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New 14, 20, for, , Cambridge, , IGCSE, Physics, , ®, , Third Edition, , 9781444176421_FM_00.indd 1, , 20/06/14 7:29 AM
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New 14, 20, r, o, f, , Cambridge, , IGCSE, Physics, , ®, , Third Edition, , Tom Duncan, and Heather Kennett, , iii, , 9781444176421_FM_00.indd 3, , 20/06/14 7:29 AM
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® IGCSE is the registered trademark of Cambridge International Examinations. The questions, example answers, marks, awarded and/or comments that appear in this book/CD were written by the authors. In examination the way marks, would be awarded to answers like these may be different., Past examination questions reproduced by permission of Cambridge International Examinations., Cambridge International Examinations bears no responsibility for the example answers to questions taken from its past, question papers which are contained in this publication., Although every effort has been made to ensure that website addresses are correct at time of going to press, Hodder, Education cannot be held responsible for the content of any website mentioned in this book. It is sometimes possible to, find a relocated web page by typing in the address of the home page for a website in the URL window of your browser., Hachette UK’s policy is to use papers that are natural, renewable and recyclable products and made from wood grown in, sustainable forests. The logging and manufacturing processes are expected to conform to the environmental regulations, of the country of origin., Orders: please contact Bookpoint Ltd, 130 Milton Park, Abingdon, Oxon OX14 4SB. Telephone: (44) 01235 827720., Fax: (44) 01235 400454. Lines are open 9.00–5.00, Monday to Saturday, with a 24-hour message answering service., Visit our website at www.hoddereducation.com, Proudly sourced and uploaded by [StormRG], © Tom Duncan and Heather Kennett 2002, Kickass Torrents | TPB | ET | h33t, First published in 2002 by, Hodder Education, an Hachette UK Company,, 338 Euston Road, London NW1 3BH, This third edition published 2014, Impression number 5 4 3 2 1, Year, , 2018 2017 2016 2015 2014, , All rights reserved. Apart from any use permitted under UK copyright law, no part of this publication may be reproduced, or transmitted in any form or by any means, electronic or mechanical, including photocopying and recording, or held, within any information storage and retrieval system, without permission in writing from the publisher or under licence, from the Copyright Licensing Agency Limited. Further details of such licences (for reprographic reproduction) may be, obtained from the Copyright Licensing Agency Limited, Saffron House, 6–10 Kirby Street, London EC1N 8TS., Cover photo © robertkoczera – Fotolia, Illustrations by Fakenham Prepress Solutions, Wearset and Integra Software Services Pvt. Ltd., Typeset in 11/13pt ITC Galliard Std by Integra Software Services Pvt. Ltd., Pondicherry, India, Printed and bound in Italy., A catalogue record for this title is available from the British Library, ISBN 978 1 4441 76421, , 9781444176421_FM_00.indd 4, , 20/06/14 7:29 AM
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Contents, Preface, Physics and technology, Scientific enquiry, Section 1, , General physics, Measurements and motion, 1 Measurements, 2 Speed, velocity and acceleration, 3 Graphs of equations, 4 Falling bodies, 5 Density, Forces and momentum, 6 Weight and stretching, 7 Adding forces, 8 Force and acceleration, 9 Circular motion, 10 Moments and levers, 11 Centres of mass, 12 Momentum, Energy, work, power and pressure, 13 Energy transfer, 14 Kinetic and potential energy, 15 Energy sources, 16 Pressure and liquid pressure, , Section 2, , vii, viii, x, , 2, 9, 13, 17, 21, 24, 27, 30, 35, 39, 43, 47, 50, 56, 60, 66, , Thermal physics, Simple kinetic molecular model of matter, 17 Molecules, 18 The gas laws, Thermal properties and temperature, 19 Expansion of solids, liquids and gases, 20 Thermometers, 21 Specific heat capacity, 22 Specific latent heat, Thermal processes, 23 Conduction and convection, 24 Radiation, , 72, 76, 81, 85, 88, 91, 97, 102, , v, , 9781444176421_FM_00.indd 5, , 20/06/14 7:29 AM
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Section 3 Properties of waves, General wave properties, 25 Mechanical waves, Light, 26 Light rays, 27 Reflection of light, 28 Plane mirrors, 29 Refraction of light, 30 Total internal reflection, 31 Lenses, 32 Electromagnetic radiation, Sound, 33 Sound waves, , 106, 113, 116, 119, 122, 126, 129, 135, 140, , Section 4 Electricity and magnetism, Simple phenomena of magnetism, 34 Magnetic fields, Electrical quantities and circuits, 35 Static electricity, 36 Electric current, 37 Potential difference, 38 Resistance, 39 Capacitors, 40 Electric power, 41 Electronic systems, 42 Digital electronics, Electromagnetic effects, 43 Generators, 44 Transformers, 45 Electromagnets, 46 Electric motors, 47 Electric meters, 48 Electrons, , 146, 150, 157, 162, 167, 174, 177, 185, 193, 199, 204, 209, 215, 219, 222, , Section 5 Atomic physics, 49 Radioactivity, 50 Atomic structure, , 230, 238, , Revision questions, Cambridge IGCSE exam questions, Mathematics for physics, Further experimental investigations, Practical test questions, Alternative to practical test questions, , 245, 251, 279, 283, 285, 291, , Answers, Index, Photo acknowledgements, , 299, 308, 315, , vi, , 9781444176421_FM_00.indd 6, , 20/06/14 7:29 AM
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Preface, IGCSE Physics Third Edition aims to provide an, up-to-date and comprehensive coverage of the Core, and Extended curriculum in Physics specified in, the current Cambridge International Examinations, IGCSE syllabus., As you read through the book, you will notice four, sorts of shaded area in the text., Material highlighted in green is for the Cambridge, IGCSE Extended curriculum., Areas highlighted in yellow contain material that, is not part of the Cambridge IGCSE syllabus. It is, extension work and will not be examined., , The book has been completely restructured to, align chapters and sections with the order of the, IGCSE syllabus. A new chapter on momentum has, been included and the checklists at the end of each, chapter are all aligned more closely with the syllabus, requirements. New questions from recent exam, papers are included at the end of the book in the, sections entitled Cambridge IGCSE exam questions,, Practical test questions and Alternative to practical test, questions. These can be used for quick comprehensive, revision before exams., The accompanying Revision CD-ROM provides, invaluable exam preparation and practice. Interactive, tests, organised by syllabus topic, cover both the, Core and Extended curriculum., T.D. and H.K., , Areas highlighted in blue contain important facts., Questions are highlighted by a box like this., , vii, , 9781444176421_FM_00.indd 7, , 20/06/14 7:29 AM
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Physics and technology, Physicists explore the Universe. Their investigations, range from particles that are smaller than atoms to, stars that are millions and millions of kilometres away,, as shown in Figures 1a and 1b., As well as having to find the facts by observation, and experiment, physicists also must try to discover, the laws that summarise these facts (often as, mathematical equations). They then have to, make sense of the laws by thinking up and testing, theories (thought-models) to explain the laws. The, reward, apart from satisfied curiosity, is a better, understanding of the physical world. Engineers, and technologists use physics to solve practical, problems for the benefit of people, though, in, solving them, social, environmental and other, problems may arise., In this book we will study the behaviour of matter, (the stuff things are made of) and the different kinds, of energy (such as light, sound, heat, electricity)., We will also consider the applications of physics in, the home, in transport, medicine, research, industry,, , Figure 1b The many millions of stars in the Universe, of which the, Sun is just one, are grouped in huge galaxies. This photograph of two, interacting spiral galaxies was taken with the Hubble Space Telescope., This orbiting telescope is enabling astronomers to tackle one of the most, , energy production and electronics. Figure 2 shows, some examples., Mathematics is an essential tool of physics and a, ‘reference section’ for some of the basic mathematics, is given at the end of the book along with suggested, methods for solving physics problems., , Figure 1a This image, produced by a scanning tunnelling microscope,, shows an aggregate of gold just three atoms thick on a graphite, substrate. Individual graphite (carbon) atoms are shown as green., , fundamental questions in science, i.e. the age and scale of the Universe,, by giving much more detailed information about individual stars than is, possible with ground-based telescopes., , viii, , 9781444176421_FM_00.indd 8, , 20/06/14 7:29 AM
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Physics and technology, , Figure 2a The modern technology of laser surgery enables very, delicate operations to be performed. Here the surgeon is removing, thin sheets of tissue from the surface of the patient’s cornea, in, order to alter its shape and correct severe short-sightedness., , Figure 2c The manned exploration of space is such an expensive, operation that international co-operation is seen as the way forward. This, is the International Space Station, built module by module in orbit around, the Earth. It is operated as a joint venture by the USA and Russia., , Figure 2b Mobile phones provide us with the convenience, of instant communication wherever we are – but does the, electromagnetic radiation they use pose a hidden risk to our, health?, , Figure 2d In the search for alternative energy sources, ‘wind farms’ of, 20 to 100 wind turbines have been set up in suitable locations, such as, this one in North Wales, to generate at least enough electricity for the, local community., , ix, , 9781444176421_FM_00.indd 9, , 20/06/14 7:29 AM
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Scientific enquiry, During your course you will have to carry out a few, experiments and investigations aimed at encouraging, you to develop some of the skills and abilities that, scientists use to solve real-life problems., Simple experiments may be designed to measure,, for example, the temperature of a liquid or the, electric current in a circuit. Longer investigations, may be designed to establish or verify a relationship, between two or more physical quantities., Investigations may arise from the topic you are, currently studying in class, or your teacher may, provide you with suggestions to choose from, or you, may have your own ideas. However an investigation, arises, it will probably require at least one hour of, laboratory time, but often longer, and will involve the, following four aspects., 1 Planning how you are going to set about finding, answers to the questions the problem poses. Making, predictions and hypotheses (informed guesses) may, help you to focus on what is required at this stage., 2 Obtaining the necessary experimental data, safely and accurately. You will have to decide, what equipment is needed, what observations, and measurements have to be made and what, variable quantities need to be manipulated. Do not, dismantle the equipment until you have completed, your analysis and you are sure you do not need to, repeat any of the measurements!, 3 Presenting and interpreting the evidence in a way, that enables any relationships between quantities to, be established., 4 Considering and evaluating the evidence by, drawing conclusions, assessing the reliability of data, and making comparisons with what was expected., , A written report of the investigation would normally, be made. This should include:, l, l, , l, , l, , l, , l, , Figure 3 Girls from Copthall School, London, with their winning entry, for a contest to investigate, design and build the most efficient, elegant, and cost-effective windmill., , The aim of the work., A list of all items of apparatus used and a record of, the smallest division of the scale of each measuring, device. For example, the smallest division on a, metre rule is 1 mm. The scale of the rule can be, read to the nearest mm. So when used to measure, a length of 100 mm (0.1 m), the length is measured, to the nearest 1 mm, the degree of accuracy of the, measurement being 1 part in 100. When used to, measure 10 mm (0.01 m), the degree of accuracy, of the measurement is 1 part in 10. A thermometer, is calibrated in degrees Celsius and may be read to, the nearest 1 °C. A temperature may be measured, to the nearest 1 °C. So when used to measure a, temperature of 20 °C, the degree of accuracy is, 1 part in 20 (this is 5 parts in 100)., Details of procedures, observations and, measurements made. A clearly labelled diagram, will be helpful here; any difficulties encountered, or precautions taken to achieve accuracy should be, mentioned., Presentation of results and calculations. If several, measurements of a quantity are made, draw up a, table in which to record your results. Use the column, headings, or start of rows, to name the measurement, and state its unit; for example ‘Mass of load/kg’., Repeat the measurement of each observation;, record each value in your table, then calculate an, average value. Numerical values should be given to, the number of significant figures appropriate to the, measuring device (see Chapter 1)., If you decide to make a graph of your results you, will need at least eight data points taken over as, large a range as possible; be sure to label each axis, of a graph with the name and unit of the quantity, being plotted (see Chapter 3)., Conclusions which can be drawn from the, evidence. These can take the form of a numerical, value (and unit), the statement of a known law, a, relationship between two quantities or a statement, related to the aim of the experiment (sometimes, experiments do not achieve the intended objective)., An evaluation and discussion of the findings which, should include:, (i) a comparison with expected outcomes,, (ii) a comment on the reliability of the readings,, especially in relation to the scale of the, measuring apparatus,, , x, , 9781444176421_FM_00.indd 10, , 20/06/14 7:29 AM
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Ideas and evidence in science, , (iii) a reference to any apparatus that was, unsuitable for the experiment,, (iv) a comment on any graph drawn, its shape and, whether the graph points lie on the line,, (v) a comment on any trend in the readings,, usually shown by the graph,, (vi) how the experiment might be modified to, give more reliable results, for example in an, electrical experiment by using an ammeter, with a more appropriate scale., , ●● Suggestions for, investigations, Investigations which extend the practical work or, theory covered in some chapters are listed below., The section Further experimental investigations on, p. 283 details how you can carry out some of these, investigations., 1 Pitch of a note from a vibrating wire, (Chapter 33)., 2 Stretching of a rubber band (Chapter 6 and, Further experimental investigations, p. 283)., 3 Stretching of a copper wire – wear safety glasses, (Chapter 6)., 4 Toppling (Further experimental investigations,, p. 283)., 5 Friction – factors affecting (Chapter 7)., 6 Energy values from burning fuel, e.g. a firelighter, (Chapter 13)., 7 Model wind turbine design (Chapter 15)., 8 Speed of a bicycle and its stopping distance, (Chapter 14)., 9 Circular motion using a bung on a string, (Chapter 9)., 10 Heat loss using different insulating materials, (Chapter 23)., 11 Cooling and evaporation (Further experimental, investigations, pp. 283–84)., 12 Variation of the resistance of a thermistor with, temperature (Chapter 38)., 13 Variation of the resistance of a wire with, length (Further experimental investigations,, p. 284)., 14 Heating effect of an electric current (Chapter 36)., 15 Strength of an electromagnet (Chapter 45)., 16 Efficiency of an electric motor (Chapter 46)., , ●● Ideas and evidence in, science, In some of the investigations you perform in the, school laboratory, you may find that you do not, interpret your data in the same way as your friends, do; perhaps you will argue with them as to the best, way to explain your results and try to convince them, that your interpretation is right. Scientific controversy, frequently arises through people interpreting, evidence differently., Observations of the heavens led the ancient Greek, philosophers to believe that the Earth was at the, centre of the planetary system, but a complex system, of rotation was needed to match observations of the, apparent movement of the planets across the sky. In, 1543 Nicolaus Copernicus made the radical suggestion, that all the planets revolved not around the Earth, but around the Sun. (His book On the Revolutions of, the Celestial Spheres gave us the modern usage of the, word ‘revolution’.) It took time for his ideas to gain, acceptance. The careful astronomical observations, of planetary motion documented by Tycho Brahe, were studied by Johannes Kepler, who realised that, the data could be explained if the planets moved, in elliptical paths (not circular) with the Sun at one, focus. Galileo’s observations of the moons of Jupiter, with the newly invented telescope led him to support, this ‘Copernican view’ and to be imprisoned by the, Catholic Church in 1633 for disseminating heretical, views. About 50 years later, Isaac Newton introduced, the idea of gravity and was able to explain the motion, of all bodies, whether on Earth or in the heavens,, which led to full acceptance of the Copernican, model. Newton’s mechanics were refined further at, the beginning of the 20th century when Einstein, developed his theories of relativity. Even today, data, from the Hubble Space Telescope is providing new, evidence which confirms Einstein’s ideas., Many other scientific theories have had to wait, for new data, technological inventions, or time and, the right social and intellectual climate for them to, become accepted. In the field of health and medicine,, for example, because cancer takes a long time to, develop it was several years before people recognised, that X-rays and radioactive materials could be, dangerous (Chapter 49)., , xi, , 9781444176421_FM_00.indd 11, , 20/06/14 7:29 AM
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Scientific enquiry, , At the beginning of the 20th century scientists, were trying to reconcile the wave theory and the, particle theory of light by means of the new ideas of, quantum mechanics., Today we are collecting evidence on possible, health risks from microwaves used in mobile phone, networks. The cheapness and popularity of mobile, phones may make the public and manufacturers, , reluctant to accept adverse findings, even if risks are, made widely known in the press and on television., Although scientists can provide evidence and, evaluation of that evidence, there may still be room, for controversy and a reluctance to accept scientific, findings, particularly if there are vested social or, economic interests to contend with. This is most, clearly shown today in the issue of global warming., , xii, , 9781444176421_FM_00.indd 12, , 20/06/14 7:29 AM
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Section, , 1, , General physics, , Chapters, Measurements and motion, 1 Measurements, 2 Speed, velocity and acceleration, 3 Graphs of equations, 4 Falling bodies, 5 Density, Forces and momentum, 6 Weight and stretching, 7 Adding forces, , 9781444176421_Section_01.indd 1, , 8, 9, 10, 11, 12, , Force and acceleration, Circular motion, Moments and levers, Centres of mass, Momentum, , Energy, work, power and pressure, 13 Energy transfer, 14 Kinetic and potential energy, 15 Energy sources, 16 Pressure and liquid pressure, , 20/06/14 7:30 AM
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1 Measurements, l, l, l, l, l, l, , Units and basic quantities, Powers of ten shorthand, Length, Significant figures, Area, Volume, , ●● Units and basic, quantities, Before a measurement can be made, a standard or, unit must be chosen. The size of the quantity to be, measured is then found with an instrument having a, scale marked in the unit., Three basic quantities we measure in physics are, length, mass and time. Units for other quantities, are based on them. The SI (Système International, d’Unités) system is a set of metric units now used in, many countries. It is a decimal system in which units, are divided or multiplied by 10 to give smaller or, larger units., , l, l, l, l, l, , Mass, Time, Systematic errors, Vernier scales and micrometers, Practical work: Period of a simple pendulum, , 4000 = 4 × 10 × 10 × 10, 400 = 4 × 10 × 10, 40 = 4 × 10, 4=4×1, 0.4 = 4/10, = 4/101, 0.04 = 4/100 = 4/102, 0.004 = 4/1000 = 4/103, , = 4 × 103, = 4 × 102, = 4 × 101, = 4 × 100, = 4 × 10−1, = 4 × 10−2, = 4 × 10−3, , The small figures 1, 2, 3, etc., are called powers of, ten. The power shows how many times the number, has to be multiplied by 10 if the power is greater than, 0 or divided by 10 if the power is less than 0. Note, that 1 is written as 100., This way of writing numbers is called standard, notation., , ●● Length, The unit of length is the metre (m) and is the, distance travelled by light in a vacuum during, a specific time interval. At one time it was the, distance between two marks on a certain metal bar., Submultiples are:, 1 decimetre (dm), 1 centimetre (cm), 1 millimetre (mm), 1 micrometre (µm), 1 nanometre (nm), Figure 1.1 Measuring instruments on the flight deck of a passenger jet, provide the crew with information about the performance of the aircraft., , ●● Powers of ten shorthand, This is a neat way of writing numbers, especially if they are, large or small. The example below shows how it works., , = 10−1 m, = 10−2 m, = 10−3 m, = 10−6 m, = 10−9 m, , A multiple for large distances is, 1 kilometre (km) = 103 m ( 58 mile approx.), Many length measurements are made with rulers;, the correct way to read one is shown in Figure 1.2., The reading is 76 mm or 7.6 cm. Your eye must be, directly over the mark on the scale or the thickness of, the ruler causes a parallax error., , 2, , 9781444176421_Section_01.indd 2, , 20/06/14 7:30 AM
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Area, , wrong, , correct, , If a number is expressed in standard notation, the, number of significant figures is the number of digits, before the power of ten. For example, 2.73 × 103 has, three significant figures., , ●● Area, 80, , 70, , The area of the square in Figure 1.3a with sides 1 cm, long is 1 square centimetre (1 cm2). In Figure 1.3b, the rectangle measures 4 cm by 3 cm and has an area, of 4 × 3 = 12 cm2 since it has the same area as twelve, squares each of area 1 cm2. The area of a square or, rectangle is given by, area = length × breadth, , object, Figure 1.2 The correct way to measure with a ruler, , To obtain an average value for a small distance,, multiples can be measured. For example, in ripple, tank experiments (Chapter 25) measure the distance, occupied by five waves, then divide by 5 to obtain the, average wavelength., , ●● Significant figures, Every measurement of a quantity is an attempt to, find its true value and is subject to errors arising from, limitations of the apparatus and the experimenter., The number of figures, called significant figures,, given for a measurement indicates how accurate we, think it is and more figures should not be given than, is justified., For example, a value of 4.5 for a measurement has, two significant figures; 0.0385 has three significant, figures, 3 being the most significant and 5 the least,, i.e. it is the one we are least sure about since it might, be 4 or it might be 6. Perhaps it had to be estimated, by the experimenter because the reading was between, two marks on a scale., When doing a calculation your answer should, have the same number of significant figures as the, measurements used in the calculation. For example,, if your calculator gave an answer of 3.4185062, this, would be written as 3.4 if the measurements had, two significant figures. It would be written as 3.42, for three significant figures. Note that in deciding, the least significant figure you look at the next figure, to the right. If it is less than 5 you leave the least, significant figure as it is (hence 3.41 becomes 3.4) but, if it equals or is greater than 5 you increase the least, significant figure by 1 (hence 3.418 becomes 3.42)., , The SI unit of area is the square metre (m2) which is, the area of a square with sides 1 m long. Note that, 1 m2 = 10−4 m2, 1 cm2 = 1 m × 1 m =, 100, 100, 10 000, 1 cm, , a, 1 cm, , 3 cm, , b, , 4 cm, , Figure 1.3, , Sometimes we need to know the area of a triangle, (Chapter 3). It is given by, area of triangle =, , 1, 2, , × base × height, , 1, 2, 1, 2, , × AB × AC, , 1, 2, 1, 2, , × PQ × SR, , For example in Figure 1.4, area ∆ABC =, =, , and, , area ∆PQR =, =, , C, , × 4 cm × 6 cm = 12 cm2, , × 5 cm × 4 cm = 10 cm2, R, , 6 cm, , 4 cm, 90°, , A, , 4 cm, , B, , P, , S, 5 cm, , Q, , Figure 1.4, 3, , 9781444176421_Section_01.indd 3, , 20/06/14 7:31 AM
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1, , Measurements, , The area of a circle of radius r is πr2 where, π = 22/7 or 3.14; its circumference is 2πr., , ●● Volume, Volume is the amount of space occupied. The unit of, volume is the cubic metre (m3) but as this is rather, large, for most purposes the cubic centimetre (cm3), is used. The volume of a cube with 1 cm edges is, 1 cm3. Note that, 1 cm3 = 1 m × 1 m × 1 m, 100, 100, 100, =, , The volume of a sphere of radius r is 34 πr3 and that, of a cylinder of radius r and height h is πr2h., The volume of a liquid may be obtained by, pouring it into a measuring cylinder, Figure 1.6a., A known volume can be run off accurately from a, burette, Figure 1.6b. When making a reading both, vessels must be upright and your eye must be level, with the bottom of the curved liquid surface, i.e. the, meniscus. The meniscus formed by mercury is curved, oppositely to that of other liquids and the top is read., Liquid volumes are also expressed in litres (l);, 1 litre = 1000 cm3 = 1 dm3. One millilitre (1 ml) = 1 cm3., , 1, m3 = 10−6 m3, 1000000, , For a regularly shaped object such as a rectangular, block, Figure 1.5 shows that, volume = length × breadth × height, , meniscus, 5 cm, , b, , a, 3 cm, , Figure 1.6a A measuring cylinder; b a burette, , 4 cm, , ●● Mass, The mass of an object is the measure of the amount, of matter in it. The unit of mass is the kilogram (kg), and is the mass of a piece of platinum–iridium alloy, at the Office of Weights and Measures in Paris. The, gram (g) is one-thousandth of a kilogram., 1g =, , 3 4 5 cubes, Figure 1.5, , 1 kg = 10–3 kg = 0.001 kg, 1000, , The term weight is often used when mass is really, meant. In science the two ideas are distinct and have, different units, as we shall see later. The confusion is, not helped by the fact that mass is found on a balance, by a process we unfortunately call ‘weighing’!, There are several kinds of balance. In the beam, balance the unknown mass in one pan is balanced, against known masses in the other pan. In the lever, balance a system of levers acts against the mass when, , 4, , 9781444176421_Section_01.indd 4, , 20/06/14 7:31 AM
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Systematic errors, , it is placed in the pan. A direct reading is obtained, from the position on a scale of a pointer joined to, the lever system. A digital top-pan balance is shown, in Figure 1.7., , Figure 1.7 A digital top-pan balance, , Practical work, Period of a simple pendulum, In this investigation you have to make time measurements using, a stopwatch or clock., Attach a small metal ball (called a bob) to a piece of string, and, suspend it as shown in Figure 1.8. Pull the bob a small distance, to one side, and then release it so that it oscillates to and fro, through a small angle., Find the time for the bob to make several complete oscillations;, one oscillation is from A to O to B to O to A (Figure 1.8). Repeat, the timing a few times for the same number of oscillations, and work out the average. The time for one oscillation is the, period T. What is it for your system? The frequency f of the, oscillations is the number of complete oscillations per second and, equals 1/T. Calculate f., How does the amplitude of the oscillations change with time?, Investigate the effect on T of (i) a longer string, (ii) a heavier, bob. A motion sensor connected to a datalogger and computer, (Chapter 2) could be used instead of a stopwatch for these, investigations., , ●● Time, The unit of time is the second (s) which used to, be based on the length of a day, this being the time, for the Earth to revolve once on its axis. However,, days are not all of exactly the same duration and, the second is now defined as the time interval for a, certain number of energy changes to occur in the, caesium atom., Time-measuring devices rely on some kind of, constantly repeating oscillation. In traditional clocks, and watches a small wheel (the balance wheel), oscillates to and fro; in digital clocks and watches the, oscillations are produced by a tiny quartz crystal. A, swinging pendulum controls a pendulum clock., To measure an interval of time in an experiment,, first choose a timer that is accurate enough for, the task. A stopwatch is adequate for finding the, period in seconds of a pendulum, see Figure 1.8,, but to measure the speed of sound (Chapter 33),, a clock that can time in milliseconds is needed. To, measure very short time intervals, a digital clock that, can be triggered to start and stop by an electronic, signal from a microphone, photogate or mechanical, switch is useful. Tickertape timers or dataloggers are, often used to record short time intervals in motion, experiments (Chapter 2)., Accuracy can be improved by measuring longer time, intervals. Several oscillations (rather than just one) are, timed to find the period of a pendulum. ‘Tenticks’, (rather than ‘ticks’) are used in tickertape timers., , metal plates, , string, support, stand, , B, , O, , A, , pendulum, bob, , Figure 1.8, , ●● Systematic errors, Figure 1.9 shows a part of a rule used to measure the, height of a point P above the bench. The rule chosen, has a space before the zero of the scale. This is shown, as the length x. The height of the point P is given, by the scale reading added to the value of x. The, equation for the height is, height = scale reading + x, height = 5.9 + x, 5, , 9781444176421_Section_01.indd 5, , 20/06/14 7:31 AM
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Measurements, , a) Vernier scale, , 8, , 1, , 4, , 5, , P•, , 6, , 7, , The calipers shown in Figure 1.10 use a vernier, scale. The simplest type enables a length to be, measured to 0.01 cm. It is a small sliding scale which, is 9 mm long but divided into 10 equal divisions, (Figure 1.11a) so, 9, 10, , 3, , 1 vernier division =, , mm, , 0, , 1, , 2, , = 0.9 mm, = 0.09 cm, , x, bench, Figure 1.9, , By itself the scale reading is not equal to the height., It is too small by the value of x., This type of error is known as a systematic error., The error is introduced by the system. A half-metre, rule has the zero at the end of the rule and so can be, used without introducing a systematic error., When using a rule to determine a height, the rule, must be held so that it is vertical. If the rule is at an, angle to the vertical, a systematic error is introduced., , ●● Vernier scales and, micrometers, Lengths can be measured with a ruler to an accuracy, of about 1 mm. Some investigations may need a, more accurate measurement of length, which can be, achieved by using vernier calipers (Figure 1.10) or a, micrometer screw gauge., , One end of the length to be measured is made to, coincide with the zero of the millimetre scale and, the other end with the zero of the vernier scale., The length of the object in Figure 1.11b is between, 1.3 cm and 1.4 cm. The reading to the second place, of decimals is obtained by finding the vernier mark, which is exactly opposite (or nearest to) a mark on, the millimetre scale. In this case it is the 6th mark, and the length is 1.36 cm, since, OA = OB – AB, OA = (1.90 cm) – (6 vernier divisions), = 1.90 cm – 6(0.09) cm, = (1.90 – 0.54) cm, = 1.36 cm, , ∴, , Vernier scales are also used on barometers, travelling, microscopes and spectrometers., vernier scale, , mm scale, , 5, , 1, , mm, , 2, , a, O, , object, , A, , B, 10, , 5, , mm, , 1, , 2, , b, Figure 1.11 Vernier scale, , b) Micrometer screw gauge, Figure 1.10 Vernier calipers in use, , This measures very small objects to 0.001 cm. One, revolution of the drum opens the accurately flat,, , 6, , 9781444176421_Section_01.indd 6, , 20/06/14 7:31 AM
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Vernier scales and micrometers, , parallel jaws by one division on the scale on the, shaft of the gauge; this is usually 12 mm, i.e. 0.05 cm., If the drum has a scale of 50 divisions round it, then, rotation of the drum by one division opens the jaws, by 0.05/50 = 0.001 cm (Figure 1.12). A friction, clutch ensures that the jaws exert the same force, when the object is gripped., jaws, , shaft, , 0 1 2, mm, , drum, , 35, 30, , friction, clutch, , object, , 5 The pages of a book are numbered 1 to 200 and each, leaf is 0.10 mm thick. If each cover is 0.20 mm thick, what, is the thickness of the book?, 6 How many significant figures are there in a length, measurement of:, a 2.5 cm, b 5.32 cm, c 7.180 cm, d 0.042 cm?, 7 A rectangular block measures 4.1 cm by 2.8 cm by 2.1 cm., Calculate its volume giving your answer to an appropriate, number of significant figures., 8 A metal block measures 10 cm × 2 cm × 2 cm. What is its, volume? How many blocks each 2 cm × 2 cm × 2 cm have, the same total volume?, 9 How many blocks of ice cream each 10 cm × 10 cm × 4 cm, can be stored in the compartment of a freezer measuring, 40 cm × 40 cm × 20 cm?, 10 A Perspex container has a 6 cm square base and contains, water to a height of 7 cm (Figure 1.13)., a What is the volume of the water?, b A stone is lowered into the water so as to be, completely covered and the water rises to a height of, 9 cm. What is the volume of the stone?, , Figure 1.12 Micrometer screw gauge, , The object shown in Figure 1.12 has a length of, 2.5 mm on the shaft scale +, 33 divisions on the drum scale, = 0.25 cm + 33(0.001) cm, = 0.283 cm, Before making a measurement, check to ensure, that the reading is zero when the jaws are closed., Otherwise the zero error must be allowed for when, the reading is taken., , 6 cm, 6 cm, Figure 1.13, , 11 What are the readings on the vernier scales in, Figures 1.14a and b?, , Questions, 1 How many millimetres are there in, a 1 cm, b 4 cm, c 0.5 cm, d 6.7 cm,, , 7 cm, , 50, , 60, , mm scale, , e 1 m?, , 2 What are these lengths in metres:, a 300 cm,, b 550 cm,, c 870 cm,, d 43 cm,, e 100 mm?, 3 a Write the following as powers of ten with one figure, before the decimal point:, 100 000 3500 428 000 000 504 27 056, , 5, object, , vernier scale, , a, 90, , 100, , mm scale, , b Write out the following in full:, 103 2 × 106 6.92 × 104 1.34 × 102 109, 5, , 4 a Write these fractions as powers of ten:, 1/1000 7/100 000 1/10 000 000 3/60 000, , object, , vernier scale, , b, Figure 1.14, , ▲, ▲, , b Express the following decimals as powers of ten with, one figure before the decimal point:, 0.5 0.084 0.000 36 0.001 04, , 7, , 9781444176421_Section_01.indd 7, , 20/06/14 7:32 AM
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1, , MeAsureMents, , 12 What are the readings on the micrometer screw gauges in, Figures 1.15a and b?, , 0, , 1, , 35, , 2, , 30, , mm, , 25, , a, , 11, mm, , 12, , 13, , 14, , 0, 45, 40, , Checklist, After studying this chapter you should be able to, • recall three basic quantities in physics,, • write a number in powers of ten (standard notation),, • recall the unit of length and the meaning of the prefixes, kilo, centi, milli, micro, nano,, • use a ruler to measure length so as to minimise errors,, • give a result to an appropriate number of significant, figures,, • measure areas of squares, rectangles, triangles and circles,, • measure the volume of regular solids and of liquids,, • recall the unit of mass and how mass is measured,, • recall the unit of time and how time is measured,, • describe the use of clocks and devices, both analogue and, digital, for measuring an interval of time,, • describe an experiment to find the period of a pendulum,, • understand how a systematic error may be introduced when, measuring,, • take measurements with vernier calipers and a micrometer, screw gauge., , b, Figure 1.15, , 13 a Name the basic units of: length, mass, time., b What is the difference between two measurements of, the same object with values of 3.4 and 3.42?, c Write expressions for, (i) the area of a circle,, (ii) the volume of a sphere,, (iii) the volume of a cylinder., , 8, , 9781444176421_Section_01.indd 8, , 20/06/14 7:32 AM
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2, ●, ●, ●, , Speed, velocity and acceleration, , Speed, Velocity, Acceleration, , ●, ●, , Timers, Practical work: Analysing motion, , ●● Speed, , ●● Velocity, , If a car travels 300 km from Liverpool to London, in five hours, its average speed is 300 km/5 h =, 60 km/h. The speedometer would certainly not, read 60 km/h for the whole journey but might vary, considerably from this value. That is why we state, the average speed. If a car could travel at a constant, speed of 60 km/h for five hours, the distance covered, would still be 300 km. It is always true that, , Speed is the distance travelled in unit time;, velocity is the distance travelled in unit time in, a stated direction. If two trains travel due north, at 20 m/s, they have the same speed of 20 m/s, and the same velocity of 20 m/s due north. If one, travels north and the other south, their speeds, are the same but not their velocities since their, directions of motion are different. Speed is a, scalar quantity and velocity a vector quantity, (see Chapter 7)., , average speed =, , distance moved, time taken, , To find the actual speed at any instant we would need, to know the distance moved in a very short interval, of time. This can be done by multiflash photography., In Figure 2.1 the golfer is photographed while a, flashing lamp illuminates him 100 times a second., The speed of the club-head as it hits the ball is about, 200 km/h., , velocity =, , distance moved in a stated directtion, time taken, , The velocity of a body is uniform or constant if it, moves with a steady speed in a straight line. It is not, uniform if it moves in a curved path. Why?, The units of speed and velocity are the same,, km/h, m/s., 60 km /h =, , 6000 m, = 17 m /s, 3600 s, , Distance moved in a stated direction is called the, displacement. It is a vector, unlike distance which is, a scalar. Velocity may also be defined as, velocity =, , displacement, time taken, , ●● Acceleration, , Figure 2.1 Multiflash photograph of a golf swing, , When the velocity of a body changes we say the body, accelerates. If a car starts from rest and moving due, north has velocity 2 m/s after 1 second, its velocity, has increased by 2 m/s in 1 s and its acceleration is, 2 m/s per second due north. We write this as 2 m/s2., , 9, , 9781444176421_Section_01.indd 9, , 20/06/14 7:32 AM
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2, , sPeed, VeloCity And ACCelerAtion, , Acceleration is the change of velocity in unit, time, or, , acceleration =, , vibrating, marker, , change of velocity, time taken for change, , tickertape, , U, , N I L AB, Blackburn, , Engladn, , 2 V a.c., , ®, , ma2x.V, , For a steady increase of velocity from 20 m/s to, 50 m/s in 5 s, acceleration =, , onlay.c., , TICKER TIM, , ER, , (50 − 20) m /s, = 6 m /s2, 5s, , Acceleration is also a vector and both its magnitude, and direction should be stated. However, at present, we will consider only motion in a straight line and so, the magnitude of the velocity will equal the speed,, and the magnitude of the acceleration will equal the, change of speed in unit time., The speeds of a car accelerating on a straight road, are shown below., Time/s, , 0, , 1, , 2, , 3, , 4, , 5, , 6, , Speed/m/s, , 0, , 5, , 10, , 15, , 20, , 25, , 30, , The speed increases by 5 m/s every second and the, acceleration of 5 m/s2 is said to be uniform., An acceleration is positive if the velocity increases, and negative if it decreases. A negative acceleration is, also called a deceleration or retardation., , ●● Timers, A number of different devices are useful for analysing, motion in the laboratory., , a) Motion sensors, Motion sensors use the ultrasonic echo technique, (see p. 143) to determine the distance of an object, from the sensor. Connection of a datalogger and, computer to the motion sensor then enables a, distance–time graph to be plotted directly (see, Figure 2.6). Further data analysis by the computer, allows a velocity–time graph to be obtained, as in, Figures 3.1 and 3.2, p. 13., , b) Tickertape timer: tape charts, , Figure 2.2 Tickertape timer, , a marker that vibrates 50 times a second and makes, 1, s intervals on the paper tape being pulled, dots at 50, 1, s is called a ‘tick’., through it; 50, The distance between successive dots equals the, average speed of whatever is pulling the tape in,, 1, s, i.e. cm per tick. The ‘tentick’ ( 15 s), say, cm per 50, is also used as a unit of time. Since ticks and tenticks, are small we drop the ‘average’ and just refer to the, ‘speed’., Tape charts are made by sticking successive strips, of tape, usually tentick lengths, side by side. That in, Figure 2.3a represents a body moving with uniform, speed since equal distances have been moved in each, tentick interval., The chart in Figure 2.3b is for uniform, acceleration: the ‘steps’ are of equal size showing, that the speed increased by the same amount in every, tentick ( 15 s). The acceleration (average) can be found, from the chart as follows., The speed during the first tentick is 2 cm for every, 1, s, or 10 cm/s. During the sixth tentick it is 12 cm, 5, per 15 s or 60 cm/s. And so during this interval of, 5 tenticks, i.e. 1 second, the change of speed is, (60 − 10) cm/s = 50 cm/s., acceleration =, =, , change of speed, time taken, 50 cm /s, 1s, , = 50 cm /s2, , A tickertape timer also enables us to measure speeds, and hence accelerations. One type, Figure 2.2, has, , 10, , 9781444176421_Section_01.indd 10, , 20/06/14 7:33 AM
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Timers, , Practical work, , 12, ‘step’, 10, distance/ cm, , tentick tape, , distance/ cm, , 8, 6, , a) Your own motion, , 6, , Pull a 2 m length of tape through a tickertape timer as you walk, away from it quickly, then slowly, then speeding up again and, finally stopping., Cut the tape into tentick lengths and make a tape chart. Write, labels on it to show where you speeded up, slowed down, etc., , 4, , 4, , 2, , 2, 0, , Analysing motion, , 8, , 0, , 1 2 3 4 5, time/ tenticks, , a, , b, , 1, , 2, , 3 4, 1s, , 5, , 6, , time / tenticks, , Figure 2.3 Tape charts: a uniform speed; b uniform acceleration, , c) Photogate timer, , b) Trolley on a sloping runway, Attach a length of tape to a trolley and release it at the top of a, runway (Figure 2.5). The dots will be very crowded at the start –, ignore those; but beyond them cut the tape into tentick lengths., Make a tape chart. Is the acceleration uniform? What is its, average value?, tickertape timer, , runway, , trolley, , Photogate timers may be used to record the, time taken for a trolley to pass through the gate,, Figure 2.4. If the length of the ‘interrupt card’ on, the trolley is measured, the velocity of the trolley, can then be calculated. Photogates are most useful, in experiments where the velocity at only one or two, positions is needed., , Figure 2.5, , c) Datalogging, Replace the tickertape timer with a motion sensor connected to, a datalogger and computer (Figure 2.6). Repeat the experiments, in a) and b) and obtain distance–time and velocity–time graphs, for each case; identify regions where you think the acceleration, changes or remains uniform., , Distance/m, , 0.3, , computer, , motion, sensor, , 0.2, 0.1, , datalogger, , 0.5 1.0 1.5 2.0, Time/s, , Figure 2.4 Use of a photogate timer, , A, , CHANNELS, ANALOG B, , C, , MOTION, MOTION SENSOR, SENSOR IIII, , LOG, , 1, , 2, , ON, , LS, CHANNE, DIGITAL, , Figure 2.6 Use of a motion sensor, , 11, , 9781444176421_Section_01.indd 11, , 20/06/14 7:33 AM
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2, , sPeed, VeloCity And ACCelerAtion, , Questions, 1 What is the average speed of, a a car that travels 400 m in 20 s,, b an athlete who runs 1500 m in 4 minutes?, 2 A train increases its speed steadily from 10 m/s to 20 m/s in, 1 minute., a What is its average speed during this time, in m/s?, b How far does it travel while increasing its speed?, 3 A motorcyclist starts from rest and reaches a speed of 6 m/s, after travelling with uniform acceleration for 3 s. What is his, acceleration?, 4 An aircraft travelling at 600 km/h accelerates steadily, at 10 km/h per second. Taking the speed of sound as, 1100 km/h at the aircraft’s altitude, how long will it take to, reach the ‘sound barrier’?, 5 A vehicle moving with a uniform acceleration of 2 m/s2 has, a velocity of 4 m/s at a certain time. What will its velocity be, a 1 s later,, b 5 s later?, 6 If a bus travelling at 20 m/s is subject to a steady, deceleration of 5 m/s2, how long will it take to come to rest?, 7 The tape in Figure 2.7 was pulled through a timer by a, trolley travelling down a runway. It was marked off in, tentick lengths., a What can you say about the trolley’s motion?, b Find its acceleration in cm/s2., , 2 cm, , tape length/cm, , 50, 40, 30, 20, 10, 0, , O, , A, time, , B, , Figure 2.8, , 9 The speeds of a car travelling on a straight road are given, below at successive intervals of 1 second., Time/s, , 0, , 1, , 2, , 3, , 4, , Speed/m/s, , 0, , 2, , 4, , 6, , 8, , The car travels, 1 with an average velocity of 4 m/s, 2 16 m in 4 s, 3 with a uniform acceleration of 2 m/s2., Which statement(s) is (are) correct?, A 1, 2, 3 B 1, 2 C 2, 3 D 1 E 3, 10 If a train travelling at 10 m/s starts to accelerate at 1 m/s2, for 15 s on a straight track, its final velocity in m/s is, A 5 B 10 C 15 D 20 E 25, , 7cm, , 15 cm, 26 cm, Figure 2.7, , 8 Each strip in the tape chart of Figure 2.8 is for a time, interval of 1 tentick., a If the timer makes 50 dots per second, what time, intervals are represented by OA and AB?, b What is the acceleration between O and A in, (i) cm/tentick2,, (ii) cm/s per tentick,, (iii) cm/s2?, c What is the acceleration between A and B?, , Checklist, After studying this chapter you should be able to, • explain the meaning of the terms speed and acceleration,, • distinguish between speed and velocity,, • describe how speed and acceleration may be found using, tape charts and motion sensors., , 12, , 9781444176421_Section_01.indd 12, , 20/06/14 7:33 AM
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Graphs of equations, , 3, ●, ●, , Velocity–time graphs, Distance–time graphs, , ●, , Equations for uniform acceleration, , ●● Velocity–time graphs, , Q, , 40, velocity/m/s, , If the velocity of a body is plotted against the time, the, graph obtained is a velocity–time graph. It provides, a way of solving motion problems. Tape charts are, crude velocity–time graphs that show the velocity, changing in jumps rather than smoothly, as occurs in, practice. A motion sensor gives a smoother plot., , 30, P, 20, , R, , 10, , The area under a velocity–time graph measures the distance, travelled., , S, O, , 1, , 2, , 3, , 4, , 5, , time/s, Figure 3.2a Uniform acceleration, , A, , 20, , B, , 10, , C, O, , 1, , 2, 3, time/s, , 4, , 30, , velocity/m/s, , velocity/m/s, , 30, , 20, , 10, , 5, , 0, , Figure 3.1 Uniform velocity, , Y, 0, , 1, , 2, , 3, , 4, , 5, , time/s, , In Figure 3.1, AB is the velocity–time graph for a, body moving with a uniform velocity of 20 m/s., Since distance = average velocity × time, after 5 s it, will have moved 20 m/s × 5 s = 100 m. This is the, shaded area under the graph, i.e. rectangle OABC., In Figure 3.2a, PQ is the velocity–time graph for a, body moving with uniform acceleration. At the start of, the timing the velocity is 20 m/s but it increases steadily, to 40 m/s after 5 s. If the distance covered equals the, area under PQ, i.e. the shaded area OPQS, then, distance = area of rectangle OPRS, + area of triangle PQR, = OP × OS + 12 × PR × QR, (area of a triangle = 12 base × height), = 20 m/s × 5 s +, , X, , 1, 2, , × 5 s × 20 m/s, , = 100 m + 50 m = 150 m, , Figure 3.2b Non-uniform acceleration, , Notes, 1 When calculating the area from the graph, the unit, of time must be the same on both axes., 2 This rule for finding distances travelled is true even, if the acceleration is not uniform. In Figure 3.2b,, the distance travelled equals the shaded area OXY., The slope or gradient of a velocity–time graph represents the, acceleration of the body., , In Figure 3.1, the slope of AB is zero, as is the, acceleration. In Figure 3.2a, the slope of PQ is, QR/PR = 20/5 = 4: the acceleration is 4 m/s2., In Figure 3.2b, when the slope along OX changes,, so does the acceleration., 13, , 9781444176421_Section_01.indd 13, , 20/06/14 7:34 AM
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3, , grAPHs oF equAtions, , ●● Distance–time graphs, A body travelling with uniform velocity covers, equal distances in equal times. Its distance–time, graph is a straight line, like OL in Figure 3.3, for a velocity of 10 m/s. The slope of the graph is, LM/OM = 40 m/4 s = 10 m/s, which is the value, of the velocity. The following statement is true in, general:, The slope or gradient of a distance–time graph represents the, velocity of the body., , ●● Equations for uniform, acceleration, Problems involving bodies moving with uniform, acceleration can often be solved quickly using the, equations of motion., , First equation, If a body is moving with uniform acceleration a and, its velocity increases from u to v in time t, then, a=, , L, , 40, , ∴, , distance/m, , at = v − u, , or, , 30, , v = u + at, , 20, 10, M, O, , 1, , 2, 3, time/s, , 4, , When the velocity of the body is changing,, the slope of the distance–time graph varies, as, in Figure 3.4, and at any point equals the slope, of the tangent. For example, the slope of the, tangent at T is AB/BC = 40 m/2 s = 20 m/s., The velocity at the instant corresponding to T is, therefore 20 m/s., A, , 40, , Note that the initial velocity u and the final velocity v, refer to the start and the finish of the timing and do, not necessarily mean the start and finish of the motion., The velocity of a body moving with uniform, acceleration increases steadily. Its average velocity, therefore equals half the sum of its initial and final, velocities, that is,, average velocity = u + v, 2, If s is the distance moved in time t, then since, average velocity = distance/time = s/t,, s = u+v, t, 2, or, , 30, , s =, , 20, , (u + v ), t, 2, , (2), , T, , Third equation, , 10, B, , C, O, , (1), , Second equation, , Figure 3.3 Uniform velocity, , distance/m, , change of velocity v − u, =, t, time taken, , 1, , 2, , 3, time/s, , 4, , 5, , From equation (1), v = u + at, From equation (2),, s = u +v, t, 2, , Figure 3.4 Non-uniform velocity, , 14, , 9781444176421_Section_01.indd 14, , 20/06/14 7:35 AM
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Worked example, , s u + u + at 2u + at, =, =, 2, t, 2, 1, = u + at, 2, , Second stage, u = 20 m/s (constant), , t = 60 s, , distance moved = speed × time = 20 m/s × 60 s, , and so, , = 1200 m, s = ut +, , 1 2, at, 2, , (3), , u = 20 m/s, , Fourth equation, This is obtained by eliminating t from equations (1), and (3). Squaring equation (1) we have, v2 = (u + at)2, ∴, , v2 = u2 + 2uat + a2t2, = u2 + 2a (ut + 1 at2), 2, 1, 2, s = ut + at, 2, , But, ∴, , Third stage, v = 0 a = −2 m/s2 (a deceleration), , We have, v2 = u2 + 2as, ∴, , 2, 2, 0 − 202 m2 /s2, − 400 m2 /s2, =, s = v −u =, 2, 2a, 2 × (−2) m/s, − 4 m/s2, , = 100 m, , Answers, Maximum speed = 72 km/h, Total distance covered = 200 m + 1200 m + 100 m, = 1500 m, , v2 = u2 + 2as, , If we know any three of u, v, a, s and t, the others, can be found from the equations., , ●● Worked example, A sprint cyclist starts from rest and accelerates at, 1 m/s2 for 20 seconds. He then travels at a constant, speed for 1 minute and finally decelerates at 2 m/s2, until he stops. Find his maximum speed in km/h, and the total distance covered in metres., , Questions, 1 The distance–time graph for a girl on a cycle ride is shown, in Figure 3.5., a How far did she travel?, b How long did she take?, c What was her average speed in km/h?, d How many stops did she make?, e How long did she stop for altogether?, f What was her average speed excluding stops?, g How can you tell from the shape of the graph, when she travelled fastest? Over which stage did, this happen?, , First stage, u = 0 a = 1 m/s2, , t = 20 s, , 50, , v = u + at = 0 + 1 m/s2 × 20 s, = 20 m/s, = 20 × 60 × 60 = 72 km /h, 1000, , distance/km, , We have, , F, , 60, , The distance s moved in the first stage is given by, , 40, B C, , 30, 20, , A, , 10, , s = ut + 1 at2 = 0 × 20 s + 1 × 1 m/s2 × 202 s2, 2, 2, , 0, 1pm 2pm 3pm 4pm 5pm 6pm, Figure 3.5, , time of, day, , ▲, ▲, , = 1 × 1 m/s2 × 400 s2 = 200 m, 2, , E, D, , 15, , 9781444176421_Section_01.indd 15, , 20/06/14 7:35 AM
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3, , grAPHs oF equAtions, , 2 The graph in Figure 3.6 represents the distance travelled by, a car plotted against time., a How far has the car travelled at the end of 5 seconds?, b What is the speed of the car during the first, 5 seconds?, c What has happened to the car after A?, d Draw a graph showing the speed of the car plotted, against time during the first 5 seconds., , a State in which of the regions OA, AB, BC, CD, DE the, car is (i) accelerating, (ii) decelerating, (iii) travelling, with uniform velocity., b Calculate the value of the acceleration, deceleration or, constant velocity in each region., c What is the distance travelled over each region?, d What is the total distance travelled?, e Calculate the average velocity for the whole journey., C, , 100, A, , 100, distance/m, , speed/(km/h), , 120, 80, 60, 40, , A, , 80, , D, , B, , 60, 40, 20, , O, , E, , 0, , 1, , 20, , 2, 3, time/hours, , 4, , 5, , Figure 3.8, 1, , 2, , 3 4, time/s, , 5, , 6, , Figure 3.6, , 3 Figure 3.7 shows an incomplete velocity–time graph for a, boy running a distance of 100 m., a What is his acceleration during the first 4 seconds?, b How far does the boy travel during (i) the first, 4 seconds, (ii) the next 9 seconds?, c Copy and complete the graph showing clearly at what, time he has covered the distance of 100 m. Assume, his speed remains constant at the value shown by the, horizontal portion of the graph., , 5 The distance–time graph for a motorcyclist riding off from, rest is shown in Figure 3.9., a Describe the motion., b How far does the motorbike move in 30 seconds?, c Calculate the speed., , 600, 500, distance/m, , 0, , velocity/m/s, , 7.5, , 300, 200, 100, , 5.0, , 0, , 2.5, , 0, , 400, , 10, , 20, , 30, , time/s, , Figure 3.9, , 2, , 4, , 6, , 8 10 12 14, time/s, , Figure 3.7, , Checklist, After studying this chapter you should be able to, , 4 The approximate velocity–time graph for a car on a 5-hour, journey is shown in Figure 3.8. (There is a very quick driver, change midway to prevent driving fatigue!), , • draw, interpret and use velocity–time and distance–time, graphs to solve problems., , 16, , 9781444176421_Section_01.indd 16, , 20/06/14 7:36 AM
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4 Falling bodies, l, l, l, , Acceleration of free fall, Measuring g, Distance–time graphs, , l, l, , Projectiles, Practical work: Motion of a falling body, , In air, a coin falls faster than a small piece of paper., In a vacuum they fall at the same rate, as may, be shown with the apparatus of Figure 4.1. The, difference in air is due to air resistance having, a greater effect on light bodies than on heavy, bodies. The air resistance to a light body is large, when compared with the body’s weight. With a, dense piece of metal the resistance is negligible at, low speeds., There is a story, untrue we now think, that, in the 16th century the Italian scientist Galileo, dropped a small iron ball and a large cannonball, ten times heavier from the top of the Leaning, Tower of Pisa (Figure 4.2). And we are told that,, to the surprise of onlookers who expected the, cannonball to arrive first, they reached the ground, almost simultaneously. You will learn more about air, resistance in Chapter 8., rubber, stopper, , Perspex or, Pyrex tube, paper, 1.5 m, , coin, , pressure, tubing, screw clip, , to vacuum, pump, , Figure 4.1 A coin and a piece of paper fall at the same, rate in a vacuum., , Figure 4.2 The Leaning Tower of Pisa, where Galileo is said to have, experimented with falling objects, 17, , 9781444176421_Section_01.indd 17, , 20/06/14 7:36 AM
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4, , Falling bodies, , Practical work, , (i.e. a = g = +10 m/s2) and a negative sign for rising, bodies since they are decelerating (i.e. a = −g = –10 m/s2)., , Motion of a falling body, Arrange things as shown in Figure 4.3 and investigate the motion, of a 100 g mass falling from a height of about 2 m., Construct a tape chart using one-tick lengths. Choose as dot, ‘0’ the first one you can distinguish clearly. What does the tape, chart tell you about the motion of the falling mass? Repeat the, experiment with a 200 g mass; what do you notice?, 2 V a.c., , ticker, timer, , retort, stand, , tickertape, , ●● Measuring g, Using the arrangement in Figure 4.4 the time, for a steel ball-bearing to fall a known distance is, measured by an electronic timer., When the two-way switch is changed to the, ‘down’ position, the electromagnet releases the ball, and simultaneously the clock starts. At the end of, its fall the ball opens the ‘trap-door’ on the impact, switch and the clock stops., The result is found from the third equation of, motion s = ut + 12 at 2, where s is the distance fallen, (in m), t is the time taken (in s), u = 0 (the ball, starts from rest) and a = g (in m/s2). Hence, s = 1 gt2, 2, or, g = 2s/t2, Air resistance is negligible for a dense object such as, a steel ball-bearing falling a short distance., electromagnet, , ballbearing, 100 g, mass, , to floor, , Figure 4.3, electronic timer, , ●● Acceleration of free fall, All bodies falling freely under the force of gravity, do so with uniform acceleration if air resistance is, negligible (i.e. the ‘steps’ in the tape chart from the, practical work should all be equal)., This acceleration, called the acceleration of free fall,, is denoted by the italic letter g. Its value varies slightly, over the Earth but is constant in each place; in India, for example, it is about 9.8 m/s2 or near enough 10 m/s2., The velocity of a free-falling body therefore increases, by 10 m/s every second. A ball shot straight upwards, with a velocity of 30 m/s decelerates by 10 m/s every, second and reaches its highest point after 3 s., In calculations using the equations of motion, g, replaces a. It is given a positive sign for falling bodies, , EXT, , two-way, switch, , COM , CLOCK, OPERATING, , magnet, , 12 V a.c., adjustable, terminal, , hinge trap-door of, impact switch, , Figure 4.4, , 18, , 9781444176421_Section_01.indd 18, , 20/06/14 7:36 AM
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Projectiles, , ●● Worked example, , a We have u = 30 m/s, a =, (a, deceleration) and v = 0 since the ball is, momentarily at rest at its highest point., Substituting in v2 = u2 + 2as,, , distance/m, , A ball is projected vertically upwards with an initial, velocity of 30 m/s. Find a its maximum height and, b the time taken to return to its starting point., Neglect air resistance and take g = 10 m/s2., , 80, 60, 40, 20, , −10 m/s2, , or, , 0 = 302 m2/s2 + 2(−10 m/s2) × s, , s =, , −900 m2 /s2, = 45 m, −20 m/s2, , b If t is the time to reach the highest point, we, have, from v = u + at,, , ∴, , 8, , 4, , 12, , 16, , (time)2/s2, Figure 4.5b A graph of distance against (time)2 for a body falling freely, from rest, , −900 m2/s2 = −s × 20 m/s2, , ∴, , or, , 0, , 0 = 30 m/s + (−10 m/s2) × t, −30 m/s = −t × 10 m/s2, t =, , −30 m/s, = 3s, −10 m/s2, , The downward trip takes exactly the same time as, the upward one and so the answer is 6 s., , ●● Projectiles, The photograph in Figure 4.6 was taken while a lamp, emitted regular flashes of light. One ball was dropped, from rest and the other, a ‘projectile’, was thrown, sideways at the same time. Their vertical accelerations, (due to gravity) are equal, showing that a projectile, falls like a body which is dropped from rest. Its, horizontal velocity does not affect its vertical motion., The horizontal and vertical motions of a body are independent, and can be treated separately., , ●● Distance–time graphs, For a body falling freely from rest we have, s=, , 1, 2, , gt2, , A graph of distance s against time t is shown in Figure, 4.5a and for s against t 2 in Figure 4.5b. The second, graph is a straight line through the origin since s ∝ t2, ( g being constant at one place)., , distance/m, , 80, 60, 40, 20, , 0, , 1, , 2, , 3, , 4, , time/s, Figure 4.5a A graph of distance against time for a body falling freely, from rest, , Figure 4.6 Comparing free fall and projectile motion using multiflash, photography, 19, , 9781444176421_Section_01.indd 19, , 20/06/14 7:36 AM
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4, , FAlling bodies, , For example if a ball is thrown horizontally from, the top of a cliff and takes 3 s to reach the beach, below, we can calculate the height of the cliff by, considering the vertical motion only. We have u = 0, (since the ball has no vertical velocity initially),, a = g = +10 m/s2 and t = 3 s. The height s of the, cliff is given by, s = ut + 1 at2, 2, 1, = 0 × 3 s + (+10 m/s2)32 s2, 2, = 45 m, Projectiles such as cricket balls and explosive shells, are projected from near ground level and at an, angle. The horizontal distance they travel, i.e. their, range, depends on, (i) the speed of projection – the greater this is, the, greater the range, and, (ii) the angle of projection – it can be shown, that, neglecting air resistance, the range is a, maximum when the angle is 45º (Figure 4.7)., , Questions, 1 A stone falls from rest from the top of a high tower. Ignore, air resistance and take g = 10 m/s2., a What is its velocity after, (i) 1 s,, (ii) 2 s,, (iii) 3 s,, (iv) 5 s?, b How far has it fallen after, (i) 1 s,, (ii) 2 s,, (iii) 3 s,, (iv) 5 s?, 2 An object falls from a hovering helicopter and hits the, ground at a speed of 30 m/s. How long does it take the, object to reach the ground and how far does it fall? Sketch, a velocity–time graph for the object (ignore air resistance)., , Checklist, After studying this chapter you should be able to, • describe the behaviour of falling objects,, • state that the acceleration of free fall for a body near the, Earth is constant., , 45°, Figure 4.7 The range is greatest for an angle of projection of 45º, , 20, , 9781444176421_Section_01.indd 20, , 20/06/14 7:37 AM
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Density, , 5, ●, ●, , Calculations, Simple density measurements, , ●, , In everyday language, lead is said to be ‘heavier’, than wood. By this it is meant that a certain volume, of lead is heavier than the same volume of wood., In science such comparisons are made by using the, term density. This is the mass per unit volume of a, substance and is calculated from, density =, , Floating and sinking, , ●● Calculations, Using the symbols ρ (rho) for density, m for mass and, V for volume, the expression for density is, , ρ =m, V, Rearranging the expression gives, , mass, volume, , m = V ×ρ, The density of lead is 11 grams per cubic centimetre, (11 g/cm3) and this means that a piece of lead of, volume 1 cm3 has mass 11 g. A volume of 5 cm3, of lead would have mass 55 g. If the density of a, substance is known, the mass of any volume of it, can be calculated. This enables engineers to work, out the weight of a structure if they know from the, plans the volumes of the materials to be used and, their densities. Strong enough foundations can then, be made., The SI unit of density is the kilogram per, cubic metre. To convert a density from g/cm3,, normally the most suitable unit for the size of, sample we use, to kg/m3, we multiply by 103., For example the density of water is 1.0 g/cm3 or, 1.0 × 103 kg/m3., The approximate densities of some common, substances are given in Table 5.1., , and, , V =, , m, ρ, , These are useful if ρ is known and m or V have, to be calculated. If you do not see how they are, obtained refer to the Mathematics for physics section, on p. 279. The triangle in Figure 5.1 is an aid to, remembering them. If you cover the quantity you, want to know with a finger, such as m, it equals what, you can still see, i.e. ρ × V. To find V, cover V and, you get V = m/ρ., , m, , ρ V, , Figure 5.1, Table 5.1, , Densities of some common substances, , Solids, , Density/g/cm3, , Liquids, , Density/g/cm3, , aluminium, , 2.7, , paraffin, , 0.80, , copper, , 8.9, , petrol, , 0.80, , iron, , 7.9, , pure water, , 1.0, , gold, , 19.3, , glass, , mercury, , 13.6, , 2.5, , Gases, , Density/kg/m3, , wood (teak), , 0.80, , air, , 1.3, , ice, , 0.92, , hydrogen, , 0.09, , polythene, , 0.90, , carbon dioxide, , 2.0, , ●● Worked example, Taking the density of copper as 9 g/cm3, find a the, mass of 5 cm3 and b the volume of 63 g., a ρ = 9 g/cm3, V = 5 cm3 and m is to be found., m = V × ρ = 5 cm3 × 9 g/cm3 = 45 g, b ρ = 9 g/cm3, m = 63 g and V is to be found., ∴, , 63 g, V = m =, = 7cm3, ρ, 9 g/cm3, , 21, , 9781444176421_Section_01.indd 21, , 20/06/14 7:37 AM
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5 Density, , ●● Simple density, measurements, , water, , If the mass m and volume V of a substance are known,, its density can be found from ρ = m/V., , a) Regularly shaped solid, , displacement can, (filled to overflowing before, solid inserted), , The mass is found on a balance and the volume by, measuring its dimensions with a ruler., , b) Irregularly shaped solid, such as a, pebble or glass stopper, , measuring cylinder, , The mass of the solid is found on a balance. Its, volume is measured by one of the methods shown in, Figures 5.2a and b. In Figure 5.2a the volume is the, difference between the first and second readings. In, Figure 5.2b it is the volume of water collected in the, measuring cylinder., , solid, , water, , Figure 5.2b Measuring the volume of an irregular solid: method 2, , measuring cylinder, , 2nd reading, , 1st reading, , water, , solid, , c) Liquid, The mass of an empty beaker is found on a balance., A known volume of the liquid is transferred from a, burette or a measuring cylinder into the beaker. The, mass of the beaker plus liquid is found and the mass, of liquid is obtained by subtraction., , d) Air, Using a balance, the mass of a 500 cm3 roundbottomed flask full of air is found and again after, removing the air with a vacuum pump; the difference, gives the mass of air in the flask. The volume of air, is found by filling the flask with water and pouring it, into a measuring cylinder., , ●● Floating and sinking, Figure 5.2a Measuring the volume of an irregular solid: method 1, , An object sinks in a liquid of lower density than its, own; otherwise it floats, partly or wholly submerged., For example, a piece of glass of density 2.5 g/cm3, sinks in water (density 1.0 g/cm3) but floats in, mercury (density 13.6 g/cm3). An iron nail sinks, in water but an iron ship floats because its average, density is less than that of water., , 22, , 9781444176421_Section_01.indd 22, , 20/06/14 7:37 AM
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Floating and sinking, , Checklist, After studying this chapter you should be able to, • define density and perform calculations using ρ = m/V,, • describe experiments to measure the density of solids,, liquids and air,, • predict whether an object will float based on density data., , Figure 5.3 Why is it easy to float in the Dead Sea?, , Questions, 1 a If the density of wood is 0.5 g/cm3 what is the mass of, (i) 1 cm3,, (ii) 2 cm3,, (iii) 10 cm3?, b What is the density of a substance of, (i) mass 100 g and volume 10 cm3,, (ii) volume 3 m3 and mass 9 kg?, c The density of gold is 19 g/cm3. Find the volume of, (i) 38 g,, (ii) 95 g of gold., 2 A piece of steel has a volume of 12 cm3 and a mass of 96 g., What is its density in, a g/cm3,, b kg/m3?, 3 What is the mass of 5 m3 of cement of density 3000 kg/m3?, 4 What is the mass of air in a room measuring 10 m × 5.0 m ×, 2.0 m if the density of air is 1.3 kg/m3?, 5 When a golf ball is lowered into a measuring cylinder of, water, the water level rises by 30 cm3 when the ball is, completely submerged. If the ball weighs 33 g in air, find its, density., 6 Why does ice float on water?, , 23, , 9781444176421_Section_01.indd 23, , 20/06/14 7:37 AM
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6, ●, ●, ●, , Weight and stretching, , Force, Weight, The newton, , ●● Force, A force is a push or a pull. It can cause a body at, rest to move, or if the body is already moving it can, change its speed or direction of motion. A force can, also change a body’s shape or size., , ●, ●, , Hooke’s law, Practical work: Stretching a spring, , For a body above or on the Earth’s surface, the, nearer it is to the centre of the Earth, the more the, Earth attracts it. Since the Earth is not a perfect, sphere but is flatter at the poles, the weight of a body, varies over the Earth’s surface. It is greater at the, poles than at the equator., Gravity is a force that can act through space, i.e., there does not need to be contact between the Earth, and the object on which it acts as there does when we, push or pull something. Other action-at-a-distance, forces which, like gravity, decrease with distance are:, (i) magnetic forces between magnets, and, (ii) electric forces between electric charges., , ●● The newton, The unit of force is the newton (N). It will be defined, later (Chapter 8); the definition is based on the change, of speed a force can produce in a body. Weight is a, force and therefore should be measured in newtons., The weight of a body can be measured by hanging, it on a spring balance marked in newtons (Figure 6.2), and letting the pull of gravity stretch the spring in, the balance. The greater the pull, the more the spring, stretches., , 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, , 1 newton, , spring balance, , Figure 6.1 A weightlifter in action exerts first a pull and then a push., , ●● Weight, We all constantly experience the force of gravity,, in other words. the pull of the Earth. It causes an, unsupported body to fall from rest to the ground., The weight of a body is the force of gravity on it., , Figure 6.2 The weight of an average-sized apple is about 1 newton., , On most of the Earth’s surface:, The weight of a body of mass 1 kg is 9.8 N., , 24, , 9781444176421_Section_01.indd 24, , 20/06/14 7:38 AM
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Hooke’s law, , Often this is taken as 10 N. A mass of 2 kg has a, weight of 20 N, and so on. The mass of a body is, the same wherever it is and, unlike weight, does not, depend on the presence of the Earth., , Practical work, Stretching a spring, Arrange a steel spring as in Figure 6.3. Read the scale opposite, the bottom of the hanger. Add 100 g loads one at a time (thereby, increasing the stretching force by steps of 1 N) and take the readings, after each one. Enter the readings in a table for loads up to 500 g., Note that at the head of columns (or rows) in data tables it is, usual to give the name of the quantity or its symbol followed by /, and the unit., Stretching force/N, , Scale reading/mm, , Total extension/mm, , Do the results suggest any rule about how the spring behaves, when it is stretched?, Sometimes it is easier to discover laws by displaying the results, on a graph. Do this on graph paper by plotting stretching force, readings along the x-axis (horizontal axis) and total extension, readings along the y-axis (vertical axis). Every pair of readings will, give a point; mark them by small crosses and draw a smooth line, through them. What is its shape?, , steel, spring, , 10, , hanger, mm, scale, , 20, , 30, , Using the sign for proportionality, ∝, we can write, Hooke’s law as, extension ∝ stretching force, , It is true only if the elastic limit or ‘limit of, proportionality’ of the spring is not exceeded. In, other words, the spring returns to its original length, when the force is removed., The graph of Figure 6.4 is for a spring stretched, beyond its elastic limit, E. OE is a straight line, passing through the origin O and is graphical proof, that Hooke’s law holds over this range. If the force, for point A on the graph is applied to the spring,, the proportionality limit is passed and on removing, the force some of the extension (OS) remains. Over, which part of the graph does a spring balance work?, The force constant, k, of a spring is the force, needed to cause unit extension, i.e. 1 m. If a force F, produces extension x then, k = F, x, Rearranging the equation gives, F = kx, This is the usual way of writing Hooke’s law in, symbols., Hooke’s law also holds when a force is applied, to a straight metal wire or an elastic band, provided, they are not permanently stretched. Force–extension, graphs similar to Figure 6.4 are obtained. You should, label each axis of your graph with the name of the, quantity or its symbol followed by / and the unit, as, shown in Figure 6.4., For a rubber band, a small force causes a large, extension., , 90, , A, , Figure 6.3, stretching force/N, , ●● Hooke’s law, Springs were investigated by Robert Hooke nearly, 350 years ago. He found that the extension was, proportional to the stretching force provided the, spring was not permanently stretched. This means, that doubling the force doubles the extension,, trebling the force trebles the extension, and so on., , E, , O, , S, , total extension/mm, , Figure 6.4, 25, , 9781444176421_Section_01.indd 25, , 20/06/14 7:38 AM
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6, , WeigHt And stretCHing, , ●● Worked example, A spring is stretched 10 mm (0.01 m) by a weight of, 2.0 N. Calculate: a the force constant k, and b the, weight W of an object that causes an extension of, 80 mm (0.08 m)., a k = F = 2.0 N = 200 N/m, x, 0.01 m, , Checklist, After studying this chapter you should be able to, • recall that a force can cause a change in the motion, size or, shape of a body,, • recall that the weight of a body is the force of gravity on it,, • recall the unit of force and how force is measured,, • describe an experiment to study the relation between force, and extension for springs,, • draw conclusions from force–extension graphs,, • recall Hooke’s law and solve problems using it,, • recognise the significance of the term limit of, proportionality., , b W = stretching force F, =k×x, = 200 N/m × 0.08 m, = 16 N, , Questions, 1 A body of mass 1 kg has weight 10 N at a certain place., What is the weight of, a 100 g,, b 5 kg,, c 50 g?, 2 The force of gravity on the Moon is said to be one-sixth of, that on the Earth. What would a mass of 12 kg weigh, a on the Earth, and, b on the Moon?, 3 What is the force constant of a spring which is stretched, a 2 mm by a force of 4 N,, b 4 cm by a mass of 200 g?, 4 The spring in Figure 6.5 stretches from 10 cm to 22 cm, when a force of 4 N is applied. If it obeys Hooke’s law, its, total length in cm when a force of 6 N is applied is, A 28 B 42, , C 50, , D 56, , E 100, , 10 cm, , 22 cm, , 4N, Figure 6.5, , 26, , 9781444176421_Section_01.indd 26, , 20/06/14 7:39 AM
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7 Adding forces, l, l, l, , Forces and resultants, Examples of addition of forces, Vectors and scalars, , l, l, , Friction, Practical work: Parallelogram law, , ●● Forces and resultants, Force has both magnitude (size) and direction. It, is represented in diagrams by a straight line with an, arrow to show its direction of action., Usually more than one force acts on an object. As a, simple example, an object resting on a table is pulled, downwards by its weight W and pushed upwards by, a force R due to the table supporting it (Figure 7.1)., Since the object is at rest, the forces must balance,, i.e. R = W., R, , Figure 7.2 The design of an offshore oil platform requires an, understanding of the combination of many forces., , 3N, , 1N, , 2N, , W, , In structures such as a giant oil platform (Figure 7.2),, two or more forces may act at the same point. It is, then often useful for the design engineer to know, the value of the single force, i.e. the resultant, which, has exactly the same effect as these forces. If the, forces act in the same straight line, the resultant is, found by simple addition or subtraction as shown in, Figure 7.3; if they do not they are added by using the, parallelogram law., , 2N, , 3N, , Figure 7.3 The resultant of forces acting in the same straight line is, found by addition or subtraction., , Remove the paper and, using a scale of 1 cm to represent 1 N,, draw OA, OB and OD to represent the three forces P, Q and W, which act at O, as in Figure 7.4b. (W = weight of the 1 kg, mass = 9.8 N; therefore OD = 9.8 cm.), , Practical work, , spring balance, (0–10 N), string, , Parallelogram law, Arrange the apparatus as in Figure 7.4a with a sheet of paper, behind it on a vertical board. We have to find the resultant of, forces P and Q., Read the values of P and Q from the spring balances. Mark on, the paper the directions of P, Q and W as shown by the strings., , 1N, , , , Figure 7.1, , P, , Q, O, , W, 1 kg, , Figure 7.4a, 27, , 9781444176421_Section_01.indd 27, , 20/06/14 7:39 AM
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7, , Adding ForCes, , C, , ●● Examples of addition, of forces, , B, A, , Q, , 1 Two people carrying a heavy bucket. The, weight of the bucket is balanced by the force F,, the resultant of F1 and F2 (Figure 7.6a)., , P, O, Use the scale 1 cm 1 N, W, 9.8 cm, , 2 Two tugs pulling a ship. The resultant of T1, and T2 is forwards in direction (Figure 7.6b),, and so the ship moves forwards (as long as the, resultant is greater than the resistance to motion, of the sea and the wind)., , D, Figure 7.4b Finding a resultant by the parallelogram law, , P and Q together are balanced by W and so their resultant must, be a force equal and opposite to W., Complete the parallelogram OACB. Measure the diagonal OC;, if it is equal in size (i.e. 9.8 cm) and opposite in direction to W, then it represents the resultant of P and Q., The parallelogram law for adding two forces is:, If two forces acting at a point are represented in size, and direction by the sides of a parallelogram drawn, from the point, their resultant is represented in size and, direction by the diagonal of the parallelogram drawn from, the point., , F1, , T1, , Find the resultant of two forces of 4.0 N and 5.0 N, acting at an angle of 45º to each other., Using a scale of 1.0 cm = 1.0 N, draw, parallelogram ABDC with AB = 5.0 cm, AC = 4.0 N, and angle CAB = 45º (Figure 7.5). By the, parallelogram law, the diagonal AD represents the, resultant in magnitude and direction; it measures, 8.3 cm, and angle BAD = 20º., ∴ Resultant is a force of 8.3 N acting at an angle, of 20º to the force of 5.0 N., D, , 4.0 N, 45°, A, Figure 7.5, , 5.0 N, , B, , F2, , a, , ●● Worked example, , Scale: 1.0 cm 1.0 N, C, , F, , T2, tugs, , b, Figure 7.6, , ●● Vectors and scalars, A vector quantity is one such as force which, is described completely only if both its size, (magnitude) and direction are stated. It is not, enough to say, for example, a force of 10 N, but, rather a force of 10 N acting vertically downwards., A vector can be represented by a straight line, whose length represents the magnitude of the, quantity and whose direction gives its line of action., An arrow on the line shows which way along the, line it acts., , 28, , 9781444176421_Section_01.indd 28, , 20/06/14 7:40 AM
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Friction, , A scalar quantity has magnitude only. Mass is a, scalar and is completely described when its value is, known. Scalars are added by ordinary arithmetic;, vectors are added geometrically, taking account of, their directions as well as their magnitudes., , ●● Friction, Friction is the force that opposes one surface moving,, or trying to move, over another. It can be a help or a, hindrance. We could not walk if there was no friction, between the soles of our shoes and the ground., Our feet would slip backwards, as they tend to if, we walk on ice. On the other hand, engineers try to, reduce friction to a minimum in the moving parts of, machinery by using lubricating oils and ball-bearings., When a gradually increasing force P is applied, through a spring balance to a block on a table, (Figure 7.7), the block does not move at first. This is, because an equally increasing but opposing frictional, force F acts where the block and table touch. At any, instant P and F are equal and opposite., If P is increased further, the block eventually, moves; as it does so F has its maximum value, called, starting or static friction. When the block is moving, at a steady speed, the balance reading is slightly less, than that for starting friction. Sliding or dynamic, friction is therefore less than starting or static, friction., Placing a mass on the block increases the force, pressing the surfaces together and increases friction., When work is done against friction, the, temperatures of the bodies in contact rise (as you can, test by rubbing your hands together); mechanical, energy is being changed into heat energy (see, Chapter 13)., block, , F, , Questions, 1 Jo, Daniel and Helen are pulling a metal ring. Jo pulls with, a force of 100 N in one direction and Daniel with a force, of 140 N in the opposite direction. If the ring does not, move, what force does Helen exert if she pulls in the same, direction as Jo?, 2 A boy drags a suitcase along the ground with a force of, 100 N. If the frictional force opposing the motion of the, suitcase is 50 N, what is the resultant forward force on the, suitcase?, 3 A picture is supported by two vertical strings; if the weight, of the picture is 50 N what is the force exerted by each, string?, 4 Using a scale of 1 cm to represent 10 N, find the size and, direction of the resultant of forces of 30 N and 40 N acting, at right angles to each other., 5 Find the size of the resultant of two forces of 5 N and 12 N, acting, a in opposite directions to each other,, b at 90° to each other., , Checklist, After studying this chapter you should be able to, • combine forces acting along the same straight line to find, their resultant,, • add vectors graphically to determine a resultant,, • distinguish between vectors and scalars and give examples, of each,, • understand friction as the force between two surfaces that, impedes motion and results in heating., , spring balance, , P, , Figure 7.7 Friction opposes motion between surfaces in contact., , 29, , 9781444176421_Section_01.indd 29, , 20/06/14 7:40 AM
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8, ●, ●, ●, ●, , Force and acceleration, , Newton’s first law, Mass and inertia, Newton’s second law, Weight and gravity, , ●● Newton’s first law, Friction and air resistance cause a car to come to rest, when the engine is switched off. If these forces were, absent we believe that a body, once set in motion,, would go on moving forever with a constant speed in, a straight line. That is, force is not needed to keep a, body moving with uniform velocity provided that no, opposing forces act on it., This idea was proposed by Galileo and is summed, up in Newton’s first law of motion:, A body stays at rest, or if moving it continues to move with, uniform velocity, unless an external force makes it behave, differently., , It seems that the question we should ask about a, moving body is not ‘what keeps it moving’ but ‘what, changes or stops its motion’., The smaller the external forces opposing a moving, body, the smaller is the force needed to keep it, moving with uniform velocity. An ‘airboard’, which is, supported by a cushion of air (Figure 8.1), can skim, across the ground with little frictional opposition,, so that relatively little power is needed to maintain, motion., , ●, ●, ●, ●, , Gravitational field, Newton’s third law, Air resistance: terminal velocity, Practical work: Effect of force and mass on acceleration, , ●● Mass and inertia, Newton’s first law is another way of saying that all, matter has a built-in opposition to being moved if, it is at rest or, if it is moving, to having its motion, changed. This property of matter is called inertia, (from the Latin word for laziness)., Its effect is evident on the occupants of a car that, stops suddenly; they lurch forwards in an attempt, to continue moving, and this is why seat belts are, needed. The reluctance of a stationary object to, move can be shown by placing a large coin on a, piece of card on your finger (Figure 8.2). If the card, is flicked sharply the coin stays where it is while the, card flies off., coin, , card, , Figure 8.2 Flick the card sharply, , The larger the mass of a body, the greater is its, inertia, i.e. the more difficult it is to move it, when at rest and to stop it when in motion. Because, of this we consider that the mass of a body, measures its inertia. This is a better definition, of mass than the one given earlier (Chapter 1) in, which it was stated to be the ‘amount of matter’, in a body., Figure 8.1 Friction is much reduced for an airboard., 30, , 9781444176421_Section_01.indd 30, , 20/06/14 7:40 AM
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newton’s second law, , Practical work, , Find the accelerations from the tape charts or computer, plots and tabulate the results. Do they suggest any relationship, between a and m?, , Effect of force and mass on, acceleration, , Mass (m)/(no. of trolleys), , The apparatus consists of a trolley to which a force is applied by a, stretched length of elastic (Figure 8.3). The velocity of the trolley, is found from a tickertape timer or a motion sensor, datalogger, and computer (see Figure 2.6, p.11)., First compensate the runway for friction: raise one end until, the trolley runs down with uniform velocity when given a push., The dots on the tickertape should be equally spaced, or a, horizontal trace obtained on a velocity–time graph. There is now, no resultant force on the trolley and any acceleration produced, later will be due only to the force caused by the stretched elastic., , a) Force and acceleration (mass constant), Fix one end of a short length of elastic to the rod at the back, of the trolley and stretch it until the other end is level with the, front of the trolley. Practise pulling the trolley down the runway,, keeping the same stretch on the elastic. After a few trials you, should be able to produce a steady accelerating force., tickertape timer, (or motion sensor), , trolley stretched elastic, , 1, , 2, , 3, , Acceleration (a)/cm/tentick2 or m/s2, , ●● Newton’s second law, The previous experiment should show roughly that, the acceleration a is, (i) directly proportional to the applied force F for a, fixed mass, i.e., a ∝ F, and, (ii) inversely proportional to the mass m for a fixed, force, i.e., a ∝ 1/m., Combining the results into one equation, we get, a ∝, Therefore, , F, m, , or, , F ∝ ma, , F = kma, , where k is the constant of proportionality., One newton is defined as the force which gives a mass of 1 kg, an acceleration of 1 m/s2, i.e., 1 N = 1 kg m/s2., , Figure 8.3, , Repeat using first two and then three identical pieces of elastic,, stretched side by side by the same amount, to give two and three, units of force., If you are using tickertape, make a tape chart for each force and, use it to find the acceleration produced in cm/tentick2 (see Chapter, 2). Ignore the start of the tape (where the dots are too close) and, the end (where the force may not be steady). If you use a motion, sensor and computer to plot a velocity–time graph, the acceleration, can be obtained in m/s2 from the slope of the graph (Chapter 3)., Does a steady force cause a steady acceleration? Put the, results in a table. Do they suggest any relationship between, acceleration, a, and force F?, Force (F)/(no. of pieces of elastic), , 1, , 2, , Acceleration (a)/cm/tentick2 or m/s2, , b) Mass and acceleration (force constant), Do the experiment as in a) using two pieces of elastic (i.e., constant F ) to accelerate first one trolley, then two (stacked, one above the other) and finally three. Check the friction, compensation of the runway each time., , 3, , So if m = 1 kg and a = 1 m/s2, then F = 1 N., Substituting in F = kma, we get k = 1 and so we, can write, F = ma, , This is Newton’s second law of motion. When, using it two points should be noted. First, F is, the resultant (or unbalanced) force causing the, acceleration a. Second, F must be in newtons, m, in kilograms and a in metres per second squared,, otherwise k is not 1. The law shows that a will be, largest when F is large and m small., You should now appreciate that when the forces, acting on a body do not balance there is a net, (resultant) force which causes a change of motion,, i.e. the body accelerates or decelerates. If the forces, balance, there is no change in the motion of the body., However, there may be a change of shape, in which, case internal forces in the body (i.e. forces between, neighbouring atoms) balance the external forces., 31, , 9781444176421_Section_01.indd 31, , 20/06/14 7:40 AM
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8, , ForCe And ACCelerAtion, , ●● Worked example, , ●● Gravitational field, , A block of mass 2 kg has a constant velocity when it, is pushed along a table by a force of 5 N. When the, push is increased to 9 N what is, , The force of gravity acts through space and can, cause a body, not in contact with the Earth, to fall, to the ground. It is an invisible, action-at-a-distance, force. We try to ‘explain’ its existence by saying that, the Earth is surrounded by a gravitational field, which exerts a force on any body in the field. Later,, magnetic and electric fields will be considered., , a the resultant force,, b the acceleration?, When the block moves with constant velocity the, forces acting on it are balanced. The force of friction, opposing its motion must therefore be 5 N., a When the push is increased to 9 N the resultant, (unbalanced) force F on the block is (9 − 5) N =, 4 N (since the frictional force is still 5 N)., b The acceleration a is obtained from F = ma where, F = 4 N and m = 2 kg., ∴ a =, , 4N, 4 kg m/s2, F, =, =, = 2 m/s2, m, 2 kg, 2 kg, , The strength of a gravitational field is defined as the force, acting on unit mass in the field., , Measurement shows that on the Earth’s surface a, mass of 1 kg experiences a force of 9.8 N, i.e. its, weight is 9.8 N. The strength of the Earth’s field, is therefore 9.8 N/kg (near enough 10 N/kg). It, is denoted by g, the letter also used to denote the, acceleration of free fall. Hence, g = 9.8 N/kg = 9.8 m/s2, , ●● Weight and gravity, The weight W of a body is the force of gravity acting, on it which gives it an acceleration g when it is falling, freely near the Earth’s surface. If the body has mass, m, then W can be calculated from F = ma. We put, F = W and a = g to give, W = mg, , Taking g = 9.8 m/s2 and m = 1 kg, this gives, W = 9.8 N, i.e. a body of mass 1 kg has weight, 9.8 N, or near enough 10 N. Similarly a body of, mass 2 kg has weight of about 20 N, and so on., While the mass of a body is always the same, its, weight varies depending on the value of g. On the, Moon the acceleration of free fall is only about, 1.6 m/s2, and so a mass of 1 kg has a weight of just, 1.6 N there., The weight of a body is directly proportional, to its mass, which explains why g is the same, for all bodies. The greater the mass of a body,, the greater is the force of gravity on it but it, does not accelerate faster when falling because, of its greater inertia (i.e. its greater resistance to, acceleration)., , We now have two ways of regarding g. When, considering bodies falling freely, we can think of, it as an acceleration of 9.8 m/s2. When a body of, known mass is at rest and we wish to know the force, of gravity (in N) acting on it we think of g as the, Earth’s gravitational field strength of 9.8 N/kg., , ●● Newton’s third law, If a body A exerts a force on body B, then body B exerts an, equal but opposite force on body A., , This is Newton’s third law of motion and states, that forces never occur singly but always in pairs, as a result of the action between two bodies. For, example, when you step forwards from rest your, foot pushes backwards on the Earth, and the Earth, exerts an equal and opposite force forward on you., Two bodies and two forces are involved. The small, force you exert on the large mass of the Earth gives, no noticeable acceleration to the Earth but the, equal force it exerts on your very much smaller mass, causes you to accelerate., Note that the pair of equal and opposite forces do, not act on the same body; if they did, there could, , 32, , 9781444176421_Section_01.indd 32, , 20/06/14 7:40 AM
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Air resistance: terminal velocity, , never be any resultant forces and acceleration would, be impossible. For a book resting on a table, the, book exerts a downward force on the table and the, table exerts an equal and opposite upward force on, the book; this pair of forces act on different objects, and are represented by the red arrows in Figure 8.4., The weight of the book (blue arrow) does not form, a pair with the upward force on the book (although, they are equal numerically) as these two forces act on, the same body., An appreciation of the third law and the effect of, friction is desirable when stepping from a rowing, boat (Figure 8.5). You push backwards on the boat, and, although the boat pushes you forwards with, an equal force, it is itself now moving backwards, , contact, force pair, , (because friction with the water is slight). This, reduces your forwards motion by the same amount –, so you may fall in!, , NE, , WT, , O N I II, , Figure 8.5 The boat moves backwards when you step forwards!, , push of table, on book, pull of Earth, on book, , push of book, on table, , gravitational, force pair, pull of book, on Earth, Figure 8.4 Forces between book and table, , ●● Air resistance: terminal velocity, When an object falls in air, the air resistance (fluid, friction) opposing its motion increases as its speed, rises, so reducing its acceleration. Eventually, air, resistance acting upwards equals the weight of the, object acting downwards. The resultant force on the, object is then zero since the gravitational force balances, the frictional force. The object falls at a constant, velocity, called its terminal velocity, whose value, depends on the size, shape and weight of the object., A small dense object, such as a steel ball-bearing,, has a high terminal velocity and falls a considerable, distance with a constant acceleration of 9.8 m/s2, before air resistance equals its weight. A light object,, like a raindrop, or an object with a large surface area,, such as a parachute, has a low terminal velocity and, only accelerates over a comparatively short distance, before air resistance equals its weight. A skydiver, (Figure 8.6) has a terminal velocity of more than, 50 m/s (180 km/h) before the parachute is opened., , Objects falling in liquids behave similarly to those, falling in air., , Figure 8.6 Synchronised skydivers, 33, , 9781444176421_Section_01.indd 33, , 20/06/14 7:40 AM
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8, , ForCe And ACCelerAtion, , Questions, 1 Which one of the diagrams in Figure 8.7 shows the, arrangement of forces that gives the block of mass M the, greatest acceleration?, A, 10 N, , M, , B, 12 N, , 2N, , 40 N, , 20 N, , C, 20 N, , M, , M, , 4N, , D, M, , 30 N, , E, 3N, , M, , 7 A rocket has a mass of 500 kg., a What is its weight on Earth where g = 10 N/kg?, b At lift-off the rocket engine exerts an upward force of, 25 000 N. What is the resultant force on the rocket?, What is its initial acceleration?, 8 Figure 8.9 shows the forces acting on a raindrop which is, falling to the ground., a (i) A is the force which causes the raindrop to fall., What is this force called?, (ii) B is the total force opposing the motion of the, drop. State one possible cause of this force., b What happens to the drop when force A = force B?, B, , 15 N, , raindrop, , Figure 8.7, , 2 In Figure 8.8 if P is a force of 20 N and the object moves, with constant velocity, what is the value of the opposing, force F ?, P, , object, , F, , Figure 8.8, , 3 a What resultant force produces an acceleration of 5 m/s2, in a car of mass 1000 kg?, b What acceleration is produced in a mass of 2 kg by a, resultant force of 30 N?, 4 A block of mass 500 g is pulled from rest on a horizontal, frictionless bench by a steady force F and travels 8 m in 2 s., Find, a the acceleration,, b the value of F., 5 Starting from rest on a level road a girl can reach a speed of, 5 m/s in 10 s on her bicycle. Find, a the acceleration,, b the average speed during the 10 s,, c the distance she travels in 10 s., Eventually, even though she is still pedalling as fast as, she can, she stops accelerating and her speed reaches a, maximum value. Explain in terms of the forces acting why, this happens., 6 What does an astronaut of mass 100 kg weigh, a on Earth where the gravitational field strength is, 10 N/kg,, b on the Moon where the gravitational field strength is, 1.6 N/kg?, , A, Figure 8.9, , 9 Explain the following using F = ma., a A racing car has a powerful engine and is made of, strong but lightweight material., b A car with a small engine can still accelerate rapidly., , Checklist, After studying this chapter you should be able to, • describe an experiment to investigate the relationship, between force, mass and acceleration,, • state the unit of force,, • state Newton’s second law of motion and use it to solve, problems,, • recall and use the equation W = mg, • define the strength of the Earth’s gravitational field,, • describe the motion of an object falling in air., , 34, , 9781444176421_Section_01.indd 34, , 20/06/14 7:41 AM
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Circular motion, , 9, ●, ●, ●, , Centripetal force, Rounding a bend, Looping the loop, , ●, ●, , There are many examples of bodies moving in, circular paths – rides at a funfair, clothes being, spun dry in a washing machine, the planets going, round the Sun and the Moon circling the Earth., When a car turns a corner it may follow an arc of a, circle. ‘Throwing the hammer’ is a sport practised at, highland games in Scotland (Figure 9.1), in which, the hammer is whirled round and round before it is, released., , Satellites, Practical work: Investigating circular motion, , ●● Centripetal force, In Figure 9.2 a ball attached to a string is being, whirled round in a horizontal circle. Its direction of, motion is constantly changing. At A it is along the, tangent at A; shortly afterwards, at B, it is along the, tangent at B; and so on., Velocity has both size and direction; speed has, only size. Velocity is speed in a stated direction, and if the direction of a moving body changes,, even if its speed does not, then its velocity has, changed. A change of velocity is an acceleration,, and so during its whirling motion the ball is, accelerating., It follows from Newton’s first law of motion, that if we consider a body moving in a circle to be, accelerating then there must be a force acting on it, to cause the acceleration. In the case of the whirling, ball it is reasonable to say the force is provided, by the string pulling inwards on the ball. Like the, acceleration, the force acts towards the centre of the, circle and keeps the body at a fixed distance from, the centre., A larger force is needed if, (i) the speed v of the ball is increased,, (ii) the radius r of the circle is decreased,, (iii) the mass m of the ball is increased., The rate of change of direction, and so the acceleration, a, is increased by (i) and (ii). It can be shown that, a = v2/r and so, from F = ma, we can write, F =, , Figure 9.1 ‘Throwing the hammer’, , string, A, , B, , This force, which acts towards the centre and, keeps a body moving in a circular path, is called the, centripetal force (centre-seeking force)., Should the force be greater than the string can, bear, the string breaks and the ball flies off with, ▲, ▲, , Figure 9.2, , force in string pulls, ball into a, circular path, , mv 2, r, , 35, , 9781444176421_Section_01.indd 35, , 20/06/14 7:41 AM
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9, , Circular motion, , steady speed in a straight line along the tangent,, i.e. in the direction of travel when the string broke, (as Newton’s first law of motion predicts). It is not, thrown outwards., Whenever a body moves in a circle (or circular, arc) there must be a centripetal force acting on it. In, throwing the hammer it is the pull of the athlete’s, arms acting on the hammer towards the centre of the, whirling path. When a car rounds a bend a frictional, force is exerted inwards by the road on the car’s tyres., , Practical work, , therefore, depends on the tyres and the road surface, being in a condition that enables them to provide, a sufficiently large frictional force – otherwise, skidding occurs., Safe cornering that does not rely entirely on, friction is achieved by ‘banking’ the road as in, Figure 9.4b. Some of the centripetal force is then, supplied by the part of the contact force N, from, the road surface on the car, that acts horizontally., A bend in a railway track is banked, so that the, outer rail is not strained by having to supply the, centripetal force by pushing inwards on the wheel, flanges., contact force N, , Investigating circular motion, Use the apparatus in Figure 9.3 to investigate the various, factors that affect circular motion. Make sure the rubber, bung is tied securely to the string and that the area around, you is clear of other students. The paper clip acts as an, indicator to aid keeping the radius of the circular motion, constant., Spin the rubber bung at a constant speed while adding more, weights to the holder; it will be found that the radius of the, orbit decreases. Show that if the rubber bung is spun faster,, more weights must be added to the holder to keep the radius, constant. Are these findings in agreement with the formula given, on p. 35 for the centripetal force, F = mv2/r ?, string, rubber bung, rubber tube, glass tube, paper clip (indicator), hanger and 10 g slotted weights, Figure 9.3, , ●● Rounding a bend, When a car rounds a bend, a frictional force is, exerted inwards by the road on the car’s tyres,, so providing the centripetal force needed to keep it, in its curved path (Figure 9.4a). Here friction, acts as an accelerating force (towards the centre, of the circle) rather than a retarding force (p. 29)., The successful negotiation of a bend on a flat road,, , a, , friction , centripetal force, , b, , horizontal effect, of N centripetal, force, , Figure 9.4, , ●● Looping the loop, A pilot who is not strapped into his aircraft can still, loop the loop without falling downwards at the top, of the loop. A bucket of water can be swung round, in a vertical circle without spilling. Some amusement, park rides (Figure 9.5) give similar effects. Can you, suggest what provides the centripetal force for each, of these three cases (i) at the top of the loop and (ii), at the bottom of the loop?, , ●● Satellites, For a satellite of mass m orbiting the Earth at, radius r with orbital speed v, the centripetal force,, F = mv2/r , is provided by gravity., To put an artificial satellite in orbit at a certain, height above the Earth it must enter the orbit at the, correct speed. If it does not, the force of gravity, which, decreases as height above the Earth increases, will not, be equal to the centripetal force needed for the orbit., This can be seen by imagining a shell fired, horizontally from the top of a very high mountain, (Figure 9.6). If gravity did not pull it towards the, centre of the Earth it would continue to travel, horizontally, taking path A. In practice it might take, path B. A second shell fired faster might take path C, , 36, , 9781444176421_Section_01.indd 36, , 20/06/14 7:41 AM
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Satellites, , The orbital period T (the time for one orbit), of a satellite = distance/velocity. So for a, circular orbit, T = 2πr, v, Satellites in high orbits have longer periods than, those in low orbits., The Moon is kept in a circular orbit round the, Earth by the force of gravity between it and the, Earth. It has an orbital period of 27 days., , a) Communication satellites, , Figure 9.5 Looping the loop at an amusement park, , and travel further. If a third shell is fired even faster,, it might never catch up with the rate at which the, Earth’s surface is falling away. It would remain at the, same height above the Earth (path D) and return to, the mountain top, behaving like a satellite., shell, A, mountain, , B, C, Earth, , Figure 9.6, , D, , These circle the Earth in orbits above the equator., Geostationary satellites have an orbit high above, the equator (36 000 km); they travel with the, same speed as the Earth rotates, so appear to be, stationary at a particular point above the Earth’s, surface – their orbital period is 24 hours. They are, used for transmitting television, intercontinental, telephone and data signals. Geostationary satellites, need to be well separated so that they do not, interfere with each other; there is room for, about 400., Mobile phone networks use many satellites in, much lower equatorial orbits; they are slowed, by the Earth’s atmosphere and their orbit has to, be regularly adjusted by firing a rocket engine., Eventually they run out of fuel and burn up in the, atmosphere as they fall to Earth., , b) Monitoring satellites, These circle the Earth rapidly in low polar orbits,, i.e. passing over both poles; at a height of 850 km, the orbital period is only 100 minutes. The Earth, rotates below them so they scan the whole surface, at short range in a 24-hour period and can be, used to map or monitor regions of the Earth’s, surface which may be inaccessible by other means., They are widely used in weather forecasting to, continuously transmit infrared pictures of cloud, patterns down to Earth (Figure 9.7), which are, picked up in turn by receiving stations around, the world., ▲, ▲, 37, , 9781444176421_Section_01.indd 37, , 20/06/14 7:41 AM
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9, , CirCulAr Motion, , Checklist, After studying this chapter you should be able to, • explain circular motion in terms of an unbalanced, centripetal force,, • describe an experiment to investigate the factors affecting, circular motion,, • explain how the centripetal force arises for a car rounding, a bend,, • understand satellite motion., , Figure 9.7 Satellite image of cloud over Europe, , Questions, 1 An apple is whirled round in a horizontal circle on the end, of a string which is tied to the stalk. It is whirled faster and, faster and at a certain speed the apple is torn from the, stalk. Why?, 2 A car rounding a bend travels in an arc of a circle., a What provides the centripetal force?, b Is a larger or a smaller centripetal force required if, (i) the car travels faster,, (ii) the bend is less curved,, (iii) the car has more passengers?, 3 Racing cars are fitted with tyres called ‘slicks’, which have, no tread pattern, for dry tracks, and with ‘tread’ tyres for, wet tracks. Why?, 4 A satellite close to the Earth (at a height of about 200 km), has an orbital speed of 8 km/s. Taking the radius of the orbit, as approximately equal to the Earth’s radius of 6400 km,, calculate the time it takes to make one orbit., , 38, , 9781444176421_Section_01.indd 38, , 20/06/14 7:41 AM
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10, ●, ●, ●, , Moments and levers, , Moment of a force, Balancing a beam, Levers, , ●, ●, , Conditions for equilibrium, Practical work: Law of moments, , ●● Moment of a force, , ●● Balancing a beam, , The handle on a door is at the outside edge so that it, opens and closes easily. A much larger force would be, needed if the handle were near the hinge. Similarly it, is easier to loosen a nut with a long spanner than with, a short one., The turning effect of a force is called the, moment of the force. It depends on both the, size of the force and how far it is applied from the, pivot or fulcrum. It is measured by multiplying the, force by the perpendicular distance of the line of, action of the force from the fulcrum. The unit is the, newton metre (N m)., , To balance a beam about a pivot, like the ruler in, Figure 10.2, the weights must be moved so that the, clockwise turning effect equals the anticlockwise, turning effect and the net moment on the beam, becomes zero. If the beam tends to swing clockwise,, m1 can be moved further from the pivot to increase its, turning effect; alternatively m2 can be moved nearer to, the pivot to reduce its turning effect. What adjustment, would you make to the position of m2 to balance the, beam if it is tending to swing anticlockwise?, , moment of a force = force × perpendicular distance of the line, of action of the force from fulcrum, , Practical work, Law of moments, , In Figure 10.1a, a force F acts on a gate at its edge,, and in Figure 10.1b it acts at the centre., In Figure 10.1a:, , d1, , moment of F about O = 5 N × 3 m = 15 N m, In Figure 10.1b:, , fulcrum (nail through, hole in ruler), , m1, , moment of F about O = 5 N × 1.5 m = 7.5 N m, The turning effect of F is greater in the first case; this, agrees with the fact that a gate opens most easily when, pushed or pulled at the edge furthest from the hinge., 3m, O, , hinge (fulcrum), , d2, , m2, , Figure 10.2, , Balance a half-metre ruler at its centre, adding Plasticine to one, side or the other until it is horizontal., Hang unequal loads m1 and m2 from either side of the fulcrum, and alter their distances d1 and d2 from the centre until the ruler, is again balanced (Figure 10.2). Forces F1 and F2 are exerted by, gravity on m1 and m2 and so on the ruler; the force on 100 g, is 1 N. Record the results in a table and repeat for other loads, and distances., , gate, m1/g, F 5 N, , F1/N, , d1/cm, , F1 × d1, /N cm, , m2/g, , F2/N, , d2/cm, , F2 × d2, / N cm, , a, , 1.5 m, , b, Figure 10.1, , 1.5 m, , F 5 N, , O, , F1 is trying to turn the ruler anticlockwise and F1 × d1 is, its moment. F2 is trying to cause clockwise turning and its, moment is F2 × d2. When the ruler is balanced or, as we say, in, equilibrium, the results should show that the anticlockwise, moment F1 × d1 equals the clockwise moment F2 × d2., , 39, , 9781444176421_Section_01.indd 39, , 20/06/14 7:42 AM
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10 MoMents And leVers, The law of moments (also called the law of the lever) is stated, as follows., When a body is in equilibrium the sum of the clockwise, moments about any point equals the sum of the anticlockwise, moments about the same point. There is no net moment on a, body which is in equilibrium., , can be calculated from the law of moments. As, the boulder just begins to move we can say, taking, moments about O, that, clockwise moment = anticlockwise moment, effort × 200 cm = 1000 N × 10 cm, 10000 N cm, = 50 N, 200 cm, , effort =, , ●● Worked example, The see-saw in Figure 10.3 balances when Shani of, weight 320 N is at A, Tom of weight 540 N is at B, and Harry of weight W is at C. Find W., 3m, A, , Examples of other levers are shown in Figure 10.5., How does the effort compare with the load for, scissors and a spanner in Figures 10.5c and d?, B, OA 10 cm, OB 200 cm, effort, , 3m, B, , O, 1m, , C, pivot, A, , 320 N, , 540 N, , O, fulcrum, , W, , Figure 10.3, , load, , Taking moments about the fulcrum, O:, anticlockwise moment = (320 N × 3 m) + (540 N × 1 m), = 960 N m + 540 N m, = 1500 N m, , Figure 10.4 Crowbar, effort, , clockwise moment = W × 3 m, By the law of moments,, clockwise moments = anticlockwise moments, ∴, , W × 3 m = 1500 N m, , ∴, , 1500 N m, W =, = 500 N, 3m, , fulcrum, , load, , Figure 10.5a Wheelbarrow, , ●● Levers, A lever is any device which can turn about a pivot., In a working lever a force called the effort is used, to overcome a resisting force called the load. The, pivotal point is called the fulcrum., If we use a crowbar to move a heavy boulder, (Figure 10.4), our hands apply the effort at one, end of the bar and the load is the force exerted, by the boulder on the other end. If distances, from the fulcrum O are as shown and the load, is 1000 N (i.e. the part of the weight of the, boulder supported by the crowbar), the effort, , effort, , biceps, muscle, , fulcrum, , load, , Figure 10.5b Forearm, , 40, , 9781444176421_Section_01.indd 40, , 20/06/14 7:42 AM
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Conditions for equilibrium, , clockwise moment = P × 5 m, , fulcrum, , effort, , anticlockwise moment = 400 N × 2 m, = 800 N m, Since the plank is in equilibrium we have from, (ii) above:, P × 5 m = 800 N m, , load, , ∴, , P =, , 800 N m, = 160 N, 5m, , From equation (1), , Figure 10.5c Scissors, , Q = 240 N, , fulcrum, 1m, , 1m, A, , effort, plank, load, , 2m, P, , 1m, O, , 1m, B, , trestle, , 500 N, , 2m, Q, C, , trestle, 400 N 700 N, , Figure 10.6, , Figure 10.5d Spanner, , Questions, , ●● Conditions for, equilibrium, Sometimes a number of parallel forces act on a body, so that it is in equilibrium. We can then say:, (i) The sum of the forces in one direction equals the sum, of the forces in the opposite direction., (ii) The law of moments must apply., , P + Q = 400 N, , 50 cm, , M, Figure 10.7, , 40 cm, , 100 g, , ▲, ▲, , A body is in equilibrium when there is no resultant, force and no resultant turning effect acting on it., As an example consider a heavy plank resting on, two trestles, as in Figure 10.6. In the next chapter we, will see that the whole weight of the plank (400 N), may be taken to act vertically downwards at its, centre, O. If P and Q are the upward forces exerted, by the trestles on the plank (called reactions) then we, have from (i) above:, , 1 The metre rule in Figure 10.7 is pivoted at its centre., If it balances, which of the following equations gives the, mass of M?, A M + 50 = 40 + 100, B M × 40 = 100 × 50, C M/50 = 100/40, D M/50 = 40/100, E M × 50 = 100 × 40, , (1), , Moments can be taken about any point but if we take, them about C, the moment due to force Q is zero., , 41, , 9781444176421_Section_01.indd 41, , 20/06/14 7:43 AM
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10 MoMents And leVers, , 2 Figure 10.8 shows three positions of the pedal on a bicycle, which has a crank 0.20 m long. If the cyclist exerts the same, vertically downward push of 25 N with his foot, in which, case, A, B or C, is the turning effect, (i) 25 × 0.2 = 5 N m,, (ii) 0,, (iii) between 0 and 5 N m?, Explain your answers., , Checklist, After studying this chapter you should be able to, • define the moment of a force about a point,, • describe qualitatively the balancing of a beam about a pivot,, • describe an experiment to verify that there is no net, moment on a body in equilibrium,, • state the law of moments and use it to solve problems,, • explain the action of common tools and devices as levers,, • state the conditions for equilibrium when parallel forces act, on a body., , force, chain, crank, , A, , B, , C, Figure 10.8, , 42, , 9781444176421_Section_01.indd 42, , 20/06/14 7:43 AM
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11 Centres of mass, l, l, , Toppling, Stability, , l, l, , Balancing tricks and toys, Practical work: Centre of mass using a plumb line, , A body behaves as if its whole mass were, concentrated at one point, called its centre of mass, or centre of gravity, even though the Earth attracts, every part of it. The body’s weight can be considered, to act at this point. The centre of mass of a uniform, ruler is at its centre and when supported there it can, be balanced, as in Figure 11.1a. If it is supported at, any other point it topples because the moment of its, weight W about the point of support is not zero, as, in Figure 11.1b., 0, , 50, , ruler, , 100, , 0, , 50, , 100, , support, W, , a, , b, , Figure 11.3 A tightrope walker using a long pole, , The centre of mass of a regularly shaped body that, has the same density throughout is at its centre. In, other cases it can be found by experiment., , Figure 11.1, , Your centre of mass is near the centre of your body, and the vertical line from it to the floor must be, within the area enclosed by your feet or you will, fall over. You can test this by standing with one, arm and the side of one foot pressed against a wall, (Figure 11.2). Now try to raise the other leg sideways., , raise this leg, , Figure 11.2 Can you do this without falling over?, , A tightrope walker has to keep his centre of mass, exactly above the rope. Some carry a long pole to, help them to balance (Figure 11.3). The combined, weight of the walker and pole is then spread out, more and if the walker begins to topple to one side,, he moves the pole to the other side., , Practical work, Centre of mass using a plumb line, Suppose we have to find the centre of mass of an irregularly, shaped lamina (a thin sheet) of cardboard., Make a hole A in the lamina and hang it so that it can swing, freely on a nail clamped in a stand. It will come to rest with, its centre of mass vertically below A. To locate the vertical line, through A, tie a plumb line (a thread and a weight) to the nail, (Figure 11.4), and mark its position AB on the lamina. The centre, of mass lies somewhere on AB., Hang the lamina from another position, C, and mark the, plumb line position CD. The centre of mass lies on CD and must, be at the point of intersection of AB and CD. Check this by, hanging the lamina from a third hole. Also try balancing it at its, centre of mass on the tip of your forefinger., Devise a method using a plumb line for finding the centre of, mass of a tripod., A, , hole, , C, , lamina, , nail clamped, in stand, centre of mass, , D, , B, plumb line, , Figure 11.4, , 43, , 9781444176421_Section_01.indd 43, , 20/06/14 7:43 AM
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11 Centres of mass, , ●● Toppling, The position of the centre of mass of a body, affects whether or not it topples over easily. This is, important in the design of such things as tall vehicles, (which tend to overturn when rounding a corner),, racing cars, reading lamps and even drinking glasses., A body topples when the vertical line through, its centre of mass falls outside its base, as in, Figure 11.5a. Otherwise it remains stable, as in, Figure 11.5b, where the body will not topple., , Racing cars have a low centre of mass and a wide, wheelbase for maximum stability., , centre of, mass, base, Figure 11.6a A tractor under test to find its centre of mass, , a Topples, , b Will not topple (stable), , Figure 11.5, , Toppling can be investigated by placing an empty can, on a plank (with a rough surface to prevent slipping), which is slowly tilted. The angle of tilt is noted when, the can falls over. This is repeated with a mass of 1 kg in, the can. How does this affect the position of the centre, of mass? The same procedure is followed with a second, can of the same height as the first but of greater width., It will be found that the second can with the mass in it, can be tilted through the greater angle., The stability of a body is therefore increased by, (i) lowering its centre of mass, and, (ii) increasing the area of its base., In Figure 11.6a the centre of mass of a tractor is, being found. It is necessary to do this when testing, a new design since tractors are often driven over, sloping surfaces and any tendency to overturn must, be discovered., The stability of double-decker buses is being, tested in Figure 11.6b. When the top deck only is, fully laden with passengers (represented by sand bags, in the test), it must not topple if tilted through an, angle of 28º., , Figure 11.6b A double-decker bus being tilted to test its stability, , ●● Stability, Three terms are used in connection with stability., , a) Stable equilibrium, A body is in stable equilibrium if when slightly, displaced and then released it returns to its previous, , 44, , 9781444176421_Section_01.indd 44, , 20/06/14 7:44 AM
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Balancing tricks and toys, , position. The ball at the bottom of the dish in Figure, 11.7a is an example. Its centre of mass rises when, it is displaced. It rolls back because its weight has, a moment about the point of contact that acts to, reduce the displacement., , b) Unstable equilibrium, A body is in unstable equilibrium if it moves, further away from its previous position when slightly, displaced and released. The ball in Figure 11.7b, behaves in this way. Its centre of mass falls when it is, displaced slightly because there is a moment which, increases the displacement. Similarly in Figure 11.1a, (p. 43) the balanced ruler is in unstable equilibrium., , c) Neutral equilibrium, A body is in neutral equilibrium if it stays in its new, position when displaced (Figure 11.7c). Its centre of, mass does not rise or fall because there is no moment, to increase or decrease the displacement., dish, , ●● Balancing tricks and toys, Some tricks that you can try or toys you can make, are shown in Figure 11.8. In each case the centre, of mass is vertically below the point of support and, equilibrium is stable., needle, cork, fork, , can, , a Balancing a needle on its point, , ball, point of contact, , card, centre, of mass, , spar, , weight, , bull-dog clip, , a Stable, centre of mass, b The perched parrot, , card, , point of, contact, , cork, , weight, , thick, wire, , b Unstable, matchsticks, iron nut, c Neutral, , c A rocking horse, , Figure 11.7 States of equilibrium, , Figure 11.8 Balancing tricks, , bar, , 45, , 9781444176421_Section_01.indd 45, , 20/06/14 7:44 AM
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11 Centres oF MAss, , A self-righting toy (Figure 11.9) has a heavy, base and, when tilted, the weight acting through, the centre of mass has a moment about the point, of contact. This restores it to the upright position., , Checklist, After studying this chapter you should be able to, • recall that an object behaves as if its whole mass were, concentrated at its centre of mass,, • recall that an object’s weight acts through the centre of, mass (or centre of gravity),, • describe an experiment to find the centre of mass of an, object,, • connect the stability of an object to the position of its centre, of mass., , Figure 11.9 A self-righting toy, , Questions, 1 Figure 11.10 shows a Bunsen burner in three different, positions. State in which position it is in, a stable equilibrium,, b unstable equilibrium,, c neutral equilibrium., , A, , B, , C, , Figure 11.10, , 2 The weight of the uniform bar in Figure 11.11 is 10 N. Does, it balance, tip to the right or tip to the left?, 0 10, , 40 50, , 100, , 3N, Figure 11.11, , 46, , 9781444176421_Section_01.indd 46, , 20/06/14 7:44 AM
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12, ●, ●, ●, , Momentum, , Conservation of momentum, Explosions, Rockets and jets, , ●, ●, , Momentum is a useful quantity to consider when, bodies are involved in collisions and explosions. It, is defined as the mass of the body multiplied by, its velocity and is measured in kilogram metre per, second (kg m/s) or newton second (N s)., , Repeat the experiment with another trolley stacked on top, of the one to be pushed so that two are moving before the, collision and three after., Copy and complete the tables of results., Before collision (m2 at rest), Mass, m1, (no. of trolleys), , momentum = mass × velocity, , A 2 kg mass moving at 10 m/s has momentum, 20 kg m/s, the same as the momentum of a 5 kg, mass moving at 4 m/s., , Momentum, m1v, , 2, After collision (m1 and m2 together), Velocity, v1/m/s, , Momentum, (m1 + m2)v1, , 2, , Collisions and momentum, , 3, , Figure 12.1 shows an arrangement which can be used to find, the velocity of a trolley before and after a collision. If a trolley, of length l takes time t to pass through a photogate, its velocity, = distance/time = l/t. Two photogates are needed, placed each, side of the collision point, to find the velocities before and after, the collision. Set them up so that they will record the time taken, for the passage of a trolley., , photogate 2, sloping, runway, , Velocity, v/m/s, , 1, , Mass, m1 + m2, (no. of trolleys), , Practical work, , trolley with, ‘interrupt card’, photogate 1, , Force and momentum, Sport: impulse and collision time, Practical work: Collisions and momentum, , ●, , to timer, , Figure 12.1, , ●● Conservation of, momentum, When two or more bodies act on one another, as in a, collision, the total momentum of the bodies remains constant,, provided no external forces act (e.g. friction)., , This statement is called the principle of, conservation of momentum. Experiments like, those in the Practical work section show that it is, true for all types of collisions., As an example, suppose a truck of mass 60 kg, moving with velocity 3 m/s collides and couples, with a stationary truck of mass 30 kg (Figure 12.2a)., The two move off together with the same velocity v, which we can find as follows (Figure 12.2b)., Total momentum before is, (60 kg × 3 m/s) + (30 kg × 0 m/s) = 180 kg m/s, ▲, ▲, , A tickertape timer or motion sensor, placed at the top end of the, runway, could be used instead of the photogates if preferred., Attach a strip of Velcro to each trolley so that they ‘stick’ to each, other on collision and compensate the runway for friction (see, Chapter 8). Place one trolley at rest halfway down the runway and, another at the top; give the top trolley a push. It will move forwards, with uniform velocity and should hit the second trolley so that they, travel on as one. Using the times recorded by the photogate timer,, calculate the velocity of the moving trolley before the collision and, the common velocity of both trolleys after the collision., , Do the results suggest any connection between the momentum, before the collision and after it in each case?, , 47, , 9781444176421_Section_01.indd 47, , 20/06/14 7:44 AM
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12 MoMentuM, , Total momentum after is, (60 kg + 30 kg) × v = 90 kg × v, Since momentum is not lost, 90 kg × v = 180 kg m/s or v = 2 m/s, 3m /s, 60 kg, , v, , at rest, 30 kg, , a Before, , 60 kg, , air, , balloon, , 30 kg, , b After, , Figure 12.2, , ●● Explosions, Momentum, like velocity, is a vector since it has both, magnitude and direction. Vectors cannot be added, by ordinary addition unless they act in the same, direction. If they act in exactly opposite directions,, such as east and west, the smaller subtracts from the, greater, or if the same they cancel out., Momentum is conserved in an explosion such as, occurs when a rifle is fired. Before firing, the total, momentum is zero since both rifle and bullet are, at rest. During the firing the rifle and bullet receive, equal but opposite amounts of momentum so, that the total momentum after firing is zero. For, example, if a rifle fires a bullet of mass 0.01 kg with, a velocity of 300 m/s,, forward momentum of bullet = 0.01 kg × 300 m/s, = 3 kg m/s, ∴, , by burning fuel and leaves the exhaust with large, momentum. The rocket or jet engine itself acquires, an equal forward momentum. Space rockets carry, their own oxygen supply; jet engines use the, surrounding air., , backward momentum of rifle = 3 kg m/s, , If the rifle has mass m, it recoils (kicks back) with a, velocity v such that, mv = 3 kg m/s, Taking m = 6 kg gives v = 3/6 m/s = 0.5 m/s., , ●● Rockets and jets, If you release an inflated balloon with its neck open,, it flies off in the opposite direction to that of the, escaping air. In Figure 12.3 the air has momentum, to the left and the balloon moves to the right with, equal momentum., This is the principle of rockets and jet engines. In, both, a high-velocity stream of hot gas is produced, , Figure 12.3 A deflating balloon demonstrates the principle of a rocket, or a jet engine., , ●● Force and momentum, If a steady force F acting on a body of mass m, increases its velocity from u to v in time t, the, acceleration a is given by, a = (v − u)/t, , (from v = u + at), , Substituting for a in F = ma,, F =, , m (v − u ) mv − mu, =, t, t, , Therefore, force =, , change of momentum = rate of change of, time, momentum, , This is another version of Newton’s second law. For, some problems it is more useful than F = ma., We also have, , Ft = mv − mu, , where mv is the final momentum, mu the initial, momentum and Ft is called the impulse., , ●● Sport: impulse and, collision time, The good cricketer or tennis player ‘follows, through’ with the bat or racket when striking, the ball (Figure 12.4a). The force applied then, acts for a longer time, the impulse is greater and, so also is the gain of momentum (and velocity), of the ball., When we want to stop a moving ball such as, a cricket ball, however, its momentum has to be, , 48, , 9781444176421_Section_01.indd 48, , 20/06/14 7:44 AM
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sport: impulse and collision time, , reduced to zero. An impulse is then required in, the form of an opposing force acting for a certain, time. While any number of combinations of force, and time will give a particular impulse, the ‘sting’, can be removed from the catch by drawing back the, hands as the ball is caught (Figure 12.4b). A smaller, average force is then applied for a longer time., , Figure 12.5 Sand reduces the athlete’s momentum more gently., , Questions, , Figure 12.4a Batsman ‘following through’ after hitting the ball, , Figure 12.4b Cricketer drawing back the hands to catch the ball, , The use of sand gives a softer landing for longjumpers (Figure 12.5), as a smaller stopping force, is applied over a longer time. In a car crash the, car’s momentum is reduced to zero in a very short, time. If the time of impact can be extended by, using crumple zones (see Figure 14.6, p. 58) and, extensible seat belts, the average force needed to, stop the car is reduced so the injury to passengers, should also be less., , 1 What is the momentum in kg m/s of a 10 kg truck travelling at, a 5 m/s,, b 20 cm/s,, c 36 km/h?, 2 A ball X of mass 1 kg travelling at 2 m/s has a head-on, collision with an identical ball Y at rest. X stops and Y, moves off. What is Y’s velocity?, 3 A boy with mass 50 kg running at 5 m/s jumps on to a 20 kg, trolley travelling in the same direction at 1.5 m/s. What is, their common velocity?, 4 A girl of mass 50 kg jumps out of a rowing boat of mass, 300 kg on to the bank, with a horizontal velocity of 3 m/s., With what velocity does the boat begin to move backwards?, 5 A truck of mass 500 kg moving at 4 m/s collides with, another truck of mass 1500 kg moving in the same, direction at 2 m/s. What is their common velocity just after, the collision if they move off together?, 6 The velocity of a body of mass 10 kg increases from 4 m/s to, 8 m/s when a force acts on it for 2 s., a What is the momentum before the force acts?, b What is the momentum after the force acts?, c What is the momentum gain per second?, d What is the value of the force?, 7 A rocket of mass 10 000 kg uses 5.0 kg of fuel and oxygen, to produce exhaust gases ejected at 5000 m/s. Calculate the, increase in its velocity., , Checklist, , After studying this chapter you should be able to, • define momentum,, • describe experiments to demonstrate the principle of, conservation of momentum,, • state and use the principle of conservation of momentum, to solve problems,, • understand the action of rocket and jet engines,, • state the relationship between force and rate of change, of momentum and use it to solve problems,, • use the definition of impulse to explain how the time of, impact affects the force acting in a collision., 49, , 9781444176421_Section_01.indd 49, , 20/06/14 7:45 AM
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13 Energy transfer, Forms of energy, Energy transfers, Energy measurements, Energy conservation, , l, l, l, l, , Energy is a theme that pervades all branches of, science. It links a wide range of phenomena and, enables us to explain them. It exists in different forms, and when something happens, it is likely to be due to, energy being transferred from one form to another., Energy transfer is needed to enable people, computers,, machines and other devices to work and to enable, processes and changes to occur. For example, in Figure, 13.1, the water skier can only be pulled along by the, boat if there is energy transfer in its engine from the, burning petrol to its rotating propeller., , l, l, l, , Energy of food, Combustion of fuels, Practical work: Measuring power, , ●● Forms of energy, a) Chemical energy, Food and fuels, like oil, gas, coal and wood, are, concentrated stores of chemical energy (see, Chapter 15). The energy of food is released by, chemical reactions in our bodies, and during the, transfer to other forms we are able to do useful jobs., Fuels cause energy transfers when they are burnt in, an engine or a boiler. Batteries are compact sources, of chemical energy, which in use is transferred to, electrical energy., , b) Potential energy (p.e.), This is the energy a body has because of its position or, condition. A body above the Earth’s surface, like water, in a mountain reservoir, has potential energy (p.e.), stored in the form of gravitational potential energy., Work has to be done to compress or stretch a, spring or elastic material and energy is transferred, to potential energy; the p.e. is stored in the form of, strain energy (or elastic potential energy). If the, catapult in Figure 13.3c were released, the strain, energy would be transferred to the projectile., , c) Kinetic energy (k.e.), Any moving body has kinetic energy (k.e.) and the, faster it moves, the more k.e. it has. As a hammer, drives a nail into a piece of wood, there is a transfer of, energy from the k.e. of the moving hammer to other, forms of energy., , d) Electrical energy, Electrical energy is produced by energy transfers at, power stations and in batteries. It is the commonest, form of energy used in homes and industry because of, the ease of transmission and transfer to other forms., , e) Heat energy, Figure 13.1 Energy transfer in action, , This is also called thermal or internal energy and is, the final fate of other forms of energy. It is transferred, by conduction, convection or radiation., , 50, , 9781444176421_Section_01.indd 50, , 20/06/14 7:45 AM
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Energy transfers, , f) Other forms, These include light energy and other forms of, electromagnetic radiation, sound and nuclear, energy., , ●● Energy transfers, a) Demonstration, The apparatus in Figure 13.2 can be used to show, a battery changing chemical energy to electrical, energy which becomes kinetic energy in the electric, motor. The motor raises a weight, giving it potential, energy. If the changeover switch is joined to the, lamp and the weight allowed to fall, the motor acts, as a generator in which there is an energy transfer, from kinetic energy to electrical energy. When this, is supplied to the lamp, it produces a transfer to heat, and light energy., , a Potential energy to kinetic energy, , lamp (1.25 V), changeover, switch, , b Electrical energy to heat and light energy, , large motor/, generator, , to 4 V battery, , line shaft, unit, , weight, (500 g), , c Chemical energy (from muscles in the arm) to p.e. (strain, energy of catapult), , Figure 13.2 Demonstrating energy transfers, , b) Other examples, Study the energy transfers shown in Figures, 13.3a to d. Some devices have been invented to, cause particular energy transfers. For example, a, microphone changes sound energy into electrical, energy; a loudspeaker does the reverse. Belts, chains, or gears are used to transfer energy between moving, parts, such as those in a bicycle., , d Potential energy of water to kinetic energy of turbine, to electrical energy from generator, Figure 13.3 Some energy transfers, 51, , 9781444176421_Section_01.indd 51, , 20/06/14 7:45 AM
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13 energy trAnsFer, , ●● Energy measurements, , 3 kg, , a) Work, In science the word work has a different, meaning from its everyday use. Work is done, when a force moves. No work is done in the, scientific sense by someone standing still holding a, heavy pile of books: an upward force is exerted, but, no motion results., If a building worker carries ten bricks up to the, first floor of a building, he does more work than if he, carries only one brick because he has to exert a larger, force. Even more work is required if he carries the, ten bricks to the second floor. The amount of work, done depends on the size of the force applied and the, distance it moves. We therefore measure work by, work = force × distance moved in direction of force, , (1), , The unit of work is the joule (J); it is the work done, when a force of 1 newton (N) moves through 1 metre, (m). For example, if you have to pull with a force, of 50 N to move a crate steadily 3 m in the direction, of the force (Figure 13.4a), the work done is, 50 N × 3 m = 150 N m = 150 J. That is, joules = newtons × metres, If you lift a mass of 3 kg vertically through 2 m, (Figure 13.4b), you have to exert a vertically upward, force equal to the weight of the body, i.e. 30 N, (approximately) and the work done is 30 N × 2 m =, 60 N m = 60 J., Note that we must always take the distance in the, direction in which the force acts., , 2m, , Figure 13.4b, , b) Measuring energy transfers, In an energy transfer, work is done. The work, done is a measure of the amount of energy, transferred. For example, if you have to exert, an upward force of 10 N to raise a stone steadily, through a vertical distance of 1.5 m, the work done, is 15 J. This is also the amount of chemical energy, transferred from your muscles to potential energy of, the stone. All forms of energy, as well as work, are, measured in joules., , c) Power, The more powerful a car is, the faster it can accelerate, or climb a hill, i.e. the more rapidly it does work., The power of a device is the work it does per second,, i.e. the rate at which it does work. This is the same, as the rate at which it transfers energy from one, form to another., power =, , work done energy transfer, =, time taken, time taken, , (2), , The unit of power is the watt (W) and is a rate, of working of 1 joule per second, i.e. 1 W =, 1 J/s. Larger units are the kilowatt (kW) and the, megawatt (MW):, 1 kW = 1000 W = 103 W, 1 mW = 1 000 000 W = 106 W, , 50 N, 3m, , If a machine does 500 J of work in 10 s, its power is, 500 J/10 s = 50 J/s = 50 W. A small car develops a, maximum power of about 25 kW., , Figure 13.4a, , 52, , 9781444176421_Section_01.indd 52, , 20/06/14 7:46 AM
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energy of food, , Practical work, , efficiency =, , useful energy output, × 100%, total energy input, , Measuring power, a) Your own power, Get someone with a stopwatch to time you running up a flight of, stairs, the more steps the better. Find your weight (in newtons)., Calculate the total vertical height (in metres) you have climbed by, measuring the height of one step and counting the number of, steps., The work you do (in joules) in lifting your weight to the top of, the stairs is (your weight) × (vertical height of stairs). Calculate, your power (in watts) from equation (2). About 0.5 kW is good., , b) Electric motor, This experiment is described in Chapter 40., , For example, for the lever shown in Figure 10.4 (p. 40), efficiency = work done on load × 100%, work done by effort, This will be less than 100% if there is friction in the, fulcrum., Table 13.1 lists the efficiencies of some devices and, the energy transfers involved., Table 13.1, , ●● Energy conservation, a) Principle of conservation of energy, This is one of the basic laws of physics and is stated as, follows., Energy cannot be created or destroyed; it is always conserved., , However, energy is continually being transferred, from one form to another. Some forms, such as, electrical and chemical energy, are more easily, transferred than others, such as heat, for which it is, hard to arrange a useful transfer., Ultimately all energy transfers result in the, surroundings being heated (as a result of doing, work against friction) and the energy is wasted, i.e., spread out and increasingly more difficult to use., For example, when a brick falls its potential energy, becomes kinetic energy; as it hits the ground, its, temperature rises and heat and sound are produced., If it seems in a transfer that some energy has, disappeared, the ‘lost’ energy is often converted, into non-useful heat. This appears to be the fate of, all energy in the Universe and is one reason why, new sources of useful energy have to be developed, (Chapter 15)., , b) Efficiency of energy transfers, , % Efficiency, , Energy transfer, , large electric motor, , 90, , electrical to k.e., , large electric generator, , 90, , k.e. to electrical, , domestic gas boiler, , 75, , chemical to heat, , compact fluorescent lamp, , 50, , electrical to light, , steam turbine, , 45, , heat to k.e., , car engine, , 25, , chemical to k.e., , filament lamp, , 10, , electrical to light, , A device is efficient if it transfers energy mainly to, useful forms and the ‘lost’ energy is small., , ●● Energy of food, When food is eaten it reacts with the oxygen we, breathe into our lungs and is slowly ‘burnt’. As, a result chemical energy stored in food becomes, thermal energy to warm the body and mechanical, energy for muscular movement., The energy value of a food substance is the amount of, energy released when 1 kg is completely oxidised., , Energy value is measured in J/kg. The energy, values of some foods are given in Figure 13.5 in, megajoules per kilogram., ▲, ▲, , The efficiency of a device is the percentage of the, energy supplied to it that is usefully transferred. It is, calculated from the expression:, , Device, , 53, , 9781444176421_Section_01.indd 53, , 20/06/14 7:46 AM
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13 energy trAnsFer, , cheese 21, beef 10, , 31, , BUTTER, , 26, , M A R GAR IN E, , Table 13.2 Heating values of fuels in kJ/g, , FLO15UR, 16, , potatoes 4, 9, , M ILK, 2.9, carrots 1.7, , apples 2.6, , A fuel for a space rocket (e.g. liquid hydrogen), must also burn very quickly so that the gases created, expand rapidly and leave the rocket at high speed., The heating values of some fuels are given in, Table 13.2 in kilojoules per gram., , eggs 7, , Figure 13.5 Energy values of some foods in MJ/kg, , Foods with high values are ‘fattening’ and if more, food is eaten than the body really needs, the extra, is stored as fat. The average adult requires about, 10 MJ per day., Our muscles change chemical energy into, mechanical energy when we exert a force – to, lift a weight, for example. Unfortunately, they, are not very good at doing this; of every 100 J of, chemical energy they use, they can convert only, 25 J into mechanical energy – that is, they are only, 25% efficient at changing chemical energy into, mechanical energy. The other 75 J becomes thermal, energy, much of which the body gets rid of by, sweating., , ●● Combustion of fuels, Fuels can be solids such as wood and coal, liquids, such as fuel oil and paraffin, or gases such as, methane and butane., Some fuels are better than others for certain jobs., For example, fuels for cooking or keeping us warm, should, as well as being cheap, have a high heating, value. This means that every gram of fuel should, produce a large amount of heat energy when burnt., , Solids, , Value, , Liquids, , Value, , Gases, , Value, , wood, , 17, , fuel oil, , 45, , methane, , 55, , coal, , 25–33, , paraffin, , 48, , butane, , 50, , The thick dark liquid called petroleum or crude oil, is the source of most liquid and gaseous fuels. It is, obtained from underground deposits at oil wells in, many parts of the world. Natural gas (methane) is, often found with it. In an oil refinery different fuels, are obtained from petroleum, including fuel oil for, industry, diesel oil for lorries, paraffin (kerosene), for jet engines, and petrol for cars, as well as butane, (bottled gas)., , Questions, 1 Name the energy transfers which occur when, a an electric bell rings,, b someone speaks into a microphone,, c a ball is thrown upwards,, d there is a picture on a television screen,, e a torch is on., 2 Name the forms of energy represented by the letters A, B,, C and D in the following statement., In a coal-fired power station, the (A) energy of coal, becomes (B) energy which changes water into steam., The steam drives a turbine which drives a generator. A, generator transfers (C) energy into (D) energy., 3 How much work is done when a mass of 3 kg (weighing, 30 N) is lifted vertically through 6 m?, 4 A hiker climbs a hill 300 m high. If she has a mass of 50 kg, calculate the work she does in lifting her body to the top of, the hill., 5 In loading a lorry a man lifts boxes each of weight 100 N, through a height of 1.5 m., a How much work does he do in lifting one box?, b How much energy is transferred when one box is lifted?, c If he lifts four boxes per minute at what power is he, working?, 6 A boy whose weight is 600 N runs up a flight of stairs 10 m, high in 12 s. What is his average power?, , 54, , 9781444176421_Section_01.indd 54, , 20/06/14 7:46 AM
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Combustion of fuels, , 7 a When the energy input to a gas-fired power station is, 1000 MJ, the electrical energy output is 300 MJ. What, is the efficiency of the power station in changing the, energy in gas into electrical energy?, b What form does the 700 MJ of ‘lost’ energy take?, c What is the fate of the ‘lost’ energy?, 8 State what energy transfers occur in, a a hairdryer,, b a refrigerator,, c an audio system., 9 An escalator carries 60 people of average mass 70 kg to, a height of 5 m in one minute. Find the power needed, to do this., , Checklist, After studying this chapter you should be able to, • recall the different forms of energy,, • describe energy transfers in given examples,, • relate work done to the magnitude of a force and the, distance moved,, • use the relation work done = force × distance moved to, calculate energy transfer,, • define the unit of work,, • relate power to work done and time taken, and give, examples,, • recall that power is the rate of energy transfer, give its unit, and solve problems,, • describe an experiment to measure your own power,, • state the principle of conservation of energy,, • understand qualitatively the meaning of efficiency,, • recall and use the equation, efficiency =, , useful energy output, × 100%, energy input, , 55, , 9781444176421_Section_01.indd 55, , 20/06/14 7:46 AM
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14, ●, ●, ●, ●, , Kinetic and potential energy, , Kinetic energy (k.e.), Potential energy (p.e.), Conservation of energy, Elastic and inelastic collisions, , ●, ●, , Energy and its different forms were discussed earlier, (Chapter 13). Here we will consider kinetic energy, (k.e.) and potential energy (p.e.) in more detail., , ●● Kinetic energy (k.e.), Kinetic energy is the energy a body has because of its motion., , A body above the Earth’s surface is considered to, have an amount of gravitational potential energy equal, to the work that has been done against gravity by the, force used to raise it. To lift a body of mass m through, a vertical height h at a place where the Earth’s, gravitational field strength is g, needs a force equal, and opposite to the weight mg of the body. Hence, work done by force = force × vertical height, = mg × h, , For a body of mass m travelling with velocity v,, kinetic energy = Ek =, , 1 2, mv, 2, , If m is in kg and v in m/s, then kinetic energy is, in J. For example, a football of mass 0.4 kg (400 g), moving with velocity 20 m/s has, 1, k.e. = 1 mv2 = × 0.4 kg × (20)2 m2/s2, 2, 2, = 0.2 × 400 kg m/s2 × m, = 80 N m = 80 J, Since k.e. depends on v2, a high-speed vehicle, travelling at 1000 km/h (Figure 14.1), has one, hundred times the k.e. it has at 100 km/h., , ●● Potential energy (p.e.), Potential energy is the energy a body has because of its position, or condition., , Driving and car safety, Practical work: Change of p.e. to k.e., , ∴, , potential energy = Ep = mgh, , When m is in kg, g in N/kg (or m/s2) and h in m,, the potential energy is in J. For example, if, g = 10 N/kg, the potential energy gained by a, 0.1 kg (100 g) mass raised vertically by 1 m is, 0.1 kg × 10 N/kg × 1 m = 1 N m = 1 J, Note Strictly speaking we are concerned with changes, in potential energy from that which a body has at, the Earth’s surface, rather than with actual values., The expression for potential energy is therefore more, correctly written, ∆Ep = mgh, , where ∆ (pronounced ‘delta’) stands for ‘change in’., , Figure 14.1 Kinetic energy depends on the square of the velocity., , 56, , 9781444176421_Section_01.indd 56, , 20/06/14 7:46 AM
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Elastic and inelastic collisions, , Practical work, , m, , p.e. mgh, k.e. 0, , m, , p.e. k.e., , Change of p.e. to k.e., Friction-compensate a runway and arrange the apparatus as in, Figure 14.2 with the bottom of the 0.1 kg (100 g) mass 0.5 m, from the floor., Start the timer and release the trolley. It will accelerate until the, falling mass reaches the floor; after that it moves with constant, velocity v., From your results calculate v in m/s (on the tickertape, 50 ticks = 1 s). Find the mass of the trolley in kg. Work out:, k.e. gained by trolley and 0.1 kg mass = ___ J, p.e. lost by 0.1 kg mass = ___ J, Compare and comment on the results., , to tickertape, timer (or, motion sensor), , trolley, , friction-compensated, runway, thread pulley, , h, , k.e. mgh, p.e. 0, Figure 14.3 Loss of p.e. = gain of k.e., , This is an example of the principle of, conservation of energy which was discussed, in Chapter 13., In the case of a pendulum (Figure 14.4), kinetic, and potential energy are interchanged continually., The energy of the bob is all potential energy at the, end of the swing and all kinetic energy as it passes, through its central position. In other positions it has, both potential and kinetic energy. Eventually all the, energy is changed to heat as a result of overcoming, air resistance., , 100 g, 0.5 m, floor, Figure 14.2, , p.e., , p.e., p.e. k.e., , ●● Conservation of, energy, , p.e. k.e., , Figure 14.4 Interchange of p.e. and k.e. for a simple pendulum, , ●● Elastic and inelastic, collisions, In all collisions (where no external force acts) there, is normally a loss of kinetic energy, usually to heat, energy and to a small extent to sound energy. The, greater the proportion of kinetic energy lost, the less, elastic is the collision, i.e. the more inelastic it is. In, a perfectly elastic collision, kinetic energy is conserved., ▲, ▲, , A mass m at height h above the ground has potential, energy = mgh (Figure 14.3). When it falls, its, velocity increases and it gains kinetic energy at the, expense of its potential energy. If it starts from rest, and air resistance is negligible, its kinetic energy on, reaching the ground equals the potential energy lost, by the mass, 1 2, mv = mgh, 2, or, loss of p.e. = gain of k.e., , k.e., , 57, , 9781444176421_Section_01.indd 57, , 20/06/14 7:46 AM
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14 KinetiC And PotentiAl energy, Table 14.1, Speed/mph, , 20, , 40, , 60, , 80, , Thinking distance/metres, , 6, , 12, , 18, , 24, , Braking distance/metres, , 6, , 24, , 54, , 96, , Total stopping distance/metres, , 12, , 36, , 72, , 120, , b) Car design and safety, , Figure 14.5 Newton’s cradle is an instructive toy for studying collisions, and conservation of energy., , ●● Driving and car safety, a) Braking distance and speed, For a car moving with speed v, the brakes must, be applied over a braking distance s to bring the, car to rest. The braking distance is directly, proportional to the square of the speed, i.e. if v, is doubled, s is quadrupled. The thinking distance, (i.e. the distance travelled while the driver is reacting, before applying the brakes) has to be added to the, braking distance to obtain the overall stopping, distance, in other words, stopping distance = thinking distance + braking distance, , Typical values taken from the Highway Code are, given in Table 14.1 for different speeds. The greater, the speed, the greater the stopping distance for, a given braking force. (To stop the car in a given, distance a greater braking force is needed for higher, speeds.), Thinking distance depends on the driver’s, reaction time – this will vary with factors such as the, driver’s degree of tiredness, use of alcohol or drugs,, eyesight and the visibility of the hazard. Braking, distance varies with both the road conditions and, the state of the car; it is longer when the road is, wet or icy, when friction between the tyres and the, road is low, than when conditions are dry. Efficient, brakes and deep tyre tread help to reduce the, braking distance., , When a car stops rapidly in a collision, large forces, are produced on the car and its passengers, and their, kinetic energy has to be dissipated., Crumple zones at the front and rear collapse, in such a way that the kinetic energy is absorbed, gradually (Figure 14.6). As we saw in Chapter 12, this extends the collision time and reduces the, decelerating force and hence the potential for injury, to the passengers., Extensible seat belts exert a backwards force (of, 10 000 N or so) over about 0.5 m, which is roughly, the distance between the front seat occupants and the, windscreen. In a car travelling at 15 m/s (34 mph), the, effect felt by anyone not using a seat belt is the same as, that produced by jumping off a building 12 m high!, Air bags in some cars inflate and protect the driver, from injury by the steering wheel., Head restraints ensure that if the car is hit from, behind, the head goes forwards with the body and, not backwards over the top of the seat. This prevents, damage to the top of the spine., All these are secondary safety devices which aid, survival in the event of an accident. Primary safety, factors help to prevent accidents and depend on the, car’s roadholding, brakes, steering, handling and, above all on the driver since most accidents are due, to driver error., The chance of being killed in an accident is, about five times less if seat belts are worn and head, restraints are installed., , Figure 14.6 Cars in an impact test showing the collapse of the front, crumple zone, , 58, , 9781444176421_Section_01.indd 58, , 20/06/14 7:47 AM
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Worked example, , ●● Worked example, A boulder of mass 4 kg rolls over a cliff and reaches, the beach below with a velocity of 20 m/s. Find: a, the kinetic energy of the boulder as it lands; b the, potential energy of the boulder when it was at the, top of the cliff and c the height of the cliff., a Mass of boulder = m = 4 kg, Velocity of boulder as it lands = v = 20 m/s, ∴, , k.e. of boulder as it lands = E k = 1 mv 2, 2, 1, = × 4 kg × ( 20)2 m2 /s2, 2, = 800 kg m/s2 × m, = 800 N m, = 800 J, , b Applying the principle of conservation of energy, (and neglecting energy lost in overcoming air, resistance),, p.e. of boulder on cliff = k.e. as it lands, ∴, , ∆Ep = Ek = 800 J, , c If h is the height of the cliff,, ∆Ep = mgh, ∴, , h =, , ∆E p, 800 J, 800 N m, =, =, mg, 4 kg × 10 m/s2, 40 kg m/s2, =, , 800 kg m/s2 × m, = 20 m, 40 kg m/s2, , Questions, 1 Calculate the k.e. of, a a 1 kg trolley travelling at 2 m/s,, b a 2 g (0.002 kg) bullet travelling at 400 m/s,, c a 500 kg car travelling at 72 km/h., 2 a What is the velocity of an object of mass 1 kg which has, 200 J of k.e.?, b Calculate the p.e. of a 5 kg mass when it is (i) 3 m, (ii), 6 m, above the ground. (g = 10 N/kg), 3 A 100 g steel ball falls from a height of 1.8 m on to a metal, plate and rebounds to a height of 1.25 m. Find, a the p.e. of the ball before the fall (g = 10 m/s2),, b its k.e. as it hits the plate,, c its velocity on hitting the plate,, d its k.e. as it leaves the plate on the rebound,, e its velocity of rebound., 4 It is estimated that 7 × 106 kg of water pours over the, Niagara Falls every second. If the falls are 50 m high, and if, all the energy of the falling water could be harnessed, what, power would be available? (g = 10 N/kg), , Checklist, After studying this chapter you should be able to, • define kinetic energy (k.e.),, • perform calculations using Ek = 21 mv2,, • define potential energy (p.e.),, • calculate changes in p.e. using ∆Ep = mgh,, • apply the principle of conservation of energy to simple, mechanical systems, such as a pendulum,, • recall the effect of speed on the braking distance of a, vehicle,, • describe secondary safety devices in cars., , 59, , 9781444176421_Section_01.indd 59, , 20/06/14 7:47 AM
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15 Energy sources, l, l, , Non-renewable energy sources, Renewable energy sources, , Energy is needed to heat buildings, to make cars, move, to provide artificial light, to make computers, work, and so on. The list is endless. This ‘useful’, energy needs to be produced in controllable energy, transfers (Chapter 13). For example, in power, stations a supply of useful energy in the form of, electricity is produced. The ‘raw materials’ for energy, production are energy sources. These may be, non-renewable or renewable. Apart from nuclear,, geothermal, hydroelectric or tidal energy, the Sun is, the source for all our energy resources., , ●● Non-renewable energy, sources, Once used up these cannot be replaced., , a) Fossil fuels, These include coal, oil and natural gas, formed, from the remains of plants and animals which lived, millions of years ago and obtained energy originally, from the Sun. At present they are our main energy, source. Predictions vary as to how long they will last, since this depends on what reserves are recoverable, and on the future demands of a world population, expected to increase from about 7000 million in, 2011 to at least 7600 million by the year 2050., Some estimates say oil and gas will run low early, in the present century but coal should last for, 200 years or so., Burning fossil fuels in power stations and in, cars pollutes the atmosphere with harmful gases, such as carbon dioxide and sulfur dioxide. Carbon, dioxide emission aggravates the greenhouse effect, (Chapter 24) and increases global warming. It is, not immediately feasible to prevent large amounts, of carbon dioxide entering the atmosphere, but, less is produced by burning natural gas than by, burning oil or coal; burning coal produces most, carbon dioxide for each unit of energy produced., When coal and oil are burnt they also produce sulfur, dioxide which causes acid rain. The sulfur dioxide, can be extracted from the waste gases so it does not, enter the atmosphere or the sulfur can be removed, , l, l, , Power stations, Economic, environmental and social issues, , from the fuel before combustion, but these are both, costly processes which increase the price of electricity, produced using these measures., , b) Nuclear fuels, The energy released in a nuclear reactor, (Chapter 50) from uranium, found as an ore in the, ground, can be used to produce electricity. Nuclear, fuels do not pollute the atmosphere with carbon, dioxide or sulfur dioxide but they do generate, radioactive waste materials with very long half-lives, (Chapter 49); safe ways of storing this waste for, perhaps thousands of years must be found. As long, as a reactor is operating normally it does not pose a, radiation risk, but if an accident occurs, dangerous, radioactive material can leak from the reactor and, spread over a large area., Two advantages of all non-renewable fuels are, (i) their high energy density (i.e. they are, concentrated sources) and the relatively small, size of the energy transfer device (e.g. a furnace), which releases their energy, and, (ii) their ready availability when energy demand, increases suddenly or fluctuates seasonally., , ●● Renewable energy, sources, These cannot be exhausted and are generally nonpolluting., , a) Solar energy, The energy falling on the Earth from the Sun is, mostly in the form of light and in an hour equals, the total energy used by the world in a year., Unfortunately its low energy density requires large, collecting devices and its availability varies. Its, greatest potential use is as an energy source for lowtemperature water heating. This uses solar panels as, the energy transfer devices, which convert light into, heat energy. They are used increasingly to produce, domestic hot water at about 70 ºC and to heat, swimming pools., , 60, , 9781444176421_Section_01.indd 60, , 20/06/14 7:47 AM
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Renewable energy sources, , Solar energy can also be used to produce hightemperature heating, up to 3000 ºC or so, if a large, curved mirror (a solar furnace) focuses the Sun’s, rays on to a small area. The energy can then be used, to turn water to steam for driving the turbine of an, electric generator in a power station., , b) Wind energy, Giant windmills called wind turbines with two or, three blades each up to 30 m long drive electrical, generators. ‘Wind farms’ of 20 to 100 turbines, spaced about 400 m apart (Figure 2d, p. ix), supply, about 400 MW (enough electricity for 250 000, homes) in the UK and provide a useful, ‘top-up’ to the National Grid., Wind turbines can be noisy and may be considered, unsightly so there is some environmental objection, to wind farms, especially as the best sites are often in, coastal or upland areas of great natural beauty., , c) Wave energy, , Figure 15.1 Solar cells on a house provide electricity., , Solar cells, made from semiconducting materials,, convert sunlight into electricity directly. A number, of cells connected together can be used to supply, electricity to homes (Figure 15.1) and to the, electronic equipment in communication and, other satellites. They are also used for small-scale, power generation in remote areas of developing, countries where there is no electricity supply. Recent, developments have made large-scale generation, more cost effective and there is now a large solar, power plant in California. There are many designs, for prototype light vehicles run on solar power, (Figure 15.2)., , Figure 15.2 Solar-powered car, , The rise and fall of sea waves has to be transferred by, some kind of wave-energy converter into the rotary, motion required to drive a generator. It is a difficult, problem and the large-scale production of electricity, by this means is unlikely in the near future, but, small systems are being developed to supply island, communities with power., , d) Tidal and hydroelectric energy, The flow of water from a higher to a lower level from, behind a tidal barrage (barrier) or the dam of a, hydroelectric scheme is used to drive a water turbine, (water wheel) connected to a generator., One of the largest working tidal schemes is the La, Grande I project in Canada (Figure 15.3). Feasibility, studies have shown that a 10-mile-long barrage, across the Severn Estuary could produce about 7% of, today’s electrical energy consumption in England and, Wales. Such schemes have significant implications for, the environment, as they may destroy wildlife habitats, of wading birds for example, and also for shipping, routes., In the UK, hydroelectric power stations generate, about 2% of the electricity supply. Most are located, in Scotland and Wales where the average rainfall is, higher than in other areas. With good management, hydroelectric energy is a reliable energy source, but, there are risks connected with the construction of, dams, and a variety of problems may result from the, impact of a dam on the environment. Land previously, used for forestry or farming may have to be flooded., , 61, , 9781444176421_Section_01.indd 61, , 20/06/14 7:47 AM
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15 Energy sources, , Figure 15.3 Tidal barrage in Canada, , Figure 15.4 Filling up with biofuel in Brazil, , e) Geothermal energy, If cold water is pumped down a shaft into hot rocks, below the Earth’s surface, it may be forced up, another shaft as steam. This can be used to drive a, turbine and generate electricity or to heat buildings., The energy that heats the rocks is constantly being, released by radioactive elements deep in the Earth as, they decay (Chapter 49)., Geothermal power stations are in operation in, the USA, New Zealand and Iceland., , f) Biomass (vegetable fuels), These include cultivated crops (e.g. oilseed rape),, crop residues (e.g. cereal straw), natural vegetation, (e.g. gorse), trees (e.g. spruce) grown for their wood,, animal dung and sewage. Biofuels such as alcohol, (ethanol) and methane gas are obtained from them, by fermentation using enzymes or by decomposition, by bacterial action in the absence of air. Liquid, biofuels can replace petrol (Figure 15.4); although, they have up to 50% less energy per litre, they are, lead- and sulfur-free and so cleaner. Biogas is a, mix of methane and carbon dioxide with an energy, content about two-thirds that of natural gas. In, developing countries it is produced from animal and, human waste in ‘digesters’ (Figure 15.5) and used for, heating and cooking., , Figure 15.5 Feeding a biogas digester in rural India, , ●● Power stations, The processes involved in the production of, electricity at power stations depend on the energy, source being used., , a) Non-renewable sources, These are used in thermal power stations to produce, heat energy that turns water into steam. The steam, drives turbines which in turn drive the generators that, produce electrical energy as described in Chapter 43., If fossil fuels are the energy source (usually coal but, , 62, , 9781444176421_Section_01.indd 62, , 20/06/14 7:48 AM
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Power stations, , natural gas is favoured in new stations), the steam is, obtained from a boiler. If nuclear fuel is used, such as, uranium or plutonium, the steam is produced in a, heat exchanger as explained in Chapter 50., The action of a steam turbine resembles that of, a water wheel but moving steam not moving water, causes the motion. Steam enters the turbine and is, directed by the stator or diaphragm (sets of fixed, blades) on to the rotor (sets of blades on a shaft that, can rotate) (Figure 15.6). The rotor revolves and, drives the electrical generator. The steam expands, as it passes through the turbine and the size of the, blades increases along the turbine to allow for this., , In gas-fired power stations, natural gas is burnt in a, gas turbine linked directly to an electricity generator., The hot exhaust gases from the turbine are not, released into the atmosphere but used to produce, steam in a boiler. The steam is then used to generate, more electricity from a steam turbine driving another, generator. The efficiency is claimed to be over 50%, without any extra fuel consumption. Furthermore,, the gas turbines have a near 100% combustion, efficiency so very little harmful exhaust gas (i.e., unburnt methane) is produced, and natural gas is, almost sulfur-free so the environmental pollution, caused is much less than for coal., , b) Renewable sources, In most cases the renewable energy source is used to, drive turbines directly, as explained earlier in the cases, of hydroelectric, wind, wave, tidal and geothermal, schemes., The block diagram and energy-transfer diagram, for a hydroelectric scheme like that in Figure 13.3d, (p. 51) are shown in Figure 15.8. The efficiency of, a large installation can be as high as 85–90% since, many of the causes of loss in thermal power stations, (e.g. water cooling towers) are absent. In some cases, the generating costs are half those of thermal stations., Figure 15.6 The rotor of a steam turbine, , The overall efficiency of thermal power stations is, only about 30%. They require cooling towers to, condense steam from the turbine to water and this, is a waste of energy. A block diagram and an energytransfer diagram for a thermal power station are given, in Figure 15.7., boiler or, heat, exchanger, , steam, turbine, , generator, , high-level, reservoir, , p.e., of water, , water, turbine, , k.e. of, falling, water, , generator, , k.e. of, rotating, turbine, , electrical, energy, , heat and sound energy lost to surroundings, Figure 15.8 Energy transfers in a hydroelectric power station, , chemical, or nuclear, energy, , heat, energy, of steam, , k.e. of, rotating, turbine, , electrical, energy, , heat energy lost to surroundings, and from cooling towers, Figure 15.7 Energy transfers in a thermal power station, , A feature of some hydroelectric stations is pumped, storage. Electrical energy cannot be stored on a, large scale but must be used as it is generated. The, demand varies with the time of day and the season, (Figure 15.9), so in a pumped-storage system, electricity generated at off-peak periods is used to, pump water back up from a low-level reservoir to, a higher-level one. It is easier to do this than to, reduce the output of the generator. At peak times, the potential energy of the water in the high-level, 63, , 9781444176421_Section_01.indd 63, , 20/06/14 7:48 AM
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15 Energy sources, , reservoir is converted back into electrical energy;, three-quarters of the electrical energy that was used, to pump the water is generated., , 5, winter, demand/W 1010, , 4, , 3, , 2, , summer, , 1, , 0, , 4h, , 8h, , 12h, , 16h, , 20h, , 24h, , time of day, Figure 15.9 Variation in power demand, , ●● Economic, environmental, and social issues, When considering the large-scale generation of, electricity, the economic and environmental costs, of using various energy sources have to be weighed, against the benefits that electricity brings to society as, a ‘clean’, convenient and fairly ‘cheap’ energy supply., Environmental problems such as polluting, emissions that arise with different energy sources, were outlined when each was discussed previously., Apart from people using less energy, how far, pollution can be reduced by, for example, installing, desulfurisation processes in coal-fired power stations,, is often a matter of cost., Although there are no fuel costs associated with, electricity generation from renewable energy sources, such as wind power, the energy is so ‘dilute’ that the, capital costs of setting up the generating installation are, high. Similarly, although fuel costs for nuclear power, stations are relatively low, the costs of building the, stations and of dismantling them at the end of their, useful lives is higher than for gas- or coal-fired stations., It has been estimated that currently it costs, between 6p and 15p to produce a unit of electricity, in a gas- or coal-fired power station in the UK., , The cost for a nuclear power station is in excess of, 8p per unit. Wind energy costs vary, depending upon, location, but are in the range 8p to 21p per unit., In the most favourable locations wind competes with, coal and gas generation., The reliability of a source has also to be considered,, as well as how easily production can be started up and, shut down as demand for electricity varies. Natural gas, power stations have a short start-up time, while coal, and then oil power stations take successively longer to, start up; nuclear power stations take longest. They are, all reliable in that they can produce electricity at any, time of day and in any season of the year as long as, fuel is available. Hydroelectric power stations are also, very reliable and have a very short start-up time which, means they can be switched on when the demand for, electricity peaks. The electricity output of a tidal power, station, although predictable, is not as reliable because, it depends on the height of the tide which varies over, daily, monthly and seasonal time scales. The wind and, the Sun are even less reliable sources of energy since, the output of a wind turbine changes with the strength, of the wind and that of a solar cell with the intensity of, light falling on it; the output may not be able to match, the demand for electricity at a particular time., Renewable sources are still only being used on, a small scale globally. The contribution of the, main energy sources to the world’s total energy, consumption at present is given in Table 15.1. (The, use of biofuels is not well documented.) The pattern, in the UK is similar but France generates nearly, three-quarters of its electricity from nuclear plants;, for Japan and Taiwan the proportion is one-third,, and it is in the developing economies of East Asia, where interest in nuclear energy is growing most, dramatically. However, the great dependence on fossil, fuels worldwide is evident. It is clear the world has an, energy problem (Figure 15.10)., Table 15.1 World use of energy sources, Oil, , Coal, , Gas, , Nuclear, , Hydroelectric, , 36%, , 29%, , 23%, , 6%, , 6%, , Consumption varies from one country to another;, North America and Europe are responsible for about, 42% of the world’s energy consumption each year., Table 15.2 shows approximate values for the annual, consumption per head of population for different areas., , 64, , 9781444176421_Section_01.indd 64, , 20/06/14 7:48 AM
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economic, environmental and social issues, , These figures include the ‘hidden’ consumption in, the manufacturing and transporting of goods. The, world average consumption is 69 × 109 J per head, per year., Table 15.2 Energy consumption per head per year/J × 109, N. America UK, , Japan, , S. America, , China, , Africa, , 335, , 172, , 60, , 55, , 20, , 156, , Questions, 1 The pie chart in Figure 15.11 shows the percentages of the, main energy sources used by a certain country., a What percentage is supplied by water power?, b Which of the sources is/are renewable?, c What is meant by ‘renewable’?, d Name two other renewable sources., e Why, if energy is always conserved, is it important to, develop renewable sources?, , oil, 40%, , natural, gas, 25%, water 2%, coal, 25%, , nuclear 8%, , Figure 15.11, , 2 List six properties which you think the ideal energy source, should have for generating electricity in a power station., 3 a List six social everyday benefits for which electrical, energy is responsible., b Draw up two lists of suggestions for saving energy, (i) in the home, and, (ii) globally., Figure 15.10 An energy supply crisis in California forces a blackout on, stock exchange traders., , Checklist, After studying this chapter you should be able to, • distinguish between renewable and non-renewable energy, sources,, • give some advantages and some disadvantages of using, non-renewable fuels,, • describe the different ways of harnessing solar, wind, wave,, tidal, hydroelectric, geothermal and biomass energy,, • describe the energy transfer processes in a thermal and a, hydroelectric power station,, • compare and contrast the advantages and disadvantages of, using different energy sources to generate electricity,, • discuss the environmental and economic issues of electricity, production and consumption., , 65, , 9781444176421_Section_01.indd 65, , 20/06/14 7:48 AM
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16, ●, ●, ●, , Pressure and liquid pressure, , Pressure, Liquid pressure, Water supply system, , ●, ●, ●, , Hydraulic machines, Expression for liquid pressure, Pressure gauges, , ●● Pressure, , ●● Liquid pressure, , To make sense of some effects in which a force acts, on a body we have to consider not only the force but, also the area on which it acts. For example, wearing, skis prevents you sinking into soft snow because, your weight is spread over a greater area. We say the, pressure is less., Pressure is the force (or thrust) acting on unit, area (i.e. 1 m2) and is calculated from, , 1 Pressure in a liquid increases with depth because, the further down you go, the greater the weight, of liquid above. In Figure 16.2a water spurts out, fastest and furthest from the lowest hole., 2 Pressure at one depth acts equally in all, directions. The can of water in Figure 16.2b has, similar holes all round it at the same level. Water, comes out equally fast and spurts equally far from, each hole. Hence the pressure exerted by the water, at this depth is the same in all directions., , pressure =, , force, area, , water, , The unit of pressure is the pascal (Pa); it equals, 1 newton per square metre (N/m2) and is quite a, small pressure. An apple in your hand exerts about, 1000 Pa., The greater the area over which a force acts, the, less the pressure. Figure 16.1 shows the pressure, exerted on the floor by the same box standing on, end (Figure 16.1a) and lying flat (Figure 16.1b). This, is why a tractor with wide wheels can move over soft, ground. The pressure is large when the area is small, and this is why nails are made with sharp points., Walnuts can be broken in the hand by squeezing two, together but not one. Why?, , weight 24 N, 4m, 2m, , 3m, , 2m, , a area 6m2, 24 N, pressure , 6m2, 4Pa, Figure 16.1, , 3m, , a, , b, , Figure 16.2, , 3 A liquid finds its own level. In the U-tube of, Figure 16.3a the liquid pressure at the foot of P is, greater than at the foot of Q because the left-hand, column is higher than the right-hand one. When, the clip is opened the liquid flows from P to Q, until the pressure and the levels are the same, i.e., the liquid ‘finds its own level’. Although the weight, of liquid in Q is now greater than in P, it acts over, a greater area because tube Q is wider., In Figure 16.3b the liquid is at the same level in each, tube and confirms that the pressure at the foot of a, liquid column depends only on the vertical depth of, the liquid and not on the tube width or shape., 4 Pressure depends on the density of the liquid., The denser the liquid, the greater the pressure at, any given depth., , 4m, , b area 12m2, 24 N, pressure , 12m2, 2Pa, , can, , liquid, , clip, a, , P, , Q, , b, , Figure 16.3, , 66, , 9781444176421_Section_01.indd 66, , 20/06/14 7:48 AM
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Hydraulic machines, , ●● Water supply system, A town’s water supply often comes from a reservoir, on high ground. Water flows from it through pipes, to any tap or storage tank that is below the level of, water in the reservoir (Figure 16.4). The lower the, place supplied, the greater the water pressure. In very, tall buildings it may be necessary first to pump the, water to a large tank in the roof., Reservoirs for water supply or for hydroelectric, power stations are often made in mountainous, regions by building a dam at one end of a valley. The, dam must be thicker at the bottom than at the top, due to the large water pressure at the bottom., reservoir, , pump, , f, pressure = force =, area, A, This pressure acts on a second piston of larger area A,, producing an upward force, F = pressure × area:, F =, or, , f, ×A, a, , F = f ×A, a, , Since A is larger than a, F must be larger than f, and the hydraulic system is a force multiplier; the, multiplying factor is A/a., 1, m2 and A = 12 m2, For example, if f = 1 N, a = 100, then, 1 m2, F = 1N× 2, 1 m2, 100, = 50 N, , Figure 16.4 Water supply system. Why is the pump needed in the, high-rise building?, , ●● Hydraulic machines, Liquids are almost incompressible (i.e. their volume, cannot be reduced by squeezing) and they ‘pass on’, any pressure applied to them. Use is made of these, facts in hydraulic machines. Figure 16.5 shows the, principle on which they work., F, , A force of 1 N could lift a load of 50 N; the hydraulic, system multiplies the force 50 times., A hydraulic jack (Figure 16.6) has a platform on, top of piston B and is used in garages to lift cars., Both valves open only to the right and they allow B, to be raised a long way when A moves up and down, repeatedly. When steel is forged using a hydraulic, press there is a fixed plate above piston B and the, sheets of steel are placed between B and the plate., reservoir, , f, , piston, A, B, load, , piston, area a, , piston, area A, , liquid, , valves, , Figure 16.5 The hydraulic principle, , Figure 16.6 A hydraulic jack, , Suppose a downward force f acts on a piston of, area a. The pressure transmitted through the liquid is, , Hydraulic fork-lift trucks and similar machines such, as loaders (Figure 16.7) work in the same way., 67, , 9781444176421_Section_01.indd 67, , 20/06/14 7:49 AM
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16 Pressure and liquid pressure, , liquid column of height h and cross-sectional area, A above it. Then, volume of liquid column = hA, Since mass = volume × density we can say, mass of liquid column = hAρ, Taking a mass of 1 kg to have weight 10 N,, weight of liquid column = 10hAρ, ∴, , As, , force on area A = 10hAρ, pressure = force/area = 10hAρ/A, , then, Figure 16.7 A hydraulic machine in action, , Hydraulic car brakes are shown in Figure 16.8., When the brake pedal is pushed, the piston in the, master cylinder exerts a force on the brake fluid and, the resulting pressure is transmitted equally to eight, other pistons (four are shown). These force the brake, shoes or pads against the wheels and stop the car., , pressure = depth × density × g, = hρg, where g is the acceleration of free fall (Chapter 4)., surface, of liquid, , ●● Expression for liquid, pressure, In designing a dam an engineer has to calculate the, pressure at various depths below the water surface., The pressure increases with depth and density., An expression for the pressure at a depth h in a, liquid of density ρ can be found by considering a, horizontal area A (Figure 16.9). The force acting, vertically downwards on A equals the weight of a, , pressure = 10hρ, , This is usually written as, , liquid, density ρ, , depth, h, area, A, Figure 16.9, , This pressure acts equally in all directions at depth h, and depends only on h and ρ. Its value will be in Pa if, h is in m and ρ in kg/m3., brake drum, , REAR WHEEL, , pistons, , brake shoe, return, spring, pad, , pistons, , master, cylinder, disc, FRONT WHEEL, , piston, , brake, fluid, , Figure 16.8 Hydraulic car brakes, 68, , 9781444176421_Section_01.indd 68, , 20/06/14 7:49 AM
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Pressure gauges, , ●● Pressure gauges, These measure the pressure exerted by a fluid, in, other words by a liquid or a gas., , a) Bourdon gauge, This works like the toy in Figure 16.10. The harder, you blow into the paper tube, the more it uncurls., In a Bourdon gauge (Figure 16.11), when a fluid, pressure is applied, the curved metal tube tries to, straighten out and rotates a pointer over a scale. Car, oil-pressure gauges and the gauges on gas cylinders, are of this type., , b) U-tube manometer, In Figure 16.12a each surface of the liquid is acted, on equally by atmospheric pressure and the levels are, the same. If one side is connected to, for example,, the gas supply (Figure 16.12b), the gas exerts a, pressure on surface A and level B rises until, pressure of gas = atmospheric pressure, + pressure due to liquid column BC, The pressure of the liquid column BC therefore, equals the amount by which the gas pressure, exceeds atmospheric pressure. It equals hρg (in, Pa) where h is the vertical height of BC (in m), and ρ is the density of the liquid (in kg/m3)., The height h is called the head of liquid and, sometimes, instead of stating a pressure in Pa, we, say that it is so many cm of water (or mercury for, higher pressures)., , atmospheric, pressure, , to gas supply, B, h, , gas pressure, C, , a, Figure 16.10 The harder you blow, the greater the pressure and the, more it uncurls., curved, metal, tube, , A, , b, , Figure 16.12 A U-tube manometer, , c) Mercury barometer, A barometer is a manometer which measures, atmospheric pressure. A simple barometer is shown, in Figure 16.13. The pressure at X due to the weight, of the column of mercury XY equals the atmospheric, pressure on the surface of the mercury in the bowl., The height XY measures the atmospheric pressure in, mm of mercury (mmHg)., The vertical height of the column is, unchanged if the tube is tilted. Would it be, different with a wider tube? The space above the, mercury in the tube is a vacuum (except for a, little mercury vapour)., , fluid, pressure, Figure 16.11 A Bourdon gauge, 69, , 9781444176421_Section_01.indd 69, , 20/06/14 7:49 AM
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16 Pressure And liquid Pressure, , Y, mercury, , 760 mm, atmospheric, pressure, X, Figure 16.13 Mercury barometer, , Questions, 1 a What is the pressure on a surface when a force of 50 N, acts on an area of, (i) 2.0 m2,, (ii) 100 m2,, (iii) 0.50 m2?, b A pressure of 10 Pa acts on an area of 3.0 m2. What is, the force acting on the area?, 2 In a hydraulic press a force of 20 N is applied to a piston of, area 0.20 m2. The area of the other piston is 2.0 m2. What is, a the pressure transmitted through the liquid,, b the force on the other piston?, 3 a Why must a liquid and not a gas be used as the ‘fluid’ in, a hydraulic machine?, b On what other important property of a liquid do, hydraulic machines depend?, 4 What is the pressure 100 m below the surface of sea water, of density 1150 kg/m3?, 5 Figure 16.14 shows a simple barometer., a What is the region A?, b What keeps the mercury in the tube?, c What is the value of the atmospheric pressure being, shown by the barometer?, d What would happen to this reading if the barometer, were taken up a high mountain? Give a reason., , A, , 6 Which of the following will damage a wood-block floor, that can withstand a pressure of 2000 kPa (2000 kN/m2)?, 1 A block weighing 2000 kN standing on an area of 2 m2., 2 An elephant weighing 200 kN standing on an area of, 0.2 m2., 3 A girl of weight 0.5 kN wearing stiletto-heeled shoes, standing on an area of 0.0002 m2., Use the answer code:, A 1, 2, 3, B 1, 2, C 2, 3, D 1, E 3, 7 The pressure at a point in a liquid, 1 increases as the depth increases, 2 increases if the density of the liquid increases, 3 is greater vertically than horizontally., Which statement(s) is (are) correct?, A 1, 2, 3, B 1, 2, C 2, 3, D 1, E 3, , Checklist, After studying this chapter you should be able to, •, •, •, •, , relate pressure to force and area and give examples,, define pressure and recall its unit,, connect the pressure in a fluid with its depth and density,, recall that pressure is transmitted through a liquid and use it, to explain the hydraulic jack and hydraulic car brakes,, , • use pressure = hρ g to solve problems,, • describe how a U-tube manometer may be used to measure, fluid pressure,, • describe and use a simple mercury barometer., , 2 cm, , 74 cm, mercury, 1 cm, 1 cm, , Figure 16.14, , 70, , 9781444176421_Section_01.indd 70, , 20/06/14 7:49 AM
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Section, , 2, , Thermal physics, , Chapters, Simple kinetic molecular model of matter, 17 Molecules, 18 The gas laws, Thermal properties and temperature, 19 Expansion of solids, liquids and gases, 20 Thermometers, , 9781444176421_Section_02.indd 71, , 21 Specific heat capacity, 22 Specific latent heat, Thermal processes, 23 Conduction and convection, 24 Radiation, , 20/06/14 7:31 AM
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17 Molecules, l, l, , Kinetic theory of matter, Crystals, , l, l, , Diffusion, Practical work: Brownian motion, , Matter is made up of tiny particles or molecules, which are too small for us to see directly. But, they can be ‘seen’ by scientific ‘eyes’. One of, these is the electron microscope. Figure 17.1 is a, photograph taken with such an instrument showing, molecules of a protein. Molecules consist of even, smaller particles called atoms and are in continuous, motion., , microscope, window, , lid, , lamp, , smoke, , a, , glass rod, , glass cell, , glass plate, smoke, b, , c, , burning match, glass cell, , Figure 17.2, , Carefully adjust the microscope until you see bright specks, dancing around haphazardly (Figure 17.2c). The specks are, smoke particles seen by reflected light; their random motion is, called Brownian motion. It is due to collisions with fast-moving, air molecules in the cell. A smoke particle is massive compared, with an air molecule but if there are more high-speed molecules, striking one side of it than the other at a given instant, the, particle will move in the direction in which there is a net force., The imbalance, and hence the direction of the net force, changes, rapidly in a random manner., , Figure 17.1 Protein molecules, , Practical work, Brownian motion, The apparatus is shown in Figure 17.2a. First fill the glass cell, with smoke using a match (Figure 17.2b). Replace the lid on the, apparatus and set it on the microscope platform. Connect the, lamp to a 12 V supply; the glass rod acts as a lens and focuses, light on the smoke., , ●● Kinetic theory of matter, As well as being in continuous motion, molecules, also exert strong electric forces on one another when, they are close together. The forces are both attractive, and repulsive. The former hold molecules together, and the latter cause matter to resist compression., The kinetic theory can explain the existence of the, solid, liquid and gaseous states., , a) Solids, The theory states that in solids the molecules are, close together and the attractive and repulsive forces, , 72, , 9781444176421_Section_02.indd 72, , 20/06/14 7:31 AM
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Kinetic theory of matter, , between neighbouring molecules balance. Also each, molecule vibrates to and fro about a fixed position., It is just as if springs, representing the electric, forces between molecules, hold the molecules, together (Figure 17.3). This enables the solid to, keep a definite shape and volume, while still allowing, the individual molecules to vibrate backwards and, forwards. The theory shows that the molecules in, a solid could be arranged in a regular, repeating, pattern like those formed by crystalline substances., , tilted, tray, , marbles, Figure 17.4 A model of molecular behaviour in a liquid, , c) Gases, , Figure 17.3 The electric forces between molecules in a solid can be, represented by springs., , b) Liquids, The theory considers that in liquids the molecules, are slightly further apart than in solids but still close, enough together to have a definite volume. As well, as vibrating, they can at the same time move rapidly, over short distances, slipping past each other in all, directions. They are never near another molecule, long enough to get trapped in a regular pattern, which would stop them from flowing and from, taking the shape of the vessel containing them., A model to represent the liquid state can be, made by covering about a third of a tilted tray, with marbles (‘molecules’) (Figure 17.4). It is then, shaken to and fro and the motion of the marbles, observed. They are able to move around but most, stay in the lower half of the tray, so the liquid, has a fairly definite volume. A few energetic ones, ‘escape’ from the ‘liquid’ into the space above. They, represent molecules that have ‘evaporated’ from, the ‘liquid’ surface and become ‘gas’ or ‘vapour’, molecules. The thinning out of the marbles near the, ‘liquid’ surface can also be seen., , The molecules in gases are much further apart than, in solids or liquids (about ten times) and so gases are, much less dense and can be squeezed (compressed), into a smaller space. The molecules dash around at very, high speed (about 500 m/s for air molecules at 0 ºC) in, all the space available. It is only during the brief spells, when they collide with other molecules or with the, walls of the container that the molecular forces act., A model of a gas is shown in Figure 17.5. The, faster the vibrator works, the more often the ballbearings have collisions with the lid, the tube and with, each other, representing a gas at a higher temperature., Adding more ball-bearings is like pumping more air, into a tyre; it increases the pressure. If a polystyrene, ball (1 cm diameter) is dropped into the tube, its, irregular motion represents Brownian motion., lid, , Perspex tube, , ball-bearings, , rubber sheet, vibrator driven, by motor, Figure 17.5 A model of molecular behaviour in a gas, , 73, , 9781444176421_Section_02.indd 73, , 20/06/14 7:31 AM
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17 Molecules, , ●● Crystals, Crystals have hard, flat sides and straight edges., Whatever their size, crystals of the same substance, have the same shape. This can be seen by observing,, through a microscope, very small cubic salt crystals, growing as water evaporates from salt solution on a, glass slide (Figure 17.6)., , These facts suggest that crystals are made of small, particles (e.g. atoms) arranged in an orderly way in, planes. Metals have crystalline structures, but many, other common solids such as glass, plastics and wood, do not., , ●● Diffusion, Smells, pleasant or otherwise, travel quickly and are, caused by rapidly moving molecules. The spreading, of a substance of its own accord is called diffusion, and is due to molecular motion., Diffusion of gases can be shown if some brown, nitrogen dioxide gas is made by pouring a mixture, of equal volumes of concentrated nitric acid and, water onto copper turnings in a gas jar. When the, reaction has stopped, a gas jar of air is inverted, over the bottom jar (Figure 17.8). The brown, colour spreads into the upper jar showing that, nitrogen dioxide molecules diffuse upwards, against gravity. Air molecules also diffuse into the, lower jar., , Figure 17.6 Salt crystals viewed under a microscope with, polarised light, , A calcite crystal will split cleanly if a trimming knife,, held exactly parallel to one side of the crystal, is, struck by a hammer (Figure 17.7)., , air molecules, , nitrogen dioxide, molecules, gas jar, Figure 17.8 Demonstrating diffusion of a gas, , Figure 17.7 Splitting a calcite crystal, , The speed of diffusion of a gas depends on the speed, of its molecules and is greater for light molecules., The apparatus of Figure 17.9 shows this. When, hydrogen surrounds the porous pot, the liquid in the, U-tube moves in the direction of the arrows. This, is because the lighter, faster molecules of hydrogen, diffuse into the pot faster than the heavier, slower, molecules of air diffuse out. The opposite happens, when carbon dioxide surrounds the pot. Why?, , 74, , 9781444176421_Section_02.indd 74, , 20/06/14 7:32 AM
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diffusion, , beaker, , hydrogen, , porous pot, , Figure 17.9 The speed of diffusion is greater for lighter molecules, , Questions, 1 Which one of the following statements is not true?, A The molecules in a solid vibrate about a fixed position., B The molecules in a liquid are arranged in a regular, pattern., C The molecules in a gas exert negligibly small forces on, each other, except during collisions., D The densities of most liquids are about 1000 times, greater than those of gases because liquid molecules are, much closer together than gas molecules., E The molecules of a gas occupy all the space available., 2 Using what you know about the compressibility, (squeezability) of the different states of matter, explain why, a air is used to inflate tyres,, b steel is used to make railway lines., , Checklist, After studying this chapter you should be able to, • describe and explain an experiment to show Brownian, motion,, • use the kinetic theory to explain the physical properties of, solids, liquids and gases., , 75, , 9781444176421_Section_02.indd 75, , 20/06/14 7:32 AM
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18 The gas laws, l, l, l, l, , Pressure of a gas, Absolute zero, The gas laws, Gases and the kinetic theory, , l, , ●● Pressure of a gas, The air forming the Earth’s atmosphere stretches, upwards a long way. Air has weight; the air in, a normal room weighs about the same as you, do, about 500 N. Because of its weight the, atmosphere exerts a large pressure at sea level,, about 100 000 N/m2 = 105 Pa (or 100 kPa)., This pressure acts equally in all directions., A gas in a container exerts a pressure on the walls, of the container. If air is removed from a can by, a vacuum pump (Figure 18.1), the can collapses, because the air pressure outside is greater than, that inside. A space from which all the air has been, removed is a vacuum. Alternatively the pressure in a, container can be increased, for example by pumping, more gas into the can; a Bourdon gauge (p. 69) is, used for measuring fluid pressures., , Practical work: Effect on volume of temperature;, Effect on pressure of temperature; Effect on, volume of pressure, , Practical work, Effect on volume of temperature, (pressure constant) – Charles’ law, Arrange the apparatus as in Figure 18.2. The index of, concentrated sulfuric acid traps the air column to be, investigated and also dries it. Adjust the capillary tube so, that the bottom of the air column is opposite a convenient, mark on the ruler., Note the length of the air column (between the lower, end of the index and the sealed end of the capillary tube), at different temperatures but, before taking a reading,, stop heating and stir well to make sure that the air, has reached the temperature of the water. Put the results, in a table., Plot a graph of volume (in cm, since the length of the air, column is a measure of it) on the y-axis and temperature (in ºC), on the x-axis., The pressure of (and on) the air column is constant, and equals atmospheric pressure plus the pressure of the, acid index., , to vacuum, pump, , can, , ruler, (30 cm), , thermometer, , capillary, tube, , can, concentrated, sulfuric acid, index, , air, column, rubber, band, , water, , Figure 18.1 Atmospheric pressure collapses the evacuated can., , When a gas is heated, as air is in a jet engine, its, pressure as well as its volume may change. To study, the effect of temperature on these two quantities we, must keep one fixed while the other is changed., , heat, Figure 18.2, , 76, , 9781444176421_Section_02.indd 76, , 20/06/14 7:32 AM
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absolute zero, , Practical work, , volume or pressure, , Effect on pressure of temperature, (volume constant) – the Pressure law, The apparatus is shown in Figure 18.3. The rubber tubing from, the flask to the pressure gauge should be as short as possible., The flask must be in water almost to the top of its neck and be, securely clamped to keep it off the bottom of the can., Record the pressure over a wide range of temperatures, but, before taking a reading, stop heating, stir and allow time for the, gauge reading to become steady; the air in the flask will then be, at the temperature of the water. Tabulate the results., Plot a graph of pressure on the y-axis and temperature on, the x-axis., rubber tubing, , Bourdon, pressure, gauge, , thermometer, , can, , water, , flask, (250 cm3), , Figure 18.3, , l● Absolute zero, , Figure 18.4, , The graphs do not pass through the Celsius, temperature origin (0 ºC). If they are produced, backwards they cut the temperature axis at about, –273 ºC. This temperature is called absolute zero, because we believe it is the lowest temperature, possible. It is the zero of the absolute or Kelvin, scale of temperature. At absolute zero molecular, motion ceases and a substance has no internal energy., Degrees on this scale are called kelvins and are, denoted by K. They are exactly the same size as, Celsius degrees. Since –273 ºC = 0 K, conversions, from ºC to K are made by adding 273. For example, 0 ºC = 273 K, 15 ºC = 273 + 15 = 288 K, 100 ºC = 273 + 100 = 373 K, Kelvin or absolute temperatures are represented by, the letter T, and if θ (Greek letter ‘theta’) stands for, a Celsius scale temperature then, in general,, T = 273 + θ, , Near absolute zero strange things occur. Liquid, helium becomes a superfluid. It cannot be kept in, an open vessel because it flows up the inside of the, vessel, over the edge and down the outside. Some, metals and compounds become superconductors, of electricity and a current once started in them, flows forever, without a battery. Figure 18.5 shows, research equipment that is being used to create, materials that are superconductors at very much, higher temperatures, such as –23 ºC., ▲, ▲, , The volume–temperature and pressure–temperature, graphs for a gas are straight lines (Figure 18.4)., They show that gases expand linearly with, temperature as measured on a mercury, thermometer, i.e. equal temperature increases cause, equal volume or pressure increases., , 0°C, temperature, 273K, , 273°C, 0K, , 77, , 9781444176421_Section_02.indd 77, , 20/06/14 7:32 AM
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18 The Gas laWs, If a graph of pressure against volume is plotted using the, results, a curve like that in Figure 18.7a is obtained. Close, examination of the graph shows that if p is doubled, V is halved., That is, p is inversely proportional to V. In symbols, p∝, , 1, V, , or p = constant ×, , ∴, , 1, V, , pV = constant, , If several pairs of readings, p1 and V1, p2 and V2, etc. are taken,, then it can be confirmed that p1V1 = p2V2 = constant. This is, Boyle’s law, which is stated as follows:, The pressure of a fixed mass of gas is inversely proportional to, its volume if its temperature is kept constant., , 0, , 0, , 10, , 10, , 20, , 20, , 30, , 30, , 40, , 40, , 50, , 50, , glass tube, air, Bourdon gauge, , to foot, oil pump, reservoir, , Figure 18.6, , p, , p, , Figure 18.5 This equipment is being used to make films of complex, composite materials that are superconducting at temperatures far, above absolute zero., , p, doubled, V, halved, 0, , Practical work, a, , Effect on volume of pressure, (temperature constant) – Boyle’s law, Changes in the volume of a gas due to pressure changes can, be studied using the apparatus in Figure 18.6. The volume V of, air trapped in the glass tube is read off on the scale behind. The, pressure is altered by pumping air from a foot pump into the, space above the oil reservoir. This forces more oil into the glass, tube and increases the pressure p on the air in it; p is measured, by the Bourdon gauge., , V, , 0, , 1, V, , b, , Figure 18.7, , Since p is inversely proportional to V, then p is directly, proportional to 1/V. A graph of p against 1/V is therefore a, straight line through the origin (Figure 18.7b)., , 78, , 9781444176421_Section_02.indd 78, , 20/06/14 7:33 AM
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Gases and the kinetic theory, , l● The gas laws, , For cases in which p, V and T all change from, say,, p1, V1 and T1 to p2, V2 and T2, then, , Using absolute temperatures, the gas laws can be, stated in a convenient form for calculations., , p1V1 p2V2, =, T1, T2, , a) Charles’ law, In Figure 18.4 (p. 77) the volume–temperature, graph passes through the origin if temperatures are, measured on the Kelvin scale, that is, if we take 0 K, as the origin. We can then say that the volume V is, directly proportional to the absolute temperature T,, i.e. doubling T doubles V, etc. Therefore, or, , V ∝ T or V = constant × T, V = constant, T, , (1), , Charles’ law may be stated as follows., , (4), , l● Worked example, A bicycle pump contains 50 cm3 of air at 17 ºC and, at 1.0 atmosphere pressure. Find the pressure when, the air is compressed to 10 cm3 and its temperature, rises to 27 ºC., We have, p1 = 1.0 atm, V1 = 50 cm3, T1 = 273 + 17 = 290 K, , p2 = ?, V2 = 10 cm3, T2 = 273 + 27 = 300 K, , From equation (4) we get, , The volume of a fixed mass of gas is directly proportional to its, absolute temperature if the pressure is kept constant., , p2 = p1 ×, , V1 T2, 50 300, ×, V2 T1 = 1 × 10 × 290 = 5.2 atm, , Notes, , b) Pressure law, From Figure 18.4 we can say similarly for the, pressure p that, or, , p ∝ T or p = constant × T, p, = constant, T, , (2), , The Pressure law may be stated as follows., The pressure of a fixed mass of gas is directly proportional to, its absolute temperature if the volume is kept constant., , For a fixed mass of gas at constant temperature, , d) Combining the laws, The three equations can be combined giving, pV, = constant, T, , l● Gases and the kinetic, theory, The kinetic theory can explain the behaviour of gases., , a) Cause of gas pressure, , c) Boyle’s law, pV = constant, , 1 All temperatures must be in K., 2 Any units can be used for p and V provided the, same units are used on both sides of the equation., 3 In some calculations the volume of the gas has to, be found at standard temperature and pressure,, or ‘s.t.p.’. This is temperature 0 ºC and pressure, 1 atmosphere (1 atm = 105 Pa)., , (3), , All the molecules in a gas are in rapid random, motion, with a wide range of speeds, and repeatedly, hit and rebound from the walls of the container, in huge numbers per second. At each rebound, a, gas molecule undergoes a change of momentum, which produces a force on the walls of the container, (see Chapter 12). The average force and hence the, pressure they exert on the walls is constant since, pressure is force on unit area., , 79, , 9781444176421_Section_02.indd 79, , 20/06/14 7:33 AM
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18 The Gas laWs, , b) Boyle’s law, If the volume of a fixed mass of gas is halved by, halving the volume of the container (Figure 18.8), the, number of molecules per cm3 will be doubled. There, will be twice as many collisions per second with the, walls, i.e. the pressure is doubled. This is Boyle’s law., , Question, 1 If a certain quantity of gas has a volume of 30 cm3 at a, pressure of 1 × 105 Pa, what is its volume when the, pressure is, a 2 × 105 Pa,, b 5 × 105 Pa?, Assume the temperature remains constant., , piston, , V, , Checklist, cylinder, , V, 2, , Figure 18.8 Halving the volume doubles the pressure., , c) Temperature, When a gas is heated and its temperature rises,, the average speed of its molecules increases. If the, volume of the gas stays constant, its pressure increases, because there are more frequent and more violent, collisions of the molecules with the walls. If the, pressure of the gas is to remain constant, the volume, must increase so that the frequency of collisions does, not go up., , After studying this chapter you should be able to, • describe experiments to study the relationships between the, pressure, volume and temperature of a gas,, • explain the establishment of the Kelvin (absolute), temperature scale from graphs of pressure or volume, against temperature and recall the equation connecting, the Kelvin and Celsius scales, i.e. T = 273 + θ,, • recall that pV = constant and use this to solve problems,, • explain the behaviour of gases using the kinetic theory., , 80, , 9781444176421_Section_02.indd 80, , 20/06/14 7:33 AM
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19, l, l, l, , Expansion of solids, liquids and gases, , Uses of expansion, Precautions against expansion, Bimetallic strip, , In general, when matter is heated it expands and, when cooled it contracts. If the changes are resisted, large forces are created which are sometimes useful, but at other times are a nuisance., According to the kinetic theory (Chapter 17), the molecules of solids and liquids are in constant, vibration. When heated they vibrate faster and force, each other a little further apart. Expansion results,, and this is greater for liquids than for solids; gases, expand even more. The linear (length) expansion of, solids is small and for the effect to be noticed, the, solid must be long and/or the temperature change, must be large., , ●● Uses of expansion, In Figure 19.1 the axles have been shrunk by cooling, in liquid nitrogen at −196 ºC until the gear wheels, can be slipped on to them. On regaining normal, temperature the axles expand to give a very tight fit., , l, l, , Linear expansivity, Unusual expansion of water, , ●● Precautions against, expansion, Gaps used to be left between lengths of railway lines to, allow for expansion in summer. They caused a familiar, ‘clickety-click’ sound as the train passed over them., These days rails are welded into lengths of about 1 km, and are held by concrete ‘sleepers’ that can withstand, the large forces created without buckling. Also, at, the joints the ends are tapered and overlap (Figure, 19.2a). This gives a smoother journey and allows some, expansion near the ends of each length of rail., For similar reasons slight gaps are left between, lengths of aluminium guttering. In central heating, pipes ‘expansion joints’ are used to join lengths of, pipe (Figure 19.2b); these allow the copper pipes to, expand in length inside the joints when carrying very, hot water., , Figure 19.2a Tapered overlap of rails, , nut, , nut, , rubber seal, Figure 19.1 ‘Shrink-fitting’ of axles into gear wheels, , In the kitchen, a tight metal lid can be removed from, a glass jar by immersing the lid in hot water so that it, expands., , pipe, , pipe, , Figure 19.2b Expansion joint, , 81, , 9781444176421_Section_02.indd 81, , 20/06/14 7:33 AM
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19 eXpansIon of solIds, lIQuIds and Gases, , l● Bimetallic strip, , b) Thermostat, , If equal lengths of two different metals, such as, copper and iron, are riveted together so that they, cannot move separately, they form a bimetallic strip, (Figure 19.3a). When heated, copper expands more, than iron and to allow this the strip bends with copper, on the outside (Figure 19.3b). If they had expanded, equally, the strip would have stayed straight., Bimetallic strips have many uses., copper, iron, a, , copper, iron, , b, Figure 19.3 A bimetallic strip: a before heating; b after heating, , a) Fire alarm, Heat from the fire makes the bimetallic strip bend, and complete the electrical circuit, so ringing the, alarm bell (Figure 19.4a)., A bimetallic strip is also used in this way to work, the flashing direction indicator lamps in a car, being, warmed by an electric heating coil wound round it., electric, bell, , contact, bimetallic, strip, , A thermostat keeps the temperature of a room or an, appliance constant. The one in Figure 19.4b uses a, bimetallic strip in the electrical heating circuit of, for, example, an iron., When the iron reaches the required temperature, the strip bends down, breaks the circuit at the, contacts and switches off the heater. After cooling a, little the strip remakes contact and turns the heater, on again. A near-steady temperature results., If the control knob is screwed down, the strip has, to bend more to break the heating circuit and this, needs a higher temperature., , l● Linear expansivity, An engineer has to allow for the linear expansion, of a bridge when designing it. The expansion can be, calculated if all the following are known:, (i) the length of the bridge,, (ii) the range of temperature it will experience, and, (iii) the linear expansivity of the material to be used., The linear expansivity α of a substance is the increase in, length of 1 m for a 1 ºC rise in temperature., , The linear expansivity of a material is found by, experiment. For steel it is 0.000 012 per ºC. This, means that 1 m will become 1.000 012 m for a, temperature rise of 1 ºC. A steel bridge 100 m long, will expand by 0.000 012 × 100 m for each 1 ºC, rise in temperature. If the maximum temperature, change expected is 60 ºC (e.g. from −15 ºC to, +45 ºC), the expansion will be 0.000 012 per ºC ×, 100 m × 60 ºC = 0.072 m, or 7.2 cm. In general,, , heat from fire, , a, , expansion = linear expansivity × original length, × temperature rise, , control knob, , insulator, , to heater, circuit, , contacts, , bimetallic strip, b, Figure 19.4 Uses of a bimetallic strip: a fire alarm; b a thermostat in an iron, , (The Greek letter delta, ∆, is often used to mean the, ‘difference’ or the change in a quantity. So in the, above calculation, the change in temperature, ∆θ, is, 60 ºC and the change in length, ∆l, is 7.2 cm.), Values of expansivity for liquids are typically about, 5 times higher than that for steel; gases have expansivity, values about 100 times that of steel. These figures, indicate that gases expand much more readily than, liquids, and liquids expand more readily than solids., , 82, , 9781444176421_Section_02.indd 82, , 20/06/14 7:34 AM
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unusual expansion of water, , l● Unusual expansion of, water, As water is cooled to 4 ºC it contracts, as we would, expect. However between 4 ºC and 0 ºC it expands,, surprisingly. Water has a maximum density at 4 ºC, (Figure 19.5)., volume, , The unusual expansion of water between 4 ºC and, 0 ºC explains why fish survive in a frozen pond. The, water at the top of the pond cools first, contracts, and being denser sinks to the bottom. Warmer, less, dense water rises to the surface to be cooled. When, all the water is at 4 ºC the circulation stops. If the, temperature of the surface water falls below 4 ºC, it, becomes less dense and remains at the top, eventually, forming a layer of ice at 0 ºC. Temperatures in the, pond are then as in Figure 19.7., , ice, ice and water, , ice at 0°C, , water, maximum density, , –4, , 0, , 4, 8, temperature/°C, , 12, , water at 0°C, 1°C, 2°C, 3°C, 4°C, , 16, , Figure 19.5 Water expands on cooling below 4 ºC., , At 0 ºC, when it freezes, a considerable volume, expansion occurs and every 100 cm3 of water, becomes 109 cm3 of ice. This accounts for the, bursting of unlagged water pipes in very cold weather, and for the fact that ice is less dense than cold water, and so floats. Figure 19.6 shows a bottle of frozen, milk, the main constituent of which is water., , Figure 19.7 Fish can survive in a frozen pond., , The volume expansion of water between 4 ºC, and 0 ºC is due to the breaking up of the groups, that water molecules form above 4 ºC. The new, arrangement requires a larger volume and more, than cancels out the contraction due to the fall in, temperature., , Questions, 1 Explain why, a the metal lid on a glass jam jar can be unscrewed easily, if the jar is inverted for a few seconds with the lid in very, hot water,, b furniture may creak at night after a warm day,, c concrete roads are laid in sections with pitch between, them., 2 A bimetallic strip is made from aluminium and copper., When heated it bends in the direction shown in Figure, 19.8., Which metal expands more for the same rise in, temperature, aluminium or copper?, Draw a diagram to show how the bimetallic strip would, appear if it were cooled to below room temperature., Figure 19.6 Result of the expansion of water on freezing, 83, , 9781444176421_Section_02.indd 83, , 20/06/14 7:34 AM
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19 eXpansIon of solIds, lIQuIds and Gases, , Checklist, After studying this chapter you should be able to, , aluminium, , • describe uses of expansion, including the bimetallic strip,, • describe precautions taken against expansion,, • recall that water has its maximum density at 4 ºC and explain, why a pond freezes at the top first,, , at room, temperature, after, heating, , copper, , • recall and explain the relative order of magnitude of the, expansion of solids, liquids and gases., , Figure 19.8, , 3 When a metal bar is heated the increase in length is, greater if, 1 the bar is long, 2 the temperature rise is large, 3 the bar has a large diameter., Which statement(s) is (are) correct?, A 1, 2, 3, B 1, 2, C 2, 3, D 1, E 3, 4 A bimetallic thermostat for use in an iron is shown in, Figure 19.9., control knob, insulator, , to heater, , contacts, metal A, , circuit, metal B, , Figure 19.9, , 1 It operates by the bimetallic strip bending away from, the contact., 2 Metal A has a greater expansivity than metal B., 3 Screwing in the control knob raises the temperature at, which the contacts open., Which statement(s) is (are) correct?, A 1, 2, 3, B 1, 2, C 2, 3, D 1, E 3, , 84, , 9781444176421_Section_02.indd 84, , 20/06/14 7:34 AM
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20, l, l, l, , Thermometers, , Liquid-in-glass thermometer, Scale of temperature, Clinical thermometer, , The temperature of a body tells us how hot the body, is. It is measured using a thermometer and usually in, degrees Celsius (ºC). The kinetic theory (Chapter, 17) regards temperature as a measure of the average, kinetic energy (k.e.) of the molecules of the body., The greater this is, the faster the molecules move and, the higher the temperature of the body., There are different kinds of thermometer, each, type being more suitable than another for a certain, job. In each type the physical property used must, vary continuously over a wide range of temperature., It must be accurately measurable with simple, apparatus and vary in a similar way to other physical, properties. Figure 20.1 shows the temperature of a, lava flow being measured., , l, l, l, , Thermocouple thermometer, Other thermometers, Heat and temperature, , Alcohol freezes at −115 ºC and boils at 78 ºC and is, therefore more suitable for low temperatures., , ●● Scale of temperature, A scale and unit of temperature are obtained by, choosing two temperatures, called the fixed points,, and dividing the range between them into a number, of equal divisions or degrees., On the Celsius scale (named after the Swedish, scientist who suggested it), the lower fixed point is the, temperature of pure melting ice and is taken as 0 ºC., The upper fixed point is the temperature of the, steam above water boiling at normal atmospheric, pressure, 105 Pa (or N/m2), and is taken as 100 ºC., When the fixed points have been marked on, the thermometer, the distance between them is, divided into 100 equal degrees (Figure 20.2). The, thermometer now has a linear scale, in other words, it has been calibrated or graduated., , 100 °C, , steam point, , Figure 20.1 Use of a thermocouple probe thermometer to measure a, temperature of about 1160 ºC in lava, 100, degrees, , ●● Liquid-in-glass, thermometer, In this type the liquid in a glass bulb expands up a, capillary tube when the bulb is heated. The liquid, must be easily seen and must expand (or contract), rapidly and by a large amount over a wide range, of temperature. It must not stick to the inside of, the tube or the reading will be too high when the, temperature is falling., Mercury and coloured alcohol are in common, use. Mercury freezes at −39 ºC and boils at 357 ºC., , 0 °C, , ice point, , Figure 20.2 A temperature scale in degrees Celsius, 85, , 9781444176421_Section_02.indd 85, , 20/06/14 7:34 AM
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20 Thermometers, , ●● Clinical thermometer, A clinical thermometer is a special type of mercuryin-glass thermometer used by doctors and nurses. Its, scale only extends over a few degrees on either side, of the normal body temperature of 37 ºC (Figure, 20.3), i.e. it has a small range. Because of the very, narrow capillary tube, temperatures can be measured, very accurately, in other words, the thermometer has, a high sensitivity., The tube has a constriction (a narrower part) just, beyond the bulb. When the thermometer is placed, under the tongue the mercury expands, forcing its, way past the constriction. When the thermometer, is removed (after 1 minute) from the mouth, the, mercury in the bulb cools and contracts, breaking, the mercury thread at the constriction. The mercury, beyond the constriction stays in the tube and shows, the body temperature. After use the mercury is, returned to the bulb by a flick of the wrist. Since, mercury is a toxic material, digital thermometers, are now replacing mercury thermometers for, clinical use., constriction, , 35 °C, , V, , AC, , digital voltmeter, , copper wires, , hot, junction, , iron wire, cold junction, , Figure 20.4 A simple thermocouple thermometer, , Thermocouples are used in industry to measure, a wide range of temperatures from −250 ºC up, to about 1500 ºC, especially rapidly changing, temperatures and those of small objects., , ●● Other thermometers, , normal body temperature, , 37 °C, , DC, , 42 °C, , Figure 20.3 A clinical thermometer, , ●● Thermocouple, thermometer, A thermocouple consists of wires of two, different materials, such as copper and iron,, joined together (Figure 20.4). When one junction, is at a higher temperature than the other, an, electric current flows and produces a reading on a, sensitive meter which depends on the temperature, difference., , One type of resistance thermometer uses the, fact that the electrical resistance (Chapter 38) of a, platinum wire increases with temperature., A resistance thermometer can measure, temperatures accurately in the range −200 ºC to, 1200 ºC but it is bulky and best used for steady, temperatures. A thermistor can also be used but over, a small range, such as −5 ºC to 70 ºC; its resistance, decreases with temperature., The constant-volume gas thermometer uses the, change in pressure of a gas to measure temperatures, over a wide range. It is an accurate but bulky, instrument, basically similar to the apparatus of, Figure 18.3 (p. 77)., Thermochromic liquids which change colour, with temperature have a limited range around room, temperatures., , 86, , 9781444176421_Section_02.indd 86, , 20/06/14 7:34 AM
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heat and temperature, , l● Heat and temperature, It is important not to confuse the temperature of, a body with the heat energy that can be obtained, from it. For example, a red-hot spark from a fire is, at a higher temperature than the boiling water in a, saucepan. In the boiling water the average k.e. of the, molecules is lower than in the spark; but since there, are many more water molecules, their total energy, is greater, and therefore more heat energy can be, supplied by the water than by the spark., Heat passes from a body at a higher, temperature to one at a lower temperature. This is, because the average k.e. (and speed) of the molecules, in the ‘hot’ body falls as a result of the collisions with, molecules of the ‘cold’ body whose average k.e., and, therefore temperature, increases. When the average, k.e. of the molecules is the same in both bodies, they, are at the same temperature. For example, if the redhot spark landed in the boiling water, heat would pass, from it to the water even though much more heat, energy could be obtained from the water., Heat is also called thermal or internal energy; it, is the energy a body has because of the kinetic energy, and the potential energy (p.e.) of its molecules., Increasing the temperature of a body increases, its heat energy because the k.e. of its molecules, increases. But as we will see later (Chapter 22), the, internal energy of a body can also be increased by, increasing the p.e. of its molecules., , 3 a How must a property behave to measure temperature?, b Name three properties that qualify., c Name a suitable thermometer for measuring, (i) a steady temperature of 1000 ºC,, (ii) the changing temperature of a small object,, (iii) a winter temperature at the North Pole., 4 Describe the main features of a clinical thermometer., , Checklist, After studying this chapter you should be able to, • define the fixed points on the Celsius scale,, • recall the properties of mercury and alcohol as liquids, suitable for use in thermometers,, • describe clinical and thermocouple thermometers,, • understand the meaning of range, sensitivity and linearity, in relation to thermometers,, • describe the structure and use of a thermocouple, thermometer,, • recall some other types of thermometer and the physical, properties on which they depend,, • distinguish between heat and temperature and recall that, temperature decides the direction of heat flow,, • relate a rise in the temperature of a body to an increase in, internal energy., , Questions, 1 1530 ºC 120 ºC 55 ºC 37 ºC 19 ºC 0 ºC −12 ºC −50 ºC, From the above list of temperatures choose the most likely, value for each of the following:, a the melting point of iron,, b the temperature of a room that is comfortably warm,, c the melting point of pure ice at normal pressure,, d the lowest outdoor temperature recorded in London in, winter,, e the normal body temperature of a healthy person., 2 In order to make a mercury thermometer that will measure, small changes in temperature accurately, would you, A decrease the volume of the mercury bulb, B put the degree markings further apart, C decrease the diameter of the capillary tube, D put the degree markings closer together, E leave the capillary tube open to the air?, , 87, , 9781444176421_Section_02.indd 87, , 20/06/14 7:34 AM
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21, l, l, l, , Specific heat capacity, , The heat equation, Thermal capacity, Importance of the high specific heat capacity of water, , If 1 kg of water and 1 kg of paraffin are heated in, turn for the same time by the same heater, the, temperature rise of the paraffin is about twice that, of the water. Since the heater gives equal amounts, of heat energy to each liquid, it seems that different, substances require different amounts of heat to, cause the same temperature rise in the same mass,, say 1 ºC in 1 kg., The ‘thirst’ of a substance for heat is measured by, its specific heat capacity (symbol c)., The specific heat capacity of a substance is the heat required to, produce a 1 ºC rise in 1 kg., , l, , Practical work: Finding specific heat capacities:, water, aluminium, , If the temperature of the substance fell by 3 °C, the, heat given out would also be 6000 J. In general, we, can write the heat equation as, heat received or given out, = mass × temperature change × specific heat capacity, In symbols, Q = m × ∆θ × c, , For example, if the temperature of a 5 kg mass of, material of specific heat capacity 400 J/(kg ºC) rises, from 15 ºC to 25 ºC, the heat received, Q , is, Q = 5 kg × (25−15) ºC × 400 J/(kg ºC), , Heat, like other forms of energy, is measured in, joules (J) and the unit of specific heat capacity is the, joule per kilogram per ºC, i.e. J/(kg ºC)., In physics, the word ‘specific’ means that ‘unit, mass’ is being considered., , l● The heat equation, If a substance has a specific heat capacity of, 1000 J/(kg ºC) then, , ∴, ∴, , 1000 J raises the temperature, of 1 kg by 1 ºC, 2 × 1000 J raises the temperature, of 2 kg by 1 ºC, 3 × 2 × 1000 J raises the temperature, of 2 kg by 3 ºC, , That is, 6000 J will raise the temperature of 2 kg, of this substance by 3 ºC. We have obtained this, answer by multiplying together:, (i) the mass in kg,, (ii) the temperature rise in ºC, and, (iii) the specific heat capacity in J/(kg ºC)., , = 5 kg × 10 ºC × 400 J/(kg ºC), = 20 000 J, , l● Thermal capacity, The thermal capacity of a body is the quantity of, heat needed to raise the temperature of the whole, body by 1 °C., For a temperature rise of 1 °C the heat equation, becomes:, heat received = mass × 1 × specific heat capacity, so that, thermal capacity = mass × specific heat capacity, =m×c, , Thermal capacity is measured in joules per ºC,, i.e. J/ºC., For a copper block of mass 0.1 kg and specific heat, capacity 390 J/(kg °C),, thermal capacity = m × c, = 0.1 kg × 390 J/(kg °C), = 39 J/°C, , 88, , 9781444176421_Section_02.indd 88, , 20/06/14 7:34 AM
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Importance of the high specific heat capacity of water, switch it on for 5 minutes. When the temperature stops rising, record its highest value., Calculate the specific heat capacity as before., , Practical work, Finding specific heat capacities, You need to know the power of the 12 V electric immersion, heater to be used. (Precaution: Do not use one with a cracked, seal.) A 40 W heater converts 40 joules of electrical energy into, heat energy per second. If the power is not marked on the, heater, ask about it.1, , a) Water, Weigh out 1 kg of water into a container, such as an aluminium, saucepan. Note the temperature of the water, insert the heater, (Figure 21.1), switch on the 12 V supply and start timing. Stir the, water and after 5 minutes switch off, but continue stirring and, note the highest temperature reached., , thermometer, , electric immersion, heater, thermometer, , 12 V, supply, , electric immersion, heater, aluminium, block, , 12 V, supply, , water, , Figure 21.2, aluminium, pan, , Figure 21.1, , Assuming that the heat supplied by the heater equals the heat, received by the water, work out the specific heat capacity of, water in J/(kg ºC), as shown below:, heat received by water (J), , = power of heater (J/s) × time heater on (s), Rearranging the ‘heat equation’ we get, specific heat = heat received by water (J), capacity of water mass (kg) × temp. rise (ºC), Suggest causes of error in this experiment., , b) Aluminium, An aluminium cylinder weighing 1 kg and having two holes, drilled in it is used. Place the immersion heater in the central hole, and a thermometer in the other hole (Figure 21.2)., Note the temperature, connect the heater to a 12 V supply and, 1The power is found by immersing the heater in water, connecting, it to a 12 V d.c. supply and measuring the current taken (usually, 3–4 amperes). Then power in watts = volts × amperes., , ●● Importance of the high, specific heat capacity of, water, The specific heat capacity of water is, 4200 J/(kg ºC) and that of soil is about, 800 J/(kg ºC). As a result, the temperature of the, sea rises and falls more slowly than that of the land., A certain mass of water needs five times more heat, than the same mass of soil for its temperature to rise, by 1 ºC. Water also has to give out more heat to fall, 1 ºC. Since islands are surrounded by water they, experience much smaller changes of temperature, from summer to winter than large land masses such, as Central Asia., The high specific heat capacity of water (as well as, its cheapness and availability) accounts for its use in, cooling engines and in the radiators of central heating, systems., , 89, , 9781444176421_Section_02.indd 89, , 20/06/14 7:35 AM
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21 specIfIc heaT capacITY, , l● Worked examples, 1 A tank holding 60 kg of water is heated by a 3 kW, electric immersion heater. If the specific heat, capacity of water is 4200 J/(kg ºC), estimate the, time for the temperature to rise from 10 ºC to, 60 ºC., A 3 kW (3000 W) heater supplies 3000 J of heat, energy per second., Let t = time taken in seconds to raise the, temperature of the water by (60−10) = 50 ºC,, ∴ heat supplied to water in time t seconds, = (3000 × t) J, From the heat equation, we can say, heat received by water = 60 kg × 4200 J/(kg ºC), × 50 ºC, Assuming heat supplied = heat received, 3000 J/s × t = (60 × 4200 × 50) J, ∴, , (60 × 4200 × 50) J = 4200 s 70 min, t =, (, ), 3000 J/s, , 2 A piece of aluminium of mass 0.5 kg is heated, to 100 ºC and then placed in 0.4 kg of water at, 10 ºC. If the resulting temperature of the mixture, is 30 ºC, what is the specific heat capacity of, aluminium if that of water is 4200 J/(kg ºC)?, , Questions, 1 How much heat is needed to raise the temperature by, 10 ºC of 5 kg of a substance of specific heat capacity, 300 J/(kg ºC)? What is the thermal capacity of the, substance?, 2 The same quantity of heat was given to different masses, of three substances A, B and C. The temperature rise in, each case is shown in the table. Calculate the specific heat, capacities of A, B and C., Material, , Mass/kg, , Heat given/J, , Temp. rise/°C, , A, , 1.0, , 2000, , 1.0, , B, , 2.0, , 2000, , 5.0, , C, , 0.5, , 2000, , 4.0, , 3 The jam in a hot pop tart always seems hotter than the, pastry. Why?, , Checklist, After studying this chapter you should be able to, • define specific heat capacity, c,, • define thermal capacity,, • solve problems on specific heat capacity using the heat, equation Q = m × ∆θ × c,, • describe experiments to measure the specific heat capacity, of metals and liquids by electrical heating,, • explain the importance of the high specific heat capacity of, water., , When two substances at different temperatures, are mixed, heat flows from the one at the higher, temperature to the one at the lower temperature, until both are at the same temperature – the, temperature of the mixture. If there is no loss of, heat, then in this case:, heat given out by aluminium = heat taken in by water, Using the heat equation and letting c be the specific, heat capacity of aluminium in J/(kg ºC), we have, heat given out = 0.5 kg × c × (100 − 30) ºC, heat taken in = 0.4 kg × 4200 J/(kg ºC) ×, (30 − 10) ºC, ∴ 0.5 kg × c × 70 ºC = 0.4 kg × 4200 J/(kg ºC) × 20 ºC, c =, , ( 4200 × 8) J = 960 J/ kg ºC, (, ), 35 kg ºC, , 90, , 9781444176421_Section_02.indd 90, , 20/06/14 7:35 AM
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22, l, l, l, l, l, , Specific latent heat, , Specific latent heat of fusion, Specific latent heat of vaporisation, Latent heat and the kinetic theory, Evaporation and boiling, Condensation and solidification, , l, l, l, , When a solid is heated, it may melt and change its, state from solid to liquid. If ice is heated it becomes, water. The opposite process, freezing, occurs when a, liquid solidifies., A pure substance melts at a definite temperature,, called the melting point; it solidifies at the same, temperature – sometimes then called the freezing, point., , Cooling by evaporation, Liquefaction of gases and vapours, Practical work: Cooling curve of ethanamide; Specific, latent heat of fusion for ice; Specific latent heat of, vaporisation for steam, , l● Specific latent heat of, fusion, The previous experiment shows that the temperature, of liquid ethanamide falls until it starts to solidify, (at 82 ºC) and remains constant until it has all, solidified. The cooling curve in Figure 22.2 is for a, pure substance; the flat part AB occurs at the melting, point when the substance is solidifying., , Cooling curve of ethanamide, Half fill a test tube with ethanamide (acetamide) and, place it in a beaker of water (Figure 22.1a). Heat the water, until all the ethanamide has melted and its temperature, reaches about 90 ºC., Remove the test tube and arrange it as in Figure 22.1b, with a, thermometer in the liquid ethanamide. Record the temperature, every minute until it has fallen to 70 ºC., Plot a cooling curve of temperature against time. What is the, freezing (melting) point of ethanamide?, , thermometer, water, ethanamide, , a, , Figure 22.1, , b, , temperature, , Practical work, , A, , B, , melting point, , time, Figure 22.2 Cooling curve, , During solidification a substance loses heat to its, surroundings but its temperature does not fall., Conversely when a solid is melting, the heat supplied, does not cause a temperature rise; heat is added but, the substance does not get hotter. For example,, the temperature of a well-stirred ice–water mixture, remains at 0 ºC until all the ice is melted., Heat that is absorbed by a solid during, melting or given out by a liquid during solidification, is called latent heat of fusion. ‘Latent’ means hidden, and ‘fusion’ means melting. Latent heat does not, cause a temperature change; it seems to disappear., The specific latent heat of fusion (lf) of a substance is the, quantity of heat needed to change unit mass from solid to, liquid without temperature change., , 91, , 9781444176421_Section_02.indd 91, , 20/06/14 7:35 AM
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22 specIfIc laTenT heaT, , Specific latent heat is measured in J/kg or J/g. In, general, the quantity of heat Q to change a mass m, from solid to liquid is given by, Q = m × lf, , Practical work, Specific latent heat of fusion for ice, Through measurement of the mass of water m produced when, energy Q is transferred to melting ice, the specific latent heat of, fusion for ice can be calculated., Insert a 12 V electric immersion heater of known power P into, a funnel, and pack crushed ice around it as shown in Figure 22.3., To correct for heat transferred from the surroundings, collect the, melted ice in a beaker for time t (e.g. 4 minutes); weigh the beaker, plus the melted ice, m1. Empty the beaker, switch on the heater, and, collect the melted ice for the same time t; re-weigh the beaker plus, the melted ice, m2. The mass of ice melted by the heater is then, m = m2 − m1, The electrical energy supplied by the heater is given by Q =, P × t, where P is in J/s and t is in seconds; Q will be in joules., Alternatively, a joulemeter can be used to record Q directly., Calculate the specific latent heat of fusion, lf, for ice using, , l● Specific latent heat of, vaporisation, Latent heat is also needed to change a liquid, into a vapour. The reading of a thermometer, placed in water that is boiling remains constant at, 100 ºC even though heat, called latent heat of, vaporisation, is still being absorbed by the water, from whatever is heating it. When steam condenses, to form water, latent heat is given out., The specific latent heat of vaporisation (lv) of a substance, is the quantity of heat needed to change unit mass from liquid, to vapour without change of temperature., , Again, the specific latent heat is measured in J/kg or, J/g. In general, the quantity of heat Q to change a, mass m from liquid to vapour is given by, Q = m × lv, , Q = m × lf, How does it compare with the accepted value of 340 J/g? How, could the experiment be improved?, , immersion heater, , funnel, , crushed ice, , beaker, water, Figure 22.3, , Figure 22.4 Why is a scald from steam often more serious than one, from boiling water?, , 92, , 9781444176421_Section_02.indd 92, , 20/06/14 7:35 AM
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Evaporation and boiling, , Practical work, Specific latent heat of vaporisation, for steam, Through measurement of the mass of vapour m produced when, energy Q is transferred to boiling water, the specific latent heat, of vaporisation for steam can be calculated., Water in the flask (Figure 22.5) is heated to boiling point by, an immersion heater of power P. Steam passes out through the, holes in the top of the flask, down the outside of the flask and, into the inner tube of a condenser, where it changes back to, liquid (because cold water is flowing through the outer tube),, and is collected in a beaker., After the water has been boiling for some time, it becomes, enclosed by a ‘jacket’ of vapour at the boiling point, which, helps to reduce loss of heat to the surroundings. The rate of, vaporisation becomes equal to the rate of condensation, and the, electrical energy is only being used to transfer latent heat to the, water (not to raise its temperature)., The electrical energy Q supplied by the heater is given by, Q = P × t = ItV, where I is the steady current through the heater and V is the, p.d. across it. Q is in joules if P is in J/s and t is in seconds., Alternatively, a joulemeter can be used to record Q directly., If a mass of water m is collected in time t, then the specific, latent heat of vaporisation lv can be calculated using, Q = m × lv, A, V, , felt, lagging, , jacket of, vapour, , water, , heating, coil, , ●● Latent heat and the, kinetic theory, a) Fusion, The kinetic theory explains latent heat of fusion as, being the energy that enables the molecules of a solid, to overcome the intermolecular forces that hold them, in place, and when it exceeds a certain value they break, free. Their vibratory motion about fixed positions, changes to the slightly greater range of movement they, have as liquid molecules, and the solid melts., The energy input is used to increase the potential, energy (p.e.) of the molecules, but not their average, kinetic energy (k.e.) as happens when the heat, causes a temperature rise., , b) Vaporisation, If liquid molecules are to overcome the forces, holding them together and gain the freedom to, move around independently as gas molecules, they, need a large amount of energy. They receive this, as latent heat of vaporisation which, like latent, heat of fusion, increases the potential energy of the, molecules but not their kinetic energy. It also gives, the molecules the energy required to push back the, surrounding atmosphere in the large expansion that, occurs when a liquid vaporises., To change 1 kg of water at 100 ºC to steam at, 100 ºC needs over five times as much heat as is needed, to raise the temperature of 1 kg of water at 0 ºC to, water at 100 ºC (see Worked example 1, p. 95)., , ●● Evaporation and boiling, a) Evaporation, condenser, , cold water in, , Figure 22.5, , A few energetic molecules close to the surface of, a liquid may escape and become gas molecules., This process occurs at all temperatures and is called, evaporation. It happens more rapidly when, (i) the temperature is higher, since then more, molecules in the liquid are moving fast enough, to escape from the surface,, (ii) the surface area of the liquid is large, so giving, more molecules a chance to escape because more, are near the surface, and, 93, , 9781444176421_Section_02.indd 93, , 20/06/14 7:36 AM
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22 Specific latent heat, , (iii) a wind or draught is blowing over the surface, carrying vapour molecules away from the surface,, thus stopping them from returning to the liquid, and making it easier for more liquid molecules, to break free. (Evaporation into a vacuum occurs, much more rapidly than into a region where, there are gas molecules.), , b) Boiling, For a pure liquid boiling occurs at a definite, temperature called its boiling point and is, accompanied by bubbles that form within the, liquid, containing the gaseous or vapour form of the, particular substance., Latent heat is needed in both evaporation and, boiling and is stored in the vapour, from which it is, released when the vapour is cooled or compressed, and changes to liquid again., , ●● Condensation and, solidification, In condensation, a gas changes to a liquid, state and latent heat of vaporisation is released., In solidification, a liquid changes to a solid and, latent heat of fusion is given out. In each case, the potential energy of the molecules decreases., Condensation of steam is easily achieved by, contact with a cold surface, for example a cold, windowpane. In Figure 22.5, the latent heat, released when the steam condenses to water is, transferred to the cold water flowing through the, condenser., , ●● Cooling by evaporation, In evaporation, latent heat is obtained by the, liquid from its surroundings, as may be shown, by the following demonstration, done in a fume, cupboard., , a) Demonstration, Dichloromethane is a volatile liquid, i.e. it has a, low boiling point and evaporates readily at room, temperature, especially when air is blown through, it (Figure 22.6). Latent heat is taken first from the, liquid itself and then from the water below the can., The water soon freezes causing the block and can to, stick together., , air, , glass tube, can, dichloromethane, water, block of wood, Figure 22.6 Demonstrating cooling by evaporation, , b) Explanation, Evaporation occurs when faster-moving, molecules escape from the surface of the liquid., The average speed and therefore the average kinetic, energy of the molecules left behind decreases, i.e. the, temperature of the liquid falls. Any body in contact, with an evaporating liquid will be cooled by the, evaporation., , c) Uses, Water evaporates from the skin when we sweat., This is the body’s way of losing unwanted heat and, keeping a constant temperature. After vigorous, exercise there is a risk of the body being overcooled,, especially in a draught; it is then less able to resist, infection., Ether acts as a local anaesthetic by chilling (as, well as cleaning) your arm when you are having an, injection. Refrigerators, freezers and air-conditioning, systems use cooling by evaporation on a large scale., Volatile liquids are used in perfumes., , ●● Liquefaction of gases, and vapours, A vapour can be liquefied if it is compressed, enough. However, a gas must be cooled below a, certain critical temperature Tc before liquefaction, by pressure can occur. The critical temperatures for, some gases are given in Table 22.1., , 94, , 9781444176421_Section_02.indd 94, , 20/06/14 7:36 AM
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Worked examples, , Table 22.1 Critical temperatures of some gases, Carbon, dioxide, , Oxygen, , Air, , Nitrogen Hydrogen Helium, , Tc/K, , 304, , 154, , 132, , 126, , 33.3, , 5.3, , Tc/ºC, , +31, , −119, , −141, , −147, , −239.7, , −267.7, , Low-temperature liquids have many uses. Liquid, hydrogen and oxygen are used as the fuel and, oxidant respectively in space rockets. Liquid, nitrogen is used in industry as a coolant in, for, example, shrink-fitting (see Figure 19.1, p. 81)., Materials that behave as superconductors (see, Chapter 18) when cooled by liquid nitrogen are, increasingly used in electrical power engineering and, electronics., , Heat lost by can in falling from 15 ºC to −5.0 ºC, = mass of can × specific heat capacity of, aluminium × temperature fall, = 100 g × 0.90 J/(g ºC) × (15 − [−5]) ºC, = 100 g × 0.90 J/(g ºC) × 20 ºC, = 1800 J, Heat lost by water in falling from 15 ºC to 0 ºC, = mass of water × specific heat capacity of water, × temperature fall, = 200 g × 4.2 J/(g ºC) × 15 ºC, = 12 600 J, Heat lost by water at 0 ºC freezing to ice at 0 ºC, = mass of water × specific latent heat of ice, = 200 g × 340 J/g, = 68 000 J, , l● Worked examples, The values in Table 22.2 are required., Table 22.2, Water, , Ice, , Aluminium, , Specific heat capacity/J/(g ºC), , 4.2, , 2.0, , 0.90, , Specific latent heat/J/g, , 2300, , 340, , 1 How much heat is needed to change 20 g of ice at, 0 ºC to steam at 100 ºC?, There are three stages in the change., Heat to change 20 g ice at 0 °C to water at 0 °C, = mass of ice × specific latent heat of ice, = 20 × 340 J/g = 6800 J, Heat to change 20 g water at 0 °C to water at, 100 °C, = mass of water × specific heat capacity of water, × temperature rise, = 20 g × 4.2 J/(g ºC) × 100 ºC = 8400 J, Heat to change 20 g water at 100 °C to steam, at 100 °C, = mass of water × specific latent heat of steam, = 20 g × 2300 J/g = 46 000 J, , Heat lost by ice in falling from 0 ºC to −5.0 ºC, = mass of ice × specific heat capacity of ice, × temperature fall, = 200 g × 2.0 J/(g ºC) × 5.0 ºC, = 2000 J, ∴ Total heat removed, = 1800 + 12 600 + 68 000 + 2000 = 84 400 J, , Questions, Use values given in Table 22.2., 1 a How much heat will change 10 g of ice at 0 ºC to water, at 0 ºC?, b What quantity of heat must be removed from 20 g of, water at 0 ºC to change it to ice at 0 ºC?, 2 a How much heat is needed to change 5 g of ice at 0 ºC to, water at 50 ºC?, b If a freezer cools 200 g of water from 20 ºC to its, freezing point in 10 minutes, how much heat is removed, per minute from the water?, 3 How long will it take a 50 W heater to melt 100 g of ice at 0 ºC?, 4 Some small aluminium rivets of total mass 170 g and at, 100 ºC are emptied into a hole in a large block of ice at 0 ºC., a What will be the final temperature of the rivets?, b How much ice will melt?, ▲, ▲, , ∴ Total heat supplied, = 6800 + 8400 + 46 000 = 61 200 J, , 2 An aluminium can of mass 100 g contains 200 g, of water. Both, initially at 15 ºC, are placed in a, freezer at −5.0 ºC. Calculate the quantity of heat, that has to be removed from the water and the, can for their temperatures to fall to −5.0 ºC., , 95, , 9781444176421_Section_02.indd 95, , 20/06/14 7:36 AM
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22 specIfIc laTenT heaT, , 5 a How much heat is needed to change 4 g of water at, 100 ºC to steam at 100 ºC?, b Find the heat given out when 10 g of steam at 100 ºC, condenses and cools to water at 50 ºC., 6 A 3 kW electric kettle is left on for 2 minutes after the, water starts to boil. What mass of water is boiled off in, this time?, 7 a Why is ice good for cooling drinks?, b Why do engineers often use superheated steam (steam, above 100 ºC) to transfer heat?, 8 Some water is stored in a bag of porous material, such as, canvas, which is hung where it is exposed to a draught, of air. Explain why the temperature of the water is lower, than that of the air., 9 Explain why a bottle of milk keeps better when it stands, in water in a porous pot in a draught., 10 A certain liquid has a specific heat capacity of, 4.0 J/(g ºC). How much heat must be supplied to raise the, temperature of 10 g of the liquid from 20 ºC to 50 ºC?, , Checklist, After studying this chapter you should be able to, • describe an experiment to show that during a change of, state the temperature stays constant,, • state the meaning of melting point and boiling point,, • describe condensation and solidification,, • define specific latent heat of fusion, lf,, • define specific latent heat of vaporisation, lv,, • explain latent heat using the kinetic theory,, • solve problems on latent heat, using Q = ml,, • distinguish between evaporation and boiling,, • describe an experiment to measure specific latent heats, for ice and steam,, • explain cooling by evaporation using the kinetic theory., , 96, , 9781444176421_Section_02.indd 96, , 20/06/14 7:36 AM
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23, l, l, l, l, , Conduction and convection, , Conduction, Uses of conductors, Conduction and the kinetic theory, Convection in liquids, , l, l, l, l, , To keep a building or a house at a comfortable, temperature in winter and in summer, if it is to, be done economically and efficiently, requires a, knowledge of how heat travels., , l● Conduction, The handle of a metal spoon held in a hot drink, soon gets warm. Heat passes along the spoon by, conduction., , Convection in air, Natural convection currents, Energy losses from buildings, Ventilation, , Most metals are good conductors of heat;, materials such as wood, glass, cork, plastics and, fabrics are bad conductors. The arrangement in, Figure 23.2 can be used to show the difference, between brass and wood. If the rod is passed, through a flame several times, the paper over the, wood scorches but not the paper over the brass. The, brass conducts the heat away from the paper quickly,, preventing the paper from reaching the temperature, at which it burns. The wood conducts the heat away, only very slowly., , Conduction is the flow of thermal energy (heat) through, matter from places of higher temperature to places of lower, temperature without movement of the matter as a whole., , A simple demonstration of the different conducting, powers of various metals is shown in Figure 23.1. A, match is fixed to one end of each rod using a little, melted wax. The other ends of the rods are heated, by a burner. When the temperatures of the far ends, reach the melting point of wax, the matches drop, off. The match on copper falls first, showing it is the, best conductor, followed by aluminium, brass and, then iron., match, iron rod, , copper rod, , aluminium rod, paraffin wax, , white gummed paper, , brass, , wood, , Figure 23.2 The paper over the brass does not burn., , Metal objects below body temperature feel colder, than those made of bad conductors – even if all, the objects are at exactly the same temperature –, because they carry heat away faster from the hand., Liquids and gases also conduct heat but only, very slowly. Water is a very poor conductor, as, shown in Figure 23.3. The water at the top of, the tube can be boiled before the ice at the, bottom melts., , tripod, steam, , brass rod, , boiling water, very little, conduction, , burner, , ice, , Figure 23.1 Comparing conducting powers, , Heat is conducted faster through a rod if it has a, large cross-sectional area, is short and has a large, temperature difference between its ends., , metal, gauze to, keep ice, down, , Figure 23.3 Water is a poor conductor of heat., , 97, , 9781444176421_Section_02.indd 97, , 20/06/14 7:36 AM
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23 Conduction and convection, , ●● Uses of conductors, a) Good conductors, These are used whenever heat is required to travel, quickly through something. Saucepans, boilers and, radiators are made of metals such as aluminium, iron, and copper., , b) Bad conductors (insulators), The handles of some saucepans are made of wood or, plastic. Cork is used for table mats., Air is one of the worst conductors and so one of, the best insulators. This is why houses with cavity, walls (two layers of bricks separated by an air space), and double-glazed windows keep warmer in winter, and cooler in summer., Materials that trap air, such as wool, felt, fur,, feathers, polystyrene foam, fibreglass, are also very, bad conductors. Some of these materials are used as, ‘lagging’ to insulate water pipes, hot water cylinders,, ovens, refrigerators and the walls and roofs of houses, (Figures 23.4a and 23.4b). Others are used to make, warm winter clothes like ‘fleece’ jackets (Figure 23.4c)., , Figure 23.4c Fleece jackets help you to retain your body warmth., , ‘Wet suits’ are worn by divers and water skiers to, keep them warm. The suit gets wet and a layer of, water gathers between the person’s body and the suit., The water is warmed by body heat and stays warm, because the suit is made of an insulating fabric, such, as neoprene, a synthetic rubber., , ●● Conduction and the, kinetic theory, Figure 23.4a Lagging in a cavity wall provides extra insulation., , Figure 23.4b Laying lagging in a house loft, , Two processes occur in metals. Metals have a large, number of ‘free’ electrons (Chapter 36) which, wander about inside them. When one part of a, metal is heated, the electrons there move faster, (their kinetic energy increases) and further. As a, result they ‘jostle’ atoms in cooler parts, so passing, on their energy and raising the temperature of these, parts. This process occurs quickly., The second process is much slower. The, atoms themselves at the hot part make ‘colder’, neighbouring atoms vibrate more vigorously. This, is less important in metals but is the only way, conduction occurs in non-metals since these do not, have ‘free’ electrons; hence non-metals are poor, conductors of heat., , 98, , 9781444176421_Section_02.indd 98, , 20/06/14 7:36 AM
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convection in air, , l● Convection in liquids, Convection is the usual method by which thermal, energy (heat) travels through fluids such as liquids, and gases. It can be shown in water by dropping, a few crystals of potassium permanganate down, a tube to the bottom of a beaker or flask of, water. When the tube is removed and the beaker, heated just below the crystals by a small flame, (Figure 23.5a), purple streaks of water rise upwards, and fan outwards., , Figure 23.5b Lava lamps make use of convection., , l● Convection in air, Figure 23.5a Convection currents shown by potassium permanganate, in water, , Streams of warm moving fluids are called convection, currents. They arise when a fluid is heated because it, expands, becomes less dense and is forced upwards by, surrounding cooler, denser fluid which moves under, it. We say ‘hot water (or hot air) rises’. Warm fluid, behaves like a cork released under water: being less, dense it bobs up. Lava lamps (Figure 23.5b) use, this principle., Convection is the flow of heat through a fluid from places, of higher temperature to places of lower temperature by, movement of the fluid itself., , Black marks often appear on the wall or ceiling above, a lamp or a radiator. They are caused by dust being, carried upwards in air convection currents produced, by the hot lamp or radiator., A laboratory demonstration of convection currents, in air can be given using the apparatus of Figure 23.6., The direction of the convection current created by, the candle is made visible by the smoke from the, touch paper (made by soaking brown paper in strong, potassium nitrate solution and drying it)., Convection currents set up by electric, gas and, oil heaters help to warm our homes. Many so-called, ‘radiators’ are really convector heaters., Where should the input and extraction ducts for, cold/hot air be located in a room?, , 99, , 9781444176421_Section_02.indd 99, , 20/06/14 7:36 AM
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23 Conduction and convection, , smoke, , sea, breeze, glass chimneys, , land, warmer, , lighted, touch paper, , sea, cooler, , box, , a, , lighted, candle, , glass, window, , land, cooler, , Figure 23.6 Demonstrating convection in air, , land, breeze, sea, warmer, , ●● Natural convection, currents, , b, Figure 23.7 Coastal breezes are due to convection: a day; b night, , a) Coastal breezes, During the day the temperature of the land increases, more quickly than that of the sea (because the, specific heat capacity of the land is much smaller; see, Chapter 21). The hot air above the land rises and is, replaced by colder air from the sea. A breeze from the, sea results (Figure 23.7a)., At night the opposite happens. The sea has more, heat to lose and cools more slowly. The air above the, sea is warmer than that over the land and a breeze, blows from the land (Figure 23.7b)., , b) Gliding, Gliders, including ‘hang-gliders’ (Figure 23.8),, depend on hot air currents, called thermals., , ●● Energy losses from, buildings, The inside of a building can only be kept at a steady, temperature above that outside by heating it at a rate, which equals the rate at which it is losing energy. The, loss occurs mainly by conduction through the walls,, roof, floors and windows. For a typical house in the, UK where no special precautions have been taken,, , Figure 23.8 Once airborne, a hang-glider pilot can stay aloft for several, hours by flying from one thermal to another., , the contribution each of these makes to the total loss, is shown in Table 23.1a., As fuels (and electricity) become more expensive, and the burning of fuels becomes of greater, environmental concern (Chapter 15), more people, are considering it worthwhile to reduce heat losses, from their homes. The substantial reduction, of this loss which can be achieved, especially, by wall and roof insulation, is shown in, Table 23.1b., , 100, , 9781444176421_Section_02.indd 100, , 20/06/14 7:37 AM
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ventilation, Table 23.1 Energy losses from a typical house, , d A vacuum is an even better heat insulator than air., Suggest one (scientific) reason why the double glazing, should not have a vacuum between the sheets of glass., e The manufacturers of roof lagging suggest that two, layers of fibreglass are more effective than one. Describe, how you might set up an experiment in the laboratory, to test whether this is true., , a, Percentage of total energy loss due to, walls, , roof, , floors, , windows, , draughts, , 35, , 25, , 15, , 10, , 15, , b, , house roof, , rafter, , Percentage of each loss saved by, insulating, walls, , insulating, roof, , carpets on, floors, , double, glazing, , draught, excluders, , 65, , 80, , ≈ 30, , 50, , ≈ 60, , Percentage of total loss saved = 60, , fibreglass laid, between rafters, , a, , cavity with, plastic foam, injected, , l● Ventilation, In addition to supplying heat to compensate for, the energy losses from a building, a heating system, has also to warm the ventilated cold air, needed for, comfort, which comes in to replace stale air., If the rate of heat loss is, say, 6000 J/s, or 6 kW,, and the warming of ventilated air requires 2 kW,, then the total power needed to maintain a certain, temperature (e.g. 20 ºC) in the building is 8 kW., Some of this is supplied by each person’s ‘body, heat’, estimated to be roughly equal to a 100 W, heater., , Questions, 1 Explain why, a newspaper wrapping keeps hot things hot, e.g. fish and, chips, and cold things cold, e.g. ice cream,, b fur coats would keep their owners warmer if they were, worn inside out,, c a string vest helps to keep a person warm even though, it is a collection of holes bounded by string., 2 Figure 23.9 illustrates three ways of reducing heat losses, from a house., a As far as you can, explain how each of the three, methods reduces heat losses. Draw diagrams where they, will help your explanations., b Why are fibreglass and plastic foam good substances to, use?, c Air is one of the worst conductors of heat. What is the, point of replacing it by plastic foam as shown in the, Figure 23.9b?, , air, , house, wall, b, , glass, , glass, , c, , Figure 23.9 a Roof insulation; b cavity wall insulation; c double, glazing, , 3 What is the advantage of placing an electric immersion, heater, a near the top,, b near the bottom,, of a tank of water?, 4 Explain why on a cold day the metal handlebars of a bicycle, feel colder than the rubber grips., , Checklist, After studying this chapter you should be able to, • describe experiments to show the different conducting, powers of various substances,, • name good and bad conductors and state uses for each,, • explain conduction using the kinetic theory,, • describe experiments to show convection in fluids (liquids, and gases),, • relate convection to phenomena such as land and sea, breezes,, • explain the importance of insulating a building., , 101, , 9781444176421_Section_02.indd 101, , 20/06/14 7:37 AM
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24, l, l, l, , Radiation, , Good and bad absorbers, Good and bad emitters, Vacuum flask, , Radiation is a third way in which heat can, travel, but whereas conduction and convection, both need matter to be present, radiation can, occur in a vacuum; particles of matter are not, involved. Radiation is the way heat reaches us, from the Sun., Radiation has all the properties of electromagnetic, waves (Chapter 32), such as it travels at the speed, of radio waves and gives interference effects. When, it falls on an object, it is partly reflected, partly, transmitted and partly absorbed; the absorbed part, raises the temperature of the object., , l, l, , The greenhouse, Rate of cooling of an object, , other dull black. The coins are stuck on the outside, of each lid with candle wax. If the heater is midway, between the lids they each receive the same amount, of radiation. After a few minutes the wax on the black, lid melts and the coin falls off. The shiny lid stays, cool and the wax unmelted., , shiny, surface, , electric, heater, , dull black, surface, , coin, , Radiation is the flow of heat from one place to another by, means of electromagnetic waves., , candle, wax, tin lid, , Radiation is emitted by all bodies above absolute zero, and consists mostly of infrared radiation (Chapter, 32) but light and ultraviolet are also present if the, body is very hot (e.g. the Sun)., Figure 24.2 Comparing absorbers of radiation, , Dull black surfaces are better absorbers of, radiation than white shiny surfaces – the latter are, good reflectors of radiation. Reflectors on electric, fires are made of polished metal because of its good, reflecting properties., , l● Good and bad emitters, Figure 24.1 Why are buildings in hot countries often painted white?, , l● Good and bad absorbers, Some surfaces absorb radiation better than others,, as may be shown using the apparatus in Figure 24.2., The inside surface of one lid is shiny and of the, , Some surfaces also emit radiation better than others, when they are hot. If you hold the backs of your hands, on either side of a hot copper sheet that has one side, polished and the other side blackened (Figure 24.3),, it will be found that the dull black surface is a better, emitter of radiation than the shiny one., The cooling fins on the heat exchangers at the, back of a refrigerator are painted black so that they, lose heat more quickly. By contrast, saucepans that, are polished are poor emitters and keep their heat, longer., , 102, , 9781444176421_Section_02.indd 102, , 20/06/14 7:37 AM
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Rate of cooling of an object, , In general, surfaces that are good absorbers of, radiation are good emitters when hot., , hot copper sheet with one, side polished and the, other blackened, back of hands, towards sheet, , Figure 24.3 Comparing emitters of radiation, , ●● Vacuum flask, A vacuum or Thermos flask keeps hot liquids hot or, cold liquids cold. It is very difficult for heat to travel, into or out of the flask., Transfer by conduction and convection is, minimised by making the flask a double-walled glass, vessel with a vacuum between the walls (Figure 24.4)., Radiation is reduced by silvering both walls on the, vacuum side. Then if, for example, a hot liquid is, stored, the small amount of radiation from the hot, inside wall is reflected back across the vacuum by the, silvering on the outer wall. The slight heat loss that, does occur is by conduction up the thin glass walls, and through the stopper., , stopper, , double-walled, glass vessel, silvered surfaces, , The warmth from the Sun is not cut off by a sheet, of glass but the warmth from a red-hot fire can be, blocked by glass. The radiation from very hot bodies, like the Sun is mostly in the form of light and shortwavelength infrared. The radiation from less hot, objects, like a fire, is largely long-wavelength infrared, which, unlike light and short-wavelength infrared,, cannot pass through glass., Light and short-wavelength infrared from the Sun, penetrate the glass of a greenhouse and are absorbed, by the soil, plants, etc., raising their temperature., These in turn emit infrared but, because of their, relatively low temperature, this has a long wavelength, and is not transmitted by the glass. The greenhouse, thus acts as a ‘heat-trap’ and its temperature rises., Carbon dioxide and other gases such as methane, in the Earth’s atmosphere act in a similar way to, the glass of a greenhouse in trapping heat; this has, serious implications for the global climate., , ●● Rate of cooling of an, object, The rate at which an object cools, i.e. at which its, temperature falls, can be shown to be proportional, to the ratio of its surface area A to its volume V., For a cube of side l, 2, A1, = 6 × l3 = 6, V1, l, l, , For a cube of side 2l, A2, l2, = 6× 43 = 3, V2, l, 8l, A, = 1×6 = 1 1, 2 l, 2 V1, The larger cube has the smaller A/V ratio and so, cools more slowly., ▲, ▲, , case, vacuum, felt pad, , ●● The greenhouse, , Figure 24.4 A vacuum flask, , 103, , 9781444176421_Section_02.indd 103, , 20/06/14 7:37 AM
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24 radIaTIon, , You could investigate this using two aluminium, cubes, one having twice the length of side of the, other. Each needs holes for a thermometer and an, electric heater to raise them to the same starting, temperature. Graphs of temperature against time for, both blocks can then be obtained. It is important, that the blocks are at the same starting temperature, because the higher the temperature a body is, above its surroundings, the greater the amount of, radiation it emits per second and the faster it cools., This can be seen from its cooling curve since the, gradient of the graph is steeper at high temperatures, than it is at low temperatures (see Figure 22.2, where the ethanamide is cooling)., , Checklist, After studying this chapter you should be able to, • describe the effect of surface colour and texture on the, emission, absorption and reflection of radiation,, • describe experiments to study factors affecting the, absorption and emission of radiation,, • recall that good absorbers are also good emitters,, • explain how a knowledge of heat transfer affects the design, of a vacuum flask,, • explain how a greenhouse acts as a ‘heat-trap’., , Questions, 1 The door canopy in Figure 24.5 shows in a striking way, the difference between white and black surfaces when, radiation falls on them. Explain why., , Figure 24.5, , 2 a The Earth has been warmed by the radiation from, the Sun for millions of years yet we think its average, temperature has remained fairly steady. Why is this?, b Why is frost less likely on a cloudy night than a clear, one?, , 104, , 9781444176421_Section_02.indd 104, , 20/06/14 7:37 AM
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Section, , 3, , Properties of waves, , Chapters, General wave properties, 25 Mechanical waves, Light, 26 Light rays, 27 Reflection of light, , 9781444176421_Section_03.indd 105, , 28, 29, 30, 31, 32, , Plane mirrors, Refraction of light, Total internal reflection, Lenses, Electromagnetic radiation, , Sound, 33 Sound waves, , 20/06/14 7:32 AM
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25 Mechanical waves, l, l, l, l, l, l, , Types of wave, Describing waves, The wave equation, Wavefronts and rays, Reflection, Refraction, , l, l, l, l, l, , Diffraction, Wave theory, Interference, Polarisation, Practical work: The ripple tank, , ●● Types of wave, , ●● Describing waves, , Several kinds of wave occur in physics. Mechanical, waves are produced by a disturbance, such as, a vibrating object, in a material medium and, are transmitted by the particles of the medium, vibrating to and fro. Such waves can be seen, or felt and include waves on a rope or spring,, water waves and sound waves in air or in other, materials., A progressive or travelling wave is a disturbance, which carries energy from one place to another, without transferring matter. There are two types,, transverse and longitudinal. Longitudinal waves are, dealt with in Chapter 33., In a transverse wave, the direction of the, disturbance is at right angles to the direction of, travel of the wave. A transverse wave can be sent, along a rope (or a spring) by fixing one end and, moving the other rapidly up and down (Figure, 25.1). The disturbance generated by the hand is, passed on from one part of the rope to the next, which performs the same motion but slightly later., The humps and hollows of the wave travel along the, rope as each part of the rope vibrates transversely, about its undisturbed position., Water waves are transverse waves., , Terms used to describe waves can be explained, with the aid of a displacement–distance graph, (Figure 25.2). It shows, at a certain instant of time,, the distance moved (sideways from their undisturbed, positions) by the parts of the medium vibrating at, different distances from the cause of the wave., , direction of wave, , hump, , rope, direction of, vibration, , Figure 25.1 A transverse wave, , hollow, , a) Wavelength, , displacement, , The wavelength of a wave, represented by the Greek, letter λ (‘lambda’), is the distance between successive, crests., wavelength, λ, , undisturbed, position, , a, A, , distance, , crest, B, , a, , C, , D, , trough, , λ, Figure 25.2 Displacement–distance graph for a wave at a particular, instant, , b) Frequency, The frequency f is the number of complete waves, generated per second. If the end of a rope is moved, up and down twice in a second, two waves are, produced in this time. The frequency of the wave is, 2 vibrations per second or 2 hertz (2 Hz; the hertz, being the unit of frequency), which is the same as the, frequency of the movement of the end of the rope., That is, the frequencies of the wave and its source are, equal., The frequency of a wave is also the number of, crests passing a chosen point per second., , 106, , 9781444176421_Section_03.indd 106, , 20/06/14 7:32 AM
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Wavefronts and rays, , c) Speed, The speed v of the wave is the distance moved in the, direction of travel of the wave by a crest or any point, on the wave in 1 second., , d) Amplitude, The amplitude a is the height of a crest or the depth, of a trough measured from the undisturbed position, of what is carrying the wave, such as a rope., , e) Phase, The short arrows at A, B, C, D on Figure 25.2 show, the directions of vibration of the parts of the rope, at these points. The parts at A and C have the same, speed in the same direction and are in phase. At B, and D the parts are also in phase with each other but, they are out of phase with those at A and C because, their directions of vibration are opposite., , ●● The wave equation, The faster the end of a rope is vibrated, the shorter, the wavelength of the wave produced. That is,, the higher the frequency of a wave, the smaller its, wavelength. There is a useful connection between f,, λ and v, which is true for all types of wave., Suppose waves of wavelength λ = 20 cm travel, on a long rope and three crests pass a certain point, every second. The frequency f = 3 Hz. If Figure 25.3, represents this wave motion then, if crest A is at P at a, particular time, 1 second later it will be at Q, a distance, from P of three wavelengths, i.e. 3 × 20 = 60 cm. The, speed of the wave is v = 60 cm per second (60 cm/s),, obtained by multiplying f by λ. Hence, or, , speed of wave = frequency × wavelength, v = fλ, P, , Q, crest A, time 0 second, , vibrator, (3 Hz), , time 1 second, 3λ, , Figure 25.3, , Practical work, The ripple tank, The behaviour of water waves can be studied in a ripple tank., It consists of a transparent tray containing water, having a light, source above and a white screen below to receive the wave, images (Figure 25.4)., Pulses (i.e. short bursts) of ripples are obtained by dipping a, finger in the water for circular ripples and a ruler for straight, ripples. Continuous ripples are generated using an electric, motor and a bar. The bar gives straight ripples if it just, touches the water or circular ripples if it is raised and has a small, ball fitted to it., , light source, ripple, generator, (motor), water, (5 mm, deep), screen, , bar touching water, for straight ripples, , hand, stroboscope, (below tank), , Figure 25.4 A ripple tank, , Continuous ripples are studied more easily if they are apparently, stopped (‘frozen’) by viewing the screen through a disc, with equally spaced slits, which can be spun by hand, i.e. a, stroboscope. If the disc speed is such that the waves have, advanced one wavelength each time a slit passes your eye, they, appear at rest., , ●● Wavefronts and rays, In two dimensions, a wavefront is a line on which, the disturbance has the same phase at all points;, the crests of waves in a ripple tank can be thought, of as wavefronts. A vibrating source produces a, succession of wavefronts, all of the same shape. In, a ripple tank, straight wavefronts are produced by a, vibrating bar (a line source) and circular wavefronts, are produced by a vibrating ball (a point source)., A line drawn at right angles to a wavefront, which, shows its direction of travel, is called a ray. Straight, wavefronts and the corresponding rays are shown, in Figure 25.5; circular wavefronts can be seen in, Figure 25.13., 107, , 9781444176421_Section_03.indd 107, , 20/06/14 7:32 AM
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25 Mechanical waves, , ●● Reflection, In Figure 25.5 straight water waves are falling on a, metal strip placed in a ripple tank at an angle of 60°,, i.e. the angle i between the direction of travel of the, waves and the normal to the strip is 60°, as is the angle, between the wavefront and the strip. (The perpendicular, to the strip at the point where the incident ray strikes, is called the normal.) The wavefronts are represented, by straight lines and can be thought of as the crests, of the waves. They are at right angles to the direction, of travel, i.e. to the rays. The angle of reflection r is, 60°. Incidence at other angles shows that the angle of, incidence and angle of reflection are always equal., , The change in the direction of travel of the waves,, which occurs when their speed and hence wavelength, changes, is termed refraction., , Figure 25.7a Waves are refracted at the boundary between deep and, shallow regions., , incident wavefront normal reflected wavefront, direction, of travel, , slow, i, , r, , r, , metal strip, shallow water, , Figure 25.5 Reflection of waves, , ●● Refraction, If a glass plate is placed in a ripple tank so that the, water over the glass plate is about 1 mm deep but is, 5 mm deep elsewhere, continuous straight waves in the, shallow region are found to have a shorter wavelength, than those in the deeper parts, i.e. the wavefronts are, closer together (Figure 25.6). Both sets of waves have, the frequency of the vibrating bar and, since v = f λ, if, λ has decreased so has v, since f is fixed. Hence waves, travel more slowly in shallow water., , deep water, i, fast, , Figure 25.7b The direction of travel is bent towards the normal in the, shallow region., , ●● Diffraction, In Figures 25.8a and 25.8b, straight water waves in, a ripple tank are meeting gaps formed by obstacles., In Figure 25.8a the gap width is about the same as, the wavelength of the waves (1 cm); the wavefronts, that pass through become circular and spread out, in all directions. In Figure 25.8b the gap is wide, (10 cm) compared with the wavelength and the waves, continue straight on; some spreading occurs but it is, less obvious., , Figure 25.6 Waves in shallower water have a shorter wavelength., , When the plate is at an angle to the waves, (Figure 25.7a), their direction of travel in the shallow, region is bent towards the normal (Figure 25.7b)., , Figure 25.8a Spreading of waves after passing through a narrow gap, , 108, , 9781444176421_Section_03.indd 108, , 20/06/14 7:33 AM
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Wave theory, , Figure 25.8b Spreading of waves after passing through a wide gap, , Figure 25.9 Model of a harbour used to study wave behaviour, , The spreading of waves at the edges of obstacles, is called diffraction; when designing harbours,, , engineers use models like that in Figure 25.9, to study it., , ●● Wave theory, , A, , C, constructed wavefront, , If the position of a wavefront is known at one, instant, its position at a later time can be found, using Huygens’ construction. Each point on the, wavefront is considered to be a source of secondary, spherical wavelets (Figure 25.10) which spread, out at the wave speed; the new wavefront is the, surface that touches all the wavelets (in the forward, direction). In Figure 25.10; the straight wavefront, AB is travelling from left to right with speed v. At a, time t later, the spherical wavelets from AB will be a, distance vt from the secondary sources and the new, surface which touches all the wavelets is the straight, wavefront CD., Wave theory can be used to explain reflection,, refraction and diffraction effects., , secondary source, , first position of, wavefront, , vt, B, , D, secondary wavelet, , Figure 25.10 Huygens’ construction for a straight wavefront, , a) Reflection and wave theory, Figure 25.11 shows a straight wavefront AB, incident at an angle i on a reflecting surface; the, , secondary wavelet from A, B, incident wavefront, , A', , reflected wavefront, , C, , D, , r, , i, i, , B', , ▲, ▲, , A, , r, , Figure 25.11 Reflection of a straight wavefront, 109, , 9781444176421_Section_03.indd 109, , 20/06/14 7:33 AM
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25 Mechanical waves, , wavefront has just reached the surface at A. The, position of the wavefront a little later, when B, reaches the reflecting surface, can be found using, Huygens’ construction. A circle of radius BB′ is, drawn about A; the reflected wavefront is then A′B′,, the tangent to the wavelet from B′. Measurements, of the angle of incidence i and the angle of, reflection r show that they are equal., , b) Refraction and wave theory, Huygens’ construction can also be used to, find the position of a wavefront when it enters a, second medium in which the speed of travel of the, wave is different from in the first (see Figure 25.7b)., In Figure 25.12, point A, on the straight wavefront, AB, has just reached the boundary between two, media. When B reaches the boundary the secondary, wavelet from A will have moved on to A′. If the, wave travels more slowly in the second medium the, distance AA′ is shorter than BB′. The new wavefront, is then A′B′, the tangent to the wavelet from B′; it, is clear that the direction of travel of the wave has, changed – refraction has occurred., , ●● Interference, When two sets of continuous circular waves cross in, a ripple tank, a pattern like that in Figure 25.13 is, obtained., At points where a crest from one source, S1, arrives, at the same time as a crest from the other source, S2,, a bigger crest is formed, and the waves are said to be, in phase. At points where a crest and a trough arrive, together, they cancel out (if their amplitudes are, equal); the waves are exactly out of phase (because, they have travelled different distances from S1 and, S2) and the water is undisturbed; in Figure 25.13 the, blurred lines radiating from between S1 and S2 join, such points., , incident wavefront, N, , C, , v1, , B, 1, , i1, i1, , v1 v2, , A, v2, , i2, , B', , i2, N', , 2, , refracted wavefront, A', secondary wavelet from A, , Figure 25.13 Interference of circular waves, , Interference or superposition is the combination of, waves to give a larger or a smaller wave (Figure, 25.14)., , crest, , Figure 25.12 Refraction of a straight wavefront, , crest, , , crest, , c) Diffraction and wave theory, Diffraction effects, such as those shown in, Figure 25.8, can be explained by describing what, happens to secondary wavelets arising from point, sources on the unrestricted part of the wavefronts in, the gaps., , , , , , , , water, at rest, , trough, , Figure 25.14, , Study this effect with two ball ‘dippers’ about 3 cm, apart on the bar of a ripple tank. Also observe the, effect of changing (i) the frequency and (ii) the, separation of the dippers; use a stroboscope when, , 110, , 9781444176421_Section_03.indd 110, , 20/06/14 7:33 AM
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Polarisation, , necessary. You will find that if the frequency is, increased, i.e. the wavelength decreased, the blurred, lines are closer together. Increasing the separation, has the same effect., Similar patterns are obtained if straight waves fall, on two small gaps: interference occurs between the, sets of emerging (circular) diffracted waves., , Questions, 1 The lines in Figure 25.16 are crests of straight ripples., a What is the wavelength of the ripples?, b If 5 seconds ago ripple A occupied the position now, occupied by ripple F, what is the frequency of the, ripples?, c What is the speed of the ripples?, , l● Polarisation, , 5 cm, , This effect occurs only with transverse waves. It, can be shown by fixing a rope at one end, D in, Figure 25.15, and passing it through two slits,, B and C. If end A is vibrated in all directions (as, shown by the short arrowed lines), vibrations of, the rope occur in every plane and transverse waves, travel towards B., At B only waves due to vibrations in a vertical, plane can emerge from the vertical slit. The, wave between B and C is said to be plane, polarised (in the vertical plane containing the, slit at B). By contrast the waves between A and, B are unpolarised. If the slit at C is vertical, the, wave travels on, but if it is horizontal as shown,, the wave is stopped and the slits are said to be, ‘crossed’., B, , F, , E, , D, , C, , B, , A, , Figure 25.16, , 2 During the refraction of a wave which two of the following, properties change?, A the speed, B the frequency, C the wavelength, 3 One side of a ripple tank ABCD is raised slightly (Figure, 25.17), and a ripple started at P by a finger. After 1 second, the shape of the ripple is as shown., a Why is it not circular?, b Which side of the tank has been raised?, , C, , A, , B, tank, , A, , D, ripple, , P, Figure 25.15 Polarising waves on a rope, , D, , C, , Figure 25.17, , ▲, ▲, 111, , 9781444176421_Section_03.indd 111, , 20/06/14 7:33 AM
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25 Mechanical Waves, , 4 Figure 25.18 gives a full-scale representation of the water, in a ripple tank 1 second after the vibrator was started. The, coloured lines represent crests., a What is represented at A at this instant?, b Estimate, (i) the wavelength,, (ii) the speed of the waves, and, (iii) the frequency of the vibrator., c Sketch a suitable attachment which could have, been vibrated up and down to produce this wave, pattern., , A, , Figure 25.18, , 5 Copy Figure 25.19 and show on it what happens to the, waves as they pass through the gap, if the water is much, shallower on the right-hand side than on the left., , Checklist, After studying this chapter you should be able to, • describe the production of pulses and progressive transverse, waves on ropes, springs and ripple tanks,, • recall the meaning of wavelength, frequency, speed and, amplitude,, • represent a transverse wave on a displacement–distance, graph and extract information from it,, • recall the wave equation v = fλ and use it to solve, problems,, • use the term wavefront,, • recall that the angle of reflection equals the angle of, incidence and draw a diagram for the reflection of straight, wavefronts at a plane surface,, • describe experiments to show reflection and refraction of, waves,, • recall that refraction at a straight boundary is due to change, of wave speed but not of frequency,, • draw a diagram for the refraction of straight wavefronts at a, straight boundary,, • explain the term diffraction,, • describe experiments to show diffraction of waves,, • draw diagrams for the diffraction of straight wavefronts at, single slits of different widths,, • predict the effect of changing the wavelength or the size, of the gap on diffraction of waves at a single slit., , Figure 25.19, , 112, , 9781444176421_Section_03.indd 112, , 20/06/14 7:34 AM
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26 Light rays, l, l, l, , Sources of light, Rays and beams, Shadows, , l, l, , ●● Sources of light, You can see an object only if light from it enters your, eyes. Some objects such as the Sun, electric lamps and, candles make their own light. We call these luminous, sources., Most things you see do not make their own light, but reflect it from a luminous source. They are nonluminous objects. This page, you and the Moon are, examples. Figure 26.1 shows some others., luminous source, emitting light, , Speed of light, Practical work: The pinhole camera, , ●● Rays and beams, Sunbeams streaming through trees (Figure 26.3), and light from a cinema projector on its way to the, screen both suggest that light travels in straight lines., The beams are visible because dust particles in the air, reflect light into our eyes., The direction of the path in which light is travelling, is called a ray and is represented in diagrams by a, straight line with an arrow on it. A beam is a stream, of light and is shown by a number of rays, as in, Figure 26.4. A beam may be parallel, diverging, (spreading out) or converging (getting narrower)., , non-luminous, objects reflecting, light, , Figure 26.1 Luminous and non-luminous objects, , Luminous sources radiate light when their atoms, become ‘excited’ as a result of receiving energy. In, a light bulb, for example, the energy comes from, electricity. The ‘excited’ atoms give off their light, haphazardly in most luminous sources., A light source that works differently is the laser,, invented in 1960. In laser light sources the excited, atoms act together and emit a narrow, very bright, beam of light. The laser has a host of applications., It is used in industry to cut through plate metal, in, scanners to read bar codes at shop-and library checkouts, in CD players, in optical fibre telecommunication, systems, in delicate medical operations on the eye or, inner ear (for example Figure 26.2), in printing and in, surveying and range-finding., , Figure 26.3 Light travels in straight lines, , ray, , parallel, Figure 26.2 Laser surgery in the inner ear, , diverging, , converging, , Figure 26.4 Beams of light, 113, , 9781444176421_Section_03.indd 113, , 20/06/14 7:34 AM
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26 Light rays, , A, , Practical work, , pinhole, , object, , The pinhole camera, A simple pinhole camera is shown in Figure 26.5a. Make a, small pinhole in the centre of the black paper. Half darken the, room. Hold the box at arm’s length so that the pinhole end is, nearer to and about 1 metre from a luminous object, such as, a carbon filament lamp or a candle. Look at the image on the, screen (an image is a likeness of an object and need not be an, exact copy)., Can you see three ways in which the image differs from the, object? What is the effect of moving the camera closer to the, object?, Make the pinhole larger. What happens to the, (i) brightness,, (ii) sharpness,, (iii) size of the image?, Make several small pinholes round the large hole (Figure 26.5b),, and view the image again., The formation of an image is shown in Figure 26.6., , B', image, A', , B, Figure 26.6 Forming an image in a pinhole camera, , ●● Shadows, Shadows are formed for two reasons. First, because, some objects, which are said to be opaque, do not, allow light to pass through them. Secondly, light, travels in straight lines., The sharpness of the shadow depends on the size, of the light source. A very small source of light, called, a point source, gives a sharp shadow which is equally, dark all over. This may be shown as in Figure 26.7a, where the small hole in the card acts as a point, source., , lid, small hole, screen, , card, screen, (greaseproof, paper over, square hole, in box), , black, paper, round, hole in, box, , sharp, shadow, , 100 watt, lamp, metal ball, to mains supply, , box, , a With a point source, , small, pinhole, a A pinhole camera, , penumbra, umbra, large, pinhole, b With an extended source, Figure 26.7 Forming a shadow, , small, pinhole, , b , Figure 26.5, , black, paper, , If the card is removed the lamp acts as a large, or extended source (Figure 26.7b). The shadow, is then larger and has a central dark region, the, umbra, surrounded by a ring of partial shadow,, the penumbra. You can see by the rays that some light, reaches the penumbra but none reaches the umbra., , 114, , 9781444176421_Section_03.indd 114, , 20/06/14 7:34 AM
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speed of light, , l● Speed of light, , Checklist, , Proof that light travels very much faster than sound, is provided by a thunderstorm. The flash of lightning, is seen before the thunder is heard. The length of the, time lapse is greater the further the observer is from, the storm., The speed of light has a definite value; light does, not travel instantaneously from one point to another, but takes a certain, very small time. Its speed is about, 1 million times greater than that of sound., , • give examples of effects which show that light travels in a, straight line,, • explain the operation of a pinhole camera and draw ray, diagrams to show the result of varying the object distance or, the length of the camera,, • draw diagrams to show how shadows are formed using, point and extended sources, and use the terms umbra and, penumbra,, • recall that light travels much faster than sound., , After studying this chapter you should be able to, , Questions, 1 How would the size and brightness of the image formed by, a pinhole camera change if the camera were made longer?, 2 What changes would occur in the image if the single, pinhole in a camera were replaced by, a four pinholes close together,, b a hole 1 cm wide?, 3 In Figure 26.8 the completely dark region on the screen is, A PQ, B PR, C QR, D QS, E RS, , P, Q, R, , lamp, , S, , object, , screen, Figure 26.8, , 4 When watching a distant firework display do you see the, cascade of lights before or after hearing the associated, bang? Explain your answer., , 115, , 9781444176421_Section_03.indd 115, , 20/06/14 7:35 AM
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27, l, l, , Reflection of light, , Law of reflection, Periscope, , l, l, , If we know how light behaves when it is, reflected, we can use a mirror to change the, direction in which the light is travelling. This, happens when a mirror is placed at the entrance, of a concealed drive to give warning of approaching, traffic., An ordinary mirror is made by depositing, a thin layer of silver on one side of a piece of, glass and protecting it with paint. The silver –, at the back of the glass – acts as the reflecting, surface., , l● Law of reflection, , Regular and diffuse reflection, Practical work: Reflection by a plane mirror, , The incident ray, the reflected ray and the normal all, lie in the same plane. (This means that they could all, be drawn on a flat sheet of paper.), , Practical work, Reflection by a plane mirror, Draw a line AOB on a sheet of paper and using a protractor mark, angles on it. Measure them from the perpendicular ON, which, is at right angles to AOB. Set up a plane (flat) mirror with its, reflecting surface on AOB., Shine a narrow ray of light along, say, the 30° line onto the, mirror (Figure 27.2)., , Terms used in connection with reflection are, shown in Figure 27.1. The perpendicular to, the mirror at the point where the incident ray, strikes it is called the normal. Note that the angle, of incidence i is the angle between the incident ray, and the normal; similarly the angle of reflection, r is the angle between the reflected ray and the, normal., plane, mirror, i, , shield, , lamp, and stand, single, slit, , r, , 45°, 30°, 15°, , 60° 75°, , A, , N, O, sheet, of paper, incident, ray, , normal, , B, , reflected, ray, , plane, mirror, , Figure 27.1 Reflection of light by a plane mirror, Figure 27.2, , The law of reflection states:, The angle of incidence equals the angle of reflection., , Mark the position of the reflected ray, remove the mirror and, measure the angle between the reflected ray and ON. Repeat for, rays at other angles. What can you conclude?, , 116, , 9781444176421_Section_03.indd 116, , 20/06/14 7:35 AM
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Regular and diffuse reflection, , ●● Periscope, A simple periscope consists of a tube containing two, plane mirrors, fixed parallel to and facing each other., Each makes an angle of 45° with the line joining, them (Figure 27.3). Light from the object is turned, through 90° at each reflection and an observer is able, to see over a crowd, for example (Figure 27.4), or, over the top of an obstacle., 45°, 45°, , Make your own periscope from a long, narrow, cardboard box measuring about 40 cm × 5 cm × 5 cm, (Such as one in which aluminium cooking foil or, clingfilm is sold), two plane mirrors (7.5 cm × 5 cm), and sticky tape. When you have got it to work, make, modifications that turn it into a ‘see-back-o-scope’,, which lets you see what is behind you., , ●● Regular and diffuse, reflection, If a parallel beam of light falls on a plane mirror it is, reflected as a parallel beam (Figure 27.5a) and regular, reflection occurs. Most surfaces, however, reflect light, irregularly and the rays in an incident parallel beam, are reflected in many directions (Figure 27.5b)., , obstacle, , Figure 27.3 Action of a simple periscope, , plane mirror, a Regular reflection, , normal, , normal, Figure 27.4 Periscopes being used by people in a crowd., , In more elaborate periscopes like those used, in submarines, prisms replace mirrors (see, Chapter 30)., ‘rough’ surface, b Diffuse reflection, Figure 27.5, , 117, , 9781444176421_Section_03.indd 117, , 20/06/14 7:35 AM
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27 reflection of light, , Irregular or diffuse reflection happens because,, unlike a mirror, the surface of an object is not, perfectly smooth. At each point on the surface, the laws of reflection are obeyed but the angle of, incidence, and so the angle of reflection, varies, from point to point. The reflected rays are scattered, haphazardly. Most objects, being rough, are seen by, diffuse reflection., , Checklist, After studying this chapter you should be able to, • state the law of reflection and use it to solve problems,, • describe an experiment to show that the angle of incidence, equals the angle of reflection,, • draw a ray diagram to show how a periscope works., , Questions, 1 Figure 27.6 shows a ray of light PQ striking a mirror AB., The mirror AB and the mirror CD are at right angles to each, other. QN is a normal to the mirror AB., A, , P, , N, D, , 50°, Q, , B, , C, , Figure 27.6, , a What is the value of the angle of incidence of the ray PQ, on the mirror AB?, b Copy the diagram, and continue the ray PQ to show the, path it takes after reflection at both mirrors., c What are the values of the angle of reflection at, AB, the angle of incidence at CD and the angle of, reflection at CD?, d What do you notice about the path of the ray PQ and, the final reflected ray?, 2 A ray of light strikes a plane mirror at an angle of incidence, of 60°, is reflected from the mirror and then strikes a, second plane mirror placed so that the angle between the, mirrors is 45°. The angle of reflection at the second mirror,, in degrees, is, A 15, B 25, C 45, D 65, E 75, 3 A person stands in front of a mirror (Figure 27.7). How, much of the mirror is used to see from eye to toes?, , Figure 27.7, , 118, , 9781444176421_Section_03.indd 118, , 20/06/14 7:35 AM
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28 Plane mirrors, l, l, l, , Real and virtual images, Lateral inversion, Properties of the image, , l, l, , When you look into a plane mirror on the wall of, a room you see an image of the room behind, the mirror; it is as if there were another room., Restaurants sometimes have a large mirror on, one wall just to make them look larger. You may, be able to say how much larger after the next, experiment., The position of the image formed by a mirror, depends on the position of the object., , Practical work, Position of the image, , Kaleidoscope, Practical work: Position of the image, , ●● Real and virtual, images, A real image is one which can be produced on a, screen (as in a pinhole camera) and is formed by rays, that actually pass through it., A virtual image cannot be formed on a screen and, is produced by rays which seem to come from it but, do not pass through it. The image in a plane mirror, is virtual. Rays from a point on an object are reflected, at the mirror and appear to our eyes to come from, a point behind the mirror where the rays would, intersect when produced backwards (Figure 28.2)., IA and IB are construction lines and are shown as, broken lines., , glass (microscope slide), I, , virtual rays, dark surface, , I, , A, , O, , B, , N, , Plasticine, , white paper, arrow, , block to support glass vertically, Figure 28.1, , Support a piece of thin glass on the bench, as in Figure 28.1. It, must be vertical (at 90° to the bench). Place a small paper arrow,, O, about 10 cm from the glass. The glass acts as a poor mirror, and an image of O will be seen in it; the darker the bench top,, the brighter the image will be., Lay another identical arrow, I, on the bench behind the, glass; move it until it coincides with the image of O. How, do the sizes of O and its image compare? Imagine a line, joining them. What can you say about it? Measure the, distances of the points of O and I from the glass along the, line joining them. How do they compare? Try placing O at, other distances., , O, real rays, Figure 28.2 A plane mirror forms a virtual image., , ●● Lateral inversion, If you close your left eye, your image in a plane, mirror seems to close the right eye. In a mirror, image, left and right are interchanged and the image, appears to be laterally inverted. The effect occurs, whenever an image is formed by one reflection, and is very evident if print is viewed in a mirror, (Figure 28.3). What happens if two reflections occur,, as in a periscope?, , 119, , 9781444176421_Section_03.indd 119, , 20/06/14 7:35 AM
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28 Plane mirrors, , Figure 28.3 The image in a plane mirror is laterally inverted., , ●● Properties of the image, The image in a plane mirror is, (i) as far behind the mirror as the object is in front,, with the line joining the object and image being, perpendicular to the mirror,, (ii) the same size as the object,, (iii) virtual,, (iv) laterally inverted., , To see how a kaleidoscope works, draw on a sheet, of paper two lines at right angles to one another., Using different coloured pens or pencils, draw a, design between them (Figure 28.5a). Place a small, mirror along each line and look into the mirrors, (Figure 28.5b). You will see three reflections which, join up to give a circular pattern. If you make the, angle between the mirrors smaller, more reflections, appear but you always get a complete design., In a kaleidoscope the two mirrors are usually kept at, the same angle (about 60°) and different designs are, made by hundreds of tiny coloured beads which can, be moved around between the mirrors., Now make a kaleidoscope using a cardboard tube, (from half a kitchen roll), some thin card, greaseproof paper, clear sticky tape, small pieces of different, coloured cellophane and two mirrors (10 cm × 3 cm) or, a single plastic mirror (10 cm × 6 cm) bent to form two, mirrors at 60° to each other, as shown in Figure 28.5c., , sheet of paper, , ●● Kaleidoscope, , Figure 28.5a, paper, , mirror, , mirror, , Figure 28.4 A kaleidoscope produces patterns using the images, formed by two plane mirrors – the patterns change as the object, moves., , Figure 28.5b, , 120, , 9781444176421_Section_03.indd 120, , 20/06/14 7:36 AM
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Kaleidoscope, , greaseproof paper, , 3 A girl stands 5 m away from a large plane mirror. How far, must she walk to be 2 m away from her image?, 4 The image in a plane mirror is, A upright, real and larger, B upright, virtual and the same size, C inverted, real and smaller, D inverted, virtual and the same size, E inverted, real and larger., , cardboard tube, , Checklist, card with, central, pinhole, , mirrors at 60°, coloured, cellophane, Figure 28.5c, , Questions, 1 In Figure 28.6 at which of the points A to E will the, observer see the image in the plane mirror of the object?, A, , After studying this chapter you should be able to, • describe an experiment to show that the image in a plane, mirror is as far behind the mirror as the object is in front,, and that the line joining the object and image is at right, angles to the mirror,, • draw a diagram to explain the formation of a virtual image, by a plane mirror,, • explain the apparent lateral inversion of an image in a plane, mirror,, • explain how a kaleidoscope works., , B, C, , E, , D, , object, Figure 28.6, , 2 Figure 28.7 shows the image in a plane mirror of a clock., The correct time is, A 2.25, B 2.35, C 6.45, D 9.25, , Figure 28.7, , 121, , 9781444176421_Section_03.indd 121, , 20/06/14 7:36 AM
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29 Refraction of light, l, l, l, , Facts about refraction, Real and apparent depth, Refractive index, , l, l, l, , If you place a coin in an empty dish and move back, until you just cannot see it, the result is surprising if, someone gently pours in water. Try it., Although light travels in straight lines in a, transparent material, such as air, if it passes into a, different material, such as water, it changes direction, at the boundary between the two, i.e. it is bent. The, bending of light when it passes from one material, (called a medium) to another is called refraction. It, causes effects such as the coin trick., , ●● Facts about refraction, (i) A ray of light is bent towards the normal when, it enters an optically denser medium at an angle,, for example from air to glass as in Figure 29.1a., The angle of refraction r is less than the angle of, incidence i., (ii) A ray of light is bent away from the normal, when it enters an optically less dense medium, for, example from glass to air., (iii) A ray emerging from a parallel-sided block is, parallel to the ray entering, but is displaced, sideways, like the ray in Figure 29.1a., (iv) A ray travelling along the normal direction at a, boundary is not refracted (Figure 29.1b)., , Refraction by a prism, Dispersion, Practical work: Refraction in glass, , Practical work, Refraction in glass, Shine a ray of light at an angle on to a glass block, (which has its lower face painted white or frosted), as in, Figure 29.2. Draw the outline ABCD of the block on the sheet, of paper under it. Mark the positions of the various rays in, air and in glass., Remove the block and draw the normals on the paper at the, points where the ray enters side AB (see Figure 29.2) and where, it leaves side CD., , shield, , sheet, of paper, , lamp, and stand, single, slit, , D, , A, , normal, , Note ‘Optically denser’ means having a greater, refraction effect; the actual density may or may not, be greater., , B, , C, glass block, , air, , normal, , i, , Figure 29.2, , r, glass, , glass, , air, , normal, a, , What two things happen to the light falling on AB? When, the ray enters the glass at AB, is it bent towards or away from, the part of the normal in the block? How is it bent at CD?, What can you say about the direction of the ray falling on AB, and the direction of the ray leaving CD?, What happens if the ray hits AB at right angles?, , b, , Figure 29.1 Refraction of light in glass, 122, , 9781444176421_Section_03.indd 122, , 20/06/14 7:36 AM
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refractive index, , l● Real and apparent, depth, Rays of light from a point O on the bottom of a, pool are refracted away from the normal at the water, surface because they are passing into an optically less, dense medium, i.e. air (Figure 29.3). On entering the, eye they appear to come from a point I that is above, O; I is the virtual image of O formed by refraction., The apparent depth of the pool is less than its, real depth., , real, depth, , apparent, depth, , I, , water, , l● Refractive index, Light is refracted because its speed changes when, it enters another medium. An analogy helps to, explain why., Suppose three people A, B, C are marching in, line, with hands linked, on a good road surface., If they approach marshy ground at an angle, (Figure 29.5a), person A is slowed down first,, followed by B and then C. This causes the whole, line to swing round and change its direction of, motion., In air (and a vacuum) light travels at, 300 000 km/s (3 × 108 m/s); in glass its speed falls, to 200 000 km/s (2 × 108 m/s) (Figure 29.5b). The, refractive index, n, of a medium, in this case glass,, is defined by the equation, refractive index, n =, , speed of light in air (or a vacuum), speed of light in medium, , O, , 300000 km/s, 3, =, 2, 200000 km/s, , for glass, n =, , Experiments also show that, Figure 29.3 A pool of water appears shallower than it is., , n =, , sine of angle between ray in air and normaal, ormal, sine of angle between ray in glass and no, , = sin i, sin r, , ( see Figure 29.1a), , The more light is slowed down when it enters a, medium from air, the greater is the refractive index, of the medium and the more the light is bent., road, C, , C, , B, , B, , C, , Figure 29.4 A pencil placed in water seems to bend at the water, surface. Why?, , marsh, , A, , B, A, A, , ▲, ▲, , Figure 29.5a, , 123, , 9781444176421_Section_03.indd 123, , 20/06/14 7:37 AM
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29 Refraction of light, , ●● Dispersion, 300000 km/s, air, glass, 200 000 km/s, n , , When sunlight (white light) falls on a triangular, glass prism (Figure 29.7a), a band of colours, called a spectrum is obtained (Figure 29.7b)., The effect is termed dispersion. It arises because, white light is a mixture of many colours; the prism, separates the colours because the refractive index, of glass is different for each colour (it is greatest for, violet light)., , Figure 29.5b, , white, screen, , We saw earlier (Chapter 25) that water waves are, refracted when their speed changes. The change in, the direction of travel of a light ray when its speed, changes on entering another medium suggests that, light may also be a type of wave motion., , sunlight, , prism, spectrum, , red, orange, yellow, green, blue, indigo, violet, , Figure 29.7a Forming a spectrum with a prism, , ●● Refraction by a prism, In a triangular glass prism (Figure 29.6a), the, bending of a ray due to refraction at the first surface, is added to the bending of the ray at the second, surface (Figure 29.6b); the overall change in, direction of the ray is called the deviation., The bendings of the ray do not cancel out as they, do in a parallel-sided block where the emergent ray,, although displaced, is parallel to the incident ray., a, , b, , angle of, deviation, , Figure 29.7b White light shining through cut crystal can produce, several spectra., , Figure 29.6, 124, , 9781444176421_Section_03.indd 124, , 20/06/14 7:37 AM
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dispersion, , Questions, 1 Figure 29.8 shows a ray of light entering a rectangular, block of glass., a Copy the diagram and draw the normal at the point of, entry., b Sketch the approximate path of the ray through the, block and out of the other side., , 6 Which diagram in Figure 29.11 shows the ray of light, refracted correctly?, A, , B, , water, air, , C, , air, glass, , glass, water, , D, , E, , glass, air, , water, glass, , Figure 29.8, , 2 Draw two rays from a point on a fish in a stream to show, where someone on the bank will see the fish. Where must, the person aim to spear the fish?, 3 What is the speed of light in a medium of refractive index, 6/5 if its speed in air is 300 000 km/s?, 4 Figure 29.9 shows a ray of light OP striking a glass prism, and then passing through it. Which of the rays A to D is the, correct representation of the emerging ray?, , Figure 29.11, , 7 Which diagram in Figure 29.12 shows the correct path of, the ray through the prism?, A, , B, , D, , A, , C, , E, , B, Figure 29.12, , C, , D, , P, , Checklist, After studying this chapter you should be able to, •, •, •, •, , O, Figure 29.9, , 5 A beam of white light strikes the face of a prism. Copy, Figure 29.10 and draw the path taken by red and blue, rays of light as they pass through the prism and on to the, screen AB., A, , state what the term refraction means,, give examples of effects that show light can be refracted,, describe an experiment to study refraction,, draw diagrams of the passage of light rays through, rectangular blocks and recall that lateral displacement occurs, for a parallel-sided block,, • recall that light is refracted because it changes speed when, it enters another medium,, • recall the definition of refractive index as, n = speed in air/speed in medium,, • recall and use the equation n = sin i/sin r, • draw a diagram for the passage of a light ray through a, prism,, • explain the terms spectrum and dispersion,, • describe how a prism is used to produce a spectrum from, white light., , white light, , glass prism, , B, , Figure 29.10, , 125, , 9781444176421_Section_03.indd 125, , 20/06/14 7:37 AM
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30 Total internal reflection, l, l, l, , Critical angle, Refractive index and critical angle, Multiple images in a mirror, , ●● Critical angle, When light passes at small angles of incidence from, an optically dense to a less dense medium, such as, from glass to air, there is a strong refracted ray and, a weak ray reflected back into the denser medium, (Figure 30.1a). Increasing the angle of incidence, increases the angle of refraction., air, glass, , l, l, l, , Totally reflecting prisms, Light pipes and optical fibres, Practical work: Critical angle of glass, , Practical work, Critical angle of glass, Place a semicircular glass block on a sheet of paper (Figure 30.2),, and draw the outline LOMN where O is the centre and ON the, normal at O to LOM. Direct a narrow ray (at an angle of about, 30° to the normal ON) along a radius towards O. The ray is not, refracted at the curved surface. Why? Note the refracted ray, emerging from LOM into the air and also the weak internally, reflected ray in the glass., Slowly rotate the paper so that the angle of incidence on LOM, increases until total internal reflection just occurs. Mark the incident, ray. Measure the angle of incidence; this is the critical angle., , ray of, light, , a, , L, sheet of, paper, , air, glass, c, , N, , c, , c critical angle, b, , semicircular, glass block, , O, , angle of, incidence, , M, , air, glass, , c, Figure 30.1, , At a certain angle of incidence, called the critical, angle, c, the angle of refraction is 90° (Figure 30.1b)., For angles of incidence greater than c, the refracted, ray disappears and all the incident light is reflected, inside the denser medium (Figure 30.1c). The light, does not cross the boundary and is said to undergo, total internal reflection., , Figure 30.2, , ●● Refractive index and, critical angle, From Figure 30.1b and the definition of refractive, index:, , n =, , sine of angle between ray in air and normaal, sine of angle between ray in glass and no, ormal, , 126, , 9781444176421_Section_03.indd 126, , 20/06/14 7:38 AM
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Totally reflecting prisms, , =, , si n 90°, sin c, , =, , 1, sin c, , (because sin 90° = 1), , 3, 2, So, if n = , then sin c = , and c must be 42°., 2, 3, , Worked example, If the critical angle for diamond is 24°, calculate its, refractive index., Critical angle, c = 24°, sin 24° = 0.4, , 1, n = sin 90° =, sin c, sin 24°, =, , 1, = 2.5, 0.4, , ●● Multiple images in, a mirror, An ordinary mirror silvered at the back forms, several images of one object, because of multiple, reflections inside the glass (Figure 30.3a and, Figure 30.3b). These blur the main image I (which, is formed by one reflection at the silvering),, especially if the glass is thick. The problem is absent, in front-silvered mirrors but such mirrors are easily, damaged., , ●● Totally reflecting prisms, The defects of mirrors are overcome if 45°, right-angled glass prisms are used. The, critical angle of ordinary glass is about 42° and a, ray falling normally on face PQ of such a prism, (Figure 30.4a) hits face PR at 45°. Total internal, reflection occurs and the ray is turned through 90°., Totally reflecting prisms replace mirrors in good, periscopes., Light can also be reflected through 180° by a, prism (Figure 30.4b); this happens in binoculars., P, 45°, 45°, 45°, Q, , main, image, , glass, O, object, , Figure 30.3b The multiple images in a mirror cause blurring., , I1, , I, , I2, , R, , a, , silvering, , b, Figure 30.4 Reflection of light by a prism, , ▲, ▲, , Figure 30.3a Multiple reflections in a mirror, , 127, , 9781444176421_Section_03.indd 127, , 20/06/14 7:39 AM
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30 total internal reflection, , l● Light pipes and optical, fibres, , Questions, 1 Figure 30.7 shows rays of light in a semicircular glass block., B, , Light can be trapped by total internal reflection, inside a bent glass rod and ‘piped’ along a curved, path (Figure 30.5). A single, very thin glass fibre, behaves in the same way., , A, , 20°, C, , Figure 30.7, , Figure 30.5 Light travels through a curved glass rod or fibre by total, internal reflection., , If several thousand such fibres are taped together,, a flexible light pipe is obtained that can be used,, for example, by doctors as an ‘endoscope’ (Figure, 30.6a), to obtain an image from inside the body, (Figure 30.6b), or by engineers to light up some, awkward spot for inspection. The latest telephone, ‘cables’ are optical (very pure glass) fibres carrying, information as pulses of laser light., , a Explain why the ray entering the glass at A is not bent as, it enters., b Explain why the ray AB is reflected at B and not, refracted., c Ray CB does not stop at B. Copy the diagram and draw, its approximate path after it leaves B., 2 Copy Figures 30.8a and 30.8b and complete the paths of, the rays through the glass prisms., , 60°, glass, , glass, air, 45°, , 60°, a, , b, , Figure 30.8, , 3 Name two instruments that use prisms to reflect light., 4 Light travels up through a pond of water of critical angle, 49°. What happens at the surface if the angle of incidence, is: a 30°; b 60°?, 4, 5 Calculate the critical angle for water if n = ., 3, , Figure 30.6a Endoscope in use, , Checklist, After studying this chapter you should be able to, • explain with the aid of diagrams what is meant by critical, angle and total internal reflection,, • describe an experiment to find the critical angle of glass or, Perspex,, • draw diagrams to show the action of totally reflecting, prisms in periscopes and binoculars,, • explain the action of optical fibres,, • recall and use n = 1/sin c to determine the critical angle., , Figure 30.6b Trachea (windpipe) viewed by an endoscope, 128, , 9781444176421_Section_03.indd 128, , 20/06/14 7:40 AM
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31 Lenses, l, l, l, l, l, , Converging and diverging lenses, Principal focus, Ray diagrams, Magnification, Power of a lens, , l, l, l, , Magnifying glass, Spectacles, Practical work: Focal length, f, of a converging lens;, Images formed by a converging lens, , ●● Converging and, diverging lenses, Lenses are used in optical instruments such as, cameras, spectacles, microscopes and telescopes;, they often have spherical surfaces and there are two, types. A converging (or convex) lens is thickest in, the centre and bends light inwards (Figure 31.1a)., You may have used one as a magnifying glass, (Figure 31.2a) or as a burning glass. A diverging (or, concave) lens is thinnest in the centre and spreads, light out (Figure 31.1b); it always gives a diminished, image (Figure 31.2b)., The centre of a lens is its optical centre, C; the, line through C at right angles to the lens is the, principal axis., The action of a lens can be understood by treating, it as a number of prisms (most with the tip removed),, each of which bends the ray towards its base, as in, Figure 31.1c and 31.1d. The centre acts as a parallelsided block., , Figure 31.1d, , Figure 31.2a A converging lens forms a magnified image of a close object., principal, axis, , F, , C, , F, f, , Figure 31.1a, , principal, axis, , F, , C, , F, , f, , Figure 31.1b, , Figure 31.2b A diverging lens always forms a diminished image., Figure 31.1c, 129, , 9781444176421_Section_03.indd 129, , 20/06/14 7:40 AM
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31 Lenses, , ●● Principal focus, , Practical work, , When a beam of light parallel to the principal axis, passes through a converging lens it is refracted so as, to converge to a point on the axis called the principal, focus, F. It is a real focus. A diverging lens has a, virtual principal focus behind the lens, from which, the refracted beam seems to diverge., Since light can fall on both faces of a lens it has two, principal foci, one on each side, equidistant from C., The distance CF is the focal length f of the lens (see, Figure 31.1a); it is an important property of a lens., The more curved the lens faces are, the smaller is f, and the more powerful is the lens., , Practical work, , Images formed by a converging, lens, In the formation of images by lenses, two important points on, the principal axis are F and 2F; 2F is at a distance of twice the, focal length from C., First find the focal length of the lens by the ‘distant object, method’ just described, then fix the lens upright with Plasticine, at the centre of a metre rule. Place small pieces of Plasticine at, the points F and 2F on both sides of the lens, as in Figure 31.4., Place a small light source, such as a torch bulb, as the object, supported on the rule beyond 2F and move a white card, on, the other side of the lens from the light, until a sharp image is, obtained on the card., torch, , converging lens, , screen, , Focal length, f, of a converging lens, We use the fact that rays from a point on a very distant object,, i.e. at infinity, are nearly parallel (Figure 31.3a)., 2F, , F, , F, , 2F, , close point, diverging beam, , Plasticine, , distant point, , Figure 31.4, , almost parallel beam, very, distant, point, , Note and record, in a table like the one below, the image position, as ‘beyond 2F’, ‘between 2F and F’ or ‘between F and lens’. Also, note whether the image is ‘larger’ or ‘smaller’ than the actual, bulb or ‘same size’ and if it is ‘upright’ or ‘inverted’. Now repeat, with the light at 2F, then between 2F and F., , parallel beam, , Figure 31.3a, , Object position, light from window at, , metre rule, , Image position Larger, smaller Upright or, or same size?, inverted?, , beyond 2F, , lens, , other side of room, , at 2F, ruler, , screen, or wall, , Figure 31.3b, , Move the lens, arranged as in Figure 31.3b, until a sharp image, of a window at the other side of the room is obtained on the, screen. The distance between the lens and the screen is then f,, roughly. Why?, , between 2F and F, between F and lens, , So far all the images have been real since they can be obtained, on a screen. When the light is between F and the lens, the image, is virtual and is seen by looking through the lens at the light. Do, this. Is the virtual image larger or smaller than the object? Is it, upright or inverted? Record your findings in your table., , 130, , 9781444176421_Section_03.indd 130, , 20/06/14 7:40 AM
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Magnifying glass, , l● Ray diagrams, , B, , Information about the images formed by a lens can, be obtained by drawing two of the following rays., A, , 1 A ray parallel to the principal axis which is refracted, through the principal focus, F., 2 A ray through the optical centre, C, which is, undeviated for a thin lens., 3 A ray through the principal focus, F, which is refracted, parallel to the principal axis., , In diagrams a thin lens is represented by a straight, line at which all the refraction is considered to occur., In each ray diagram in Figure 31.5, two rays are, drawn from the top A of an object OA. Where these, rays intersect after refraction gives the top B of the, image IB. The foot I of each image is on the axis, since ray OC passes through the lens undeviated., In Figure 31.5d, the broken rays, and the image,, are virtual. In all parts of Figure 31.5, the lens is a, converging lens., , F, , O, , C, , F, , Image is behind object, virtual, erect, larger, Figure 31.5d Object between F and C, , l● Magnification, The linear magnification, m is given by, m =, , height of image, height of object, , It can be shown that in all cases, , A, , F, O, , I, , F, , 2F, , I, , C, , 2F, , l● Power of a lens, , Image is between F and 2F, real, inverted, smaller, , The shorter the focal length of a lens, the stronger, it is, i.e. the more it converges or diverges a beam, of light. We define the power, P, of a lens to be, 1/focal length of the lens, where the focal length is, measured in metres:, P = 1, f, , Figure 31.5a Object beyond 2F, A, F, F, , distance of image from lens, distance of objject from lens, , image, B, , 2F O, , m =, , 2F I, , C, image, , l● Magnifying glass, , B, , Image is beyond 2F, real, inverted, larger, Figure 31.5b Object at 2F, A, , F, , O, 2F, , F, , C, , 2F, I, image, , Image is at 2F, real, inverted, same size, Figure 31.5c Object between 2F and F, , 9781444176421_Section_03.indd 131, , ▲, ▲, , B, , The apparent size of an object depends on its actual, size and on its distance from the eye. The sleepers, on a railway track are all the same length but those, nearby seem longer. This is because they enclose, a larger angle at your eye than more distant ones:, their image on the retina is larger, so making them, appear bigger., , 131, , 20/06/14 7:41 AM
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31 Lenses, , A converging lens gives an enlarged, upright, virtual image of an object placed between the lens, and its principal focus F (Figure 31.6a). It acts as a, magnifying glass since the angle β made at the eye, by the image, formed at the near point (see next, section), is greater than the angle α made by the, object when it is viewed directly at the near point, without the magnifying glass (Figure 31.6b)., converging lens, image, object, , F, , F, , β, , The average adult eye can focus objects comfortably, from about 25 cm (the near point) to infinity (the, far point). Your near point may be less than 25 cm;, it gets further away with age., , a) Short sight, A short-sighted person sees near objects, clearly but distant objects appear blurred., The image of a distant object is formed in, front of the retina because the eyeball is too, long or because the eye lens cannot be made, thin enough (Figure 31.8a). The problem, is corrected by a diverging spectacle lens (or, contact lens) which diverges the light before it, enters the eye, to give an image on the retina, (Figure 31.8b)., , a, , from point, on distant, object, , I, , α, , object, , a, , b, Figure 31.6 Magnification by a converging lens: angle β is larger than, angle α, , The fatter (more curved) a converging lens is, the, shorter its focal length and the more it magnifies., Too much curvature, however, distorts the image., , ●● Spectacles, , b, , From the ray diagrams shown in Figure 31.5, (p. 131) we would expect that the converging lens in, the eye will form a real inverted image on the retina, as shown in Figure 31.7. Since an object normally, appears upright, the brain must invert the image., eye, , object, , I, , retina of eye, inverted, image, , Figure 31.8 Short sight and its correction by a diverging lens, , b) Long sight, A long-sighted person sees distant objects clearly, but close objects appear blurred. The image of a, near object is focused behind the retina because the, eyeball is too short or because the eye lens cannot, be made thick enough (Figure 31.9a). A converging, spectacle lens (or contact lens) corrects the problem, (Figure 31.9b)., , Figure 31.7 Inverted image on the retina, , 132, , 9781444176421_Section_03.indd 132, , 20/06/14 7:41 AM
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spectacles, , I, near, object, , b Copy the diagrams and complete them to show the, path of the light after passing through the lens., c Figure 31.11 shows an object AB 6 cm high placed, 18 cm in front of a lens of focal length 6 cm. Draw the, diagram to scale and, by tracing the paths of rays from, A, find the position and size of the image formed., A, , a, , B, I, , focus, 18 cm, , 6 cm, , Figure 31.11, , b, Figure 31.9 Long sight and its correction by a converging lens, , Questions, 1 A small torch bulb is placed at the focal point of a, converging lens. When the bulb is switched on, does the, lens produce a convergent, divergent or parallel beam of, light?, 2 a What kind of lens is shown in Figure 31.10?, , focus, , focus, , principal, axis, , 3 Where must the object be placed for the image formed by, a converging lens to be, a real, inverted and smaller than the object,, b real, inverted and same size as the object,, c real, inverted and larger than the object,, d virtual, upright and larger than the object?, 4 Figure 31.12 shows a camera focused on an object in the, middle distance. Should the lens be moved towards or, away from the film so that the image of a more distant, object is in focus?, , film, Figure 31.12, , 5 a Three converging lenses are available, having focal, lengths of 4 cm, 40 cm and 4 m, respectively. Which one, would you choose as a magnifying glass?, b An object 2 cm high is viewed through a converging lens, of focal length 8 cm. The object is 4 cm from the lens., By means of a ray diagram find the position, nature and, magnification of the image., 6 An object is placed 10 cm in front of a lens, A; the details, of the image are given below. The process is repeated for a, different lens, B., Lens A Real, inverted, magnified and at a great distance., Lens B Real, inverted and same size as the object., Estimate the focal length of each lens and state whether it, is converging or diverging., , Figure 31.10, , 133, , 9781444176421_Section_03.indd 133, , 20/06/14 7:41 AM
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31 Lenses, , Checklist, After studying this chapter you should be able to, • explain the action of a lens in terms of refraction by a, number of small prisms,, • draw diagrams showing the effects of a converging lens on, a beam of parallel rays,, • recall the meaning of optical centre, principal axis, principal, focus and focal length,, • describe an experiment to measure the focal length of a, converging lens,, • draw ray diagrams to show formation of a real image by a, converging lens,, • draw scale diagrams to solve problems about converging, lenses,, • draw ray diagrams to show formation of a virtual image, by a single lens,, • show how a single lens is used as a magnifying glass., , 134, , 9781444176421_Section_03.indd 134, , 20/06/14 7:41 AM
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32 Electromagnetic radiation, l, l, l, l, , Properties, Light waves, Infrared radiation, Ultraviolet radiation, , l, l, l, , frequency increases, gamma, rays, typical, wavelength:, , 0.01 nm, , frequency decreases, , light, , X-rays, , 1 nm, , Radio waves, X-rays, Practical work: Wave nature of microwaves, , ultraviolet, , 0.1, µm, , infrared, , 0.4, µm, , (microwaves, , 0.7 0.01 mm, µm, , radiowaves, TV, , radio), , 1m, , 1 km, , 1 cm, , wavelength increases, , wavelength decreases, 1 nm = 10–9 m, 1 µm = 10–6 m, , source:, , radioactive, matter, , X-ray, tube, , mercury Sun, lamp, , electric, fire, , microwave, oven, , transmitting TV, and radio aerials, , Figure 32.1 The electromagnetic spectrum and sources of each type of radiation, , Light is one member of the family of electromagnetic, radiation which forms a continuous spectrum, beyond both ends of the visible (light) spectrum, (Figure 32.1). While each type of radiation has a, different source, all result from electrons in atoms, undergoing an energy change and all have certain, properties in common., , ●● Properties, 1 All types of electromagnetic radiation travel, through a vacuum at 300 000 km/s, (3 × 108 m/s), i.e. with the speed of light., 2 They exhibit interference, diffraction and, polarisation, which suggests they have a transverse, wave nature., 3 They obey the wave equation, v = f λ, where v is the, speed of light, f is the frequency of the waves and λ, is the wavelength. Since v is constant for a particular, medium, it follows that large f means small λ., 4 They carry energy from one place to another, and can be absorbed by matter to cause heating, and other effects. The higher the frequency and, the smaller the wavelength of the radiation, the, greater is the energy carried, i.e. gamma rays are, more ‘energetic’ than radio waves. This is shown, , by the photoelectric effect in which electrons are, ejected from metal surfaces when electromagnetic, waves fall on them. As the frequency of the waves, increases so too does the speed (and energy) with, which electrons are emitted., Because of its electrical origin, its ability to travel, in a vacuum (e.g. from the Sun to the Earth), and its wave-like properties (i.e. point 2 above),, electromagnetic radiation is regarded as a progressive, transverse wave. The wave is a combination of, travelling electric and magnetic fields. The fields vary, in value and are directed at right angles to each other, and to the direction of travel of the wave, as shown, by the representation in Figure 32.2., magnetic field, , electric field, , direction, of travel, , Figure 32.2 An electromagnetic wave, 135, , 9781444176421_Section_03.indd 135, , 20/06/14 7:41 AM
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32 Electromagnetic radiation, , ●● Light waves, Red light has the longest wavelength, which is about, 0.0007 mm (7 × 10−7 m = 0.7 µm), while violet light, has the shortest wavelength of about 0.0004 mm, (4 × 10−7 m = 0.4 µm). Colours between these in the, spectrum of white light have intermediate values., Light of one colour and so of one wavelength is, called monochromatic light., Since v = f λ for all waves including light, it, follows that red light has a lower frequency, f, than, violet light since (i) the wavelength, λ, of red light, is greater, and (ii) all colours travel with the same, speed, v, of 3 × 108 m/s in air (strictly, in a vacuum)., It is the frequency of light which decides its colour,, rather than its wavelength which is different in, different media, as is the speed (Chapter 29)., Different frequencies of light travel at different, speeds through a transparent medium and so, are refracted by different amounts. This explains, dispersion (Chapter 29), in other word why the, refractive index of a material depends on the, wavelength of the light., The amplitude of a light (or any other) wave is, greater the higher the intensity of the source; in the, case of light the greater the intensity the brighter it is., , ●● Infrared radiation, Our bodies detect infrared radiation (IR) by its, heating effect on the skin. It is sometimes called, ‘radiant heat’ or ‘heat radiation’., Anything which is hot but not glowing, i.e. below, 500 °C, emits IR alone. At about 500 °C a body, becomes red hot and emits red light as well as, IR – the heating element of an electric fire, a toaster, or a grill are examples. At about 1500 °C, things such, as lamp filaments are white hot and radiate IR and, white light, i.e. all the colours of the visible spectrum., Infrared is also detected by special temperaturesensitive photographic films which allow pictures, to be taken in the dark. Infrared sensors are used, on satellites and aircraft for weather forecasting,, monitoring of land use (Figure 32.3), assessing heat, loss from buildings, intruder alarms and locating, victims of earthquakes., Infrared lamps are used to dry the paint on cars, during manufacture and in the treatment of muscular, complaints. The remote control for an electronic device, contains a small infrared transmitter to send signals to, the device, such as a television or DVD player., , Figure 32.3 Infrared aerial photograph of Washington DC, , ●● Ultraviolet radiation, Ultraviolet (UV) rays have shorter wavelengths, than light. They cause sun tan and produce, vitamins in the skin but can penetrate deeper,, causing skin cancer. Dark skin is able to absorb, more UV, so reducing the amount reaching, deeper tissues. Exposure to the harmful UV rays, present in sunlight can be reduced by wearing, protective clothing such as a hat or by using, sunscreen lotion., Ultraviolet causes fluorescent paints and clothes, washed in some detergents to fluoresce (Figure 32.4)., They glow by re-radiating as light the energy they, absorb as UV. This effect may be used to verify, ‘invisible’ signatures on bank documents., , Figure 32.4 White clothes fluorescing in a club, , 136, , 9781444176421_Section_03.indd 136, , 20/06/14 7:42 AM
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Radio waves, , A UV lamp used for scientific or medical, purposes contains mercury vapour and this, emits UV when an electric current passes through, it. Fluorescent tubes also contain mercury, vapour and their inner surfaces are coated, with special powders called phosphors which, radiate light., , b) VHF (very high frequency) and, UHF (ultra high frequency) waves, (wavelengths of 10 m to 10 cm), , ●● Radio waves, , c) Microwaves (wavelengths of, a few cm), , Radio waves have the longest wavelengths in the, electromagnetic spectrum. They are radiated from, aerials and used to ‘carry’ sound, pictures and other, information over long distances., , a) Long, medium and, short waves (wavelengths of 2 km, to 10 m), These diffract round obstacles so can be, received even when hills are in their way, (Figure 32.5a). They are also reflected by layers, of electrically charged particles in the upper, atmosphere (the ionosphere), which makes, long-distance radio reception possible, (Figure 32.5b)., , These shorter wavelength radio waves need a clear,, straight-line path to the receiver. They are not, reflected by the ionosphere. They are used for local, radio and for television., , These are used for international telecommunications, and television relay via geostationary satellites and for, mobile phone networks via microwave aerial towers, and low-orbit satellites (Chapter 9). The microwave, signals are transmitted through the ionosphere by dish, aerials, amplified by the satellite and sent back to a, dish aerial in another part of the world., Microwaves are also used for radar detection of, ships and aircraft, and in police speed traps., Microwaves can be used for cooking since they cause, water molecules in the moisture of the food to vibrate, vigorously at the frequency of the microwaves. As a, result, heating occurs inside the food which cooks itself., Living cells can be damaged or killed by the heat, produced when microwaves are absorbed by water, in the cells. There is some debate at present as to, whether their use in mobile phones is harmful;, ‘hands-free’ mode, where separate earphones are used,, may be safer., , Practical work, a Diffraction of radio waves, , Wave nature of microwaves, ionosphere, , transmitter, , b Reflection of radio waves, , ▲, ▲, , Figure 32.5, , receiver, , The 3 cm microwave transmitter and receiver shown in, Figure 32.6 can be used. The three metal plates can be set up for, double-slit interference with ‘slits’ about 3 cm wide; the reading, on the meter connected to the horn receiver rises and falls as it is, moved across behind the plates., Diffraction can be shown similarly using the two wide metal, plates to form a single slit., If the grid of vertical metal wires is placed in front of the, transmitter, the signal is absorbed but transmission occurs, when the wires are horizontal, showing that the microwaves, are vertically polarised. This can also be shown by rotating the, receiver through 90° in a vertical plane from the maximum signal, position, when the signal decreases to a minimum., , 137, , 9781444176421_Section_03.indd 137, , 20/06/14 7:42 AM
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32 electroMagnetic radiation, , Figure 32.6, , l● X-rays, These are produced when high-speed electrons are, stopped by a metal target in an X-ray tube. X-rays, have smaller wavelengths than UV., They are absorbed to some extent by living cells, but can penetrate some solid objects and affect, a photographic film. With materials like bones,, teeth and metals which they do not pass through, easily, shadow pictures can be taken, like that in, Figure 32.7 of a hand on an alarm clock. They, are widely used in dentistry and in medicine, for, example to detect broken bones. X-rays are also, used in security machines at airports for scanning, luggage; some body scanners, now being introduced, to screen passengers, use very low doses of X-rays., In industry X-ray photography is used to inspect, welded joints., X-ray machines need to be shielded with lead since, normal body cells can be killed by high doses and, made cancerous by lower doses., Gamma rays (Chapter 49) are more penetrating, and dangerous than X-rays. They are used to kill, cancer cells and also harmful bacteria in food and on, surgical instruments., , Figure 32.7 X-rays cannot penetrate bone and metal., , Questions, 1 Give the approximate wavelength in micrometres (µm) of, a red light,, b violet light., 2 Which of the following types of radiation has, a the longest wavelength,, b the highest frequency?, A UV, B radio waves, C light, D X-rays, E IR, 3 Name one type of electromagnetic radiation which, a causes sun tan,, b is used for satellite communication,, c is used to sterilise surgical instruments,, d is used in a TV remote control,, e is used to cook food,, f is used to detect a break in a bone., 4 A VHF radio station transmits on a frequency of 100 MHz, (1 MHz = 106 Hz). If the speed of radio waves is 3 × 108 m/s,, a what is the wavelength of the waves,, b how long does the transmission take to travel 60 km?, , 138, , 9781444176421_Section_03.indd 138, , 20/06/14 7:42 AM
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X-rays, , 5 In the diagram in Figure 32.8 light waves are incident on an, air–glass boundary. Some are reflected and some are refracted, in the glass. One of the following is the same for the incident, wave and the refracted wave inside the glass. Which?, A speed, B wavelength, C direction, D brightness, E frequency, , air, , glass, , Figure 32.8, , Checklist, After studying this chapter you should be able to, • recall the types of electromagnetic radiation,, • recall that all electromagnetic waves have the same speed in, space and are progressive transverse waves,, • recall that the colour of light depends on its frequency, that, red light has a lower frequency (but longer wavelength), than blue light and that all colours travel at the same speed, in air,, • use the term monochromatic,, • distinguish between infrared radiation, ultraviolet radiation,, radio waves and X-rays in terms of their wavelengths,, properties and uses,, • be aware of the harmful effects of different types of, electromagnetic radiation and of how exposure to them can, be reduced., , 139, , 9781444176421_Section_03.indd 139, , 20/06/14 7:42 AM
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33 Sound waves, l, l, l, l, l, , Origin and transmission of sound, Longitudinal waves, Reflection and echoes, Speed of sound, Limits of audibility, , l, l, l, l, , ●● Origin and transmission, of sound, Sources of sound all have some part that vibrates. A, guitar has strings (Figure 33.1), a drum has a stretched, skin and the human voice has vocal cords. The sound, travels through the air to our ears and we hear it. That, the air is necessary may be shown by pumping the, air out of a glass jar containing a ringing electric bell, (Figure 33.2); the sound disappears though the striker, can still be seen hitting the gong. Evidently sound, cannot travel in a vacuum as light can. Other materials,, including solids and liquids, transmit sound., , Musical notes, Ultrasonics, Seismic waves, Practical work: Speed of sound in air, , Sound also gives interference and diffraction effects., Because of this and its other properties, we believe it, is a form of energy (as the damage from supersonic, booms shows) which travels as a progressive wave,, but of a type called longitudinal., , ●● Longitudinal waves, a) Waves on a spring, In a progressive longitudinal wave the particles of, the transmitting medium vibrate to and fro along, the same line as that in which the wave is travelling, and not at right angles to it as in a transverse wave., A longitudinal wave can be sent along a spring,, stretched out on the bench and fixed at one end, if, the free end is repeatedly pushed and pulled sharply,, as shown in Figure 33.3. Compressions C (where, the coils are closer together) and rarefactions, R (where the coils are further apart) travel along, the spring., C, , R, , C, , R, , C, , wave, Figure 33.1 A guitar string vibrating. The sound waves produced are, amplified when they pass through the circular hole into the guitar’s, sound box., , fixed end, Figure 33.3 A longitudinal wave, , b) Sound waves, glass jar, ringing electric, bell, sponge pad, , to, battery, to vacuum pump, , Figure 33.2 Sound cannot travel through a vacuum, , A sound wave, produced for example by a, loudspeaker, consists of a train of compressions, (‘squashes’) and rarefactions (‘stretches’) in the air, (Figure 33.4)., The speaker has a cone which is made to vibrate, in and out by an electric current. When the cone, moves out, the air in front is compressed; when it, moves in, the air is rarefied (goes ‘thinner’). The, wave progresses through the air but the air as a whole, does not move. The air particles (molecules) vibrate, , 140, , 9781444176421_Section_03.indd 140, , 20/06/14 7:43 AM
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Limits of audibility, , backwards and forwards a little as the wave passes., When the wave enters your ear the compressions, and rarefactions cause small, rapid pressure changes, on the eardrum and you experience the sensation of, sound., The number of compressions produced per, second is the frequency f of the sound wave (and, equals the frequency of the vibrating loudspeaker, cone); the distance between successive compressions, is the wavelength λ. As with transverse waves, the, speed, v, = f λ., C, , R, , C, , R, , C, wave, , loudspeaker, cone, , , , In air the speed increases with temperature and, at high altitudes, where the temperature is lower,, it is less than at sea level. Changes of atmospheric, pressure do not affect it., An estimate of the speed of sound can be made, directly if you stand about 100 metres from a high, wall or building and clap your hands. Echoes are, produced. When the clapping rate is such that each, clap coincides with the echo of the previous one,, the sound has travelled to the wall and back in the, time between two claps, i.e. one interval. By timing, 30 intervals with a stopwatch, the time t for one, interval can be found. Also, knowing the distance, d to the wall, a rough value is obtained from, speed of sound in air = 2d, t, , , , Figure 33.4 Sound travels as a longitudinal wave., , ●● Reflection and echoes, Sound waves are reflected well from hard, flat, surfaces such as walls or cliffs and obey the same, laws of reflection as light. The reflected sound forms, an echo., If the reflecting surface is nearer than 15 m from, the source of sound, the echo joins up with the, original sound which then seems to be prolonged., This is called reverberation. Some is desirable in a, concert hall to stop it sounding ‘dead’, but too much, causes ‘confusion’. Modern concert halls are designed, for the optimal amount of reverberation. Seats and, some wall surfaces are covered with sound-absorbing, material., , ●● Speed of sound, The speed of sound depends on the material, through which it is passing. It is greater in solids than, in liquids or gases because the molecules in a solid are, closer together than in a liquid or a gas. Some values, are given in Table 33.1., Table 33.1 Speed of sound in different materials, Material, , air (0 °C), , water, , concrete, , steel, , Speed/m/s, , 330, , 1400, , 5000, , 6000, , The speed of sound in air can be found directly by, measuring the time t taken for a sound to travel past, two microphones separated by a distance d:, distance travelled by the sound, time taken, d, =, t, , speed of sound in air =, , ●● Limits of audibility, Humans hear only sounds with frequencies from, about 20 Hz to 20 000 Hz. These are the limits of, audibility; the upper limit decreases with age., , Practical work, Speed of sound in air, Set two microphones about a metre apart, and attach one to the, ‘start’ terminal and the other to the ‘stop’ terminal of a digital, timer, as shown in Figure 33.5. The timer should have millisecond, accuracy. Measure and record the distance d between the centres, of the microphones with a metre ruler. With the small hammer, and metal plate to one side of the ‘start’ microphone, produce, a sharp sound. When the sound reaches the ‘start’ microphone,, the timer should start; when it reaches the ‘stop’ microphone,, the timer should stop. The time displayed is then the time taken, for the sound to travel the distance d. Record the time and then, reset the timer; repeat the experiment a few times and work out, an average value for t., Calculate the speed of sound in air from d/t. How does your, value compare with that given in Table 33.1?, ▲, ▲, 141, , 9781444176421_Section_03.indd 141, , 20/06/14 7:43 AM
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33 Sound waves, , digital timer, , ‘start’, microphone, , sharp, sound, , ‘stop’, microphone, , A set of tuning forks with frequencies marked on, them can also be used. A tuning fork (Figure 33.7),, has two steel prongs which vibrate when struck;, the prongs move in and out together, generating, compressions and rarefactions., , d, , prong, , direction of sound, , stem, , Figure 33.5 Measuring the speed of sound, Figure 33.7 A tuning fork, , ●● Musical notes, Irregular vibrations such as those of motor engines, cause noise; regular vibrations such as occur in the, instruments of a brass band (Figure 33.6), produce, musical notes which have three properties – pitch,, loudness and quality., , b) Loudness, A note becomes louder when more sound, energy enters our ears per second than before., This will happen when the source is vibrating with, a larger amplitude. If a violin string is bowed more, strongly, its amplitude of vibration increases as does, that of the resulting sound wave and the note heard, is louder because more energy has been used to, produce it., , c) Quality, , Figure 33.6 Musical instruments produce regular sound vibrations., , a) Pitch, The pitch of a note depends on the frequency of the, sound wave reaching the ear, i.e. on the frequency of, the source of sound. A high-pitched note has a high, frequency and a short wavelength. The frequency of, middle C is 256 vibrations per second or 256 Hz and, that of upper C is 512 Hz. Notes are an octave apart, if the frequency of one is twice that of the other., Pitch is like colour in light; both depend on the, frequency., Notes of known frequency can be produced in the, laboratory by a signal generator supplying alternating, electric current (a.c.) to a loudspeaker. The cone of, the speaker vibrates at the frequency of the a.c. which, can be varied and read off a scale on the generator., , The same note on different instruments sounds, different; we say the notes differ in quality or, timbre. The difference arises because no instrument, (except a tuning fork and a signal generator) emits, a ‘pure’ note, i.e. of one frequency. Notes consist, of a main or fundamental frequency mixed with, others, called overtones, which are usually weaker, and have frequencies that are exact multiples of, the fundamental. The number and strength of the, overtones decides the quality of a note. A violin has, more and stronger higher overtones than a piano., Overtones of 256 Hz (middle C) are 512 Hz, 768 Hz, and so on., The waveform of a note played near a microphone, connected to a cathode ray oscilloscope (CRO; see, Chapter 48) can be displayed on the CRO screen., Those for the same note on three instruments are, shown in Figure 33.8. Their different shapes show, that while they have the same fundamental frequency,, their quality differs. The ‘pure’ note of a tuning, fork has a sine waveform and is the simplest kind of, sound wave., Note Although the waveform on the CRO screen, is transverse, it represents a longitudinal sound wave., , 142, , 9781444176421_Section_03.indd 142, , 20/06/14 7:43 AM
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Ultrasonics, , tuning fork (sine wave), , piano, , transmitter, , receiver, , violin, Figure 33.8 Notes of the same frequency (pitch) but different quality, ultrasonic, waves, , ●● Ultrasonics, Sound waves with frequencies above 20 kHz, are called ultrasonic waves; their frequency is, too high to be detected by the human ear but, they can be detected electronically and displayed, on a CRO., , a) Quartz crystal oscillators, Ultrasonic waves are produced by a quartz crystal, which is made to vibrate electrically at the required, frequency; they are emitted in a narrow beam in the, direction in which the crystal oscillates. An ultrasonic, receiver also consists of a quartz crystal but it, works in reverse, i.e. when it is set into vibration, by ultrasonic waves it generates an electrical signal, which is then amplified. The same quartz crystal can, act as both a transmitter and a receiver., , Figure 33.9 A ship using sonar, , In medical ultrasound imaging, used in antenatal, clinics to monitor the health and sometimes to, determine the sex of an unborn baby, an ultrasonic, transmitter/receiver is scanned over the mother’s, abdomen and a detailed image of the fetus is built, up (Figure 33.10). Reflection of the ultrasonic, pulses occurs from boundaries of soft tissue, in, addition to bone, so images can be obtained of, internal organs that cannot be seen by using X-rays., Less detail of bone structure is seen than with, X-rays, as the wavelength of ultrasonic waves is, larger, typically about 1 mm, but ultrasound has no, harmful effects on human tissue., , b) Ultrasonic echo techniques, Ultrasonic waves are partially or totally reflected, from surfaces at which the density of the medium, changes; this property is exploited in techniques such, as the non-destructive testing of materials, sonar, and medical ultrasound imaging. A bat emitting, ultrasonic waves can judge the distance of an object, from the time taken by the reflected wave or ‘echo’, to return., Ships with sonar can determine the depth of a, shoal of fish or the sea bed (Figure 33.9) in the same, way; motion sensors (Chapter 2) also work on this, principle., , Figure 33.10 Checking the development of a fetus using ultrasound, imaging, , ▲, ▲, 143, , 9781444176421_Section_03.indd 143, , 20/06/14 7:43 AM
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33 sound Waves, , c) Other uses, Ultrasound can also be used in ultrasonic drills, to cut holes of any shape or size in hard materials, such as glass and steel. Jewellery, or more mundane, objects such as street lamp covers, can be cleaned, by immersion in a tank of solvent which has an, ultrasonic vibrator in the base., , l● Seismic waves, Earthquakes produce both longitudinal waves, (P-waves) and transverse waves (S-waves) that are, known as seismic waves. These travel through the, Earth at speeds of up to 13 000 m/s., When seismic waves pass under buildings, severe, structural damage may occur. If the earthquake occurs, under the sea, the seismic energy can be transmitted to, the water and produce tsunami waves that may travel, for very large distances across the ocean. As a tsunami, wave approaches shallow coastal waters, it slows down, (see Chapter 25) and its amplitude increases, which, can lead to massive coastal destruction. This happened, in Sri Lanka (see Figure 33.11) and Thailand after, the great 2004 Sumatra–Andaman earthquake. The, time of arrival of a tsunami wave can be predicted if its, speed of travel and the distance from the epicentre of, the earthquake are known; it took about 2 hours for, tsunami waves to cross the ocean to Sri Lanka from, Indonesia. A similar time was needed for the tsunami, waves to travel the shorter distance to Thailand. This, was because the route was through shallower water, and the waves travelled more slowly. If an earlywarning system had been in place, many lives could, have been saved., , Questions, 1 If 5 seconds elapse between a lightning flash and the, clap of thunder, how far away is the storm? (Speed of, sound = 330 m/s.), 2 a A girl stands 160 m away from a high wall and claps, her hands at a steady rate so that each clap coincides, with the echo of the one before. If her clapping rate is, 60 per minute, what value does this give for the speed, of sound?, b If she moves 40 m closer to the wall she finds the, clapping rate has to be 80 per minute. What value do, these measurements give for the speed of sound?, c If she moves again and finds the clapping rate becomes, 30 per minute, how far is she from the wall if the speed, of sound is the value you found in a?, 3 a What properties of sound suggest it is a wave motion?, b How does a progressive transverse wave differ from a, longitudinal one? Which type of wave is a sound wave?, 4 a Draw the waveform of, (i) a loud, low-pitched note, and, (ii) a soft, high-pitched note., b If the speed of sound is 340 m/s what is the wavelength, of a note of frequency, (i) 340 Hz,, (ii) 170 Hz?, , Checklist, After studying this chapter you should be able to, • recall that sound is produced by vibrations,, • describe an experiment to show that sound is not, transmitted through a vacuum,, • describe how sound travels in a medium as progressive, longitudinal waves,, • recall the limits of audibility (i.e. the range of frequencies), for the normal human ear,, • explain echoes and reverberation,, • describe an experiment to measure the speed of sound, in air,, • solve problems using the speed of sound, e.g. distance away, of thundercloud,, • state the order of magnitude of the speed of sound in air,, liquid and solids,, • relate the loudness and pitch of sound waves to amplitude, and frequency., , Figure 33.11 This satellite image shows the tsunami that hit the southwestern coast of Sri Lanka on 26 December 2004 as it pulled back out to, sea, having caused utter devastation in coastal areas., 144, , 9781444176421_Section_03.indd 144, , 20/06/14 7:44 AM
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Section, , 4, , Electricity and magnetism, , Chapters, Simple phenomena of magnetism, 34 Magnetic fields, Electrical quantities and circuits, 35 Static electricity, 36 Electric current, 37 Potential difference, 38 Resistance, 39 Capacitors, , 9781444176421_Section_04.indd 145, , 40 Electric power, 41 Electronic systems, 42 Digital electronics, Electromagnetic effects, 43 Generators, 44 Transformers, 45 Electromagnets, 46 Electric motors, 47 Electric meters, 48 Electrons, , 20/06/14 7:38 AM
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34, ●, ●, ●, , Magnetic fields, , Properties of magnets, Magnetisation of iron and steel, Magnetic fields, , ●● Properties of magnets, a) Magnetic materials, , ●, ●, , Earth’s magnetic field, Practical work: Plotting lines of force, , When the same is done with the steel chain, it, does not collapse; magnetism induced in steel is, permanent., , Magnets attract strongly only certain materials such, as iron, steel, nickel and cobalt, which are called, ferro-magnetics., , b) Magnetic poles, The poles are the places in a magnet to which, magnetic materials, such as iron filings, are attracted., They are near the ends of a bar magnet and occur in, pairs of equal strength., , c) North and south poles, If a magnet is supported so that it can swing in a, horizontal plane it comes to rest with one pole, the, north-seeking or N pole, always pointing roughly, towards the Earth’s north pole. A magnet can, therefore be used as a compass., , d) Law of magnetic poles, If the N pole of a magnet is brought near the N pole, of another magnet, repulsion occurs. Two S (southseeking) poles also repel. By contrast, N and S poles, always attract. The law of magnetic poles summarises, these facts and states:, Like poles repel, unlike poles attract., The force between magnetic poles decreases as their separation, increases., , ●● Magnetisation of iron, and steel, Chains of small iron nails and steel paper clips can be, hung from a magnet (Figure 34.1). Each nail or clip, magnetises the one below it and the unlike poles so, formed attract., If the iron chain is removed by pulling the top nail, away from the magnet, the chain collapses, showing, that magnetism induced in iron is temporary., , N, , S, , S, , N, , iron nails, N, , S, , S, , N, , N, , steel paper, clips, , S, , S, , N, , N, , S, , S, , N, , N, , S, , Figure 34.1 Investigating the magnetisation of iron and steel, , Magnetic materials such as iron that magnetise, easily but readily lose their magnetism (are easily, demagnetised) are said to be soft. Those such as, steel that are harder to magnetise than iron but stay, magnetised are hard. Both types have their uses;, very hard ones are used to make permanent magnets., Solenoids can be used to magnetise and demagnetise, magnetic materials (p. 210); dropping or heating a, magnet also causes demagnetisation. Hammering, a magnetic material in a magnetic field causes, magnetisation but in the absence of a field it causes, demagnetisation. ‘Stroking’ a magnetic material, several times in the same direction with one pole of a, magnet will also cause it to become magnetised., , ●● Magnetic fields, The space surrounding a magnet where it produces a, magnetic force is called a magnetic field. The force, around a bar magnet can be detected and shown to, vary in direction, using the apparatus in Figure 34.2., If the floating magnet is released near the N pole of, the bar magnet, it is repelled to the S pole and moves, along a curved path known as a line of force or a, , 146, , 9781444176421_Section_04.indd 146, , 20/06/14 7:38 AM
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Magnetic fields, , field line. It moves in the opposite direction if its, south pole is uppermost., S, , bar magnet, , N, , line of force, N, cork, bowl of, water, , Lay a bar magnet on a sheet of paper. Place the plotting, compass at a point such as A (Figure 34.3b), near one pole of, the magnet. In Figure 34.3b it is the N pole. Mark the position, of the poles (n, s) of the compass by pencil dots B, A. Move the, compass so that pole s is exactly over B, mark the new position of, n by dot C., Continue this process until the other pole of the bar, magnet is reached (in Figure 34.3b it is the S pole). Join the dots, to give one line of force and show its direction by putting an, arrow on it. Plot other lines by starting at different points round, the magnet., A typical field pattern is shown in Figure 34.4., , magnetised, steel needle, or rod, , S, Figure 34.2 Detecting magnetic force, , It is useful to consider that a magnetic field has a, direction and to represent the field by lines of force. It, has been decided that the direction of the field at any, point should be the direction of the force on a N, pole. To show the direction, arrows are put on the lines, of force and point away from a N pole towards a S pole., The magnetic field is stronger in regions where the field, lines are close together than where they are further apart., The force between two magnets is a result of the, interaction of their magnetic fields., , Practical work, , S, , N, , Figure 34.4 Magnetic field lines around a bar magnet, , The combined field due to two neighbouring magnets can also, be plotted to give patterns like those in Figures 34.5a, b. In part, a, where two like poles are facing each other, the point X is, called a neutral point. At X the field due to one magnet cancels, out that due to the other and there are no lines of force., , Plotting lines of force, a) Plotting compass method, A plotting compass is a small pivoted magnet in a glass case with, non-magnetic metal walls (Figure 34.3a)., , compass, needle, , X, , N, , N, , a, , a, C, n, , S, , N, , s, B, A, S, , plotting, compass, , b, Figure 34.5 Field lines due to two neighbouring magnets, , ▲, ▲, , b, Figure 34.3, , N, , 147, , 9781444176421_Section_04.indd 147, , 20/06/14 7:39 AM
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34 Magnetic fields, b) Iron filings method, Place a sheet of paper on top of a bar magnet and sprinkle iron, filings thinly and evenly on to the paper from a ‘pepper pot’., Tap the paper gently with a pencil and the filings should form, patterns showing the lines of force. Each filing turns in the, direction of the field when the paper is tapped., This method is quick but no use for weak fields. Figures 34.6a, b, show typical patterns with two magnets. Why are they different?, What combination of poles would give the observed patterns?, , ●● Earth’s magnetic field, If lines of force are plotted on a sheet of paper, with no magnets nearby, a set of parallel straight, lines is obtained. They run roughly from S to N, geographically (Figure 34.7), and represent a small, part of the Earth’s magnetic field in a horizontal plane., , north, , Figure 34.7 Lines of force due to the Earth’s field, , a, , At most places on the Earth’s surface a, magnetic compass points slightly east or west, of true north, i.e. the Earth’s geographical and, magnetic north poles do not coincide. The, angle between magnetic north and true north is, called the declination (Figure 34.8). In Hong, Kong in 2014 it was 2º 35′ W of N and changing, slowly., geographical, north, magnetic, north, , b, , declination, , Figure 34.6 Field lines round two bar magnets shown by iron filings, , Figure 34.8 The Earth’s geographical and magnetic poles do not, coincide., , 148, , 9781444176421_Section_04.indd 148, , 20/06/14 7:39 AM
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earth’s magnetic field, , Questions, 1 Which one of these statements is true?, A magnet attracts, A plastics, B any metal C iron and steel, D aluminium E carbon, 2 Copy Figure 34.9 which shows a plotting compass and a, magnet. Label the N pole of the magnet and draw the field, line on which the compass lies., , Figure 34.9, , Checklist, After studying this chapter you should be able to, • state the properties of magnets,, • explain what is meant by soft and hard magnetic materials,, • recall that a magnetic field is the region round a magnet, where a magnetic force is exerted and is represented by, lines of force whose direction at any point is the direction of, the force on a N pole,, • map magnetic fields (by the plotting compass and iron, filings methods) round (a) one magnet, (b) two magnets,, • recall that at a neutral point the field due to one magnet, cancels that due to another., , 149, , 9781444176421_Section_04.indd 149, , 20/06/14 7:39 AM
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35, ●, ●, ●, ●, ●, , Static electricity, , Positive and negative charges, Charges, atoms and electrons, Electrons, insulators and conductors, Electrostatic induction, Attraction between uncharged and charged objects, , ●, ●, ●, ●, ●, , Dangers of static electricity, Uses of static electricity, van de Graaff generator, Electric fields, Practical work: Gold-leaf electroscope, , ●● Positive and negative, charges, When a strip of polythene is rubbed with a cloth, it becomes charged. If it is hung up and another, rubbed polythene strip is brought near, repulsion, occurs (Figure 35.2). Attraction occurs when a, rubbed strip of cellulose acetate is brought near., , thread, , paper stirrup, rubbed, polythene, strips, , like, charges, repel, , Figure 35.2 Investigating charges, , Figure 35.1 A flash of lightning is nature’s most spectacular static, electricity effect., , Clothes containing nylon often crackle when they, are taken off. We say they are ‘charged with static, electricity’; the crackles are caused by tiny electric, sparks which can be seen in the dark. Pens and combs, made of certain plastics become charged when rubbed, on your sleeve and can then attract scraps of paper., , This shows there are two kinds of electric, charge. That on cellulose acetate is taken as, positive (+) and that on polythene is negative (–)., It also shows that:, Like charges (+ and +, or – and –) repel, while unlike charges, (+ and –) attract., , The force between electric charges decreases as their, separation increases., , 150, , 9781444176421_Section_04.indd 150, , 20/06/14 7:40 AM
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Charges, atoms and electrons, , ●● Charges, atoms and, electrons, There is evidence (Chapter 50) that we, can picture an atom as being made up of a, small central nucleus containing positively, charged particles called protons, surrounded, by an equal number of negatively charged, electrons. The charges on a proton and an, electron are equal and opposite so an atom as, a whole is normally electrically neutral, i.e. has, no net charge., Hydrogen is the simplest atom with one, proton and one electron (Figure 35.3). A, copper atom has 29 protons in the nucleus and, 29 surrounding electrons. Every nucleus except, hydrogen also contains uncharged particles called, neutrons., , Practical work, Gold-leaf electroscope, metal cap, metal rod, insulating, plug, metal plate, gold leaf, glass window, wooden or, metal case, earthed by, resting on, bench, Figure 35.4 Gold-leaf electroscope, , A gold-leaf electroscope consists of a metal cap on a metal rod at, the foot of which is a metal plate with a leaf of gold foil attached, (Figure 35.4). The rod is held by an insulating plastic plug in a, case with glass sides to protect the leaf from draughts., , nucleus of one proton, , a) Detecting a charge, , , one electron moving, around nucleus, , Bring a charged polythene strip towards the cap: the leaf rises, away from the plate. When you remove the charged strip, the, leaf falls again. Repeat with a charged acetate strip., , b) Charging by contact, Figure 35.3 Hydrogen atom, , The production of charges by rubbing can, be explained by supposing that electrons are, transferred from one material to the other. For, example, when cellulose acetate is rubbed with a, cloth, electrons go from the acetate to the cloth,, leaving the acetate short of electrons, i.e. positively, charged. The cloth now has more electrons than, protons and becomes negatively charged. Note that, it is only electrons which move; the protons remain, fixed in the nucleus., How does polythene become charged when, rubbed?, , Draw a charged polythene strip firmly across the edge of the cap., The leaf should rise and stay up when the strip is removed. If it, does not, repeat the process but press harder. The electroscope, has now become negatively charged by contact with the, polythene strip, from which electrons have been transferred., , c) Insulators and conductors, Touch the cap of the charged electroscope with different things,, such as a piece of paper, a wire, your finger, a comb, a cotton, handkerchief, a piece of wood, a glass rod, a plastic pen, rubber, tubing. Record your results., When the leaf falls, charge is passing to or from the ground, through you and the material touching the cap. If the fall is, rapid the material is a good conductor; if the leaf falls slowly,, the material is a poor conductor. If the leaf does not alter, the, material is a good insulator., , 151, , 9781444176421_Section_04.indd 151, , 20/06/14 7:40 AM
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35 Static electricity, , ●● Electrons, insulators, and conductors, In an insulator all electrons are bound firmly to, their atoms; in a conductor some electrons can, move freely from atom to atom. An insulator can be, charged by rubbing because the charge produced, cannot move from where the rubbing occurs, i.e. the, electric charge is static. A conductor will become, charged only if it is held with an insulating handle;, otherwise electrons are transferred between the, conductor and the ground via the person’s body., Good insulators include plastics such as polythene,, cellulose acetate, Perspex and nylon. All metals, and carbon are good conductors. In between are, materials that are both poor conductors and (because, they conduct to some extent) poor insulators., Examples are wood, paper, cotton, the human body, and the Earth. Water conducts and if it were not, present in materials like wood and on the surface of,, for example, glass, these would be good insulators., Dry air insulates well., , ●● Electrostatic, induction, This effect may be shown by bringing a negatively, charged polythene strip near to an insulated metal, sphere X which is touching a similar sphere Y, (Figure 35.5a). Electrons in the spheres are repelled, to the far side of Y., If X and Y are separated, with the charged strip, still in position, X is left with a positive charge, (deficient of electrons) and Y with a negative, charge (excess of electrons) (Figure 35.5b). The, signs of the charges can be tested by removing the, charged strip (Figure 35.5c), and taking X up to the, cap of a positively charged electroscope. Electrons, will be drawn towards X, making the leaf more, positive so that it rises. If Y is taken towards the cap, of a negatively charged electroscope the leaf again, rises; can you explain why, in terms of electron, motion?, , metal spheres, , , X, , , charged polythene strip, , , X, , , , , Y , , , a, , , , Y , , , b, , X, , , , Y, , insulator, , c, Figure 35.5 Electrostatic induction, , ●● Attraction between, uncharged and charged, objects, The attraction of an uncharged object by a, charged object near it is due to electrostatic, induction., In Figure 35.6a a small piece of aluminium, foil is attracted to a negatively charged polythene, rod held just above it. The charge on the rod, pushes free electrons to the bottom of the foil, (aluminium is a conductor), leaving the top of the, foil short of electrons, i.e. with a net positive charge,, and the bottom negatively charged. The top of the, foil is nearer the rod than the bottom. Hence the, force of attraction between the negative charge on, the rod and the positive charge on the top of the, foil is greater than the force of repulsion between, the negative charge on the rod and the negative, charge on the bottom of the foil. The foil is pulled, to the rod., A small scrap of paper, although an insulator, is, also attracted by a charged rod. There are no free, electrons in the paper but the charged rod pulls the, electrons of the atoms in the paper slightly closer, (by electrostatic induction) and so distorts the, atoms. In the case of a negatively charged polythene, , 152, , 9781444176421_Section_04.indd 152, , 20/06/14 7:40 AM
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Dangers of static electricity, , rod, the paper behaves as if it had a positively, charged top and a negative charge at the bottom., charged, polythene rod, , , , , , , , , , , , , from the spike. This effect, called action at points,, results in an ‘electric wind’ of positive air molecules, streaming upwards which can neutralise electrons, discharging from the thundercloud in a lightning, flash. If a flash occurs it is now less violent and the, conductor gives it an easy path to ground., , attraction, induced, charges, , , , , , , , , , , , thundercloud, , , , , , , , , aluminium, foil, , repulsion, Figure 35.6a An uncharged object is attracted to a charged one., tall, building, , , , , , , , , , , , stream of, positive air, molecules, spikes, copper, strip, , , , , , electrons, repelled, to Earth, metal plate, in ground, , Figure 35.6b A slow stream of water is bent by electrostatic attraction., Figure 35.7 Lightning conductor, , In Figure 35.6b a slow, uncharged stream of water, is attracted by a charged polythene rod, due to, the polar nature of water molecules (one end of a, molecule is negatively charged while the other end, is positively charged)., , ●● Dangers of static, electricity, a) Lightning, , Sparks from static electricity can be dangerous, when flammable vapour is present. For this reason,, the tanks in an oil tanker may be cleaned in an, atmosphere of nitrogen – otherwise oxygen in the, air could promote a fire., An aircraft in flight may become charged by, ‘rubbing’ the air. Its tyres are made of conducting, rubber which lets the charge pass harmlessly to, ground on landing, otherwise an explosion could, be ‘sparked off’ when the aircraft refuels. What, precautions are taken at petrol pumps when a car is, refuelled?, , c) Operating theatres, Dust and germs are attracted by charged objects, and so it is essential to ensure that equipment, and medical personnel are well ‘earthed’ allowing, electrons to flow to and from the ground, for, example by conducting rubber., ▲, ▲, , A tall building is protected by a lightning conductor, consisting of a thick copper strip fixed on the, outside of the building connecting metal spikes at, the top to a metal plate in the ground (Figure 35.7)., Thunderclouds carry charges; a negatively, charged cloud passing overhead repels electrons, from the spikes to the Earth. The points of the, spikes are left with a large positive charge (charge, concentrates on sharp points) which removes, electrons from nearby air molecules, so charging, them positively and causing them to be repelled, , b) Refuelling, , 153, , 9781444176421_Section_04.indd 153, , 20/06/14 7:40 AM
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35 Static electricity, , d) Computers, , inkjet nozzle, , Computers require similar ‘anti-static’ conditions as, they are vulnerable to electrostatic damage., , electrostatic, charging unit, , ●● Uses of static electricity, a) Flue-ash precipitation, An electrostatic precipitator removes the dust and, ash that goes up the chimneys of coal-burning, power stations. It consists of a charged fine wire, mesh which gives a similar charge to the rising, particles of ash. They are then attracted to plates, with an opposite charge. These are tapped from, time to time to remove the ash, which falls to the, bottom of the chimney from where it is removed., , b) Photocopiers, These contain a charged drum and when the paper, to be copied is laid on the glass plate, the light, reflected from the white parts of the paper causes, the charge to disappear from the corresponding, parts of the drum opposite. The charge pattern, remaining on the drum corresponds to the darkcoloured printing on the original. Special toner, powder is then dusted over the drum and sticks to, those parts which are still charged. When a sheet of, paper passes over the drum, the particles of toner, are attracted to it and fused into place by a short, burst of heat., , c) Inkjet printers, In an inkjet printer tiny drops of ink are forced out, of a fine nozzle, charged electrostatically and then, passed between two oppositely charged plates; a, negatively charged drop will be attracted towards, the positive plate causing it to be deflected as shown, in Figure 35.8. The amount of deflection and hence, the position at which the ink strikes the page is, determined by the charge on the drop and the p.d., between the plates; both of these are controlled by, a computer. About 100 precisely located drops are, needed to make up an individual letter but very fast, printing speeds can be achieved., , deflecting, plates, negative, , positive, , path of negatively, charged ink drop, paper, , Figure 35.8 Inkjet printer, , ●● van de Graaff, generator, This produces a continuous supply of charge on, a large metal dome when a rubber belt is driven, by an electric motor or by hand, as shown in, Figure 35.9a., , a) Demonstrations, In Figure 35.9a sparks jump between the dome, and the discharging sphere. Electrons flow round, a complete path (circuit) from the dome. Can, you trace it? In part Figure 35.9b why does the, ‘hair’ stand on end? In Figure 35.9c the ‘windmill’, revolves due to the reaction that arises from the, ‘electric wind’ caused by the action at points effect,, explained on p. 153 for the lightning conductor., In Figure 35.9d the ‘body’ on the insulating stool, first gets charged by touching the dome and then, lights a neon lamp., The dome can be discharged harmlessly by, bringing your elbow close to it., , b) Action, Initially a positive charge is produced on the, motor-driven Perspex roller because it is rubbing, the belt. This induces a negative charge on the, ‘comb’ of metal points P (Figure 35.9a). The, charges are sprayed off by ‘action at points’ on, , 154, , 9781444176421_Section_04.indd 154, , 20/06/14 7:41 AM
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Electric fields, , to the outside of the belt and carried upwards., A positive charge is then induced in the comb of, metal points, Q, and negative charge is repelled to, the dome., −, , −, , discharging, sphere, , −, , dome, Q +, , −, −, rubber belt, , Perspex roller, motor, a, , −, , −, , +, , −, spark, , +, , −, , +, , −, +, + +, −, P, , ‘hair’, , connecting, wire, , ●● Electric fields, When an electric charge is placed near to another, electric charge it experiences a force. The electric force, does not require contact between the two charges, so we call it an ‘action-at-a-distance force’ – it acts, through space. The region of space where an electric, charge experiences a force due to other charges is, called an electric field. If the electric force felt by a, charge is the same everywhere in a region, the field is, uniform; a uniform electric field is produced between, two oppositely charged parallel metal plates (Figure, 35.10). It can be represented by evenly spaced parallel, lines drawn perpendicular to the metal surfaces., The direction of the field, denoted by arrows, is the, direction of the force on a small positive charge placed, in the field (negative charges experience a force in the, opposite direction to the field)., , windmill, , ‘electric, wind’, point, charged, dome, Figure 35.10 Uniform electric field, , b, , c, , charged, ‘body’, neon, lamp, , Moving charges are deflected by an electric field due, to the electric force exerted on them; this occurs in, the inkjet printer (Figure 35.8)., The electric field lines radiating from an isolated, positively charged conducting sphere and a point, charge are shown in Figures 35.11a, b; again the, field lines emerge at right angles to the conducting, surface., , insulating, stool, , d, Figure 35.11a, Figure 35.9, , 155, , 9781444176421_Section_04.indd 155, , 20/06/14 7:41 AM
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35 static electricity, , Checklist, After studying this chapter you should be able to, , +, , • describe how positive and negative charges are produced by, rubbing,, • recall that like charges repel and unlike charges attract,, • explain the charging of objects in terms of the motion of, negatively charged electrons,, • describe the gold-leaf electroscope, and explain how it can, be used to compare electrical conductivities of different, materials,, • explain the differences between insulators and conductors,, • describe how a conductor can be charged by induction,, , Figure 35.11b Radial electric field, , • explain how a charged object can attract uncharged, objects,, • give examples of the dangers and the uses of static, electricity,, • explain what is meant by an electric field., , Questions, 1 Two identical conducting balls, suspended on nylon, threads, come to rest with the threads making equal angles, with the vertical, as shown in Figure 35.12., Which of these statements is true?, This shows that:, A the balls are equally and oppositely charged, B the balls are oppositely charged but not necessarily, equally charged, C one ball is charged and the other is uncharged, D the balls both carry the same type of charge, E one is charged and the other may or may not be, charged., , Figure 35.12, , 2 Explain in terms of electron movement what happens when, a polythene rod becomes charged negatively by being, rubbed with a cloth., 3 Which of statements A to E is true?, In the process of electrostatic induction, A a conductor is rubbed with an insulator, B a charge is produced by friction, C negative and positive charges are separated, D a positive charge induces a positive charge, E electrons are ‘sprayed’ into an object., , 156, , 9781444176421_Section_04.indd 156, , 20/06/14 7:41 AM
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36 Electric current, l, l, l, , Effects of a current, The ampere and the coulomb, Circuit diagrams, , l, l, l, , An electric current consists of moving electric, charges. In Figure 36.1, when the van de Graaff, machine is working, the table-tennis ball shuttles, rapidly to and fro between the plates and the, meter records a small current. As the ball touches, each plate it becomes charged and is repelled to the, other plate. In this way charge is carried across the, gap. This also shows that ‘static’ charges, produced, by friction, cause a deflection on a meter just as, current electricity produced by a battery does., In a metal, each atom has one or more loosely, held electrons that are free to move. When a van de, Graaff or a battery is connected across the ends of, such a conductor, the free electrons drift slowly along, it in the direction from the negative to the positive, terminal of a battery. There is then a current of, negative charge., , Series and parallel circuits, Direct and alternating current, Practical work: Measuring current, , ●● Effects of a current, An electric current has three effects that reveal its, existence and which can be shown with the circuit of, Figure 36.2., battery, (1.5 V cells), , thick, copper, wire, , plotting, compass, , lamp, , thread, , table-tennis, ball coated, with ‘Aquadag‘, to make it, conducting, , metal, plates, , insulating, handle, , dilute, sulfuric, acid, , van de Graaff, generator, circuit board, Figure 36.2 Investigating the effects of a current, , a) Heating and lighting, 5 cm, , The lamp lights because the small wire inside (the, filament) is made white hot by the current., , b) Magnetic, The plotting compass is deflected when it is placed, near the wire because a magnetic field is produced, around any wire carrying a current., , c) Chemical, picoammeter, Figure 36.1 Demonstrating that an electric current consists of moving, charges, , Bubbles of gas are given off at the wires in, the acid because of the chemical action of the, current., , 157, , 9781444176421_Section_04.indd 157, , 20/06/14 7:41 AM
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36 electric cUrrent, , ●● The ampere and the, coulomb, The unit of current is the ampere (A) which is, defined using the magnetic effect. One milliampere, (mA) is one-thousandth of an ampere. Current is, measured by an ammeter., The unit of charge, the coulomb (C), is defined in, terms of the ampere., One coulomb is the charge passing any point in a circuit, when a steady current of 1 ampere flows for 1 second. That is,, 1 C = 1 A s., , A charge of 3 C would pass each point in 1 s if the, current were 3 A. In 2 s, 3 A × 2 s = 6 A s = 6 C would, pass. In general, if a steady current I (amperes) flows, for time t (seconds) the charge Q (coulombs) passing, any point is given by, Q=I×t, , This is a useful expression connecting charge and, current., , ●● Circuit diagrams, , Before the electron was discovered scientists, agreed to think of current as positive charges moving, round a circuit in the direction from positive to, negative of a battery. This agreement still stands., Arrows on circuit diagrams show the direction of, what we call the conventional current, i.e. the, direction in which positive charges would flow., Electrons flow in the opposite direction to the, conventional current., , Practical work, Measuring current, (a) Connect the circuit of Figure 36.4a (on a circuit board, if possible) ensuring that the + of the cell (the metal, stud) goes to the + of the ammeter (marked red). Note the, current., (b) Connect the circuit of Figure 36.4b. The cells are in series, (+ of one to – of the other), as are the lamps. Record the, current. Measure the current at B, C and D by disconnecting, the circuit at each point in turn and inserting the ammeter., What do you find?, (c) Connect the circuit of Figure 36.4c. The lamps are in, parallel. Read the ammeter. Also measure the currents at P,, Q and R. What is your conclusion?, , Current must have a complete path (a circuit) of, conductors if it is to flow. Wires of copper are used, to connect batteries, lamps, etc. in a circuit since, copper is a good electrical conductor. If the wires are, covered with insulation, such as plastic, the ends are, bared for connecting up., The signs or symbols used for various parts of an, electric circuit are shown in Figure 36.3., , (1.5 V cell), , , (0–1 A), , A, , (1.25 V), Figure 36.4a, connecting, wire, , wires joined, , wires crossing, (not joined), , D, , , , , , , cell, , , , battery (two or more cells), , A, , or, , ammeter, , lamp, , Figure 36.3 Circuit symbols, , switch, , C, , A, , B, Figure 36.4b, , 158, , 9781444176421_Section_04.indd 158, , 20/06/14 7:41 AM
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direct and alternating current, , ●● Direct and alternating, current, , , , R, , A, , Q, , a) Difference, In a direct current (d.c.) the electrons flow in one, direction only. Graphs for steady and varying d.c. are, shown in Figure 36.5., , P, current, , Figure 36.4c, , steady d.c., , ●● Series and parallel circuits, , time, , In a series circuit, such as the one shown in Figure, 36.4b, the different parts follow one after the other, and there is just one path for the current to follow., You should have found in the previous experiment, that the reading on the ammeter (e.g. 0.2 A) when in, the position shown in the diagram is also obtained at, B, C and D. That is, current is not used up as it goes, round the circuit., The current is the same at all points in a series circuit., , current, , a) Series, , varying d.c., time, Figure 36.5 Direct current (d.c.), , In an alternating current (a.c.) the direction of flow, reverses regularly, as shown in the graph in Figure 36.6., The circuit sign for a.c. is given in Figure 36.7., , b) Parallel, , a.c., current, , In a parallel circuit, as in Figure 36.4c, the lamps, are side by side and there are alternative paths for, the current. The current splits: some goes through, one lamp and the rest through the other. The, current from the source is larger than the current in, each branch. For example, if the ammeter reading, was 0.4 A in the position shown, then if the lamps, are identical, the reading at P would be 0.2 A, and, so would the reading at Q, giving a total of 0.4 A., Whether the current splits equally or not depends on, the lamps (as we will see later); for example, it might, divide so that 0.3 A goes one way and 0.1 A by the, other branch., , 0, , ¹⁄₂, , 1, , time/seconds, , , 1 cycle, Figure 36.6 Alternating current (a.c.), , Figure 36.7 Symbol for alternating current, , The sum of the currents in the branches of a parallel circuit, equals the current entering or leaving the parallel section., , The pointer of an ammeter for measuring d.c. is, deflected one way by the direct current. Alternating, 159, , 9781444176421_Section_04.indd 159, , 20/06/14 7:42 AM
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36 electric cUrrent, , current makes the pointer move to and fro about the, zero if the changes are slow enough; otherwise no, deflection can be seen., Batteries give d.c.; generators can produce either, d.c. or a.c., , 4 Using the circuit in Figure 36.9, which of the following, statements is correct?, A When S1 and S2 are closed, lamps A and B are lit., B With S1 open and S2 closed, A is lit and B is not lit., C With S2 open and S1 closed, A and B are lit., , b) Frequency of a.c., The number of complete alternations or cycles in, 1 second is the frequency of the alternating current., The unit of frequency is the hertz (Hz). The frequency, of the a.c. in Figure 36.6 is 2 Hz, which means there, are two cycles per second, or one cycle lasts 1/2 = 0.5 s., The mains supply in the UK is a.c. of frequency 50 Hz;, each cycle lasts 1/50th of a second. This regularity was, used in the tickertape timer (Chapter 2) and is relied, upon in mains-operated clocks., , , S1, , P, , S, , Q, , R, , P, , S, , A, , P, , B, , Figure 36.9, , 5 If the lamps are both the same in Figure 36.10 and if, ammeter A1 reads 0.50 A, what do ammeters A2, A3, A4, and A5 read?, A1, A2, , A4, , A3, , A5, , Figure 36.10, , R, , B, , S, , Q, , Q, , A, , S2, , Questions, 1 If the current in a floodlamp is 5 A, what charge passes in, a 1 s,, b 10 s,, c 5 minutes?, 2 What is the current in a circuit if the charge passing each, point is, a 10 C in 2 s,, b 20 C in 40 s,, c 240 C in 2 minutes?, 3 Study the circuits in Figure 36.8. The switch S is open (there, is a break in the circuit at this point). In which circuit would, lamps Q and R light but not lamp P?, , , , R, , P, , Q, , R, , S, C, , D, , P, , Q, , R, , S, , E, Figure 36.8, , 160, , 9781444176421_Section_04.indd 160, , 20/06/14 7:42 AM
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Direct and alternating current, , Checklist, After studying this chapter you should be able to, • describe a demonstration which shows that an electric, current is a flow of charge,, • recall that an electric current in a metal is a flow of electrons, from the negative to the positive terminal of the battery, round a circuit,, • state the three effects of an electric current,, • state the unit of electric current and recall that current is, measured by an ammeter,, • define the unit of charge in terms of the unit of current,, • recall the relation Q = It and use it to solve problems,, • use circuit symbols for wires, cells, switches, ammeters and, lamps,, • draw and connect simple series and parallel circuits,, observing correct polarities for meters,, • recall that the current in a series circuit is the same, everywhere in the circuit,, • state that for a parallel circuit, the current from the source, is larger than the current in each branch,, • recall that the sum of the currents in the branches of a, parallel circuit equals the current entering or leaving the, parallel section,, • distinguish between electron flow and conventional, current,, • distinguish between direct current and alternating current,, • recall that frequency of a.c. is the number of cycles per, second., , 161, , 9781444176421_Section_04.indd 161, , 20/06/14 7:42 AM
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37 Potential difference, l, l, l, , Energy transfers and p.d., Model of a circuit, The volt, , l, l, l, , A battery transforms chemical energy to electrical, energy. Because of the chemical action going on, inside it, it builds up a surplus of electrons at one of, its terminals (the negative) and creates a shortage at, the other (the positive). It is then able to maintain, a flow of electrons, i.e. an electric current, in any, circuit connected across its terminals for as long as, the chemical action lasts., The battery is said to have a potential difference, (p.d. for short) at its terminals. Potential difference, is measured in volts (V) and the term voltage is, sometimes used instead of p.d. The p.d. of a car, battery is 12 V and the domestic mains supply in the, UK is 230 V., , Cells, batteries and e.m.f., Voltages round a circuit, Practical work: Measuring voltage, , Evidently the p.d. across a device affects the rate at, which it transfers electrical energy. This gives us a way, of defining the unit of potential difference: the volt., , ●● Model of a circuit, It may help you to understand the definition of the, volt, i.e. what a volt is, if you imagine that the current, in a circuit is formed by ‘drops’ of electricity, each, having a charge of 1 coulomb and carrying equalsized ‘bundles’ of electrical energy. In Figure 37.2,, Mr Coulomb represents one such ‘drop’. As a ‘drop’, moves around the circuit it gives up all its energy, which is changed to other forms of energy. Note that, electrical energy, not charge or current, is ‘used up’., , ●● Energy transfers, and p.d., In an electric circuit electrical energy is supplied from, a source such as a battery and is transferred to other, forms of energy by devices in the circuit. A lamp, produces heat and light., When each one of the circuits of Figure 37.1 is, connected up, it will be found from the ammeter, readings that the current is about the same (0.4 A) in, each lamp. However, the mains lamp with a potential, difference of 230 V applied to it gives much more, light and heat than the car lamp with 12 V across it., In terms of energy, the mains lamp transfers a great, deal more electrical energy in a second than the, car lamp., a.c. ammeters (0–1 A), mains lamp, (100 W), , 230 V mains, , car, side-lamp, (6 W), , 12 V a.c. supply, , Figure 37.1 Investigating the effect of p.d. (potential difference) on, energy transfer, , ‘bundle’ of, electrical, energy, , Mr Coulomb, , Figure 37.2 Model of a circuit, , In our imaginary representation, Mr Coulomb travels, round the circuit and unloads energy as he goes,, most of it in the lamp. We think of him receiving, a fresh ‘bundle’ every time he passes through the, battery, which suggests he must be travelling very, fast. In fact, as we found earlier (Chapter 36), the, electrons drift along quite slowly. As soon as the, circuit is complete, energy is delivered at once to the, lamp, not by electrons directly from the battery but, from electrons that were in the connecting wires. The, model is helpful but is not an exact representation., , 162, , 9781444176421_Section_04.indd 162, , 20/06/14 7:42 AM
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cells, batteries and e.m.f., , ●● The volt, The demonstrations of Figure 37.1 show that the, greater the voltage at the terminals of a supply, the, larger is the ‘bundle’ of electrical energy given to, each coulomb and the greater is the rate at which, light and heat are produced in a lamp., The p.d. between two points in a circuit is 1 volt if 1 joule of, electrical energy is transferred to other forms of energy when, 1 coulomb passes from one point to the other., , That is, 1 volt = 1 joule per coulomb (1 V = 1 J/C)., If 2 J are given up by each coulomb, the p.d. is, 2 V. If 6 J are transferred when 2 C pass, the p.d. is, 6 J/2 C = 3 V., In general if E (joules) is the energy transferred, (i.e. the work done) when charge Q (coulombs), passes between two points, the p.d. V (volts) between, the points is given by, V = E/Q, , or, , Figure 37.3 Compact batteries, , 1.5 V, , 1.5 V, , 1.5 V, , A, , B, , a, 1.5 V, , E=Q×V, , If Q is in the form of a steady current I (amperes), flowing for time t (seconds) then Q = I × t, (Chapter 36) and, E=I×t×V, , ●● Cells, batteries and, e.m.f., A ‘battery’ (Figure 37.3) consists of two or more, electric cells. Greater voltages are obtained when, cells are joined in series, i.e. + of one to – of next., In Figure 37.4a the two 1.5 V cells give a voltage of, 3 V at the terminals A, B. Every coulomb in a circuit, connected to this battery will have 3 J of electrical, energy., The cells in Figure 37.4b are in opposition and the, voltage at X, Y is zero., If two 1.5 V cells are connected in parallel, as in, Figure 37.4c, the voltage at terminals P, Q is still, 1.5 V but the arrangement behaves like a larger cell, and will last longer., , X, , Y, 1.5 V, , b, , 1.5 V, c, , P, , Q, , Figure 37.4, , The p.d. at the terminals of a battery decreases, slightly when current is drawn from it. This effect is, due to the internal resistance of the battery which, transfers electrical energy to heat as current flows, through it. The greater the current drawn, the larger, the ‘lost’ voltage. When no current is drawn from, a battery it is said to be an ‘open circuit’ and its, terminal p.d. is a maximum. This maximum voltage, is termed the electromotive force (e.m.f.) of the, battery. Like potential difference, e.m.f. is measured, in volts and can be written as, e.m.f. = ‘lost’ volts + terminal p.d., In energy terms, the e.m.f. is defined as the number, of joules of chemical energy transferred to electrical, energy and heat when one coulomb of charge passes, through the battery (or cell)., , 163, , 9781444176421_Section_04.indd 163, , 20/06/14 7:42 AM
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37 Potential difference, , In Figure 37.2 the size of the energy bundle Mr, Coulomb is carrying when he leaves the cell would, be smaller if the internal resistance were larger., , Practical work, Measuring voltage, A voltmeter is an instrument for measuring voltage or p.d. It, looks like an ammeter but has a scale marked in volts. Whereas, an ammeter is inserted in series in a circuit to measure the, current, a voltmeter is connected across that part of the circuit, where the voltage is required, i.e. in parallel. (We will see later, that a voltmeter should have a high resistance and an ammeter a, low resistance.), To prevent damage the + terminal (marked red) must be, connected to the point nearest the + of the battery., (a) Connect the circuit of Figure 37.5a. The voltmeter gives the, voltage across the lamp. Read it., 1.5 V cell, , , (b) Connect the circuit of Figure 37.5b. Measure:, (i) the voltage V between X and Y,, (ii) the voltage V1 across lamp L1,, (iii) the voltage V2 across lamp L2,, (iv) the voltage V3 across lamp L3., How does the value of V compare with, V1 + V2 + V3?, (c) Connect the circuit of Figure 37.5c, so that two lamps L1 and, L2 are in parallel across one 1.5 V cell. Measure the voltages,, V1 and V2, across each lamp in turn. How do V1 and V2, compare?, , ●● Voltages round, a circuit, a) Series, In the previous experiment you should have found, in the circuit of Figure 37.5b that, V = V1 + V2 + V3, , lamp, (1.25 V), , For example, if V1 = 1.4 V, V2 = 1.5 V and, V3 = 1.6 V, then V will be (1.4 + 1.5 + 1.6) V = 4.5 V., The voltage at the terminals of a battery equals the sum of, the voltages across the devices in the external circuit from one, battery terminal to the other., , V, , , voltmeter (0–5 V), a, , b) Parallel, , 4.5 V, , In the circuit of Figure 37.5c, X, , L2, , L1, , L3, , Y, , V1 = V2, The voltages across devices in parallel in a circuit are equal., , b, 1.5 V, V1, , L1, L2, , V2, c, Figure 37.5, , 164, , 9781444176421_Section_04.indd 164, , 20/06/14 7:43 AM
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Voltages round a circuit, , Questions, 1 The p.d. across the lamp in Figure 37.6 is 12 V. How many, joules of electrical energy are changed into light and heat, when, a a charge of 1 C passes through it,, b a charge of 5 C passes through it,, c a current of 2 A flows in it for 10 s?, , d, , e, , f, , Figure 37.8, , 12 V, Figure 37.6, , 2 Three 2 V cells are connected in series and used as the, supply for a circuit., a What is the p.d. at the terminals of the supply?, b How many joules of electrical energy does 1 C gain on, passing through, (i) one cell,, (ii) all three cells?, 3 Each of the cells shown in Figure 37.7 has a p.d. of 1.5 V., Which of the arrangements would produce a battery with a, p.d. of 6 V?, , 5 Three voltmeters V, V1 and V2 are connected as in, Figure 37.9., a If V reads 18 V and V1 reads 12 V, what does V2 read?, b If the ammeter A reads 0.5 A, how much electrical energy, is changed to heat and light in lamp L1 in one minute?, c Copy Figure 37.9 and mark with a + the positive, terminals of the ammeter and voltmeters for correct, connection., , L1, , L2, , V1, , V2, , A, , V, B, , 1.5 V, , Figure 37.9, , 6 Three voltmeters are connected as in Figure 37.10., , A, , V1, C, , V, V2, , D, Figure 37.7, , 4 The lamps and the cells in all the circuits of Figure 37.8 are the, same. If the lamp in a has its full, normal brightness, what can, you say about the brightness of the lamps in b, c, d, e and f?, , Figure 37.10, , What are the voltmeter readings x, y and z in the, table below (which were obtained with three different, batteries)?, V/V, , a, , b, , c, , V1/V, , V2/V, , x, , 12, , 6, , 6, , 4, , y, , 12, , z, , 4, , 165, , 9781444176421_Section_04.indd 165, , 20/06/14 7:43 AM
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37 Potential difference, , Checklist, After studying this chapter you should be able to, • describe simple experiments to show the transfer of, electrical energy to other forms (e.g. in a lamp),, • recall the definition of the unit of p.d. and that p.d. (also, called ‘voltage’) is measured by a voltmeter,, • demonstrate that the sum of the voltages across any, number of components in series equals the voltage across, all of those components,, • demonstrate that the voltages across any number of, components in parallel are the same,, • work out the voltages of cells connected in series and, parallel,, • explain the meaning of the term electromotive, force (e.m.f.)., , 166, , 9781444176421_Section_04.indd 166, , 20/06/14 7:43 AM
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38, ●, ●, ●, ●, ●, , Resistance, , The ohm, Resistors, I–V graphs: Ohm’s law, Resistors in series, Resistors in parallel, , ●, ●, ●, ●, , Resistor colour code, Resistivity, Potential divider, Practical work: Measuring resistance, , Electrons move more easily through some conductors, than others when a p.d. is applied. The opposition of, a conductor to current is called its resistance. A good, conductor has a low resistance and a poor conductor, has a high resistance. The resistance of a wire of a, certain material, (i) increases as its length increases,, (ii) increases as its cross-sectional area decreases,, (iii) depends on the material., A long thin wire has more resistance than a short, thick one of the same material. Silver is the best, conductor, but copper, the next best, is cheaper and, is used for connecting wires and for domestic electric, cables., , ●● The ohm, If the current in a conductor is I when the voltage, across it is V, as shown in Figure 38.1a, its resistance, R is defined by, R=, , V, I, , This is a reasonable way to measure resistance since, the smaller I is for a given V, the greater is R. If V is, in volts and I in amperes, then R is in ohms (symbol, Ω, the Greek letter omega). For example, if I = 2 A, when V = 12 V, then R = 12 V/2 A, that is, R = 6 Ω., The ohm is the resistance of a conductor in which the current is, 1 ampere when a voltage of 1 volt is applied across it., , I, , R, , V, , V, , I, , , , R, , Figure 38.1b, , Alternatively, if R and I are known, V can be found, from, V = IR, Also, when V and R are known, I can be calculated, from, I=, , V, R, , The triangle in Figure 38.1b is an aid to, remembering the three equations. It is used like the, ‘density triangle’ in Chapter 5., , ●● Resistors, Conductors intended to have resistance are called, resistors (Figure 38.2a) and are made either from, wires of special alloys or from carbon. Those used in, radio and television sets have values from a few ohms, up to millions of ohms (Figure 38.2b)., , Figure 38.2a Circuit symbol for a resistor, , I, , Figure 38.2b Resistor, , Figure 38.1a, 167, , 9781444176421_Section_04.indd 167, , 20/06/14 7:43 AM
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38 Resistance, , Figure 38.5 Circuit symbol for a variable resistor used as a rheostat, , Practical work, , Figure 38.2c Variable resistor (potentiometer), , Variable resistors are used in electronics (and are, then called potentiometers) as volume and other, controls (Figure 38.2c). Variable resistors that take, larger currents, like the one shown in Figure 38.3,, are useful in laboratory experiments. These consist of, a coil of constantan wire (an alloy of 60% copper, 40%, nickel) wound on a tube with a sliding contact on a, metal bar above the tube., tube, , metal bar, , Measuring resistance, The resistance R of a conductor can be found by measuring, the current I in it when a p.d. V is applied across it and then, using R = V/I. This is called the ammeter–voltmeter method., , , to three 1.5 V(4.5 V) cells in series, , , , sliding contact, , R, , terminals, , , , A, , crocodile, clip, , coil of constantan wire, terminal, , Figure 38.3 Large variable resistor, , There are two ways of using such a variable resistor., It may be used as a rheostat for changing the current, in a circuit; only one end connection and the sliding, contact are then required. In Figure 38.4a moving the, sliding contact to the left reduces the resistance and, increases the current. This variable resistor can also act, as a potential divider for changing the p.d. applied to, a device; all three connections are then used. In Figure, 38.4b any fraction from the total p.d. of the battery to, zero can be ‘tapped off’ by moving the sliding contact, down. Figure 38.5 shows the circuit diagram symbol, for a variable resistor being used in rheostat mode., , potential, divider, rheostat, , a, , b, , ammeter, (0–1 A), circuit, board, , rheostat, (0–25 Ω), , , V, , voltmeter, (0–5 V), , Figure 38.6, , Set up the circuit of Figure 38.6 in which the unknown resistance, R is 1 metre of SWG 34 constantan wire. Altering the rheostat, changes both the p.d. V and the current I. Record in a table, with, three columns, five values of I (e.g. 0.10, 0.15, 0.20, 0.25 and, 0.3 A) and the corresponding values of V. Work out R for each, pair of readings., Repeat the experiment, but instead of the wire use (i) a lamp, (e.g. 2.5 V, 0.3 A), (ii) a semiconductor diode (e.g. 1 N4001), connected first one way then the other way round, (iii) a, thermistor (e.g. TH 7). (Semiconductor diodes and thermistors, are considered in Chapter 41 in more detail.), , Figure 38.4 A variable resistor can be used as a rheostat or as a potential, divider., , 168, , 9781444176421_Section_04.indd 168, , 20/06/14 7:44 AM
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resistors in series, , ●● i–V graphs: Ohm’s law, , c) Filament lamp, , The results of the previous experiment allow graphs, of I against V to be plotted for different conductors., I, , I, , A filament lamp is a non-ohmic conductor at, high temperatures. For a filament lamp the I–V graph, bends over as V and I increase (Figure 38.7c). That, is, the resistance (V/I ) increases as I increases and, makes the filament hotter., , d) Variation of resistance with, temperature, 0, a Ohmic conductor, , 0, , V, , b Semiconductor diode, , I, , 0, c Filament lamp, , V, , I, , V, , 0, d Thermistor, , V, , Figure 38.7 I–V graphs, , In general, an increase of temperature increases, the resistance of metals, as for the filament lamp, in Figure 38.7c, but it decreases the resistance of, semiconductors. The resistance of semiconductor, thermistors (see Chapter 41) decreases if their, temperature rises, i.e. their I–V graph bends upwards,, as in Figure 38.7d., If a resistor and a thermistor are connected as a, potential divider (Figure 38.8), the p.d. across the, resistor increases as the temperature of the thermistor, increases; the circuit can be used to monitor, temperature, for example in a car radiator., , a) Metallic conductors, Metals and some alloys give I–V graphs that are a, straight line through the origin, as in Figure 38.7a,, provided that their temperature is constant. I is, directly proportional to V, i.e. I ∝ V. Doubling V, doubles I, etc. Such conductors obey Ohm’s law,, stated as follows., The current in a metallic conductor is directly proportional to, the p.d. across its ends if the temperature and other conditions, are constant., , They are called ohmic or linear conductors and, since I ∝ V, it follows that V/I = a constant (obtained, from the slope of the I–V graph). The resistance of, an ohmic conductor therefore does not change when, the p.d. does., , b) Semiconductor diode, The typical I–V graph in Figure 38.7b shows that, current passes when the p.d. is applied in one, direction but is almost zero when it acts in the, opposite direction. A diode has a small resistance, when connected one way round but a very large, resistance when the p.d. is reversed. It conducts in, one direction only and is a non-ohmic conductor., , thermistor, Figure 38.8 Potential divider circuit for monitoring temperature, , e) Variation of resistance with light, intensity, The resistance of some semiconducting materials, decreases when the intensity of light falling on them, increases. This property is made use of in lightdependent resistors (LDRs) (see Chapter 41). The, I–V graph for an LDR is similar to that shown in, Figure 38.7d for a thermistor. Both thermistors and, LDRs are non-ohmic conductors., , ●● Resistors in series, The resistors in Figure 38.9 are in series. The same, current I flows through each and the total voltage, V across all three is the sum of the separate voltages, across them, i.e., V = V1 + V2 + V3, 169, , 9781444176421_Section_04.indd 169, , 20/06/14 7:44 AM
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38 resistance, , Dividing both sides by V,, , V, R1, , I, , R2, , R3, , I, , 1, 1, 1, 1, =, +, +, R R1 R2 R3, V1, , V2, , V3, , For the simpler case of two resistors in parallel, , Figure 38.9 Resistors in series, , But V1 = IR1, V2 = IR2 and V3 = IR3. Also, if R is the, combined resistance, V = IR, and so, , 1 = 1 + 1 = R2 + R1, R, R1 R2, R1R2 R1R2, , IR = IR1 + IR2 + IR3, , ∴, , Dividing both sides by I,, , 1 = R2 + R1, R, R1R2, , Inverting both sides,, , R = R1 + R2 + R3, , R =, , ●● Resistors in parallel, The resistors in Figure 38.10 are in parallel. The, voltage V between the ends of each is the same, and the total current I equals the sum of the currents, in the separate branches, i.e., , product of resistances, R1R2, =, R1 + R2, sum of ressistances, , The combined resistance of two resistors in parallel is, less than the value of either resistor alone. Check this, is true in the following Worked example. Lamps are, connected in parallel rather than in series in a lighting, circuit. Can you suggest why? (See p.180 for the, advantages.), , I = I1 + I2 + I3, I1, , I, , I2, , I3, , R1, , R2, , ●● Worked example, I, , R3, , A p.d. of 24 V from a battery is applied to the, network of resistors in Figure 38.11a., a What is the combined resistance of the 6 Ω and, 12 Ω resistors in parallel?, b What is the current in the 8 Ω resistor?, c What is the voltage across the parallel network?, d What is the current in the 6 Ω resistor?, , V, 24 V, , Figure 38.10 Resistors in parallel, , But I1 = V/R1, I2 = V/R2 and I3 = V/R3. Also, if R, is the combined resistance, I = V/R,, , 6Ω, 8Ω, , V = V + V + V, R, R1 R2 R3, , 12 Ω, , Figure 38.11a, , 170, , 9781444176421_Section_04.indd 170, , 20/06/14 7:44 AM
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resistivity, , a Let R1 = resistance of 6 Ω and 12 Ω in parallel. Then, , 1st, figure, , 2nd, number of, figure noughts, , 1 = 1+ 1 = 2 + 1 = 3, R1, 6 12 12 12 12, R1 = 12 = 4 Ω, 3, , ∴, , b Let R = total resistance of circuit = 4 + 8, that, is, R = 12 Ω. The equivalent circuit is shown in, Figure 38.11b, and if I is the current in it then,, since V = 24 V, , red, 2, , violet, 7, , Figure Colour, tolerance, (accuracy), , silver, 10%, orange, 000, , resistor value 27 000 ( 10%), 27 k ( 10%), , 0, , black, , 1, , brown, , 2, , red, , 3, , orange, , 4, , yellow, , 5, , green, , 6, , blue, , 7, , violet, , 8, , grey, , 9, , white, , Tolerance, 5%, , gold, , 10% silver, , I = V = 24 V = 2 A, R, 12 Ω, , 20% no band, Figure 38.12 Colour code for resistors, , ∴ current in 8 Ω resistor = 2 A, 24 V, , ●● Resistivity, I, , I, 4Ω, , 8Ω, , Experiments show that the resistance R of a wire of a, given material is, (i) directly proportional to its length l, i.e. R ∝ l,, (ii) inversely proportional to its cross-sectional area, A, i.e. R ∝ 1/A (doubling A halves R)., , Figure 38.11b, , c Let V1 = voltage across parallel network in Figure, 38.11a. Then, V1 = I × R1 = 2 A × 4 Ω = 8 V, d Let I1 = current in 6 Ω resistor, then since, V1 = 8 V, I1 =, , V1, 8V, 4, =, = A, 6Ω, 6Ω, 3, , ●● Resistor colour code, Resistors have colour coded bands as shown in, Figure 38.12. In the orientation shown the first two, bands on the left give digits 2 and 7; the third band, gives the number of noughts (3) and the fourth band, gives the resistor’s ‘tolerance’ (or accuracy, here ±10%)., So the resistor has a value of 27 000 Ω (±10%)., , Combining these two statements, we get, R∝ 1, A, , or R =, , ρl, A, , where ρ is a constant, called the resistivity of, the material. If we put l = 1 m and A = 1 m2,, then ρ = R., The resistivity of a material is numerically equal to the, resistance of a 1 m length of the material with cross-sectional, area 1 m2., , The unit of ρ is the ohm-metre (Ω m), as can be, seen by rearranging the equation to give ρ = AR/l, and inserting units for A, R and l. Knowing ρ for, a material, the resistance of any sample of it can, be calculated. The resistivities of metals increase at, higher temperatures; for most other materials they, decrease., , 171, , 9781444176421_Section_04.indd 171, , 20/06/14 7:44 AM
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38 resistance, , I, , ●● Worked example, Calculate the resistance of a copper wire 1.0 km long, and 0.50 mm diameter if the resistivity of copper is, 1.7 × 10–8 Ω m., , R1, , V1, , R2, , V2, , V, , Converting all units to metres, we get, length l = 1.0 km = 1000 m =, diameter d = 0.50 mm = 0.50 × 10–3 m, 103 m, , If r is the radius of the wire, the cross-sectional area, A = πr2 = π(d/2)2 = (π/4)d2, so, 2, A = π (0.50 × 10−3 ) m2 ≈ 0.20 × 10−6 m2, 4, , Then, R =, , (1.7 × 10−8 Ω m ) × (103 m ) = 85 Ω, ρl, =, 0.20 × 10−6 m2, A, , ●● Potential divider, In the circuit shown in Figure 38.13, two resistors R1, and R2 are in series with a supply of voltage V. The, current in the circuit is, I =, , supply voltage, V, =, total resistance (R1 + R2 ), , I, Figure 38.13 Potential divider circuit, , Returning to Figure 38.8 (p. 169), can you now, explain why the voltage across the resistor increases, when the resistance of the thermistor decreases?, , Questions, 1 What is the resistance of a lamp when a voltage of 12 V, across it causes a current of 4 A?, 2 Calculate the p.d. across a 10 Ω resistor carrying a, current of 2 A., 3 The p.d. across a 3 Ω resistor is 6 V. What is the current, flowing (in ampere)?, 1, A, B 1, C 2, D 6, E 8, 2, 4 The resistors R1, R2, R3 and R4 in Figure 38.14 are all equal, in value. What would you expect the voltmeters A, B and, C to read, assuming that the connecting wires in the circuit, have negligible resistance?, A, , B, , R1, , R2, , C, , So the voltage across R1 is, V1 = I × R1 =, , V × R1, R1, =V ×, (R1 + R2 ), (R1 + R2 ), , and the voltage across R2 is, V2 = I × R2 =, , R2, V × R2, =V ×, (R1 + R2 ), (R1 + R2 ), , Also the ratio of the voltages across the two, resistors is, V1, R, = 1, V2, R2, , R3, , R4, , 12 V, Figure 38.14, , 5 Calculate the effective resistance between A and B in, Figure 38.15., 4Ω, , A, , 4Ω, , B, , Figure 38.15, , 172, , 9781444176421_Section_04.indd 172, , 20/06/14 7:45 AM
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Potential divider, , Checklist, , 6 What is the effective resistance in Figure 38.16 between, a A and B,, b C and D?, , After studying this chapter you should be able to, •, •, •, •, , 6Ω, 3Ω, , 6Ω, , 6Ω, , A, , 6Ω, B, , C, , 3Ω, , D, , Figure 38.16, , 7 Figure 38.17 shows three resistors. Their combined, resistance in ohms is, 1, 2, A 15, D 71, E 6, B 14, C 1, 5, 3, 2, 7, 6Ω, , define resistance and state the factors on which it depends,, recall the unit of resistance,, solve simple problems using R = V/I,, describe experiments using the ammeter–voltmeter, method to measure resistance, and study the relationship, between current and p.d. for (a) metallic conductors,, (b) semiconductor diodes, (c) filament lamps, (d) thermistors,, (e) LDRs,, • plot I–V graphs from the results of such experiments and, draw appropriate conclusions from them,, • use the formulae for resistors in series,, • recall that the combined resistance of two resistors in, parallel is less than that of either resistor alone,, • calculate the effective resistance of two resistors in, parallel,, • relate the resistance of a wire to its length and diameter,, • calculate voltages in a potential divider circuit., , 6Ω, 2Ω, , Figure 38.17, , 8 a The graph in Figure 38.18 illustrates how the p.d. across, the ends of a conductor is related to the current in it., (i) What law may be deduced from the graph?, (ii) What is the resistance of the conductor?, b Draw diagrams to show how six 2 V lamps could be lit to, normal brightness when using a, (i) 2 V supply,, (ii) 6 V supply,, (iii) 12 V supply., , +, , p.d./V, , 6, , +, , 4, +, 2, +, 0, , 1, , 2, current/A, , 3, , Figure 38.18, , 9 When a 4 Ω resistor is connected across the terminals of a, 12 V battery, the number of coulombs passing through the, resistor per second is, A 0.3, B 3, C 4, D 12, E 48, , 173, , 9781444176421_Section_04.indd 173, , 20/06/14 7:45 AM
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39 Capacitors, l, l, , Capacitance, Types of capacitor, , l, l, , A capacitor stores electric charge and is useful in, many electronic circuits. In its simplest form it, consists of two parallel metal plates separated by an, insulator, called the dielectric (Figure 39.1a). Figure, 39.1b shows the circuit symbol for a capacitor., a, , dielectric, , Charging and discharging a capacitor, Effect of capacitors in d.c. and a.c. circuits, , ●● Types of capacitor, Practical capacitors, with values ranging from, about 0.01 µF to 100 000 µF, often consist of two, long strips of metal foil separated by long strips, of dielectric, rolled up like a ‘Swiss roll’, as in, Figure 39.2. The arrangement allows plates of large, area to be close together in a small volume. Plastics, (e.g. polyesters) are commonly used as the dielectric,, with films of metal being deposited on the plastic to, act as the plates (Figure 39.3)., , connections, to plates, , metal, foil, , dielectric, , connections to plates, Figure 39.2 Construction of a practical capacitor, , Figure 39.3 Polyester capacitor, , metal plates, , b, , Figure 39.1a A parallel-plate capacitor; b symbol for a capacitor, , The electrolytic type of capacitor shown in Figure, 39.4a has a very thin layer of aluminium oxide as, the dielectric between two strips of aluminium foil,, giving large capacitances. It is polarised, i.e. it has, positive and negative terminals (Figure 39.4b), and, these must be connected to the + and − terminals,, respectively, of the voltage supply., , ●● Capacitance, The more charge a capacitor can store, the greater is, its capacitance (C). The capacitance is large when the, plates have a large area and are close together. It is, measured in farads (F) but smaller units such as the, microfarad (µF) are more convenient., 1 µF = 1 millionth of a farad = 10−6 F, , a, , , , b, Figure 39.4a Electrolytic capacitor; b symbol showing polarity, , 174, , 9781444176421_Section_04.indd 174, , 20/06/14 7:46 AM
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Charging and discharging a capacitor, , ●● Charging and, discharging a capacitor, a) Charging, A capacitor can be charged by connecting a battery, across it. In Figure 39.5a, the + terminal of the, battery attracts electrons (since they have a negative, charge) from plate X and the − terminal of the, battery repels electrons to plate Y. A positive charge, builds up on plate X (since it loses electrons) and an, equal negative charge builds up on Y (since it gains, electrons)., During the charging, there is a brief flow of, electrons round the circuit from X to Y (but not, through the dielectric). A momentary current, would be detected by a sensitive ammeter. The, voltage builds up between X and Y and opposes, the battery voltage. Charging stops when these, two voltages are equal; the electron flow, i.e. the, charging current, is then zero. The variation of, current with time (for both charging or discharging, a capacitor) has a similar shape to the curve shown, in Figure 39.7b., During the charging process, electrical energy is, transferred from the battery to the capacitor, which, then stores the energy., metal, plate Y, , , b) Discharging, When a conductor is connected across a charged, capacitor, as in Figure 39.5b, there is a brief flow of, electrons from the negatively charged plate to the, positively charged one, i.e. from Y to X. The charge, stored by the capacitor falls to zero, as does the, voltage across it. The capacitor has transferred its, stored energy to the conductor. The ‘delay’ time taken, for a capacitor to fully charge or discharge through a, resistor is made use of in many electronic circuits., , c) Demonstration, The circuit in Figure 39.6 has a two-way switch, S. When S is in position 1 the capacitor C charges, up, and discharges when S is in position 2. The, larger the values of R and C the longer it takes, for the capacitor to charge or discharge; with the, values shown in Figure 39.6, the capacitor will, take 2 to 3 minutes to fully charge or discharge., The direction of the deflection of the centrezero milliammeter reverses for each process., The corresponding changes of capacitor charge, (measured by the voltage across it) with time are, shown by the graphs in Figures 39.7a and b. These, can be plotted directly if the voltmeter is replaced, by a datalogger and computer., , metal, plate X, , , centre-zero, milliammeter, , 1, , 6V, , , , 2, , A, , S, , C, 500 µF, , , , , V, , R, , dielectric, battery, , 100 kΩ, , electron flow (in wire), to charge capacitor, , Figure 39.6 Demonstration circuit for charging and discharging a, capacitor, , Y X, , , , , , , , , a, electron flow to discharge capacitor, Figure 39.5b Discharging a capacitor, , 0, , capacitor fully, charged to 6 V, , time, , voltage or charge, , voltage or charge, , Figure 39.5a Charging a capacitor, , b, , 0, , time, , Figure 39.7 Graphs: a charging; b discharging, , 175, , 9781444176421_Section_04.indd 175, , 20/06/14 7:46 AM
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39 caPacitors, , ●● Effect of capacitors in, d.c. and a.c. circuits, a) Direct current circuit, In Figure 39.8a the supply is d.c. but the lamp does, not light, that is, a capacitor blocks direct current., , b) Alternating current circuit, , Checklist, After studying this chapter you should be able to, • state what a capacitor does,, • state the unit of capacitance,, • describe in terms of electron motion how a capacitor can be, charged and discharged, and sketch graphs of the capacitor, voltage with time for charging and discharging through a, resistor,, • recall that a capacitor blocks d.c. but passes a.c. and, explain why., , In Figure 39.8b the supply is a.c. and the lamp, lights, suggesting that a capacitor passes alternating, current. In fact, no current actually passes through, the capacitor since its plates are separated by an, insulator. But as the a.c. reverses direction, the, capacitor charges and discharges, causing electrons, to flow to and fro rapidly in the wires joining the, plates. Thus, effectively, a.c. flows round the circuit,, lighting the lamp., 1000 µF, , , 2V, , a, , 1000 µF, , , 2.5 V, 0.3 A, , 2V, a.c., , 2.5 V, 0.3 A, , b, , Figure 39.8 A capacitor blocks direct current and allows a flow of, alternating current., , Questions, 1 a Describe the basic construction of a capacitor., b What does a capacitor do?, c State two ways of increasing the capacitance of a, capacitor., d Name a unit of capacitance., 2 a When a capacitor is being charged, is the value of the, charging current maximum or zero, (i) at the start, or, (ii) at the end of charging?, b When a capacitor is discharging, is the value of the, current in the circuit maximum or zero, (i) at the start, or, (ii) at the end of charging?, 3 How does a capacitor behave in a circuit with, a a d.c. supply,, b an a.c. supply?, , 176, , 9781444176421_Section_04.indd 176, , 20/06/14 7:46 AM
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40, ●, ●, ●, ●, , Electric power, , Power in electric circuits, Electric lighting, Electric heating, Joulemeter, , ●, ●, ●, ●, , House circuits, Paying for electricity, Dangers of electricity, Practical work: Measuring electric power., , ●● Power in electric, circuits, , A, , In many circuits it is important to know the, rate at which electrical energy is transferred into, other forms of energy. Earlier (Chapter 13) we, said that energy transfers were measured by, the work done and power was defined by the, equation, power =, , Figure 40.1, , work done energy transfer, =, time taken, time taken, , In symbols, P =, , E, t, , (1), , where if E is in joules (J) and t in seconds (s) then, P is in J/s or watts (W)., From the definition of p.d. (Chapter 37) we saw, that if E is the electrical energy transferred when, there is a steady current I (in amperes) for time t, (in seconds) in a device (e.g. a lamp) with a p.d., V (in volts) across it, as in Figure 40.1, then, E = ItV, , V, , (2), , Therefore to calculate the power P of an electrical, appliance we multiply the current I in it by the, p.d. V across it. For example if a lamp on a 240 V, supply has a current of 0.25 A in it, its power is, 240 V × 0.25 A = 60 W. The lamp is transferring, 60 J of electrical energy into heat and light each, second. Larger units of power are the kilowatt, (kW) and the megawatt (MW) where, 1 kW = 1000 W and 1 MW = 1 000 000 W, In units, watts = amperes × volts, It follows from (3) that since, volts =, , Substituting for E in (1) we get, P = E = ItV, t, t, or, P = IV, , (3), , watts, amperes, , (4), , the volt can be defined as a watt per ampere and, p.d. calculated from (4)., If all the energy is transferred to heat in a, resistor of resistance R, then V = IR and the rate of, production of heat is given by, P = V × I = IR × I = I 2R, That is, if the current is doubled, four times as, much heat is produced per second. Also, P = V 2/R., , 177, , 9781444176421_Section_04.indd 177, , 20/06/14 7:46 AM
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40 Electric power, , Practical work, Measuring electric power, a) Lamp, Connect the circuit of Figure 40.2. Note the ammeter and, voltmeter readings and work out the electric power supplied to, the lamp in watts., , greater is the proportion of electrical energy transferred, to light and for this reason it is made of tungsten, a, metal with a high melting point (3400 ºC)., Most lamps are gas-filled and contain nitrogen, and argon, not air. This reduces evaporation of the, tungsten which would otherwise condense on the, bulb and blacken it. The coil is coiled compactly so, that it is cooled less by convection currents in the gas., glass bulb, , 3V, , argon and, nitrogen, , filament, lead-in, wires, torch, lamp, , A, (0–1 A), , bayonet, cap, , V, (0–5 V), , connections to lamp, Figure 40.3 A filament lamp, , b) Fluorescent strips, , Figure 40.2, , b) Motor, Replace the lamp in Figure 40.2 by a small electric motor., Attach a known mass m (in kg) to the axle of the motor with a, length of thin string and find the time t (in s) required to raise, the mass through a known height h (in m) at a steady speed., Then the power output Po (in W) of the motor is given by, Po =, , work done in raising mass mgh, =, t, time taken, , If the ammeter and voltmeter readings I and V are noted while the, mass is being raised, the power input Pi (in W) can be found from, Pi = IV, The efficiency of the motor is given by, efficiency =, , Po, × 100%, Pi, , Also investigate the effect of a greater mass on: (i) the speed, (ii) the, power output and (iii) the efficiency of the motor at its rated p.d., , A filament lamp transfers only 10% of the electrical, energy supplied to light; the other 90% becomes heat., Fluorescent strip lamps (Figure 40.4a) are five times, as efficient and may last 3000 hours compared with, the 1000-hour life of filament lamps. They cost more, to install but running costs are less., When a fluorescent strip lamp is switched on, the, mercury vapour emits invisible ultraviolet radiation, which makes the powder on the inside of the tube, fluoresce (glow), i.e. visible light is emitted. Different, powders give different colours., , c) Compact fluorescent lamps, These energy-saving fluorescent lamps (Figure, 40.4b) are available to fit straight into normal light, sockets, either bayonet or screw-in. They last up to, eight times longer (typically 8000 hours) and use, about five times less energy than filament lamps for, the same light output. For example, a 20 W compact, fluorescent is equivalent to a 100 W filament lamp., electrodes, , ●● Electric lighting, a) Filament lamps, The filament is a small coil of tungsten wire (Figure, 40.3) which becomes white hot when there is a current, in it. The higher the temperature of the filament, the, , a, , mercury, vapour, , glass, tube, , fluorescent, powder, , b, , Figure 40.4 Fluorescent lamps, , 178, , 9781444176421_Section_04.indd 178, , 20/06/14 7:47 AM
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Electric heating, , ●● Electric heating, , only current in one (Figure 40.6b); on ‘low’, they are, in series (Figure 40.6c)., , a) Heating elements, , switch, , In domestic appliances such as electric fires, cookers,, kettles and irons the ‘elements’ (Figure 40.5) are, made from Nichrome wire. This is an alloy of nickel, and chromium which does not oxidise (and so, become brittle) when the current makes it red hot., The elements in radiant electric fires are at red, heat (about 900 ºC) and the radiation they emit is, directed into the room by polished reflectors. In, convector types the element is below red heat (about, 450 ºC) and is designed to warm air which is drawn, through the heater by natural or forced convection., In storage heaters the elements heat fire-clay bricks, during the night using ‘off-peak’ electricity. On the, following day these cool down, giving off the stored, heat to warm the room., element, , elements, , mains, , a High, , mains, , b Medium, , mains, c Low, Figure 40.6 Three-heat switch, , c) Fuses, , cooker hob, radiant fire, , iron, , A fuse protects a circuit. It is a short length of wire, of material with a low melting point, often ‘tinned, copper’, which melts and breaks the circuit when the, current in it exceeds a certain value. Two reasons, for excessive currents are ‘short circuits’ due to, worn insulation on connecting wires and overloaded, circuits. Without a fuse the wiring would become hot, in these cases and could cause a fire. A fuse should, ensure that the current-carrying capacity of the, wiring is not exceeded. In general the thicker a, cable is, the more current it can carry, but each size, has a limit., Two types of fuse are shown in Figure 40.7a., Always switch off before replacing a fuse,, and always replace with one of the same value as, recommended by the manufacturer of the appliance., , element, kettle, , fuse, wire, , Figure 40.5 Heating elements, , cartridge, fuse, , b) Three-heat switch, This is sometimes used to control heating appliances., It has three settings and uses two identical elements., On ‘high’, the elements are in parallel across the, supply voltage (Figure 40.6a); on ‘medium’, there is, , b, a, , insulating, holder, , Figure 40.7a Two types of fuse; b the circuit symbol for a fuse, 179, , 9781444176421_Section_04.indd 179, , 20/06/14 7:47 AM
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40 Electric power, , ●● Joulemeter, , (i) The p.d. across each lamp is fixed (at the, mains p.d.), so the lamp shines with the same, brightness irrespective of how many other lamps, are switched on., (ii) Each lamp can be turned on and off, independently; if one lamp fails, the others can, still be operated., , Instead of using an ammeter and a voltmeter to, measure the electrical energy transferred by an, appliance, a joulemeter can be used to measure, it directly in joules. The circuit connections are, shown in Figure 40.8. A household electricity meter, (Figure 40.12) is a joulemeter., , b) Switches and fuses, electrical, supply, , joulemeter, , input, , output, , These are always in the live wire. If they were in the, neutral, light switches and power sockets would be, ‘live’ when switches were ‘off’ or fuses ‘blown’. A, fatal shock could then be obtained by, for example,, touching the element of an electric fire when it was, switched off., , appliance, , Figure 40.8 Connections to a joulemeter, , ●● House circuits, , c) Staircase circuit, , Electricity usually comes to our homes by an, underground cable containing two wires, the live, (L) and the neutral (N). The neutral is earthed at, the local sub-station and so there is no p.d. between, it and earth. The supply is a.c. (Chapter 36) and the, live wire is alternately positive and negative. Study the, typical house circuits shown in Figure 40.9., , a) Circuits in parallel, Every circuit is connected in parallel with the supply, i.e., across the live and neutral, and receives the full mains, p.d. of 230 V (in the UK). The advantages of having, appliances connected in parallel, rather than in series, can, be seen by studying the lighting circuit in Figure 40.9., , supply, company’s, main, fuse, , supply, cable, , d) Ring main circuit, The live and neutral wires each run in two complete, rings round the house and the power sockets, each, rated at 13 A, are tapped off from them. Thinner, wires can be used since the current to each socket, flows by two paths, i.e. from both directions in the, ring. The ring has a 30 A fuse and if it has, say, ten, sockets, then all can be used so long as the total, current does not exceed 30 A, otherwise the wires, overheat. A house may have several ring circuits, each, serving a different area., , CONSUMER UNIT, meter, N, , N, , The light is controlled from two places by the two, two-way switches., , 5A, , L, , 15 A, , 30 A, N, , L, , main, switch, , immersion, heater, , N, , to, earth, , 30 A, , L, cooker, E, N, , L, , L, N, LIGHTING CIRCUIT, two-way, switches, , RING MAIN, CIRCUIT, , L, L, , N, , L, , L, , E, , E, L, , N, E, , Figure 40.9 Electric circuits in a house, 180, , 9781444176421_Section_04.indd 180, , 20/06/14 7:47 AM
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House circuits, , e) Fused plug, , Circuit breakers, , Only one type of plug is used in a UK ring, main circuit. It is wired as in Figure 40.10a., Note the colours of the wire coverings: L – brown,, N – blue, E – green and yellow. It has its own, cartridge fuse, 3 A (red) for appliances with powers, up to 720 W, or 13 A (brown) for those between, 720 W and 3 kW., E, cartridge fuse, , E, , 13A, , L, , N, N, a, , cord grip, , L, , b, Figure 40.11 Circuit breakers, , Figure 40.10 a Wiring of a plug; b socket, , Typical power ratings for various appliances are, shown in Table 40.1, p. 182. Calculation of a current, in a device allows the correct size of fuse to be, chosen., In some countries the fuse is placed in the, appliance rather than in the plug., , f) Safety in electrical circuits, Earthing, A ring main has a third wire which goes to the top, sockets on all power points (Figure 40.9) and is, earthed by being connected either to a metal water, pipe entering the house or to an earth connection on, the supply cable. This third wire is a safety precaution, to prevent electric shock should an appliance develop, a fault., The earth pin on a three-pin plug is connected, to the metal case of the appliance which is, thus joined to earth by a path of almost zero, resistance. If then, for example, the element of an, electric fire breaks or sags and touches the case, a, large current flows to earth and ‘blows’ the fuse., Otherwise the case would become ‘live’ and anyone, touching it would receive a shock which might, be fatal, especially if they were ‘earthed’ by, say,, standing in a damp environment, such as on a wet, concrete floor., , Circuit breakers (Figure 40.11) are now used, instead of fuses in consumer units. They contain, an electromagnet (Chapter 45) which, when the, current exceeds the rated value of the circuit breaker,, becomes strong enough to separate a pair of contacts, and breaks the circuit. They operate much faster than, fuses and have the advantage that they can be reset by, pressing a button., The residual current circuit breaker (RCCB),, also called a residual current device (RCD), is, an adapted circuit breaker which is used when the, resistance of the earth path between the consumer, and the substation is not small enough for a faultcurrent to blow the fuse or trip the circuit breaker., It works by detecting any difference between the, currents in the live and neutral wires; when these, become unequal due to an earth fault (i.e. some of, the current returns to the substation via the case of, the appliance and earth) it breaks the circuit before, there is any danger. They have high sensitivity and a, quick response., An RCD should be plugged into a socket supplying, power to a portable appliance such as an electric, lawnmower or hedge trimmer. In these cases the risk, of electrocution is greater because the user is generally, making a good earth connection through the feet., , Double insulation, Appliances such as vacuum cleaners, hairdryers, and food mixers are usually double insulated., , 181, , 9781444176421_Section_04.indd 181, , 20/06/14 7:47 AM
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40 electric Power, , Connection to the supply is by a two-core, insulated cable, with no earth wire, and the appliance, is enclosed in an insulating plastic case. Any metal, attachments that the user might touch are fitted, into this case so that they do not make a direct, connection with the internal electrical parts, such as a, motor. There is then no risk of a shock should a fault, develop., , ●● Paying for electricity, Electricity supply companies charge for the electrical, energy they supply. A joule is a very small amount, of energy and a larger unit, the kilowatt-hour, (kWh), is used., A kilowatt-hour is the electrical energy used by a 1 kW, appliance in 1 hour., , 1 kWh = 1000 J/s × 3600 s, = 3 600 000 J = 3.6 MJ, A 3 kW electric fire working for 2 hours uses 6 kWh of, electrical energy – usually called 6 ‘units’. Electricity, meters, which are joulemeters, are marked in kWh:, the latest have digital readouts like the one in, Figure 40.12. At present a ‘unit’ costs about 8p in, the UK., Typical powers of some appliances are given in, Table 40.1., Table 40.1 Power of some appliances, DVD player, , 20 W, , iron, , 1 kW, , laptop computer, , 50 W, , fire, , 1, 2, 3 kW, , light bulbs, , 60, 100 W, , kettle, , 2 kW, , television, , 100 W, , immersion, heater, , 3 kW, , fridge, , 150 W, , cooker, , 6.4 kW, , Note that the current required by a 6.4 kW cooker is, given by, I = P = 6400 W = 28 A, V, 230 V, This is too large a current to draw from the ring main, and so a separate circuit must be used., , Figure 40.12 Electricity meter with digital display, , ●● Dangers of electricity, a) Electric shock, Electric shock occurs if current flows from an, electric circuit through a person’s body to earth., This can happen if there is damaged insulation or, faulty wiring. The typical resistance of dry skin is, about 10 000 Ω, so if a person touches a wire carrying, electricity at 240 V, an estimate of the current, flowing through them to earth would be I = V/R =, 240/10 000 = 0.024 A = 24 mA. For wet skin, the, resistance is lowered to about 1000 Ω (since water is, a good conductor of electricity) so the current would, increase to around 240 mA., It is the size of the current (not the voltage) and, the length of time for which it acts which determine, the strength of an electric shock. The path the, current takes influences the effect of the shock; some, parts of the body are more vulnerable than others. A, current of 100 mA through the heart is likely to be, fatal., Damp conditions increase the severity of an, electric shock because water lowers the resistance, , 182, , 9781444176421_Section_04.indd 182, , 20/06/14 7:47 AM
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dangers of electricity, , of the path to earth; wearing shoes with insulating, rubber soles or standing on a dry insulating floor, increases the resistance between a person and, earth and will reduce the severity of an electric, shock., To avoid the risk of getting an electric shock:, ●, , ●, , ●, , ●, , Switch off the electrical supply to an appliance, before starting repairs., Use plugs that have an earth pin and a cord grip; a, rubber or plastic case is preferred., Do not allow appliances or cables to come, into contact with water. For example holding a, hairdryer with wet hands in a bathroom can be, dangerous. Keep electrical appliances well away, from baths and swimming pools!, Do not have long cables trailing across a room,, under a carpet that is walked over regularly or in, other situations where the insulation can become, damaged. Take particular care when using electrical, cutting devices (such as hedge cutters) not to cut, the supply cable., , In case of an electric shock, take the following action:, 1 Switch off the supply if the shocked person is still, touching the equipment., 2 Send for qualified medical assistance., 3 If breathing or heartbeat has stopped,, commence CPR (cardiopulmonary resuscitation), by applying chest compressions at the rate of, about 100 a minute until there are signs of chest, movement or medical assistance arrives., , b) Fire risks, If flammable material is placed too close to a hot, appliance such as an electric heater, it may catch fire., Similarly if the electrical wiring in the walls of a house, becomes overheated, a fire may start. Wires become, hot when they carry electrical currents – the larger, the current carried, the hotter a particular wire will, become, since the rate of production of heat equals, I2R (see p. 177)., To reduce the risk of fire through overheated, cables, the maximum current in a circuit should be, limited by taking these precautions:, ●, ●, ●, ●, , Damaged insulation or faulty wiring which leads to, a large current flowing to earth through flammable, material can also start a fire., The factors leading to fire or electric shock can be, summarised as follows:, damaged insulation, , → electric shock and fire risk, , overheated cables, , → fire risk, , damp conditions, , → increased severity of electric shocks, , Questions, 1 How much electrical energy in joules does a 100 watt lamp, transfer in, a 1 second,, b 5 seconds,, c 1 minute?, 2 a What is the power of a lamp rated at 12 V 2 A?, b How many joules of electrical energy are transferred per, second by a 6 V 0.5 A lamp?, 3 The largest number of 100 W lamps connected in parallel, which can safely be run from a 230 V supply with a 5 A fuse is, A 2, B 5, C 11, D 12, E 0, 4 What is the maximum power in kilowatts of the appliance(s), that can be connected safely to a 13 A 230 V mains socket?, 5 The circuits of Figures 40.13a and b show ‘short circuits’, between the live (L) and neutral (N) wires. In both, the, fuse has blown but whereas circuit a is now safe, b is still, dangerous even though the lamp is out which suggests the, circuit is safe. Explain., L, , fuse, , L, , N, a, , N, short circuit, , b, , fuse, short circuit, , Figure 40.13, , 6 What steps should be taken before replacing a blown fuse, in a plug?, 7 What size fuse (3 A or 13 A) should be used in a plug, connected to, a a 150 W television,, b a 900 W iron,, c a 2 kW kettle,, if the supply is 230 V?, ▲, ▲, , Use plugs that have the correct fuse., Do not attach too many appliances to a circuit., Don’t overload circuits by using too many adapters., Appliances such as heaters use large amounts of, power (and hence current), so do not connect them, , to a lighting circuit designed for low current use., (Thick wires have a lower resistance than thin wires so, are used in circuits expected to carry high currents.), , 183, , 9781444176421_Section_04.indd 183, , 20/06/14 7:47 AM
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40 electric Power, , 8 What is the cost of heating a tank of water with a 3000 W, immersion heater for 80 minutes if electricity costs 10p, per kWh?, 9 a Below is a list of wattages of various appliances., State which is most likely to be the correct one for each, of the appliances named., 60 W, 250 W, 850 W, 2 kW, 3.5 kW, (i) kettle, (ii) table lamp, (iii) iron, b What will be the current in a 920 W appliance if the, supply voltage is 230 V?, , Checklist, After studying this chapter you should be able to, • recall the relations E = ItV and P = IV and use them to solve, simple problems on energy transfers,, • describe experiments to measure electric power,, • describe electric lamps, heating elements and fuses,, • recall that a joulemeter measures electrical energy,, • describe with the aid of diagrams a house wiring system and, explain the functions and positions of switches, fuses, circuit, breakers and earth,, • state the advantages of connecting lamps in parallel in a, lighting circuit,, • wire a mains plug and recall the international insulation, colour code,, • perform calculations of the cost of electrical energy in joules, and kilowatt-hours,, • recall the hazards of damaged insulation, damp conditions, and overheating of cables and the associated risks., , 184, , 9781444176421_Section_04.indd 184, , 20/06/14 7:47 AM
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41 Electronic systems, l, l, l, l, , Electronic systems, Input transducers, Output transducers, Semiconductor diode, , The use of electronics in our homes, factories, offices,, schools, banks, shops and hospitals is growing all the, time. The development of semiconductor devices, such as transistors and integrated circuits (‘chips’), has given us, among other things, automatic banking, machines, laptop computers, programmable control, devices, robots, computer games, digital cameras, (Figure 41.1a) and heart pacemakers (Figure 41.1b)., , l, l, l, , Transistor, Transistor as a switch, Practical work: Transistor switching circuits: lightoperated, temperature-operated., , ●● Electronic systems, input, sensor, , processor, , output, transducer, , Figure 41.2 Electronic system, , Any electronic system can be considered to consist, of the three parts shown in the block diagram of, Figure 41.2, i.e., (i) an input sensor or input transducer,, (ii) a processor and, (iii) an output transducer., , Figure 41.1a Digital camera, , Figure 41.1b Heart pacemaker, , A ‘transducer’ is a device for converting a, non-electrical input into an electrical signal or, vice versa., The input sensor detects changes in the, environment and converts them from their, present form of energy into electrical energy., Input sensors or transducers include LDRs (lightdependent resistors), thermistors, microphones, and switches that respond, for instance, to pressure, changes., The processor decides on what action to take, on the electrical signal it receives from the input, sensor. It may involve an operation such as counting,, amplifying, timing or storing., The output transducer converts the electrical, energy supplied by the processor into another form., Output transducers include lamps, LEDs (lightemitting diodes), loudspeakers, motors, heaters,, relays and cathode ray tubes., In a radio, the input sensor is the aerial that, sends an electrical signal to processors in the, radio. These processors, among other things,, amplify the signal so that it can enable the output, transducer, in this case a loudspeaker, to produce, sound., , 185, , 9781444176421_Section_04.indd 185, , 20/06/14 7:48 AM
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41 Electronic systems, , ●● Input transducers, a) Light-dependent resistor (LDR), The action of an LDR depends on the fact that the, resistance of the semiconductor cadmium sulfide, decreases as the intensity of the light falling on it, increases., An LDR and a circuit showing its action are shown, in Figures 41.3a and b. Note the circuit symbol for an, LDR, sometimes seen without a circle. When light from, a lamp falls on the ‘window’ of the LDR, its resistance, decreases and the increased current lights the lamp., LDRs are used in photographic exposure meters, and in series with a resistor to provide an input signal for a, transistor (Figure 41.16, p. 190) or other switching circuit., , LDR, , the p.d. across resistor R and the relay drops below the, operating p.d. of the relay so that the relay contacts, open again; power to the bell is cut and it stops ringing., , b) Thermistor, A thermistor contains semiconducting metallic, oxides whose resistance decreases markedly when the, temperature rises. The temperature may rise either, because the thermistor is directly heated or because a, current is in it., Figure 41.4a shows one type of thermistor., Figure 41.4b shows the symbol for a thermistor in, a circuit to demonstrate how the thermistor works., When the thermistor is heated with a match, the, lamp lights., A thermistor in series with a meter marked in ºC can, measure temperatures (Chapter 38). Used in series with, a resistor it can provide an input signal to a transistor, (Figure 41.18, p. 191) or other switching circuit., thermistor, , •, relay, , R, 6V, d.c., , +, 6V, d.c, , 6V, d.c., , •, thermistor, , a, , b, , a, , •, , relay, , R, +, 6V, d.c., , bell, , 6 V 0.06 A, , •, , bell, LDR, c, Figure 41.3 a LDR; b LDR demonstration circuit; c light-operated intruder, alarm, , Figure 41.3c shows how an LDR can be used to, switch a ‘relay’ (Chapter 45.) The LDR forms part of a, potential divider across the 6 V supply. When light falls, on the LDR, the resistance of the LDR, and hence the, voltage across it, decreases. There is a corresponding, increase in the voltage across resistor R and the relay;, when the voltage across the relay coil reaches a high, enough p.d. (its operating p.d.) it acts as a switch and, the normally open contacts close, allowing current to, flow to the bell, which rings. If the light is removed,, , b, , 6 V 0.06 A, , c, , Figure 41.4 a Thermistor; b thermistor demonstration circuit;, c high-temperature alarm, , Figure 41.4c shows how a thermistor can be used, to switch a relay. The thermistor forms part of a, potential divider across the d.c. source. When the, temperature rises, the resistance of the thermistor, falls, and so does the p.d. across it. The voltage, across resistor R and the relay increases. When the, voltage across the relay reaches its operating p.d. the, normally open contacts close, so that the circuit to, the bell is completed and it rings. If a variable resistor, is used in the circuit, the temperature at which the, alarm sounds can be varied., , ●● Output transducers, a) Relays, A switching circuit cannot supply much power to, an appliance so a relay is often included; this allows, the small current provided by the switching circuit, , 186, , 9781444176421_Section_04.indd 186, , 20/06/14 7:48 AM
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Semiconductor diode, , to control the larger current needed to operate a, buzzer as in a temperature-operated switch (Figure, 41.18, p. 191) or other device. Relays controlled by, a switching circuit can also be used to switch on the, mains supply for electrical appliances in the home. In, Figure 41.5 if the output of the switching circuit is, ‘high’ (5 V), a small current flows to the relay which, closes the mains switch; the relay also isolates the low, voltage circuit from the high voltage mains supply., 0 or 5 V, output of, switching, circuit, , calculators, video recorders and measuring instruments, have seven-segment red or green numerical displays, (Figure 41.7a). Each segment is an LED and,, depending on which have a voltage across them, the, display lights up the numbers 0 to 9, as in Figure 41.7b., LEDs are small, reliable and have a long life;, their operating speed is high and their current, requirements are very low., Diode lasers operate in a similar way to LEDs but, emit coherent laser light; they are used in optical fibre, communications as transmitters., , relay, LED, segment, , ~ mains, supply, , 0V, , a, , appliance, , b, , Figure 41.7 LED numerical display, , ●● Semiconductor diode, , Figure 41.5 Use of a relay to switch mains supply, , b) Light-emitting diode (LED), An LED, shown in Figure 41.6a, is a diode made, from the semiconductor gallium arsenide phosphide., When forward biased (with the cathode C connected, to the negative terminal of the voltage supply, as, shown in Figure 41.6b), the current in it makes it, emit red, yellow or green light. No light is emitted, on reverse bias (when the anode A is connected to, the negative terminal of the voltage supply). If the, reverse bias voltage exceeds 5 V, it may cause damage., In use an LED must have a suitable resistor R in, series with it (e.g. 300 Ω on a 5 V supply) to limit, the current (typically 10 mA). Figure 41.6b shows, the symbol for an LED (again the use of the circle is, optional) in a demonstration circuit., , ‘flat’, , cathode C, , A, C, , LED, , anode A, , a, , cathode, , circle, optional, , anode, , , , Figure 41.8 A diode and its symbol, , R, coloured translucent, plastic case, , 5V, , , A diode is a device that lets current pass in one, direction only. One is shown in Figure 41.8 with, its symbol. (You will also come across the symbol, without its outer circle.) The wire nearest the, band is the cathode and the one at the other, end is the anode., , b, , Figure 41.6 LED and demonstration circuit, , ▲, ▲, , LEDs are used as indicator lamps on computers,, radios and other electronic equipment. Many clocks,, , The typical I–V graph is shown in Figure 38.7b, (p. 169). The diode conducts when the anode, goes to the + terminal of the voltage supply and, the cathode to the – terminal (Figure 41.9a). It, is then forward-biased; its resistance is small and, conventional current passes in the direction of the, arrow on its symbol. If the connections are the, other way round, it does not conduct; its resistance, is large and it is reverse-biased (Figure 41.9b)., , 187, , 9781444176421_Section_04.indd 187, , 20/06/14 7:48 AM
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41 Electronic systems, , The lamp in the circuit shows when the diode, is conducting, as the lamp lights up. It also acts, as a resistor to limit the current when the diode is, forward-biased. Otherwise the diode might overheat, and be damaged., , 1N4001, , 1.5V, 1.25V, 0.25A, , current passes, a, , ●● Transistor, Transistors are the small semiconductor devices, which have revolutionised electronics. They are, made both as separate components in their cases,, like those in Figure 41.11a, and also as parts, of integrated circuits (ICs) in which millions, may be ‘etched’ on a ‘chip’ of silicon (Figure, 41.11b)., Transistors have three connections called the, base (B), the collector (C) and the emitter (E). In, the transistor symbol shown in Figure 41.12, the, arrow indicates the direction in which conventional, current flows in it when C and B are connected to, a battery + terminal, and E to a battery – terminal., Again, the outer circle of the symbol is not always, included., , , , no current, b, Figure 41.9 Demonstrating the action of a diode, , Figure 41.11a Transistor components, , A diode is a non-ohmic conductor. It is useful as, a rectifier for changing alternating current (a.c.), to direct current (d.c.). Figure 41.10 shows the, rectified output voltage obtained from a diode when, it is connected to an a.c. supply., V, , rectified output voltage from diode, , t, , Figure 41.11b Integrated circuits which may each contain millions of, transistors, a.c. input voltage, Figure 41.10 Rectification by a diode, 188, , 9781444176421_Section_04.indd 188, , 20/06/14 7:48 AM
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Transistor as a switch, , ●● Transistor as a switch, , collector C, , a) Advantages, , base B, , emitter E, Figure 41.12 Symbol for a transistor, , There are two current paths through a, transistor. One is the base–emitter path and, the other is the collector–emitter (via base) path., The transistor’s usefulness arises from the fact that, it can link circuits connected to each path so that, the current in one controls that in the other, just, like a relay., Its action can be shown using the circuit of, Figure 41.13. When S is open, the base current, IB is zero and neither L1 nor L2 lights up, showing, that the collector current IC is also zero even, though the battery is correctly connected across the, C–E path., When S is closed, B is connected through R to, the battery + terminal and L2 lights up but not L1., This shows there is now collector current (which, is in L2) and that it is much greater than the base, current (which is in L1 but is too small to light it)., Therefore, in a transistor the base current, IB switches on and controls the much greater, collector current IC., Resistor R has to be in the circuit to limit the, base current which would otherwise create so large, a collector current as to destroy the transistor by, overheating., S, , b) ‘On’ and ‘off’ states, A transistor is considered to be ‘off’ when the, collector current is zero or very small. It is ‘on’, when the collector current is much larger. The, resistance of the collector–emitter path is large, when the transistor is ‘off’ (as it is for an ordinary, mechanical switch) and small (ideally it should be, zero) when it is ‘on’., To switch a transistor ‘on’ requires the, base voltage (and therefore the base current) to, exceed a certain minimum value (about +0.6 V, base voltage)., , c) Basic switching circuits, Two are shown in Figures 41.14a, b. The ‘on’, state is shown by the lamp in the collector circuit, becoming fully lit., base, current, , R, 100 kΩ, , 6V, 0.06 A, , , 6V, , RB, 1 kΩ, , a, , base, current, IB, , L1, , Transistors have many advantages over other, electrically operated switches such as relays. They, are small, cheap, reliable, have no moving parts,, their life is almost indefinite (in well-designed, circuits) and they can switch on and off millions of, times a second., , collector, current, IC, , L2, , B, R, , C, , , , R, 10kΩ, , 6V, , RB, E, , IC IB, , 1 kΩ, , R 10 kΩ, L1 L2 6 V 60 mA, transistor 2N3053, Figure 41.13 Demonstration circuit, , 6V, 0.06A, , b, , , 6V, , base –, emitter, p.d., , S, 10kΩ, , ▲, ▲, , Figure 41.14 Transistor switching circuits, , 189, , 9781444176421_Section_04.indd 189, , 20/06/14 7:49 AM
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41 Electronic systems, , Rheostat control is used in the circuit in, Figure 41.14a. ‘Switch-on’ occurs by reducing R, until the base current is large enough to make the, collector current light the lamp. (The base resistor RB, is essential in case R is made zero and results in +6 V, from the battery being applied directly to the base., This would produce very large base and collector, currents and destroy the transistor by overheating.), Potential divider control is used in the circuit, in Figure 41.14b. Here ‘switch-on’ is obtained by, adjusting the variable resistance S until the p.d., across S (which is the base–emitter p.d. and depends, on the value of S compared with that of R) exceeds, +0.6 V or so., Note In a potential divider the p.d.s across the, resistors are in the ratio of their resistances (see, Chapter 38). For example, in the circuit shown in, Figure 41.14b, the p.d. across R and S in series is, 6 V. If R = 10 kΩ and S is set to 5 kΩ, then the p.d., across R, that is VR, is 4 V and the p.d. across S, that, is VS, is 2 V. So VR /VS = 4 V/2 V = 2/1., In general, VR, R, S, =, and VS = (VR + VS ) ×, VS, S, (R + S ), Also see question 2 on p. 191., , BC109, tag, C, , E, B, , (1 mm bore), , PVC sleeving, , (2 mm bore), , metal ‘tag’, , SWG 22 tinned copper connecting wire, held in contact by sleeving, Figure 41.15b Lengthening transistor leads and making connections, to tags, , In many control circuits, devices such as LDRs and thermistors are, used in potential divider arrangements to detect small changes of, light intensity and temperature, respectively. These changes then, enable a transistor to act as a simple processor by controlling the, current to an output transducer, such as a lamp or a buzzer., , a) Light-operated switch, In the circuit of Figure 41.16 the LDR is part of a potential divider., The lamp comes on when the LDR is shielded: more of the battery, p.d. acts across the increased resistance of the LDR (i.e. more than, 0.6 V) and less across R. In the dark, the base–emitter p.d. increases, as does the base current and so also the collector current., , Practical work, Transistor switching circuits, , 6V, 0.06 A, , R, 10 kΩ, , The components can be mounted on a circuit board, for, example an ‘S-DeC’ as in Figure 41.15a. The diagrams in Figure, 41.15b show how to lengthen transistor leads and also how to, make connections (without soldering) to parts that have ‘tags’,, for example, variable resistors., , , RB, BC 109, 1 kΩ, LDR, , 6V, , base–, emitter, p.d., , Figure 41.16 Light-operated switch, , If the LDR and R are interchanged the lamp goes off in the dark, and the circuit could act as a light-operated intruder alarm., If a variable resistor is used for R, the light level at which, switching occurs can be changed., , b) Temperature-operated switch, Figure 41.15a Partly built transistor switching circuit, , In the low-temperature-operated switch of Figure 41.17, a, thermistor and resistor form a potential divider across the, , 190, , 9781444176421_Section_04.indd 190, , 20/06/14 7:49 AM
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transistor as a switch, , 6 V supply. When the temperature of the thermistor falls, its, resistance increases and so does the p.d. across it, i.e. the, base-emitter p.d. rises. When it reaches 0.6 V, the transistor, switches on and the collector current becomes large enough, to operate the lamp. The circuit could act as a frost-warning, device., , Questions, 1 Figure 41.19a shows a lamp, a semiconductor diode and a, cell connected in series. The lamp lights when the diode is, connected in this direction. Say what happens to each of, the lamps in b, c and d. Give reasons for your answers., , D, , D1, , L2, , L1, , D2, , L, 6V, 0.06 A, , R, 100 kΩ, , , RB, BC 109, 1 kΩ, thermistor, , a, , b, , 6V, E1, , base–, emitter, p.d., , D, , E2, , 1 kΩ, R, 100 kΩ, , relay:, contacts, normally, open, , L2, , E2, , D2, , L2, , 2 What are the readings V1 and V2 on the high-resistance, voltmeters in the potential divider circuit of Figure 41.20 if, a R1 = R2 = 10 kΩ,, b R1 = 10 kΩ, R2 = 50 kΩ,, c R1 = 20 kΩ, R2 = 10 kΩ?, R1, , R2, , V1, , V2, 6V, , Figure 41.20, , 3 A simple moisture-warning circuit is shown in Figure 41.21,, in which the moisture detector consists of two closely, spaced copper rods., , relay, relay, contacts, , , 6V, , BC 109, electric, buzzer, , moisture, detector, Figure 41.21, , ▲, ▲, , base–, emitter, p.d., , L1, , d, , D, , RB, , D1, , Figure 41.19, , If the thermistor and resistor are interchanged, the circuit can, be used as a high-temperature alarm (Figure 41.18)., When the temperature of the thermistor rises, its resistance, decreases and a larger share of the 6 V supply acts across R,, i.e. the base–emitter p.d. increases. When it exceeds 0.6 V or, so the transistor switches on and collector current (too small to, ring the buzzer directly) goes through the relay coil. The relay, contacts close, enabling the buzzer to obtain, directly from the, 6 V supply, the larger current it needs., The diode D protects the transistor from damage: when the, collector current falls to zero at switch off this induces a large, p.d. in the relay coil (see Chapter 43). The diode is forwardbiased by the induced p.d. (which tries to maintain the, current in the relay coil) and, because of its low forward, resistance (e.g. 1 Ω), offers an easy path for the current, produced. To the 6 V supply the diode is reverse-biased, and its high resistance does not short-circuit the relay coil, when the transistor is on., If R is variable the temperature at which switching occurs can, be changed., , thermistor, , E1, , c, , Figure 41.17 Low-temperature-operated switch, , D (e.g., 1N4001), , L1, , Figure 41.18 High-temperature-operated switch, , 191, , 9781444176421_Section_04.indd 191, , 20/06/14 7:49 AM
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41 electronic systeMs, , a Describe how the circuit works when the detector gets, wet., b Warning lamps are often placed in the collector circuit of, a transistor. Why is a relay used here?, c What is the function of D?, , Checklist, After studying this chapter you should be able to, • recall the functions of the input sensor, processor and, output transducer in an electronic system and give some, examples,, • describe the action of an LDR and a thermistor and show an, understanding of their use as input transducers,, • understand the use of a relay in a switching circuit,, • explain what is meant by a diode being forward biased, and reverse biased and recall that a diode can produce, rectified a.c., , 192, , 9781444176421_Section_04.indd 192, , 20/06/14 7:49 AM
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42 Digital electronics, l, l, l, , Analogue and digital electronics, Logic gates, Logic gate control systems, , l, l, , ●● Analogue and digital, electronics, There are two main types of electronic circuits,, devices or systems – analogue and digital., In analogue circuits, voltages (and currents) can, have any value within a certain range over which they, can be varied smoothly and continuously, as shown in, Figure 42.1a. They include amplifier-type circuits., , voltage, , +, , 0, time, , a, , voltage, , 0, , ‘high’, , ‘low’, time, , –, b, , ●● Logic gates, , a) NOT gate or inverter, This is the simplest gate, with one input and, one output. It produces a ‘high’ output if the, input is ‘low’, i.e. the output is then NOT high,, and vice versa. Whatever the input, the gate, inverts it. The symbol and truth table are given in, Figure 42.2., ▲, ▲, , Figure 42.1, , In digital circuits, voltages have only one of two, values, either ‘high’ (e.g. 5 V) or ‘low’ (e.g. near, 0 V), as shown in Figure 42.1b. They include, switching-type circuits such as those we have, considered in Chapter 41., A variable resistor is an analogue device, which, in a circuit with a lamp, allows the lamp, to have a wide range of light levels. A switch is a, digital device which allows a lamp to be either ‘on’, or ‘off’., Analogue meters display their readings by the, deflection of a pointer over a continuous scale (see, Figure 47.4a, p. 220). Digital meters display their, readings as digits, i.e. numbers, which change by, one digit at a time (see Figure 47.4b, p. 220)., , Logic gates are switching circuits used in, computers and other electronic systems. They, ‘open’ and give a ‘high’ output voltage, i.e. a, signal (e.g. 5 V), depending on the combination, of voltages at their inputs, of which there is usually, more than one., There are five basic types, all made from, transistors in integrated circuit form. The behaviour, of each is described by a truth table showing what, the output is for all possible inputs. ‘High’ (e.g., 5 V) and ‘low’ (e.g. near 0 V) outputs and inputs, are represented by 1 and 0, respectively, and are, referred to as logic levels 1 and 0., , –, , +, , Problems to solve, Electronics and society, , 193, , 9781444176421_Section_04.indd 193, , 20/06/14 7:49 AM
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42 Digital electronics, , Input, , Output, , 0, , 1, , 1, , 0, , NOT gate, input, , output, , c) Testing logic gates, , Figure 42.2 NOT gate symbol and truth table, , b) OR, NOR, AND, NAND gates, All these have two or more inputs and one output., The truth tables and symbols for 2-input gates are, shown in Figure 42.3. Try to remember the following., OR: output is 1 if input A OR input B OR, both are 1, NOR: output is 1 if neither input A NOR, input B is 1, AND: output is 1 if input A AND input B, are 1, NAND: output is 1 if input A AND input B are, NOT both 1, OR gate, A, B, , NOR gate, F, , A, B, , B, , F, , 0, , 0, , 0, , 0, , 0, , 1, , 0, , 1, , 1, , 0, , 1, , 0, , 1, , 0, , 1, , 1, , 0, , 0, , 1, , 1, , 1, , 1, , 1, , 0, , B, , F, , NAND gate, F, , +5 V, , +5 V, , power, supply, , A, , 0V, , 0V, , LED, indicator, module, , logic gate, module, , B, , F, , IC, , 0V, , F, , A, , A, B, , The truth tables for the various gates can be, conveniently checked by having the logic gate, integrated circuit (IC) mounted on a small board, with sockets for the power supply, inputs A and, B and output F (Figure 42.4). A ‘high’ input, (i.e. logic level 1) is obtained by connecting the, input socket to the positive of the power supply,, e.g. +5 V and a ‘low’ input (i.e. logic level 0) by, connecting to 0 V., , Figure 42.4 Modules for testing logic gates, , A, , AND gate, , Note from the truth tables that the outputs of the, NOR and NAND gates are the inverted outputs, of the OR and AND gates, respectively. They have, a small circle at the output end of their symbols to, show this inversion., , A, B, , F, , The output can be detected using an indicator, module containing an LED that lights up for a 1, and stays off for a 0., , ●● Logic gate control, systems, Logic gates can be used as processors in electronic, control systems. Many of these can be demonstrated, by connecting together commercial modules like, those in Figure 42.8b, , a) Security system, , A, , B, , F, , A, , B, , F, , 0, , 0, , 0, , 0, , 0, , 1, , 0, , 1, , 0, , 0, , 1, , 1, , 1, , 0, , 0, , 1, , 0, , 1, , 1, , 1, , 1, , 1, , 1, , 0, , A simple system that might be used by a jeweller, to protect an expensive clock is shown in the, block diagram for Figure 42.5. The clock sits on, a push switch which sends a 1 to the NOT gate,, unless the clock is lifted when a 0 is sent. In that, case the output from the NOT gate is a 1 which, rings the bell., , Figure 42.3 Symbols and truth tables for 2-input gates, , 194, , 9781444176421_Section_04.indd 194, , 20/06/14 7:49 AM
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Logic gate control systems, , CLOCK, ON = 1, , push, switch, , CLOCK, OFF = 0, , input, sensor, , NOT, gate, , 0, bell, , 1, , 0, , temperature, sensor, , NOT, gate, 1, , output, transducer, , processor, , 1, , AND, gate, , heater, control, , 1, light, sensor, , Figure 42.5 Simple alarm system, , b) S afety system for a machine, operator, , 1, , AND, gate, switch, B, , processor, , Figure 42.7 Heater control system, , A safety system could prevent a machine, (e.g. an electric motor) from being switched, on before another switch had been operated,, for example, by a protective safety guard being, in the correct position. In Figure 42.6, when, switches A and B are on, they supply a 1 to each, input of the AND gate which can then start the, motor., switch, A, , 1, , d) Street lights, A system is required that allows the street lights, either to be turned on manually by a switch at any, time, or automatically by a light sensor when it is, dark. The arrangement in Figure 42.8a achieves this, since the OR gate gives a 1 output when either or, both of its inputs are 1., The system can be demonstrated using the, module shown in Figure 42.8b., , 1, motor, , 1 or 0, , switch, , OR, gate, , 1, , 1, , street, lights, , Figure 42.6 Safety system for controlling a motor, , c) Heater control system, The heater control has to switch on the heating, system when it is, , light, sensor, , 0, , NOT, gate, , 1, , Figure 42.8a Control system with manual override, , (i) cold, i.e. the temperature is below a certain, value and the output from the temperature, sensor is 0, and, (ii) daylight, i.e. the light sensor output is 1., With these outputs from the sensors applied to, the processor in Figure 42.7, the AND gate has, two 1 inputs. The output from the AND gate, is then 1 and will turn on the heater control., Any other combination of sensor outputs, produces a 0 output from the AND gate, as you, can check., , Figure 42.8b Module for demonstrating street lights, , ▲, ▲, 195, , 9781444176421_Section_04.indd 195, , 20/06/14 7:49 AM
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42 Digital electronics, , ●● Problems to solve, Design and draw block diagrams for logic control, systems to indicate how the following jobs could be, done. If possible build them using modules., 1 Allow a doorbell to work only during the day., , (v) Speed of operation can be millions of times, greater than for other alternatives (e.g., mechanical devices)., (vi) Transducers of many different types are, available for transferring information in and out, of an electronic system., , 2 Give warning when the temperature of a domestic, hot water system is too high or when a switch is, pressed to test the alarm., , To sum up, electronic systems tend to be cheaper,, smaller, more reliable, less wasteful, much faster and, can respond to a wider range of signals than other, systems., , 3 Switch on a bathroom heater when it is cold and, light., , b) Some areas of impact, , 4 Sound an alarm when it is cold or a switch is, pressed., 5 Give warning if the temperature of a room falls, during the day and also allow a test switch to, check the alarm works., 6 Give warning of frosty conditions at night, to a gardener who is sometimes very tired, after a hard day and may want to switch off, the alarm., , ●● Electronics and society, Electronics is having an ever-increasing impact on, all our lives. Work and leisure are changing as a, result of the social, economic and environmental, influences of new technology., , At home devices such as washing machines, burglar, alarms, telephones, cookers and sewing machines, contain electronic components. Central heating, systems and garage doors may have automatic, electronic control. For home entertainment, DVD, players, interactive digital televisions or computers, with internet connections and electronic games are, finding their way into more and more homes., Medical services have benefited greatly in recent, years from the use of electronic instruments and, appliances. Electrocardiograph (ECG) recorders for, monitoring the heart, ultrasonic scanners for checks, during pregnancy, gamma ray scanners for detecting, tumours, hearing aids, heart pacemakers, artificial, kidneys, limbs and hands with electronic control, (Figure 42.9), and ‘keyhole’ surgery are some, examples., , a) Reasons for the impact, Why is electronics having such a great impact? Some, of the reasons are listed below., (i) Mass production of large quantities of, semiconductor devices (e.g. ICs) allows them to, be made very cheaply., (ii) Miniaturisation of components means that, even complex systems can be compact., (iii) Reliability of electronic components is a, feature of well-designed circuits. There are no, moving parts to wear out and systems can be, robust., (iv) Energy consumption and use of natural, resources is often much less than for their, non-electronic counterparts. For example, the, transistor uses less power than a relay., , Figure 42.9 Electronically controlled artificial hands, , In industry microprocessor-controlled equipment, is taking over. Robots are widely used for car, assembly work, and to do dull, routine, dirty jobs, such as welding and paint spraying. In many cases, production lines and even whole factories, such, , 196, , 9781444176421_Section_04.indd 196, , 20/06/14 7:50 AM
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Electronics and society, , as sugar refineries and oil refineries, are almost, entirely automated. Computer-aided design (CAD), of products is increasing (Figure 42.10), even in, the clothing industry. Three-dimensional printers, programmed by CAD files can now produce solid, objects in a variety of materials for use as prototypes, or components in industries ranging from aerospace, to entertainment., In offices, banks and shops computers are, used for word processing, data control and, communications via email: text, numbers and, pictures are transmitted by electronic means, often, by high-speed digital links. Cash dispensers and other, automated services at banks are a great convenience, for their customers. Bar codes (like the one on the, back cover of this book) on packaged products are, used by shops for stock control in conjunction with, a bar code reader (which uses a laser) and a data, recorder connected to a computer. A similar system, is operated by libraries to record the issue and return, of books. Libraries provide electronic databases and, internet facilities for research., , and here the electronic scoreboard is likely to be, in evidence. For the golf enthusiast, electronic, machines claim to analyse ‘swings’ and reduce, handicaps. For others, leisure means listening to, music, whose production, recording and listening, facilities have been transformed by the digital, revolution. Electronically synthesised music has, become the norm for popular recordings. The, lighting and sound effects in stage shows are, programmed by computer. For the cinemagoer,, special effects in film production have been vastly, improved by computer-generated animated images, (Figure 42.11). The availability of home computers, and games consoles in recent years has enabled a, huge market in computer games and home-learning, resources to develop., , Figure 42.11 Computer animation brings the tiger into the scene, , c) Consequences of the impact, , Figure 42.10 Computer-aided design of clothing, , ▲, ▲, , Communications have been transformed. Satellites, enable events on one side of the world to be seen, and heard on the other side, as they happen. Digital, telephone and communication links, smart phones,, tablets, social media and cloud computing are the, order of the day., Leisure activities have been affected by electronic, developments. For some people, leisure means, participating in or attending sporting activities, , Most of the social and economic consequences of, electronics are beneficial but a few cause problems., An improved quality of life has resulted from, the greater convenience and reliability of electronic, systems, with increased life expectancy and leisure, time, and fewer dull, repetitive jobs., Better communication has made the world a, smaller place. The speed with which news can be, reported to our homes by radio, television and the, internet enables the public to be better informed., Databases have been developed. These are, memories which can store huge amounts of, information for rapid transmission from one place, to another. For example, the police can obtain in, seconds, by radio, details of a car they are following., Databases raise questions, however, about invasion, of privacy and security., 197, , 9781444176421_Section_04.indd 197, , 20/06/14 7:50 AM
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42 digital electronics, , Employment is affected by the demand for new, equipment – new industry and jobs are created to, make and maintain it – but when electronic systems, replace mechanical ones, redundancy and/or, retraining needs arise. Conditions of employment, and long-term job prospects can also be affected for, many people, especially certain manual and clerical, workers. One industrial robot may replace four, factory workers., The public attitude to the electronics revolution is, not always positive. Modern electronics is a ‘hidden’, technology with parts that are enclosed in a tiny, package (or ‘black box’) and do not move. It is, also a ‘throwaway’ technology in which the whole, lot is discarded and replaced – by an expert – if a, part fails, and rapid advances in design technology, cause equipment to quickly become obsolete. For, these reasons it may be regarded as mysterious and, unfriendly – people feel they do not understand, what makes it tick., , • explain and use the terms analogue and digital,, , d) The future, , • state that logic gates are switching circuits containing, transistors and other components,, , The only certain prediction about the future is that, new technologies will be developed and these, like, present ones, will continue to have a considerable, influence on our lives., Today the development of ‘intelligent’ computers, is being pursued with great vigour, and voice, recognition techniques are already in use. Optical, systems, which are more efficient than electronic, ones, are being increasingly developed for data, transmission, storage and processing of information., , 2 What do the symbols A to E represent in Figure 42.12?, , A, , B, , D, , C, , E, , Figure 42.12, , 3 Design and draw the block diagrams for logic control, systems to:, a wake you at the crack of dawn and which you can also, switch off,, b protect the contents of a drawer which you can still, open without setting off the alarm., , Checklist, After studying this chapter you should be able to, , • describe the action of NOT, OR, NOR, AND and NAND, logic gates and recall their truth tables,, • design and draw block diagrams of logic control systems, for given requirements., , Questions, 1 The combined truth tables for four logic gates A, B, C, D, are given below. State what kind of gate each one is., Inputs, , Outputs, A, , B, , C, , D, , 0, , 0, , 0, , 0, , 1, , 1, , 0, , 1, , 0, , 1, , 1, , 0, , 1, , 0, , 0, , 1, , 1, , 0, , 1, , 1, , 1, , 1, , 0, , 0, , 198, , 9781444176421_Section_04.indd 198, , 20/06/14 7:50 AM
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43, ●, ●, ●, ●, , Generators, , Electromagnetic induction, Faraday’s law, Lenz’s law, Simple a.c. generator (alternator), , ●, ●, ●, , The effect of producing electricity from magnetism, was discovered in 1831 by Faraday and is called, electromagnetic induction. It led to the, construction of generators for producing electrical, energy in power stations., , ●● Electromagnetic, induction, , Simple d.c. generator (dynamo), Practical generators, Applications of electromagnetic induction, , b) Bar magnet and coil, The magnet is pushed into the coil, one pole first, (Figure 43.2), then held still inside it. It is then, withdrawn. The meter shows that current is induced, in the coil in one direction as the magnet is moved in, and in the opposite direction as it is moved out. There, is no deflection when the magnet is at rest. The, results are the same if the coil is moved instead of the, magnet, i.e. only relative motion is needed., , Two ways of investigating the effect follow., , a) Straight wire and U-shaped, magnet, First the wire is held at rest between the poles, of the magnet. It is then moved in each of the, six directions shown in Figure 43.1 and the, meter observed. Only when it is moving upwards, (direction 1) or downwards (direction 2) is there, a deflection on the meter, indicating an induced, current in the wire. The deflection is in opposite, directions in these two cases and only lasts while the, wire is in motion., , 3, , wire, , coil (600 turns), bar magnet, , Figure 43.2 A current is induced in the coil when the magnet is moved, in or out., , ●● Faraday’s law, , magnet, , N, , sensitive, centre-zero, meter, , 1, 5, , 6, , 4, 2, , S, , To ‘explain’ electromagnetic induction Faraday, suggested that a voltage is induced in a conductor, whenever it ‘cuts’ magnetic field lines, i.e. moves, across them, but not when it moves along them or, is at rest. If the conductor forms part of a complete, circuit, an induced current is also produced., Faraday found, and it can be shown with apparatus, like that in Figure 43.2, that the induced p.d. or, voltage increases with increases of, (i) the speed of motion of the magnet or coil,, (ii) the number of turns on the coil,, (iii) the strength of the magnet., , sensitive, centre-zero meter, Figure 43.1 A current is induced in the wire when it is moved up or, down between the magnet poles., , These facts led him to state a law:, The size of the induced p.d. is directly proportional to the rate, at which the conductor cuts magnetic field lines., 199, , 9781444176421_Section_04.indd 199, , 20/06/14 7:50 AM
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43 generators, , ●● Lenz’s law, , Motion, Field, , The direction of the induced current can be found, by a law stated by the Russian scientist, Lenz., The direction of the induced current is such as to oppose the, change causing it., , In Figure 43.3a the magnet approaches the coil,, north pole first. According to Lenz’s law the, induced current should flow in a direction that, makes the coil behave like a magnet with its top a, north pole. The downward motion of the magnet, will then be opposed since like poles repel., When the magnet is withdrawn, the top of the, coil should become a south pole (Figure 43.3b), and attract the north pole of the magnet, so, hindering its removal. The induced current is thus, in the opposite direction to that when the magnet, approaches., , N, , N, , N, , S, 0, , a, , induced, Current, , seCond, finger, , Figure 43.4 Fleming’s right-hand (dynamo) rule, , ●● Simple a.c. generator, (alternator), The simplest alternating current (a.c.) generator, consists of a rectangular coil between the poles of a, C-shaped magnet (Figure 43.5a). The ends of the, coil are joined to two slip rings on the axle and, against which carbon brushes press., When the coil is rotated it cuts the field lines and a, voltage is induced in it. Figure 43.5b shows how the, voltage varies over one complete rotation., As the coil moves through the vertical position, with ab uppermost, ab and cd are moving along, the lines (bc and da do so always) and no cutting, occurs. The induced voltage is zero., coil, , 0, , rotation, , b, , b, , N, , Figure 43.3 The induced current opposes the motion of the magnet., , Lenz’s law is an example of the principle of, conservation of energy. If the currents caused, opposite poles from those that they do make,, electrical energy would be created from nothing., As it is, mechanical energy is provided, by whoever, moves the magnet, to overcome the forces that arise., For a straight wire moving at right angles to a, magnetic field a more useful form of Lenz’s law is, Fleming’s right-hand rule (the ‘dynamo rule’), (Figure 43.4)., , a, , d, , alternating voltage, , slip rings, (rotate, with coil), , brushes (fixed), 1 cycle, , , voltage, , c, , S, , a, , 0, , ¹⁄₄, , ¹⁄₂, , 1, , ³⁄₄, , no. of, rotations, , , a, , Hold the thumb and first two fingers of the right hand at, right angles to each other with the First finger pointing in, the direction of the Field and the thuMb in the direction of, Motion of the wire, then the seCond finger points in the, direction of the induced Current., , thuMb, , First, finger, , d, d, , coil, vertical, b, , d, , a, , a, a, , a, , d, , field lines, d, , coil horizontal, , Figure 43.5 A simple a.c. generator and its output, 200, , 9781444176421_Section_04.indd 200, , 20/06/14 7:50 AM
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Practical generators, , coil, , rotation, , b, , N, , , , brush, , c, , S, , a, , d, , , brush, commutator, , a, , , voltage, , During the first quarter rotation the p.d. increases, to a maximum when the coil is horizontal., Sides ab and dc are then cutting the lines at the, greatest rate., In the second quarter rotation the p.d. decreases, again and is zero when the coil is vertical with dc, uppermost. After this, the direction of the p.d., reverses because, during the next half rotation,, the motion of ab is directed upwards and dc, downwards., An alternating voltage is generated which acts, first in one direction and then the other; it causes, alternating current (a.c.) to flow in a circuit, connected to the brushes. The frequency of an, a.c. is the number of complete cycles it makes each, second and is measured in hertz (Hz), i.e. 1 cycle, per second = 1 Hz. If the coil rotates twice per, second, the a.c. has frequency 2 Hz. The mains, supply is a.c. of frequency 50 Hz., , 0, , ¹⁄₄, , ¹⁄₂, , 1, , ³⁄₄, , no. of, rotations, , , a, d, , ●● Simple d.c. generator, (dynamo), An a.c. generator becomes a direct current (d.c.), one if the slip rings are replaced by a commutator, (like that in a d.c. motor, see p. 216), as shown in, Figure 43.6a., The brushes are arranged so that as the coil goes, through the vertical, changeover of contact occurs, from one half of the split ring of the commutator, to the other. But it is when the coil goes through, the vertical position that the voltage induced in the, coil reverses, so one brush is always positive and the, other negative., The voltage at the brushes is shown in Figure, 43.6b; although varying in value, it never changes, direction and would produce a direct current (d.c.), in an external circuit., In construction the simple d.c. dynamo is, the same as the simple d.c. motor and one can, be used as the other. When an electric motor is, working it also acts as a dynamo and creates a, voltage which opposes the applied voltage. The, current in the coil is therefore much less once the, motor is running., , d, , coil, vertical, , a, , d, , a, a, , d, , a, , field lines, d, , coil horizontal, b, Figure 43.6 A simple d.c. generator and its output, , ●● Practical generators, In actual generators several coils are wound in, evenly spaced slots in a soft iron cylinder and, electromagnets usually replace permanent magnets., , a) Power stations, In power station alternators the electromagnets, rotate (the rotor, Figure 43.7a) while the coils and, their iron core are at rest (the stator, Figure 43.7b)., The large p.d.s and currents (e.g. 25 kV at several, thousand amps) induced in the stator are led away, through stationary cables, otherwise they would, quickly destroy the slip rings by sparking. Instead, the relatively small d.c. required by the rotor is fed, via the slip rings from a small dynamo (the exciter), which is driven by the same turbine as the rotor., ▲, ▲, 201, , 9781444176421_Section_04.indd 201, , 20/06/14 7:50 AM
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43 Generators, , c) Bicycles, The rotor of a bicycle generator is a permanent, magnet and the voltage is induced in the coil, which, is at rest (Figure 43.9)., driving wheel, , soft iron, , output, terminal, , axle, , a Rotor (electromagnets), , metal, case, coil, cylindrical, magnet, (rotor), Figure 43.9 Bicycle generator, , b Stator (induction coils), Figure 43.7 The rotor and stator of a power station alternator, , In a thermal power station (Chapter 15), the, turbine is rotated by high-pressure steam obtained, by heating water in a coal- or oil-fired boiler or, in a nuclear reactor (or by hot gas in a gas-fired, power station). A block diagram of a thermal power, station is shown in Figure 43.8. The energy transfer, diagram was given in Figure 15.7, p. 63., stator, , a.c. output, , steam, , boiler, , turbine, , rotor, , exciter, , water, stator, , a.c. output, , Figure 43.8 Block diagram of a thermal power station, , b) Cars, Most cars are now fitted with alternators because, they give a greater output than dynamos at low, engine speeds., , ●● Applications of, electromagnetic, induction, a) Moving-coil microphone, The moving-coil loudspeaker shown in, Figure 46.7 (p. 218) can be operated in reverse, mode as a microphone. When sound is incident, on the paper cone it vibrates, causing the attached, coil to move in and out between the poles of the, magnet. A varying electric current, representative, of the sound, is then induced in the coil by, electromagnetic induction., , b) Magnetic recording, Magnetic tapes or disks are used to record, information in sound systems and computers., In the recording head shown in Figure 43.10, the, tape becomes magnetised when it passes over the, gap in the pole piece of the electromagnet and, retains a magnetic record of the electrical signal, applied to the coil from a microphone or computer., In playback mode, the varying magnetisation on, the moving tape or disk induces a corresponding, electrical signal in the coil as a result of, electromagnetic induction., , 202, , 9781444176421_Section_04.indd 202, , 20/06/14 7:50 AM
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applications of electromagnetic induction, , Checklist, signal, to be, recorded, , winding of, electromagnet, , S, , N, SS, , SN, , N, , N, N, S S very, , N, , After studying this chapter you should be able to, • describe experiments to show electromagnetic induction,, • recall Faraday’s explanation of electromagnetic induction,, • predict the direction of the induced current using Lenz’s, law or Fleming’s right-hand rule,, • draw a diagram of a simple a.c. generator and sketch a, graph of its output., , small, gap, , coated, plastic, tape, , Figure 43.10 Magnetic recording or playback head, , Questions, 1 A simple generator is shown in Figure 43.11., a What are A and B called and what is their purpose?, b What changes can be made to increase the p.d. generated?, , N, , axis of, rotation, , A, S, B, Figure 43.11, , 2 Describe the deflections observed on the sensitive, centrezero galvanometer G (Figure 43.12) when the copper rod, XY is connected to its terminals and is made to vibrate up, and down (as shown by the arrows), between the poles of, a U-shaped magnet, at right angles to the magnetic field., Explain what is happening., Y, , G, , N, S, X, , Figure 43.12, , 203, , 9781444176421_Section_04.indd 203, , 20/06/14 7:50 AM
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44 Transformers, l, l, l, , Mutual induction, Transformer equation, Energy losses in a transformer, , l, l, l, , ●● Mutual induction, , Transmission of electrical power, Applications of eddy currents, Practical work: Mutual induction with a.c., , Practical work, , When the current in a coil is switched on, or off or changed, a voltage is induced in a, neighbouring coil. The effect, called mutual, induction, is an example of electromagnetic, induction and can be shown with the arrangement, of Figure 44.1. Coil A is the primary and coil B, the secondary., Switching on the current in the primary sets, up a magnetic field and as its field lines ‘grow’, outwards from the primary they ‘cut’ the, secondary. A p.d. is induced in the secondary until, the current in the primary reaches its steady value., When the current is switched off in the primary,, the magnetic field dies away and we can imagine the, field lines cutting the secondary as they collapse,, again inducing a p.d. in it. Changing the primary, current by quickly altering the rheostat has the, same effect., The induced p.d. is increased by having a soft, iron rod in the coils or, better still, by using coils, wound on a complete iron ring. More field lines, then cut the secondary due to the magnetisation, of the iron., , Mutual induction with a.c., An alternating current is changing all the time and if it flows in a, primary coil, an alternating voltage and current are induced in a, secondary coil., Connect the circuit of Figure 44.2. The 1 V high current, power unit supplies a.c. to the primary and the lamp detects the, secondary current., Find the effect on the brightness of the lamp of, (i) pulling the C-cores apart slightly,, (ii) increasing the secondary turns to 15,, (iii) decreasing the secondary turns to 5., high current, power unit, , iron C-cores, , lamp (2.5 V 0.3 A), , 1 V a . c., , spare, wire, , to 6 V d.c., primary, (10 turns), , secondary, (10 turns), , Figure 44.2, rheostat, , sensitive, centre-zero, meter, coil A, coil B, (600 turns) (600 turns), tapping key, , Figure 44.1 A changing current in a primary coil (A) induces a current in, a secondary coil (B)., , ●● Transformer equation, A transformer transforms (changes) an alternating, voltage from one value to another of greater or, smaller value. It has a primary coil and a secondary, coil wound on a complete soft iron core, either one, on top of the other (Figure 44.3a) or on separate, limbs of the core (Figure 44.3b)., , 204, , 9781444176421_Section_04.indd 204, , 20/06/14 7:50 AM
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energy losses in a transformer, , Soft iron, a, , ●● Energy losses in a, transformer, , b, , Primary, , Secondary, , Secondary, , Primary, , Figure 44.3 Primary and secondary coils of a transformer, , An alternating voltage applied to the primary, induces an alternating voltage in the secondary., The value of the secondary voltage can be shown,, for a transformer in which all the field lines cut the, secondary, to be given by, secondary voltage secondary turns, =, primary turns, primary voltage, , A step-up transformer has more turns on, the secondary than the primary and Vs is, greater than Vp (Figure 44.4a). For example,, if the secondary has twice as many turns as, the primary, Vs is about twice Vp. In a stepdown transformer there are fewer turns on the, secondary than the primary and Vs is less than Vp, (Figure 44.4b)., , a, , Vp × Ip = Vs × Is, , where Ip and Is are the primary and secondary, currents, respectively., Vp, Is, =, Ip, Vs, , So, for the ideal transformer, if the p.d. is doubled, the current is halved. In practice, it is more than, halved, because of small energy losses in the, transformer arising from the following three causes., , Vs, N, = s, Vp, Np, , Vs, , power in primary = power in secondary, , ∴, , In symbols, , Vp, , If the p.d. is stepped up in a transformer, the current, is stepped down in proportion. This must be so if, we assume that all the electrical energy given to the, primary appears in the secondary, i.e. that energy is, conserved and the transformer is 100% efficient or, ‘ideal’ (many approach this efficiency). Then, , Vp, , a) Resistance of windings, The windings of copper wire have some resistance, and heat is produced by the current in them. Large, transformers like those in Figure 44.5 have to be, oil-cooled to prevent overheating., , Vs, , b, , Figure 44.4 Symbols for a transformer: a step-up (Vs > Vp); b step-down, (Vp > Vs), , ▲, ▲, , Figure 44.5 Step-up transformers at a power station, , 205, , 9781444176421_Section_04.indd 205, , 20/06/14 7:50 AM
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44 Transformers, , b) Eddy currents, The iron core is in the changing magnetic field of, the primary and currents, called eddy currents, are, induced in it which cause heating. These are reduced, by using a laminated core made of sheets, insulated, from one another to have a high resistance., , c) Leakage of field lines, , b Secondary turns, Ns = 100, From a,, Ns, = 1, 23, Np, , c Efficiency = 100%, , V p × I p = Vs × I s, ∴ Ip =, , Vs × I s, 10 V × 2 A = 2 A = 0.09 A, Vp =, 230 V 23, , Note In this ideal transformer the current is stepped, up in the same ratio as the voltage is stepped down., , ●● Worked example, A transformer steps down the mains supply, from 230 V to 10 V to operate an answering machine., a What is the turns ratio of the transformer windings?, b How many turns are on the primary if the, secondary has 100 turns?, c What is the current in the primary if the, transformer is 100% efficient and the current in the, answering machine is 2 A?, a Primary voltage, Vp = 230 V, Secondary voltage, Vs = 10 V, Ns, V, = s = 10 V = 1, N p Vp, 230 V 23, 275 kV, , = 2300 turns, , ∴ power in primary = power in secondary, , All the field lines produced by the primary may not, cut the secondary, especially if the core has an air, gap or is badly designed., , Turns ratio =, , Np = 23 × Ns = 23 × 100, , ∴, , ●● Transmission of, electrical power, a) Grid system, The National Grid is a network of cables throughout, Britain, mostly supported on pylons, that connects over, 100 power stations to consumers. In the largest modern, stations, electricity is generated at 25 000 V (25 kilovolts, = 25 kV) and stepped up at once in a transformer to, 275 or 400 kV to be sent over long distances on the, Supergrid. Later, the p.d. is reduced by substation, transformers for distribution to local users (Figure 44.6)., , or 400 kV, , 132 kV, , 25 kV, power station, , transformer, , Supergrid, , transformer, , grid, , towns, farms, , villages, , 415 V, , or 230 V, , transformer, , light, industry, , 11 kV, , transformer, , heavy, industry, , 33 kV, , transformer, , Figure 44.6 The National Grid transmission system in Britain, 206, , 9781444176421_Section_04.indd 206, , 20/06/14 7:51 AM
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applications of eddy currents, , The efficiency with which transformers step, alternating p.d.s up and down accounts for the use, of a.c. rather than d.c. in power transmission. High, voltages are used in the transmission of electric power, to reduce the amount of energy ‘lost’ as heat., Power cables have resistance, and so electrical, energy is transferred to heat during the, transmission of electricity from the power station, to the user. The power ‘lost’ as heat in cables of, resistance R is I 2R, so I should be kept low to, reduce energy loss. Since power = IV, if 400 000 W, of electrical power has to be sent through cables,, it might be done, for example, either as 1 A at, 400 000 V or as 1000 A at 400 V. Less energy will, be transferred to heat if the power is transmitted, at the lower current and higher voltage, i.e. 1 A at, 400 000 V. High p.d.s require good insulation but are, readily produced by a.c. generators., , pointer, , scale, , 60, , N, 80, , b) Use of high alternating p.d.s, , 40, , 20, , At the National Control Centre, engineers direct, the flow and re-route it when breakdown occurs., This makes the supply more reliable and cuts costs, by enabling smaller, less efficient stations to be shut, down at off-peak periods., , S, , aluminium, disc, cable to, gearbox, , spring magnet, Figure 44.7 Car speedometer, , b) Metal detector, The metal detector shown in Figure 44.8 consists of a, large primary coil (A), through which an a.c. current, is passed, and a smaller secondary coil (B). When the, detector is swept over a buried metal object (such, as a nail, coin or pipe) the fluctuating magnetic field, lines associated with the alternating current in coil A, ‘cut’ the hidden metal and induce eddy currents in, it. The changing magnetic field lines associated with, these eddy currents cut the secondary coil B in turn, and induce a current which can be used to operate an, alarm. The coils are set at right angles to each other, so that their magnetic fields do not interact., a.c., , ●● Applications of eddy, currents, Eddy currents are the currents induced in a piece of, metal when it cuts magnetic field lines. They can be, quite large due to the low resistance of the metal., They have their uses as well as their disadvantages., , to alarm, secondary, coil (B), , primary, coil (A), , hidden metal object, , Figure 44.8 Metal detector, , a) Car speedometer, Questions, 1 Two coils of wire, A and B, are placed near one another, (Figure 44.9). Coil A is connected to a switch and battery., Coil B is connected to a centre-reading moving-coil, galvanometer, G., a If the switch connected to coil A were closed for a few, seconds and then opened, the galvanometer connected, to coil B would be affected. Explain and describe, step, by step, what would actually happen., b What changes would you expect if a bundle of soft iron, wires was placed through the centre of the coils? Give a, reason for your answer., ▲, ▲, , The action depends on the eddy currents induced, in a thick aluminium disc (Figure 44.7), when a, permanent magnet, near it but not touching it, is, rotated by a cable driven from the gearbox of the, car. The eddy currents in the disc make it rotate in, an attempt to reduce the relative motion between, it and the magnet (see Chapter 43). The extent to, which the disc can turn, however, is controlled by, a spring. The faster the magnet rotates the more, the disc turns before it is stopped by the spring. A, pointer fixed to the disc moves over a scale marked, in mph (or km/h) and gives the speed of the car., , 207, , 9781444176421_Section_04.indd 207, , 20/06/14 7:51 AM
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44 transforMers, , c What would happen if more turns of wire were wound, on the coil B?, A, , B, , Checklist, After studying this chapter you should be able to, • explain the principle of the transformer,, • recall the transformer equation Vs/Vp = Ns/Np and use it to, solve problems,, • recall that for an ideal transformer Vp × Ip = Vs × Is and use, the relation to solve problems,, • recall the causes of energy losses in practical transformers,, , G, Figure 44.9, , • explain why high voltage a.c. is used for transmitting, electrical power., , 2 The main function of a step-down transformer is to, A decrease current, B decrease voltage, C change a.c. to d.c., D change d.c. to a.c., E decrease the resistance of a circuit., 3 a Calculate the number of turns on the secondary of a, step-down transformer which would enable a 12 V lamp, to be used with a 230 V a.c. mains power, if there are, 460 turns on the primary., b What current will flow in the secondary when the, primary current is 0.10 A? Assume there are no energy, losses., 4 A transformer has 1000 turns on the primary coil., The voltage applied to the primary coil is 230 V a.c., How many turns are on the secondary coil if the output, voltage is 46 V a.c.?, A 20, B 200, C 2000, D 4000, E 8000, , 208, , 9781444176421_Section_04.indd 208, , 20/06/14 7:51 AM
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45, ●, ●, ●, ●, ●, , Electromagnets, , Oersted’s discovery, Field due to a straight wire, Field due to a circular coil, Field due to a solenoid, Magnetisation and demagnetisation, , ●, ●, ●, ●, ●, , ●● Oersted’s discovery, In 1819 Oersted accidentally discovered the, magnetic effect of an electric current. His, experiment can be repeated by holding a wire, over and parallel to a compass needle that is, pointing N and S (Figure 45.1). The needle moves, when the current is switched on. Reversing the, current causes the needle to move in the opposite, direction., Evidently around a wire carrying a current, there is a magnetic field. As with the field due, to a permanent magnet, we represent the field, due to a current by field lines or lines of force., Arrows on the lines show the direction of, the field, i.e. the direction in which a N pole, points., Different field patterns are given by differently, shaped conductors., , Electromagnets, Electric bell, Relay, reed switch and circuit breaker, Telephone, Practical work: Simple electromagnet, , ●● Field due to a straight, wire, If a straight vertical wire passes through the centre of, a piece of card held horizontally and there is a current, in the wire (Figure 45.2), iron filings sprinkled on, the card settle in concentric circles when the card is, gently tapped., , right-handed, screw shows field, direction, , plotting, compass, , field lines, shown by iron, filings, card, , current direction, straight, wire, compass needle, , S, N, , low-voltage high-current supply, , Figure 45.1 An electric current produces a magnetic effect., , movement, of needle, , current, direction, , Figure 45.2 Field due to a straight wire, , Plotting compasses placed on the card settle along, the field lines and show the direction of the field, at different points. When the current direction, is reversed, the compasses point in the opposite, direction showing that the direction of the field, reverses when the current reverses., If the current direction is known, the direction of the, field can be predicted by the right-hand screw rule:, If a right-handed screw moves forwards in the direction of the, current (conventional), the direction of rotation of the screw, gives the direction of the field., , 209, , 9781444176421_Section_04.indd 209, , 20/06/14 7:51 AM
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45 Electromagnets, , ●● Field due to a circular coil, The field pattern is shown in Figure 45.3. At the, centre of the coil the field lines are straight and at right, angles to the plane of the coil. The right-hand screw, rule again gives the direction of the field at any point., circular coil, , (i) View from A, , (ii) View from B, , Figure 45.4c End-on views, , Inside the solenoid in Figure 45.4a, the field lines are, closer together than they are outside the solenoid., This indicates that the magnetic field is stronger, inside a solenoid than outside it., The field inside a solenoid can be made very strong if, it has a large number of turns or a large current., Permanent magnets can be made by allowing molten, ferromagnetic metal to solidify in such fields., , field, line, current, direction, Figure 45.3 Field due to a circular coil, , ●● Field due to a solenoid, A solenoid is a long cylindrical coil. It produces a, field similar to that of a bar magnet; in Figure 45.4a,, end A behaves like a N pole and end B like a S pole., The polarity can be found as before by applying the, right-hand screw rule to a short length of one turn of, the solenoid. Alternatively the right-hand grip rule, can be used. This states that if the fingers of the right, hand grip the solenoid in the direction of the current, (conventional), the thumb points to the N pole (Figure, 45.4b). Figure 45.4c shows how to link the end-on view, of the current direction in the solenoid to the polarity., solenoid, , c, , ●● Magnetisation and, demagnetisation, A ferromagnetic material can be magnetised by, placing it inside a solenoid and gradually increasing, the current. This increases the magnetic field, strength in the solenoid (the density of the field lines, increases), and the material becomes magnetised., Reversing the direction of current flow reverses, the direction of the magnetic field and reverses the, polarity of the magnetisation. A magnet can be, demagnetised by placing it inside a solenoid through, which the current is repeatedly reversed and reduced., , field line, , Practical work, A, , B, , Simple electromagnet, An electromagnet is a coil of wire wound on a soft iron core. A 5 cm, iron nail and 3 m of PVC-covered copper wire (SWG 26) are needed., , a, , current direction, , Figure 45.4a Field due to a solenoid, , N, right, hand, , b, Figure 45.4b The right right-hand grip rule, , (a) Leave about 25 cm at one end of the wire (for connecting to, the circuit) and then wind about 50 cm as a single layer on, the nail. Keep the turns close together and always wind, in the same direction. Connect the circuit of Figure 45.5,, setting the rheostat at its maximum resistance., Find the number of paper clips the electromagnet can, support when the current is varied between 0.2 A and 2.0 A., Record the results in a table. How does the ‘strength’ of the, electromagnet depend on the current?, (b) Add another two layers of wire to the nail, winding in the, same direction as the first layer. Repeat the experiment. What, can you say about the ‘strength’ of an electromagnet and, the number of turns of wire?, , 210, , 9781444176421_Section_04.indd 210, , 20/06/14 7:51 AM
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Electric bell, , wooden, stand, , electromagnet, , In C-core (or horseshoe) electromagnets, condition (iii) is achieved (Figure 45.6). Note, that the coil on each limb of the core is wound in, opposite directions., As well as being used in cranes to lift iron objects,, scrap iron, etc. (Figure 45.7), electromagnets are an, essential part of many electrical devices., , paper clips, , A, (0–2 A), , (2–3 V), (0–15 Ω), , Figure 45.5, , (c) Place the electromagnet on the bench and under a sheet of, paper. Sprinkle iron filings on the paper, tap it gently and, observe the field pattern. How does it compare with that, given by a bar magnet?, (d) Use the right-hand screw (or grip) rule to predict which end, of the electromagnet is a N pole. Check with a plotting, compass., , ●● Electromagnets, The magnetism of an electromagnet is temporary, and can be switched on and off, unlike that of a, permanent magnet. It has a core of soft iron which, is magnetised only when there is current in the, surrounding coil., The strength of an electromagnet increases if, (i) the current in the coil increases,, (ii) the number of turns on the coil increases,, (iii) the poles are moved closer together., Figure 45.7 Electromagnet being used to lift scrap metal, coil, , soft iron core, , ●● Electric bell, , S, N, field, line, current, direction, Figure 45.6 C-core or horseshoe electromagnet, , When the circuit in Figure 45.8 is completed, by, someone pressing the bell push, current flows in the, coils of the electromagnet which becomes magnetised, and attracts the soft iron bar (the armature)., The hammer hits the gong but the circuit is now, broken at the point C of the contact screw., 211, , 9781444176421_Section_04.indd 211, , 20/06/14 7:51 AM
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45 Electromagnets, , L-shaped iron armature. This rocks on its pivot and, closes the contacts at C in the circuit connected to, DE. The relay is then ‘energised’ or ‘on’., , bell push, , insulator, , springy metal, , D, springy, metal, strip, , C, , pivot, , E, , iron armature, soft iron, armature, , A, B, coil, , soft iron core, , Figure 45.9 Relay, , C, contact screw, electromagnet, , hammer, gong, Figure 45.8 Electric bell, , The electromagnet loses its magnetism (becomes, demagnetised) and no longer attracts the armature., The springy metal strip is then able to pull the, armature back, remaking contact at C and so, completing the circuit again. This cycle is repeated, so long as the bell push is depressed, and continuous, ringing occurs., , ●● Relay, reed switch and, circuit breaker, a) Relay, A relay is a switch based on the principle of, an electromagnet. It is useful if we want one circuit, to control another, especially if the current and, power are larger in the second circuit (see question, 3, p. 214). Figure 45.9 shows a typical relay. When, a current is in the coil from the circuit connected to, AB, the soft iron core is magnetised and attracts the, , The current needed to operate a relay is called, the pull-on current and the drop-off current is, the smaller current in the coil when the relay just, stops working. If the coil resistance, R, of a relay is, 185 Ω and its operating p.d. V is 12 V, then the, pull-on current I = V/R = 12/185 = 0.065 A =, 65 mA. The symbols for relays with normally, open and normally closed contacts are given in, Figure 45.10., , a, , b, , Figure 45.10 Symbols for a relay: a open; b closed, , Some examples of the use of relays in circuits appear, in Chapter 41., , b) Reed switch, One such switch is shown in Figure 45.11a., When current flows in the coil, the magnetic field, produced magnetises the strips (called reeds) of, magnetic material. The ends become opposite poles, and one reed is attracted to the other, so completing, the circuit connected to AB. The reeds separate, when the current in the coil is switched off., This type of reed switch is sometimes called a, reed relay., , 212, , 9781444176421_Section_04.indd 212, , 20/06/14 7:51 AM
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Telephone, , to move backwards and forwards. This varies the, pressure on the carbon granules between the, movable carbon dome which is attached to, the diaphragm and the fixed carbon cup at the, back. When the pressure increases, the granules, are squeezed closer together and their electrical, resistance decreases. A decrease of pressure has the, opposite effect. The current passing through the, microphone varies in a similar way to the sound, wave variations., , A, , reeds, coil, glass, tube, B, a Reed switch, , b) Receiver, , door, N, , magnet in door, , S, , S, reed, switch, , magnet, N, alarm, bell, , b Burglar alarm activated by a reed switch, Figure 45.11, , Reed switches are also operated by permanent, magnets. Figure 45.11b shows the use of a normally, open reed switch as a burglar alarm. How does it work?, , c) Circuit breaker, A circuit breaker (p. 181) acts in a similar way to, a normally closed relay; when the current in the, electromagnet exceeds a critical value, the contact, points are separated and the circuit is broken. In the, design shown in Figure 40.11, when the iron bolt, is attracted far enough towards the electromagnet,, the plunger is released and the push switch opens,, breaking contact to the rest of the circuit., , The coils are wound in opposite directions on the, two S poles of a magnet (Figure 45.13). If the, current goes round one in a clockwise direction, it, goes round the other anticlockwise, so making one, S pole stronger and the other weaker. This causes, the iron armature to rock on its pivot towards the, stronger S pole. When the current reverses, the, armature rocks the other way due to the S pole, which was the stronger before becoming the weaker., These armature movements are passed on to the, diaphragm, making it vibrate and produce sound of, the same frequency as the alternating current in the, coil (received from the microphone)., seal, aluminium, alloy, diaphragm, , A telephone contains a microphone at the speaking, end and a receiver at the listening end., , a) Carbon microphone, , carbon granules, , movable, carbon, dome, , leads, Figure 45.12 Carbon microphone, , rocking, armature, , ●● Telephone, , fixed carbon cup, , aluminium, diaphragm, S, , N, , coil, , S, coil, magnet, , Figure 45.13 Telephone receiver, , When someone speaks into a carbon microphone, (Figure 45.12), sound waves cause the diaphragm, 213, , 9781444176421_Section_04.indd 213, , 20/06/14 7:51 AM
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45 electroMagnets, , Checklist, , Questions, 1 The vertical wire in Figure 45.14 is at right angles to the, card. In what direction will a plotting compass at A point, when, a there is no current in the wire,, b the current direction is upwards?, card, , After studying this chapter you should be able to, • describe and draw sketches of the magnetic fields round, current-carrying, straight and circular conductors and, solenoids,, • recall the right-hand screw and right-hand grip rules for, relating current direction and magnetic field direction,, • describe the effect on the magnetic field of changing the, magnitude and direction of the current in a solenoid,, , N, , • identify regions of different magnetic field strength, around a solenoid,, , A, wire, Figure 45.14, , 2 Figure 45.15 shows a solenoid wound on a core of soft, iron. Will the end A be a N pole or S pole when the current, is in the direction shown?, , • make a simple electromagnet,, • describe uses of electromagnets,, • explain the action of an electric bell, a relay, a reed switch, and a circuit breaker., , A, , Figure 45.15, , 3 Part of the electrical system of a car is shown in, Figure 45.16., a Why are connections made to the car body?, b There are two circuits in parallel with the battery. What, are they?, c Why is wire A thicker than wire B?, d Why is a relay used?, contacts, , A, B, , starter, switch, , coil, starter, motor, relay, , connections, to car body, Figure 45.16, , 214, , 9781444176421_Section_04.indd 214, , 20/06/14 7:51 AM
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46 Electric motors, l, l, l, , The motor effect, Fleming’s left-hand rule, Simple d.c. electric motor, , l, l, l, , Electric motors form the heart of a whole host of, electrical devices ranging from domestic appliances, such as vacuum cleaners and washing machines to, electric trains and lifts. In a car the windscreen wipers, are usually driven by one and the engine is started by, another., , ●● The motor effect, A wire carrying a current in a magnetic, field experiences a force. If the wire can move,, it does so., , a) Demonstration, In Figure 46.1 the flexible wire is loosely supported, in the strong magnetic field of a C-shaped magnet, (permanent or electromagnet). When the switch, is closed, current flows in the wire which jumps, upwards as shown. If either the direction of the, current or the direction of the field is reversed, the, wire moves downwards. The force increases if the, strength of the field increases and if the current, increases., , Practical motors, Moving-coil loudspeaker, Practical work: A model motor, , b) Explanation, Figure 46.2a is a side view of the magnetic field, lines due to the wire and the magnet. Those due, to the wire are circles and we will assume their, direction is as shown. The dotted lines represent, the field lines of the magnet and their direction is, towards the right., The resultant field obtained by combining both, fields is shown in Figure 46.2b. There are more lines, below than above the wire since both fields act in, the same direction below but they are in opposition, above. If we suppose the lines are like stretched elastic,, those below will try to straighten out and in so doing, will exert an upward force on the wire., , N, , S, , wire, a, , motion, , force on wire, N, S, N, , S, , flexible, wire, to low-voltage, high-current supply, wire, b, Figure 46.1 A wire carrying a current in a magnetic field experiences a force., , Figure 46.2, , 215, , 9781444176421_Section_04.indd 215, , 20/06/14 7:51 AM
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46 electric Motors, , ●● Fleming’s left-hand, rule, , coil, b, , The direction of the force or thrust on the wire can, be found by this rule which is also called the motor, rule (Figure 46.3)., Hold the thumb and first two fingers of the left hand at, right angles to each other with the First finger pointing, in the direction of the Field and the seCond finger in the, direction of the Current, then the Thumb points in the, direction of the Thrust., , If the wire is not at right angles to the field, the, force is smaller and is zero if the wire is parallel to, the field., Thumb, , Thrust, , First finger, Current, , Field, , seCond finger, Figure 46.3 Fleming’s left-hand (motor) rule, , ●● Simple d.c. electric, motor, A simple motor to work from direct current (d.c.), consists of a rectangular coil of wire mounted on, an axle which can rotate between the poles of a, C-shaped magnet (Figure 46.4). Each end of the, coil is connected to half of a split ring of copper,, called a commutator, which rotates with the coil., Two carbon blocks, the brushes, are pressed lightly, against the commutator by springs. The brushes are, connected to an electrical supply., If Fleming’s left-hand rule is applied to the, coil in the position shown, we find that side ab, experiences an upward force and side cd a downward, force. (No forces act on ad and bc since they are, parallel to the field.) These two forces form a couple, which rotates the coil in a clockwise direction until it, is vertical., , N, , a, , , brush, (fixed), , c, , d, , S, , , brush, (fixed), commutator, (rotates with coil), , Figure 46.4 Simple d.c. motor, , The brushes are then in line with the gaps in the, commutator and the current stops. However,, because of its inertia, the coil overshoots the, vertical and the commutator halves change, contact from one brush to the other. This, reverses the current through the coil and so, also the directions of the forces on its sides., Side ab is on the right now, acted on by a, downward force, while cd is on the left with an, upward force. The coil thus carries on rotating, clockwise., The more turns there are on the coil, or the larger, the current through it, the greater is the couple on, the coil and the faster it turns. The coil will also, turn faster if the strength of the magnetic field is, increased., , ●● Practical motors, Practical motors have:, (a) a coil of many turns wound on a soft, iron cylinder or core which rotates with, the coil. This makes it more powerful., The coil and core together are called the, armature., (b) several coils each in a slot in the core and, each having a pair of commutator segments., This gives increased power and smoother, running. The motor of an electric drill is shown, in Figure 46.5., (c) an electromagnet (usually) to produce the field, in which the armature rotates., Most electric motors used in industry are induction, motors. They work off a.c. (alternating current) on a, different principle from the d.c. motor., , 216, , 9781444176421_Section_04.indd 216, , 20/06/14 7:51 AM
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Practical motors, , Practical work, A model motor, The motor shown in Figure 46.6 is made from a kit., 1, 2, 3, , 4, , 5, 6, , Figure 46.5 Motor inside an electric drill, , 7, , Sellotape, , Wrap Sellotape round one end of the metal tube which, passes through the wooden block., Cut two rings off a piece of narrow rubber tubing; slip them, on to the Sellotaped end of the metal tube., Remove the insulation from one end of a 1.5-metre length, of SWG 26 PVC-covered copper wire and fix it under both, rubber rings so that it is held tight against the Sellotape. This, forms one end of the coil., Wind 10 turns of the wire in the slot in the wooden block, and finish off the second end of the coil by removing the, PVC and fixing this too under the rings but on the opposite, side of the tube from the first end. The bare ends act as the, commutator., Push the axle through the metal tube of the wooden base so, that the block spins freely., Arrange two 0.5-metre lengths of wire to act as brushes, and leads to the supply, as shown. Adjust the brushes so that, they are vertical and each touches one bare end of the coil, when the plane of the coil is horizontal. The motor will not, work if this is not so., Slide the base into the magnet with opposite poles facing., Connect to a 3 V battery (or other low-voltage d.c. supply), and a slight push of the coil should set it spinning at high, speed., , brushes, , bare ends, of coil, , wooden block, , axle, , metal rubber, tube rings, split pin, base, , magnet, rivet, , yoke, , to battery, , coil in slot, Figure 46.6 A model motor, , 217, , 9781444176421_Section_04.indd 217, , 20/06/14 7:51 AM
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46 electric Motors, , ●● Moving-coil, loudspeaker, , 2 In the simple electric motor of Figure 46.9, the coil rotates, anticlockwise as seen by the eye from the position X when, current flows in the coil. Is the current flowing clockwise or, anticlockwise around the coil when viewed from above?, , casing, , ring, pole, , N, , N, N, , S, , central, pole, , S, , N, , N, , N, , coil, on, tube, , paper, cone, a End-on view, , S, , N, , Varying currents from a radio, disc player, etc. pass, through a short cylindrical coil whose turns are, at right angles to the magnetic field of a magnet, with a central pole and a surrounding ring pole, (Figure 46.7a)., A force acts on the coil which, according to, Fleming’s left-hand rule, makes it move in and, out. A paper cone attached to the coil moves with, it and sets up sound waves in the surrounding air, (Figure 46.7b., , X, , Figure 46.9, , 3 An electric motor is a device which transfers, A mechanical energy to electrical energy, B heat energy to electrical energy, C electrical energy to heat only, D heat to mechanical energy, E electrical energy to mechanical energy and heat., 4 a Draw a labelled diagram of the essential components, of a simple motor. Explain how continuous rotation is, produced and show how the direction of rotation is, related to the direction of the current., b State what would happen to the direction of rotation of, the motor you have described if, (i) the current was reversed,, (ii) the magnetic field was reversed,, (iii) both current and field were reversed simultaneously., , b, , Figure 46.7 Moving-coil loudspeaker, , Checklist, After studying this chapter you should be able to, , Questions, 1 The current direction in a wire running between the N and, S poles of a magnet lying horizontally is shown in Figure, 46.8. The force on the wire due to the magnet is directed, A from N to S, B from S to N, C opposite to the current direction, D in the direction of the current, E vertically upwards., , • describe a demonstration to show that a force acts on a, current-carrying conductor in a magnetic field, and recall, that it increases with the strength of the field and the size of, the current,, • draw the resultant field pattern for a current-carrying, conductor which is at right angles to a uniform magnetic, field,, • explain why a rectangular current-carrying coil experiences a, couple in a uniform magnetic field,, • draw a diagram of a simple d.c. electric motor and explain, how it works,, • describe a practical d.c. motor., , current, , N, , S, , Figure 46.8, , 218, , 9781444176421_Section_04.indd 218, , 20/06/14 7:52 AM
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47 Electric meters, l, l, l, , Moving-coil galvanometer, Ammeters and shunts, Voltmeters and multipliers, , l, l, , ●● Moving-coil, galvanometer, A galvanometer detects small currents or small, p.d.s, often of the order of milliamperes (mA) or, millivolts (mV)., In the moving-coil pointer-type meter, a coil is, pivoted between the poles of a permanent magnet, (Figure 47.1a). Current enters and leaves the coil by, hair springs above and below it. When there is a current,, a couple acts on the coil (as in an electric motor),, causing it to rotate until stopped by the springs. The, greater the current, the greater the deflection which, is shown by a pointer attached to the coil., , 15, , pointer, 20, , N, , concave, pole, , field lines are directed to and from the centre of, the cylinder. The scale on the meter is then even or, linear, i.e. all divisions are the same size., The sensitivity of a galvanometer is increased by, having, (i), (ii), (iii), (iv), , more turns on the coil,, a stronger magnet,, weaker hair springs or a wire suspension,, as a pointer, a long beam of light reflected from a, mirror on the coil., , The last two are used in light-beam meters which, have a full-scale deflection of a few microamperes, (µA). (1 µA = 10−6 A), , ●● Ammeters and shunts, , 10, , 5, , Multimeters, Reading a voltmeter, , coil, S, , terminals, , An ammeter is a galvanometer that has a known, low resistance, called a shunt, in parallel with it to, take most of the current (Figure 47.2). An ammeter, is placed in series in a circuit and must have a low, resistance otherwise it changes the current to be, measured., , soft iron, cylinder, , galvanometer, G, , hair, spring, a, , shunt, radial field, , Figure 47.2 An ammeter, , ●● Voltmeters and, multipliers, soft iron, cylinder, , coil, , b View from above, Figure 47.1 Moving-coil pointer-type galvanometer, , The soft iron cylinder at the centre of the coil is fixed, and along with the concave poles of the magnet, it produces a radial field (Figure 47.1b), i.e. the, , A voltmeter is a galvanometer having a known, high resistance, called a multiplier, in series with, it (Figure 47.3). A voltmeter is placed in parallel, with the part of the circuit across which the p.d. is, to be measured and must have a high resistance –, otherwise the total resistance of the whole circuit, is reduced so changing the current and the p.d., measured., 219, , 9781444176421_Section_04.indd 219, , 20/06/14 7:52 AM
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47 Electric meters, , galvanometer, G, multiplier, Figure 47.3 A voltmeter, , ●● Multimeters, A multimeter can have analogue or digital displays, (see Figures 47.4a and 47.4b) and can be used to, measure a.c. or d.c. currents or voltages and also, resistance. The required function is first selected,, say a.c. current, and then a suitable range chosen., For example if a current of a few milliamps is, expected, the 10 mA range might be selected and the, value of the current (in mA) read from the display;, if the reading is off-scale, the sensitivity should, be reduced by changing to the higher, perhaps, 100 mA, range., For the measurement of resistance, the resistance, function is chosen and the appropriate range selected., The terminals are first short-circuited to check the, zero of resistance, then the unknown resistance, is disconnected from any circuit and reconnected, across the terminals of the meter in place of the, short circuit., , Figure 47.4b Digital multimeter, , Analogue multimeters are adapted movingcoil galvanometers. Digital multimeters are, constructed from integrated circuits. On the, voltage setting they have a very high input, resistance (10 MΩ), i.e. they affect most, circuits very little and so give very accurate, readings., , ●● Reading a voltmeter, , Figure 47.4a Analogue multimeter, , The face of an analogue voltmeter is, represented in Figure 47.5. The voltmeter, has two scales. The 0–5 scale has a full-scale, deflection of 5.0 V. Each small division on, the 0–5 scale represents 0.1 V. This voltmeter, scale can be read to the nearest 0.1 V. However, the human eye is very good at judging a half, division, so we are able to estimate the voltmeter, reading to the nearest 0.05 V with considerable, precision., , 220, , 9781444176421_Section_04.indd 220, , 20/06/14 7:52 AM
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reading a voltmeter, , Checklist, , 4, , 2, , 6, , 0, 2, , After studying this chapter you should be able to, , 8, 0, , 1, , 2, , 3, , 10, , 4, 5, , 1, , volts, , • draw a diagram of a simple moving-coil galvanometer and, explain how it works,, • explain how a moving-coil galvanometer can be modified, for use as (a) an ammeter and (b) a voltmeter,, • explain why (a) an ammeter should have a very low, resistance and (b) a voltmeter should have a very high, resistance., , Figure 47.5 An analogue voltmeter scale, , Every measuring instrument has a calibrated scale., When you write an account of an experiment (see, p. x, Scientific enquiry) you should include details, about each scale that you use., , Questions, 1 What does a galvanometer do?, 2 Why should the resistance of, a an ammeter be very small,, b a voltmeter be very large?, 3 The scales of a voltmeter are shown in Figure 47.6., 2, , 0, 2, , 0, , 1, , 4, 2, , 6, 3, , 8, 10, , 4, , 1, , 5, , volts, Figure 47.6, , a What are the two ranges available when using the, voltmeter?, b What do the small divisions between the numbers 3 and, 4 represent?, c Which scale would you use to measure a voltage of, 4.6 V?, d When the voltmeter reads 4.0 V where should you, position your eye to make the reading?, e When making the reading for 4.0 V an observer’s eye is, over the 0 V mark. Explain why the value obtained by, this observer is higher than 4.0 V., , 221, , 9781444176421_Section_04.indd 221, , 20/06/14 7:52 AM
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48 Electrons, l, l, l, l, , Thermionic emission, Cathode rays, Deflection of an electron beam, Cathode ray oscilloscope (CRO), , l, l, l, l, , The discovery of the electron was a landmark in, physics and led to great technological advances., , ●● Thermionic emission, The evacuated bulb in Figure 48.1 contains a small, coil of wire, the filament, and a metal plate called, the anode because it is connected to the positive, of the 400 V d.c. power supply. The negative of the, supply is joined to the filament which is also called, the cathode. The filament is heated by current from, a 6 V supply (a.c. or d.c.)., With the circuit as shown, the meter deflects,, indicating current flow in the circuit containing the, gap between anode and cathode. The current stops, if either the 400 V supply is reversed to make the, anode negative or the filament is not heated., This demonstration shows that negative charges,, in the form of electrons, escape from the filament, when it is hot because they have enough energy to, get free from the metal surface. The process is known, as thermionic emission and the bulb as a thermionic, diode (since it has two electrodes). There is a certain, minimum threshold energy (depending on the, metal) which the electrons must have to escape. Also,, the higher the temperature of the metal, the greater, the number of electrons emitted. The electrons are, attracted to the anode if it is positive and are able to, reach it because there is a vacuum in the bulb., evacuated bulb, , Uses of the CRO, X-rays, Photoelectric effect, Waves or particles?, , ●● Cathode rays, Beams of electrons moving at high speed are called, cathode rays. Their properties can be studied using, the ‘Maltese cross tube’ (Figure 48.2)., Electrons emitted by the hot cathode are, accelerated towards the anode but most pass, through the hole in it and travel on along the, tube. Those that miss the cross cause the screen, to fluoresce with green or blue light and cast, a shadow of the cross on it. The cathode rays, evidently travel in straight lines., If the N pole of a magnet is brought up to, the neck of the tube, the rays (and the fluorescent, shadow) can be shown to move upwards. The, rays are clearly deflected by a magnetic field and,, using Fleming’s left-hand rule (Chapter 46), we, see that they behave like conventional current, (positive charge flow) travelling from anode to, cathode., , Maltese cross, 3 kV, , evacuated, bulb, , 6V, 0 kV, , filament, , 2.5–0–2.5 mA, , cathode, anode, , anode, fluorescent, screen, , power, supply, , 6V, , 400 V, , Figure 48.1 Demonstrating thermionic emission, , Figure 48.2 Maltese cross tube, , There is also an optical shadow of the cross, due to, light emitted by the cathode. This is unaffected by, the magnet., , 222, , 9781444176421_Section_04.indd 222, , 20/06/14 7:52 AM
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Deflection of an electron beam, , ●● Deflection of an, electron beam, a) By a magnetic field, In Figure 48.3 the evenly spaced crosses represent, a uniform magnetic field (i.e. one of the same, strength throughout the area shown) acting, into and perpendicular to the paper. An electron, beam entering the field at right angles to the field, experiences a force due to the motor effect (Chapter, 46) whose direction is given by Fleming’s left-hand, rule. This indicates that the force acts at right angles, to the direction of the beam and makes it follow a, circular path as shown (the beam being treated as, conventional current in the opposite direction)., , magnetic field, (into paper), , electron, beam, force on, electron, circular path, , electron, , Figure 48.3 Path of an electron beam at right angles to a magnetic field, , , , metal plate, , , , , , , , , , , , , parabolic, path, , electron, beam, , , , , , , , , , electric, field, , , , metal, plate, , , , , Figure 48.4 Path of an electron beam incident perpendicular to an, electric field, , If a beam of electrons enters the field in a direction, perpendicular to the field, the negatively charged, beam is attracted towards the positively charged, plate and follows a parabolic path, as shown. In, fact its behaviour is not unlike that of a projectile, (Chapter 4) in which the horizontal and vertical, motions can be treated separately., , c) Demonstration, The deflection tube in Figure 48.5 can be used to, show the deflection of an electron beam in electric and, magnetic fields. Electrons from a hot cathode strike, a fluorescent screen S set at an angle. A p.d. applied, across two horizontal metal plates Y1Y2 creates a vertical, electric field which deflects the rays upwards if Y1 is, positive (as shown) and downwards if it is negative., When there is current in the two coils X1X2 (in, series) outside the tube, a horizontal magnetic field is, produced across the tube. It can be used instead of a, magnet to deflect the rays, or to cancel the deflection, due to an electric field., X1, , b) By an electric field, An electric field is a region where an electric charge, experiences a force due to other charges (see p. 155)., In Figure 48.4 the two metal plates behave like a, capacitor that has been charged by connection to a, voltage supply. If the charge is evenly spread over, the plates, a uniform electric field is created between, them and is represented by parallel, equally spaced, lines; the arrows indicate the direction in which a, positive charge would move., , 3 kV, Y1, , electrons, 6V, , S, Y2, , 0 kV, X2, anode, , cathode, , Figure 48.5 Deflection tube, , 223, , 9781444176421_Section_04.indd 223, , 20/06/14 7:52 AM
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48 Electrons, , ●● Cathode ray, oscilloscope (CRO), , screen, , fluorescent, screen, , electron, , H, , beam, C G ( ) A ( ), , Y-plates X-plates vacuum, , Figure 48.6 Main parts of a CRO, , a) Electron gun, This consists of a heater H, a cathode C, another, electrode called the grid G and two or three anodes, A. G is at a negative voltage with respect to C and, controls the number of electrons passing through, its central hole from C to A; it is the brilliance or, brightness control. The anodes are at high positive, voltages relative to C; they accelerate the electrons, along the highly evacuated tube and also focus, them into a narrow beam., , b) Fluorescent screen, A bright spot of light is produced on the screen, where the beam hits it., , c) Deflecting system, Beyond A are two pairs of deflecting plates to which, p.d.s can be applied. The Y-plates are horizontal, but create a vertical electric field which deflects the, beam vertically. The X-plates are vertical and deflect, the beam horizontally., The p.d. to create the electric field between the, Y-plates is applied to the Y-input terminals (often, marked ‘high’ and ‘low’) on the front of the CRO., The input is usually amplified by an amount that, depends on the setting of the Y-amp gain control,, before it is applied to the Y-plates. It can then, be made large enough to give a suitable vertical, deflection of the beam., , a, , a.c., electrons, , Y-plates, , deflection of spot seen from front of screen, b, c, , Figure 48.7 Deflection of the electron beam, , In Figure 48.7a the p.d. between the Y-plates is, zero, as is the deflection. In part b of the figure, the, d.c. input p.d. makes the upper plate positive and, it attracts the beam of negatively charged electrons, upwards. In part c the 50 Hz a.c. input makes the, beam move up and down so rapidly that it produces, a continuous vertical line (whose length increases if, the Y-amp gain is turned up)., The p.d. applied to the X-plates is also via an, amplifier, the X-amplifier, and can either be from an, external source connected to the X-input terminal, or, more commonly, from the time base circuit in, the CRO., The time base deflects the beam horizontally in, the X-direction and makes the spot sweep across, the screen from left to right at a steady speed, determined by the setting of the time base controls, (usually ‘coarse’ and ‘fine’). It must then make the, spot ‘fly back’ very rapidly to its starting point,, ready for the next sweep. The p.d. from the time, base should therefore have a sawtooth waveform like, that in Figure 48.8. Since AB is a straight line, the, distance moved by the spot is directly proportional, to time and the horizontal deflection becomes a, measure of time, i.e. a time axis or base., , sweep, time base p.d., , deflecting system, , screen, , d.c., , , Y-input zero, , Historically the CRO is one of the most important, scientific instruments ever developed. It contains, a cathode ray tube that has three main parts, (Figure 48.6)., electron gun, , screen, , A, , B, , time, , flyback, , , , 1 cycle, , Figure 48.8 Time base waveform, , 224, , 9781444176421_Section_04.indd 224, , 20/06/14 7:52 AM
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Uses of the CRO, , In Figures 48.9a, b and c, the time base is on, applied, to the X-plates. For the trace in part a, the Y-input, p.d. is zero, for the trace in part b the Y-input is d.c., which makes the upper Y-plate positive. In both cases, the spot traces out a horizontal line which appears to, be continuous if the flyback is fast enough. For the, trace in part c the Y-input is a.c., that is, the Y-plates, are alternately positive and negative and the spot, moves accordingly., , When preparing the CRO for use, set the, brilliance, focus, X-shift and Y-shift controls, (which allow the spot to be moved ‘manually’, over the screen in the X and Y directions,, respectively) to their mid-positions. The time base, and Y-amp gain controls can then be adjusted to, suit the input., When the a.c./d.c. selector switch is in the, ‘d.c.’ (or ‘direct’) position, both d.c. and a.c. can, pass to the Y-input. In the ‘a.c.’ (or ‘via C’) position,, a capacitor blocks d.c. in the input but allows a.c., to pass., , b) Measuring p.d.s, a, , b, , c, , Figure 48.9 Deflection of the spot with time base on, , ●● Uses of the CRO, A small CRO is shown in Figure 48.10., , A CRO can be used as a d.c./a.c. voltmeter if, the p.d. to be measured is connected across the, Y-input terminals; the deflection of the spot is, proportional to the p.d., For example, if the Y-amp gain control is on, say,, 1 V/div, a deflection of one vertical division on the, screen graticule (like graph paper with squares for, measuring deflections) would be given by a 1 V, d.c. input. A line one division long (time base off), would be produced by an a.c. input of 1 V peak-topeak, i.e. peak p.d. = 0.5 V., Increasingly the CRO is being replaced by a, data-logger and computer with software which, simulates the display on a CRO screen by plotting, the p.d. against time., , c) Displaying waveforms, , Figure 48.10 Single-beam CRO, , a) Practical points, , ▲, ▲, , The brilliance or intensity control, which is, sometimes the on/off switch as well, should be, as low as possible when there is just a spot on the, screen. Otherwise screen ‘burn’ occurs which, damages the fluorescent material. If possible it is, best to defocus the spot when not in use, or draw it, into a line by running the time base., , In this widely used role, the time base is on, and the CRO acts as a ‘graph-plotter’ to show, the waveform, i.e. the variation with time, of, the p.d. applied to its Y-input. The displays in, Figures 48.11a and b are of alternating p.d.s, with sine waveforms. For the trace in part a,, the time base frequency equals that of the input, and one complete wave is obtained. For the, trace in part b, it is half that of the input, and two waves are formed. If the traces are, obtained with the Y-amp gain control on, say,, 0.5 V/div, the peak-to-peak voltage of the a.c. =, 3 divs × 0.5 V/div, that is, 1.5 V, and the peak, p.d. = 0.75 V., Sound waveforms can be displayed if a, microphone is connected to the Y-input terminals, (see Chapter 33)., , 225, , 9781444176421_Section_04.indd 225, , 20/06/14 7:52 AM
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48 Electrons, , anode by a large p.d. (up to 100 kV). The anode is a, copper block with a ‘target’ of a high-melting-point, metal such as tungsten on which the electrons are, focused by the electric field between the anode and, the concave cathode. The tube has a lead shield with, a small exit for the X-rays., The work done (see p. 163) in transferring a, charge Q through a p.d. V is, E=Q×V, , a, , b, Figure 48.11 Alternating p.d. waveforms on the CRO, , d) Measuring time intervals and, frequency, , This will equal the k.e. of the electrons reaching the, anode if Q = charge on an electron (= 1.6 × 10−19 C), and V is the accelerating p.d. Less than 1% of the, k.e. of the electrons becomes X-ray energy; the rest, heats the anode which has to be cooled., High p.d.s give short wavelength, very, penetrating (hard) X-rays. Less penetrating (soft), rays, of longer wavelength, are obtained with lower, p.d.s. The absorption of X-rays by matter is greatest, by materials of high density having a large number, of outer electrons in their atoms, i.e. of high atomic, number (Chapter 50). A more intense beam of rays, is produced if the rate of emission of electrons is, raised by increasing the filament current., high p.d., , These can be measured if the CRO has a, calibrated time base. For example, when the time base, is set on 10 ms/div, the spot takes 10 milliseconds, to move one division horizontally across the screen, graticule. If this is the time base setting for the, waveform in Figure 48.11b then, since one complete, wave occupies two horizontal divisions, we can say, time for one complete wave = 2 divs × 10 ms/div, = 20 ms, = 20 = 1 s, 1000 50, ∴ number of complete waves per second = 50, ∴ frequency of a.c. applied to Y-input = 50 Hz, , ●● X-rays, X-rays are produced when high-speed electrons are, stopped by matter., , a) Production, In an X-ray tube, Figure 48.12, electrons from a, hot filament are accelerated across a vacuum to the, , filament, , low, p.d., , target, , cooling anode, fins, lead shield, , X-rays, , cathode, electrons, , Figure 48.12 X-ray tube, , b) Properties and nature, X-rays:, (i) readily penetrate matter – up to 1 mm of lead,, (ii) are not deflected by electric or magnetic fields,, (iii) ionise a gas, making it a conductor, e.g. a, charged electroscope discharges when X-rays, pass through the surrounding air,, (iv) affect a photographic film,, , 226, , 9781444176421_Section_04.indd 226, , 20/06/14 7:52 AM
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waves or particles?, , (v) cause fluorescence,, (vi) give interference and diffraction effects., These facts (and others) suggest that X-rays are, electromagnetic waves of very short wavelength., , c) Uses, These were considered earlier (Chapter 32)., , ●● Photoelectric effect, Electrons are emitted by certain metals when, electromagnetic radiation of small enough, wavelength falls on them. The effect is called, photoelectric emission. It happens, for example,, when zinc is exposed to ultraviolet., The photoelectric effect only occurs for a given, metal if the frequency of the incident electromagnetic, radiation exceeds a certain threshold frequency. We, can explain this by assuming that, (i) all electromagnetic radiation is emitted, and absorbed as packets of energy, called, photons, and, (ii) the energy of a photon is directly proportional, to its frequency., Ultraviolet (UV) photons would therefore have, more energy than light photons since UV has a, higher frequency than light. The behaviour of, zinc (and most other substances) in not giving, photoelectric emission with light but with UV, would therefore be explained: a photon of light has, less than the minimum energy required to cause the, zinc to emit an electron., The absorption of a photon by an atom results, in the electron gaining energy and the photon, disappearing. If the photon has more than the, minimum amount of energy required to enable an, electron to escape, the excess appears as k.e. of the, emitted electron., energy of photon = energy needed for electron to escape, + k.e. of electron, , ●● Waves or particles?, The wave theory of electromagnetic radiation, can account for properties such as interference,, diffraction and polarisation which the photon, theory cannot. On the other hand, the wave theory, does not explain the photoelectric effect and the, photon theory does., It would seem that electromagnetic radiation, has a dual nature and has to be regarded as waves, on some occasions and as ‘particles’ (photons) on, others., , Questions, 1 a In Figure 48.13a, to which terminals on the power, supply must plates A and B be connected to deflect the, cathode rays downwards?, b In Figure 48.13b, in which direction will the cathode rays, be deflected?, , a, , A, , cathode, , B, , rays, , cathode rays, , b, , magnetic field, into page, , Figure 48.13, , 2 An electron, charge e and mass m, is accelerated in a, cathode ray tube by a p.d. of 1000 V. Calculate, a the kinetic energy gained by the electron,, b the speed it acquires., (e = 1.6 × 10−19 C, m = 9.1 × 10−31 kg), , Checklist, After studying this chapter you should be able to, • explain the term cathode rays,, • describe experiments to show that cathode rays are, deflected by magnetic and electric fields., , The photoelectric effect is the process by which, X-ray photons are absorbed by matter; in effect, it causes ionisation (Chapter 49) since electrons, are ejected and positive ions remain. Photons not, absorbed by the metal pass through with unchanged, energy., 227, , 9781444176421_Section_04.indd 227, , 20/06/14 7:52 AM
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Section, , 5, , Chapters, 49 Radioactivity, , 9781444176421_Section_05.indd 229, , Atomic physics, , 50 Atomic structure, , 20/06/14 7:38 AM
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49 Radioactivity, l, l, l, l, , Ionising effect of radiation, Geiger–Müller (GM) tube, Alpha, beta and gamma radiation, Particle tracks, , l, l, l, , The discovery of radioactivity in 1896 by the French, scientist Becquerel was accidental. He found that, uranium compounds emitted radiation that: (i), affected a photographic plate even when it was, wrapped in black paper, and (ii) ionised a gas. Soon, afterwards Marie Curie discovered the radioactive, element radium. We now know that radioactivity, arises from unstable nuclei (Chapter 50) which, may occur naturally or be produced in reactors., Radioactive materials are widely used in industry,, medicine and research., We are all exposed to natural background, radiation caused partly by radioactive materials in, rocks, the air and our bodies, and partly by cosmic, rays from outer space (see p. 235)., , ●● Ionising effect of, radiation, A charged electroscope discharges when a, lighted match or a radium source (held in forceps), is brought near the cap (Figures 49.1a and b)., lighted, match, , charged, electroscope, , forceps, , Radioactive decay, Uses of radioactivity, Dangers and safety, , electron, , , neutral atom, or molecule, , positive ion, , electron, , Figure 49.2 Ionisation, , ●● Geiger–Müller (GM), tube, The ionising effect is used to detect radiation., When radiation enters a GM tube (Figure 49.3),, either through a thin end-window made of mica,, or, if the radiation is very penetrating, through, the wall, it creates argon ions and electrons., These are accelerated towards the electrodes and, cause more ionisation by colliding with other argon, atoms., On reaching the electrodes, the ions produce, a current pulse which is amplified and fed either, to a scaler or a ratemeter. A scaler counts the, pulses and shows the total received in a certain, time. A ratemeter gives the counts per second, (or minute), or count-rate, directly. It usually, has a loudspeaker which gives a ‘click’ for each, pulse., , radium source, a, , , , , , cathode (metal cylinder), , b, , Figure 49.1, , In the first case the flame knocks electrons out of, surrounding air molecules leaving them as positively, charged ions, i.e. air molecules which have lost one, or more electrons (Figure 49.2); in the second case, radiation causes the same effect, called ionisation., The positive ions are attracted to the cap if it is, negatively charged; if it is positively charged the, electrons are attracted. As a result in either case the, charge on the electroscope is neutralised, i.e. it loses, its charge., , 450 V, , , , , mica, window, , argon gas at, low pressure, , anode (wire), , to scaler or, ratemeter, , Figure 49.3 Geiger–Müller (GM) tube, , 230, , 9781444176421_Section_05.indd 230, , 20/06/14 7:38 AM
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Alpha, beta and gamma radiation, , ●● Alpha, beta and, gamma radiation, Experiments to study the penetrating power, ionising, ability and behaviour of radiation in magnetic and, electric fields show that a radioactive substance emits, one or more of three types of radiation – called alpha, (α), beta (β− or β+) and gamma (γ) rays., Penetrating power can be investigated as in, Figure 49.4 by observing the effect on the count-rate, of placing one of the following in turn between the, GM tube and the lead sheet:, (i) a sheet of thick paper (the radium source, lead, and tube must be close together for this part),, (ii) a sheet of aluminium 2 mm thick,, (iii) a further sheet of lead 2 cm thick., , ionising power is much less than that of α-particles., As well as being deflected by electric fields, they, are more easily deflected by magnetic fields., Measurements show that β−-particles are streams of, high-energy electrons, like cathode rays, emitted, with a range of speeds up to that of light. Strontium, (Sr-90) emits β−-particles only., The magnetic deflection of β−-particles can be, shown as in Figure 49.5. With the GM tube at A, and without the magnet, the count-rate is noted., Inserting the magnet reduces the count-rate but, it increases again when the GM tube is moved, sideways to B., strontium, source, , Radium (Ra-226) emits α-particles, β-particles and, γ-rays. Other sources can be tried, such as americium,, strontium and cobalt., ratemeter, , 4 mm plug, , ratemeter, magnet, , N, S, , A, GM, B tube, , lead, plates, Figure 49.5 Demonstrating magnetic deflection of β−-particles, , radium, source, , GM tube, , lead sheet with 1 mm hole to prevent, overloading of GM tube, Figure 49.4 Investigating the penetrating power of radiation, , a) Alpha particles, These are stopped by a thick sheet of paper and have, a range in air of only a few centimetres since they, cause intense ionisation in a gas due to frequent, collisions with gas molecules. They are deflected by, electric and strong magnetic fields in a direction and, by an amount which suggests they are helium atoms, minus two electrons, i.e. helium ions with a double, positive charge. From a particular substance, they are, all emitted with the same speed (about 1/20th of, that of light)., Americium (Am-241) is a pure α source., , b) Beta particles, These are stopped by a few millimetres of aluminium, and some have a range in air of several metres. Their, , c) Gamma rays, These are the most penetrating and are stopped, only by many centimetres of lead. They ionise, a gas even less than β-particles and are not, deflected by electric and magnetic fields. They, give interference and diffraction effects and are, electromagnetic radiation travelling at the speed, of light. Their wavelengths are those of very, short X-rays, from which they differ only because, they arise in atomic nuclei whereas X-rays come, from energy changes in the electrons outside the, nucleus., Cobalt (Co-60) emits γ-rays and β−-particles but, can be covered with aluminium to provide pure γ-rays., , Comparing alpha, beta and gamma, radiation, In a collision, α-particles, with their relatively large, mass and charge, have more of a chance of knocking, an electron from an atom and causing ionisation, than the lighter β-particles; γ-rays, which have, no charge, are even less likely than β-particles to, produce ionisation., 231, , 9781444176421_Section_05.indd 231, , 20/06/14 7:38 AM
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49 Radioactivity, , A GM tube detects β-particles and γ-rays and, energetic α-particles; a charged electroscope detects, only α-particles. All three types of radiation cause, fluorescence., The behaviour of the three kinds of radiation in a, magnetic field is summarised in Figure 49.6a. The, deflections (not to scale) are found from Fleming’s lefthand rule, taking negative charge moving to the right as, equivalent to positive (conventional) current to the left., ( ), , alpha, , magnetic, field into, page, , beta, , gamma, , , , ●● Particle tracks, The paths of particles of radiation were first shown, up by the ionisation they produced in devices called, cloud chambers. When air containing a vapour,, alcohol, is cooled enough, saturation occurs. If, ionising radiation passes through the air, further, cooling causes the saturated vapour to condense, on the ions created. The resulting white line of tiny, liquid drops shows up as a track when illuminated., In a diffusion cloud chamber, α-particles, showed straight, thick tracks (Figure 49.7a). Very, fast β-particles produced thin, straight tracks while, slower ones gave short, twisted, thicker tracks, (Figure 49.7b). Gamma-rays eject electrons from, air molecules; the ejected electrons behaved like, β−-particles in the cloud chamber and produced, their own tracks spreading out from the γ-rays., , Figure 49.6a Deflection of α-, β- and γ-radiation in a magnetic field, , +, metal plate, +, , +, , +, , +, γ, , gamma, , alpha, β−, a α-particles, , α++, beta, –, , metal plate, , –, , –, , –, , –, , Figure 49.6b Deflection of α-, β- and γ-radiation in a uniform, electric field, , Figure 49.6b shows the behaviour of α-particles,, β−-radiation and γ-rays in a uniform electric field:, α-particles are attracted towards the negatively, charged metal plate, β−-particles are attracted, towards the positively charged plate and γ-rays pass, through undeflected., , b Fast and slow β-particles, Figure 49.7 Tracks in a cloud chamber, , 232, , 9781444176421_Section_05.indd 232, , 20/06/14 7:39 AM
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Radioactive decay, , The bubble chamber, in which the radiation, leaves a trail of bubbles in liquid hydrogen, has, now replaced the cloud chamber in research work., The higher density of atoms in the liquid gives, better defined tracks, as shown in Figure 49.8, than, obtained in a cloud chamber. A magnetic field is, usually applied across the bubble chamber which, causes charged particles to move in circular paths; the, sign of the charge can be deduced from the way the, path curves., , Half-life, The rate of decay is unaffected by temperature but, every radioactive element has its own definite decay, rate, expressed by its half-life. This is the average, time for half the atoms in a given sample to decay., It is difficult to know when a substance has lost all its, radioactivity, but the time for its activity to fall to half, its value can be found more easily., , Decay curve, , activity (disintegrations/s), , The average number of disintegrations (i.e., decaying atoms) per second of a sample is its, activity. If it is measured at different times (e.g., by finding the count-rate using a GM tube and, ratemeter), a decay curve of activity against time, can be plotted. The ideal curve for one element, (Figure 49.9) shows that the activity decreases by, the same fraction in successive equal time intervals., It falls from 80 to 40 disintegrations per second in, 10 minutes, from 40 to 20 in the next 10 minutes,, from 20 to 10 in the third 10 minutes and so on. The, half-life is 10 minutes., Half-lives vary from millionths of a second to, millions of years. For radium it is 1600 years., , 80, , 40, 20, 10, 0, , 10, , 20, , 30, , time/min, , half-lives, Figure 49.8 Charged particle track in a bubble chamber, , Figure 49.9 Decay curve, , ●● Radioactive decay, , Experiment to find the half-life, of thoron, , Radioactive atoms have unstable nuclei and, when, they emit α-particles or β-particles, they decay into, atoms of different elements that have more stable, nuclei. These changes are spontaneous and cannot, be controlled; also, it does not matter whether, the material is pure or combined chemically with, something else., , The half-life of the α-emitting gas thoron can be, found as shown in Figure 49.10. The thoron bottle, is squeezed three or four times to transfer some, thoron to the flask (Figure 49.10a). The clips are, then closed, the bottle removed and the stopper, replaced by a GM tube so that it seals the top, (Figure 49.10b)., 233, , 9781444176421_Section_05.indd 233, , 20/06/14 7:39 AM
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49 Radioactivity, , When the ratemeter reading has reached its, maximum and started to fall, the count-rate is noted, every 15 s for 2 minutes and then every 60 s for the, next few minutes. (The GM tube is left in the flask, for at least 1 hour until the radioactivity has decayed.), A measure of the background radiation is obtained, by recording the counts for a period (say 10 minutes), at a position well away from the thoron equipment., The count-rates in the thoron decay experiment, are then corrected by subtracting the average, background count-rate from each reading. A graph of, the corrected count-rate against time is plotted and, the half-life (52 s) estimated from it., , loudspeaker of the ratemeter ‘clicks’ erratically, not, at a steady rate. This is because radioactive decay, is a random process, in that it is a matter of pure, chance whether or not a particular atom will decay, during a certain period of time. All we can say is that, about half the atoms in a sample will decay during, the half-life. We cannot say which atoms these will, be, nor can we influence the process in any way., Radioactive emissions occur randomly over space, and time., , ●● Uses of radioactivity, Radioactive substances, called radioisotopes, are now, made in nuclear reactors and have many uses., , stopper, screw clip, , filter flask, thoron bottle, , a, , ratemeter, , a) Thickness gauge, If a radioisotope is placed on one side of a moving, sheet of material and a GM tube on the other,, the count-rate decreases if the thickness increases., This technique is used to control automatically the, thickness of paper, plastic and metal sheets during, manufacture (Figure 49.11). Because of their range,, β-emitters are suitable sources for monitoring the, thickness of thin sheets but γ-emitters would be, needed for thicker materials., Flaws in a material can be detected in a similar, way; the count-rate will increase where a flaw is, present., , clip closed, , GM tube, (thin end-window), b, Figure 49.10, , Random nature of decay, , Figure 49.11 Quality control in the manufacture of paper using a, radioactive gauge, , During the previous experiment it becomes, evident that the count-rate varies irregularly: the, 234, , 9781444176421_Section_05.indd 234, , 20/06/14 7:39 AM
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Dangers and safety, , b) Tracers, The progress of a small amount of a weak, radioisotope injected into a system can be ‘traced’, by a GM tube or other detector. The method is used, in medicine to detect brain tumours and internal, bleeding, in agriculture to study the uptake of, fertilisers by plants, and in industry to measure fluid, flow in pipes., A tracer should be chosen whose half-life matches, the time needed for the experiment; the activity, of the source is then low after it has been used, and so will not pose an ongoing radiation threat., For medical purposes, where short exposures are, preferable, the time needed to transfer the source, from the production site to the patient also needs to, be considered., , c) Radiotherapy, Gamma rays from strong cobalt radioisotopes are, used in the treatment of cancer., , d) Sterilisation, Gamma rays are used to sterilise medical, instruments by killing bacteria. They are also, used to ‘irradiate’ certain foods, again killing, bacteria to preserve the food for longer. They are, safe to use as no radioactive material goes into, the food., , e) Archaeology, A radioisotope of carbon present in the air,, carbon-14, is taken in by living plants and trees, along with non-radioactive carbon-12. When a, tree dies no fresh carbon is taken in. So as the, carbon-14 continues to decay, with a half-life of, 5700 years, the amount of carbon-14 compared, with the amount of carbon-12 becomes smaller., By measuring the residual radioactivity of, carbon-containing material such as wood, linen, or charcoal, the age of archaeological remains, can be estimated within the range 1000 to, 50 000 years (Figure 49.12). See Worked example, 2, on p. 236., The ages of rocks have been estimated in a, similar way by measuring the ratio of the number, of atoms of a radioactive element to those of its, decay product in a sample. See Worked example 3,, on p. 236., , Figure 49.12 The year of construction of this Viking ship has been, estimated by radiocarbon techniques to be AD 800., , ●● Dangers and safety, We are continually exposed to radiation from a range, of sources, both natural (‘background’) and artificial,, as indicated in Figure 49.13., (i) Cosmic rays (high-energy particles from outer, space) are mostly absorbed by the atmosphere, and produce radioactivity in the air we breathe,, but some reach the Earth’s surface., (ii) Numerous homes, particularly in Scotland, are, built from granite rocks that emit radioactive, radon gas; this can collect in basements or wellinsulated rooms if the ventilation is poor., (iii) Radioactive potassium-40 is present in food and, is absorbed by our bodies., (iv) Various radioisotopes are used in certain medical, procedures., (v) Radiation is produced in the emissions from, nuclear power stations and in fall-out from the, testing of nuclear bombs; the latter produce, strontium isotopes with long half-lives which are, absorbed by bone., , 235, , 9781444176421_Section_05.indd 235, , 20/06/14 7:40 AM
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49 Radioactivity, , radioactivity in the air, cosmic rays, rocks, food, medical, nuclear power stations, nuclear bombs, Figure 49.13 Radiation sources, , We cannot avoid exposure to radiation in small doses, but large doses can be dangerous to our health. The, ionising effect produced by radiation causes damage, to cells and tissues in our bodies and can also lead to, the mutation of genes. The danger from α-particles, is small, unless the source enters the body, but β- and, γ-radiation can cause radiation burns (i.e. redness, and sores on the skin) and delayed effects such as, eye cataracts and cancer. Large exposures may lead, to radiation sickness and death. The symbol used to, warn of the presence of radioactive material is shown, in Figure 49.14., , radiation dose badges that keep a check on the, amount of radiation they have been exposed to over, a period (usually one month). The badge contains, several windows which allow different types of, radiation to fall onto a photographic film; when the, film is developed it is darkest where the exposure to, radiation was greatest., , ●● Worked examples, 1 A radioactive source has a half-life of 20 minutes., What fraction is left after 1 hour?, After 20 minutes, fraction left = 1/2, After 40 minutes, fraction left = 1/2 × 1/2 = 1/4, After 60 minutes, fraction left = 1/2 × 1/4 = 1/8, 2 Carbon-14 has a half-life of 5700 years. A, 10 g sample of wood cut recently from a living, tree has an activity of 160 counts/minute. A piece, of charcoal taken from a prehistoric campsite, also weighs 10 g but has an activity of 40 counts/, minute. Estimate the age of the charcoal., After 1 × 5700 years the activity will be 160/2 = 80, counts per minute, After 2 × 5700 years the activity will be 80/2 = 40, counts per minute, The age of the charcoal is 2 × 5700 = 11 400 years, , Figure 49.14 Radiation hazard sign, , The increasing use of radioisotopes in medicine, and industry has made it important to find ways of, disposing of radioactive waste safely. One method, is to enclose the waste in steel containers which are, then buried in concrete bunkers; possible leakage is, a cause of public concern, as water supplies could be, contaminated allowing radioactive material to enter, the food chain., The weak sources used at school should always be:, ●, ●, ●, , lifted with forceps,, held away from the eyes, and, kept in their boxes when not in use., , In industry, sources are handled by long tongs, and transported in thick lead containers. Workers, are protected by lead and concrete walls, and wear, , 3 The ratio of the number of atoms of argon-40, to potassium-40 in a sample of radioactive rock, is analysed to be 1 : 3. Assuming that there was, no potassium in the rock originally and that, argon-40 decays to potassium-40 with a, half-life of 1500 million years, estimate the, age of the rock., Assume there were N atoms of argon-40 in the rock, when it was formed., After 1 × 1500 million years there will be N/2, atoms of argon left and N − (N/2) = N/2 atoms of, potassium formed, giving an Ar : K ratio of 1 : 1., After 2 × 1500 = 3000 million years, there, would be (N/2)/2 = N/4 argon atoms left and, N − (N/4) = 3N/4 potassium atoms formed, giving, an Ar : K ratio of 1 : 3 as measured., The rock must be about 3000 million years old., , 236, , 9781444176421_Section_05.indd 236, , 20/06/14 7:40 AM
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Worked examples, , Questions, 1 Which type of radiation from radioactive materials, a has a positive charge?, b is the most penetrating?, c is easily deflected by a magnetic field?, d consists of waves?, e causes the most intense ionisation?, f has the shortest range in air?, g has a negative charge?, h is not deflected by an electric field?, 2 In an experiment to find the half-life of radioactive, iodine, the count-rate falls from 200 counts per second to, 25 counts per second in 75 minutes. What is its half-life?, 3 If the half-life of a radioactive gas is 2 minutes, then after, 8 minutes the activity will have fallen to a fraction of its, initial value. This fraction is, A 1/4, B 1/6, C 1/8, D 1/16, E 1/32, , Checklist, After studying this chapter you should be able to, • recall that the radiation emitted by a radioactive substance, can be detected by its ionising effect,, • explain the principle of operation of a Geiger–Müller tube, and a diffusion cloud chamber,, • recall the nature of α-, β- and γ-radiation,, • describe experiments to compare the range and penetrating, power of α-, β- and γ-radiation in different materials,, • recall the ionising abilities of α-, β- and γ-radiation and, relate them to their ranges,, • predict how α-, β- and γ-radiation will be deflected in, magnetic and electric fields,, • define the term half-life,, • describe an experiment from which a radioactive decay, curve can be obtained,, • show from a graph that radioactive decay processes have a, constant half-life,, • solve simple problems on half-life,, • recall that radioactivity is (a) a random process, (b) due to, nuclear instability, (c) independent of external conditions,, • recall some uses of radioactivity,, • describe sources of radiation,, • discuss the dangers of radioactivity and safety precautions, necessary., , 237, , 9781444176421_Section_05.indd 237, , 20/06/14 7:40 AM
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50 Atomic structure, l, l, l, l, , Nuclear atom, Protons and neutrons, Isotopes and nuclides, Radioactive decay, , l, l, l, , The discoveries of the electron and of radioactivity, seemed to indicate that atoms contained negatively, and positively charged particles and were not, indivisible as was previously thought. The questions, then were ‘How are the particles arranged inside an, atom?’ and ‘How many are there in the atom of each, element?’, An early theory, called the ‘plum-pudding’ model,, regarded the atom as a positively charged sphere, in which the negative electrons were distributed all, over it (like currants in a pudding) and in sufficient, numbers to make the atom electrically neutral., Doubts arose about this model., , ●● Nuclear atom, While investigating radioactivity, the physicist, Rutherford noticed that not only could α-particles, pass straight through very thin metal foil as if it, weren’t there but also that some were deflected, from their initial direction. With the help of Geiger, (of GM tube fame) and Marsden, Rutherford, investigated this in detail at Manchester University, using the arrangement in Figure 50.1. The fate of the, α-particles after striking the gold foil was detected by, the scintillations (flashes of light) they produced on, a glass screen coated with zinc sulfide and fixed to a, rotatable microscope., vacuum, , -particles, , Nuclear stability, Models of the atom, Nuclear energy, , They found that most of the α-particles were, undeflected, some were scattered by appreciable, angles and a few (about 1 in 8000) surprisingly, ‘bounced’ back. To explain these results, Rutherford proposed in 1911 a ‘nuclear’ model, of the atom in which all the positive charge and, most of the mass of an atom formed a dense core, or nucleus, of very small size compared with the, whole atom. The electrons surrounded the nucleus, some distance away., He derived a formula for the number of, α-particles deflected at various angles, assuming, that the electrostatic force of repulsion between the, positive charge on an α-particle and the positive, charge on the nucleus of a gold atom obeyed, an inverse-square law (i.e. the force increases, four times if the separation is halved). Geiger, and Marsden’s experimental results completely, confirmed Rutherford’s formula and supported, the view that an atom is mostly empty space., In fact the nucleus and electrons occupy about, one million millionth of the volume of an atom., Putting it another way, the nucleus is like a sugar, lump in a very large hall and the electrons a, swarm of flies., Figure 50.2 shows the paths of three α-particles., Particle 1 is clear of all nuclei and passes straight, through the gold atoms., Particle 2 is deflected slightly., Particle 3 approaches a gold nucleus so closely that it, is violently repelled by it and ‘rebounds’, appearing, to have had a head-on ‘collision’., , gold foil, atom of, gold foil, , radium in, lead box, , 1, zinc, sulfide, screen, , , , nucleus of, gold atom, , , , 2, , , , 3, , , , , rotatable, microscope, , -particle, , Figure 50.2 Electrostatic scattering of α-particles, , Figure 50.1 Geiger and Marsden’s scattering experiment, , 238, , 9781444176421_Section_05.indd 238, , 20/06/14 7:40 AM
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Radioactive decay, , l● Protons and neutrons, We now believe as a result of other experiments, in, some of which α and other high-speed particles were, used as ‘atomic probes’, that atoms contain three, basic particles – protons, neutrons and electrons., A proton is a hydrogen atom minus an electron,, i.e. a positive hydrogen ion. Its charge is equal in, size but opposite in sign to that of an electron but its, mass is about 2000 times greater., A neutron is uncharged with almost the same mass, as a proton., Protons and neutrons are in the nucleus and are, called nucleons. Together they account for the mass, of the nucleus (and most of that of the atom); the, protons account for its positive charge. These facts, are summarised in Table 50.1., Table 50.1, Particle, , Relative mass, , Charge, , Location, , proton, , 1836, , +e, , in nucleus, , neutron, , 1839, , +0, , in nucleus, , electron, , 1, , –e, , outside nucleus, , In a neutral atom the number of protons equals the, number of electrons surrounding the nucleus. Table, 50.2 shows the particles in some atoms. Hydrogen is, simplest with one proton and one electron. Next is, the inert gas helium with two protons, two neutrons, and two electrons. The soft white metal lithium has, three protons and four neutrons., Table 50.2, Hydrogen, , Helium, , Lithium, , Oxygen, , Copper, , protons, , 1, , 2, , 3, , 8, , 29, , neutrons, , 0, , 2, , 4, , 8, , 34, , electrons, , 1, , 2, , 3, , 8, , 29, , The atomic or proton number Z of an atom is the number of, protons in the nucleus., , The atomic number is also the number of electrons, in the atom. The electrons determine the chemical, properties of an atom and when the elements are, arranged in order of atomic number in the Periodic, Table, they fall into chemical families., , In general, A = Z + N, where N is the neutron, number of the element., Atomic nuclei are represented by symbols., Hydrogen is written as 11 H, helium as 42 He and lithium, a 73 Li . In general atom X is written as AZ X , where A is, the nucleon number and Z the proton number., The mass or nucleon number A of an atom is the number of, nucleons in the nucleus., , l● Isotopes and nuclides, Isotopes of an element are atoms that have the, same number of protons but different numbers of, neutrons. That is, their proton numbers are the same, but not their nucleon numbers., Isotopes have identical chemical properties since, they have the same number of electrons and occupy, the same place in the Periodic Table. (In Greek, isos, means same and topos means place.), Few elements consist of identical atoms; most are, mixtures of isotopes. Chlorine has two isotopes; one, has 17 protons and 18 neutrons (i.e. Z = 17, A = 35), 35Cl , the other has 17 protons and 20, and is written 17, neutrons (i.e. Z = 17, A = 37) and is written 37, 17 Cl ., They are present in ordinary chlorine in the ratio of, 35Cl to one atom of 37 Cl , giving, three atoms of 17, 17, chlorine an average atomic mass of 35.5., Hydrogen has three isotopes: 11 H with one proton,, deuterium 21D with one proton and one neutron, and tritium 31T with one proton and two neutrons., Ordinary hydrogen consists 99.99 per cent of 11 H, atoms. Water made from deuterium is called ‘heavy, water’ (D2O); it has a density of 1.108 g/cm3, it, freezes at 3.8 ºC and boils at 101.4 ºC., Each form of an element is called a nuclide., Nuclides with the same Z number but different, A numbers are isotopes. Radioactive isotopes are, termed radioisotopes or radionuclides; their nuclei, are unstable., , l● Radioactive decay, Radioactive atoms have unstable nuclei which change, or ‘decay’ into atoms of a different element when, they emit α- or β-particles. The decay is spontaneous, and cannot be controlled; also it does not matter, whether the material is pure or combined chemically, with something else., 239, , 9781444176421_Section_05.indd 239, , 20/06/14 7:41 AM
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50 Atomic structure, , a) Alpha decay, An α-particle is a helium nucleus, having two protons, and two neutrons, and when an atom decays by emission, of an α-particle, its nucleon number decreases by four, and its proton number by two. For example, when, radium of nucleon number 226 and proton number, 88 emits an α-particle, it decays to radon of nucleon, number 222 and proton number 86. We can write:, →, , 222 Rn, 86, , + 42 He, , The values of A and Z must balance on both sides of, the equation since nucleons and charge are conserved., , b) Beta decay, In β− decay a neutron changes to a proton and an, electron. The proton remains in the nucleus and the, electron is emitted as a β−-particle. The new nucleus, has the same nucleon number, but its proton number, increases by one since it has one more proton., Radioactive carbon, called carbon-14, decays by, β− emission to nitrogen:, 14 C, 6, , →, , 14 N, 7, , +, , 0, −1e, , A particle called an antineutrino ( ν ), with no charge, and negligible mass, is also emitted in β− decay. Note, that a β− decay is often referred to as just a β decay., Positrons are subatomic particles with the same, mass as an electron but with opposite (positive) charge., They are emitted in some decay processes as β+particles. Their tracks can be seen in bubble chamber, photographs. The symbol for a positron is +10e . In, β+- decay a proton in a nucleus is converted to a, neutron and a positron, for example in the reaction:, 64 Cu, 29, , →, , 64 N, 28, , +, , The stability of a nucleus depends on both, the number of protons (Z) and the number of, neutrons (N) it contains. Figure 50.3 is a plot of, N against Z for all known nuclides. The blue band, indicates the region over which stable nuclides, occur; unstable nuclides occur outside this band., The continuous line, drawn through the centre of, the band, is called the stability line., It is found that for stable nuclides:, (i) N = Z for the lightest,, (ii) N > Z for the heaviest,, (iii) most nuclides have even N and Z, implying, that the α-particle combination of two, neutrons and two protons is likely to be, particularly stable., For unstable nuclides:, (i) disintegration tends to produce new nuclides, nearer the stability line and continues until a, stable nuclide is formed,, (ii) a nuclide above the stability line decays, by β− emission (a neutron changes to a, proton and electron) so that the N/Z ratio, decreases,, (iii) a nuclide below the stability line decays, by β+ emission (a proton changes to a, neutron and positron) so that the N/Z ratio, increases,, (iv) nuclei with more than 82 protons usually emit, an α-particle when they decay., , 140, , 0, +1e, , A neutrino (ν) is also emitted in β+ decay. Neutrinos, are emitted from the Sun in large numbers, but, they rarely interact with matter so are very difficult, to detect. Antineutrinos and positrons are the, ‘antiparticles’ of neutrinos and electrons, respectively., If a particle and its antiparticle collide, they annihilate, each other, producing energy in the form of γ-rays., , c) Gamma emission, , number of neutrons (N), , 226 Ra, 88, , ●● Nuclear stability, , 120, , stability line, , 100, 80, 60, , N Z, , 40, 20, , β−-, , β+-particles,, , After emitting an α-particle, or, or, some nuclei are left in an ‘excited’ state. Rearrangement, of the protons and neutrons occurs and a burst of, γ-rays is released., , 20, , 40, 60, 80, number of protons (Z), , 100, , Figure 50.3 Stability of nuclei, , 240, , 9781444176421_Section_05.indd 240, , 20/06/14 7:41 AM
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Models of the atom, , ●● Models of the atom, , Schrödinger model, , Rutherford–Bohr model, Shortly after Rutherford proposed his nuclear model, of the atom, Bohr, a Danish physicist, developed it to, explain how an atom emits light. He suggested that, the electrons circled the nucleus at high speed, being, kept in certain orbits by the electrostatic attraction of, the nucleus for them. He pictured atoms as miniature, solar systems. Figure 50.4 shows the model for three, elements., , Although it remains useful for some purposes, the, Rutherford–Bohr model was replaced by a mathematical, model developed by Erwin Schrödinger, which is, not easy to picture. The best we can do, without, using advanced mathematics, is to say that the atom, consists of a nucleus surrounded by a hazy cloud of, electrons. Regions of the atom where the mathematics, predicts that electrons are more likely to be found are, represented by denser shading (Figure 50.6)., , lithium, hydrogen, , helium, , , , , , , , , , , , , , , , , , orbits, , proton, neutron, electron, , Figure 50.6 Electron cloud, , Figure 50.4 Electron orbits, , E4, , Normally the electrons remain in their orbits but, if the atom is given energy, for example by being, heated, electrons may jump to an outer orbit. The, atom is then said to be excited. Very soon afterwards, the electrons return to an inner orbit and, as they, do, they emit energy in the form of bursts of, electromagnetic radiation (called photons), such as, infrared light, ultraviolet or X-rays (Figure 50.5). The, wavelength of the radiation emitted depends on the, two orbits between which the electrons jump. If an, atom gains enough energy for an electron to escape, altogether, the atom becomes an ion and the energy, needed to achieve this is called the ionisation energy, of the atom., inner orbit, , , , electron jump, , , , , , energy in, , outer, orbit, , electron, jump, , , , , , , , radiation out, , Figure 50.5 Bohr’s explanation of energy changes in an atom, , E3, E2, , E1, Figure 50.7 Energy levels of an atom, , This theory does away with the idea of electrons, moving in definite orbits and replaces them by, energy levels that are different for each element., When an electron ‘jumps’ from one level, say E3, in Figure 50.7, to a lower one E1, a photon of, electromagnetic radiation is emitted with energy, equal to the difference in energy of the two levels., The frequency (and wavelength) of the radiation, emitted by an atom is thus dependent on the, arrangement of energy levels. For an atom emitting, visible light, the resulting spectrum (produced for, example by a prism) is a series of coloured lines that, is unique to each element. Sodium vapour in a gas, discharge tube (such as a yellow street light) gives, two adjacent yellow–orange lines (Figure 50.8a)., Light from the Sun is due to energy changes in, many different atoms and the resulting spectrum is a, continuous one with all colours (see Figure 50.8b)., 241, , 9781444176421_Section_05.indd 241, , 20/06/14 7:41 AM
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50 Atomic structure, , colliding with surrounding atoms and raising their, average k.e., i.e. their temperature, so producing, heat., If the fission neutrons split other uranium-235, nuclei, a chain reaction is set up (Figure 50.9). In, practice some fission neutrons are lost by escaping, from the surface of the uranium before this happens., The ratio of those causing fission to those escaping, increases as the mass of uranium-235 increases. This, must exceed a certain critical value to sustain the, chain reaction., , Figure 50.8a Line spectrum due to energy changes in sodium, , Figure 50.8b A continuous spectrum, , ●● Nuclear energy, , neutron, , a) E = mc2, Einstein predicted that if the energy of a body, changes by an amount E, its mass changes by an, amount m given by the equation, , where c is the speed of light (3 × 108 m/s). The, implication is that any reaction in which there is a, decrease of mass, called a mass defect, is a source, of energy. The energy and mass changes in physical, and chemical changes are very small; those in, some nuclear reactions, Such as radioactive decay,, are millions of times greater. It appears that mass, (matter) is a very concentrated form of energy., , b) Fission, The heavy metal uranium is a mixture of, isotopes of which 235, 92 U , called uranium-235, is, the most important. Some atoms of this isotope, decay quite naturally, emitting high-speed, neutrons. If one of these hits the nucleus of a, neighbouring uranium-235 atom (being uncharged, the neutron is not repelled by the nucleus), this, may break (fission of the nucleus) into two nearly, equal radioactive nuclei, often of barium and, krypton, with the production of two or three more, neutrons:, +, , 1, 0n, , →, , 144 Ba, 56, , +, , fission, fragment, , fission neutron, U-235, , E = mc2, , 235U, 92, , U-235, , 90, 36 Kr, , +, , 2 01 n, , neutron, neutronfission, fission, fragments, fragments, neutro, neutro, ons ons, The mass defect is large and appears mostly as k.e. of, the fission fragments. These fly apart at great speed,, , U-235, , Figure 50.9 Chain reaction, , c) Nuclear reactor, In a nuclear power station heat from a nuclear, reactor produces the steam for the turbines., Figure 50.10 is a simplified diagram of one type of, reactor., The chain reaction occurs at a steady rate, which is controlled by inserting or withdrawing, neutron-absorbing rods of boron among the, uranium rods. The graphite core is called the, moderator and slows down the fission neutrons;, fission of uranium-235 occurs more readily with, slow than with fast neutrons. Carbon dioxide, gas is pumped through the core and carries, off heat to the heat exchanger where steam is, produced. The concrete shield gives workers, protection from γ-rays and escaping neutrons. The, radioactive fission fragments must be removed, periodically if the nuclear fuel is to be used, efficiently., In an atomic bomb, an increasing uncontrolled, chain reaction occurs when two pieces of, uranium-235 come together and exceed the, critical mass., , 242, , 9781444176421_Section_05.indd 242, , 20/06/14 7:42 AM
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Nuclear energy, , hot gas, , concrete shield, , steam, boron rod, , heat exchanger, uranium rod, graphite core, cold water, , cold, gas, , pump, , Figure 50.10 Nuclear reactor, , d) Fusion, If light nuclei join together to make heavier ones,, this can also lead to a loss of mass and, as a result,, the release of energy. Such a reaction has been, achieved in the hydrogen bomb. At present,, research is being done on the controlled fusion of, isotopes of hydrogen (deuterium and tritium) to, give helium., 2H, 1, , +, , deuterium, , 3H, 1, , →, , 4 He, 2, , tritium helium, , +, , 1, 0n, , neutron, , Fusion can only occur if the reacting nuclei, have enough energy to overcome their mutual, electrostatic repulsion. This can happen if they, are raised to a very high temperature (over, 100 million ºC) so that they collide at very high, speeds. If fusion occurs, the energy released is, , enough to keep the reaction going; since heat is, required, it is called thermonuclear fusion., The source of the Sun’s energy is nuclear, fusion. The temperature in the Sun is high enough, for the conversion of hydrogen into helium to, occur, in a sequence of thermonuclear fusion, reactions known as the ‘hydrogen burning’, sequence., 1H, 1, , + 11Η → 21H + positron ( 01e) + neutrino ( ν), 1H, 1, 3, 2 He, , + 21Η → 23 He + γ − ray, , + 23Ηe → 42 He + 11H+ 11H, , Each of these fusion reactions results in a loss of, mass and a release of energy. Overall, tremendous, amounts of energy are created that help to maintain, the very high temperature of the Sun., , 243, , 9781444176421_Section_05.indd 243, , 20/06/14 7:42 AM
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50 Atomic stRuctuRe, , Questions, 1 Which one of the following statements is not true?, A An atom consists of a tiny nucleus surrounded by, orbiting electrons., B The nucleus always contains protons and neutrons,, called nucleons, in equal numbers., C A proton has a positive charge, a neutron is uncharged, and their mass is about the same., D An electron has a negative charge of the same size as, the charge on a proton but it has a much smaller mass., E The number of electrons equals the number of protons, in a normal atom., 2 A lithium atom has a nucleon (mass) number of 7 and a, proton (atomic) number of 3., 1 Its symbol is 47Li ., 2 It contains three protons, four neutrons and three, electrons., 3 An atom containing three protons, three neutrons and, three electrons is an isotope of lithium., Which statement(s) is (are) correct?, A 1, 2, 3, B 1, 2, C 2, 3, D 1, E 3, , Checklist, After studying this chapter you should be able to, • describe how Rutherford and Bohr contributed to views, about the structure of the atom,, • describe the Geiger–Marsden experiment which, established the nuclear model of the atom,, • recall the charge, relative mass and location in the atom of, protons, neutrons and electrons,, • define the terms proton number (Z), neutron number (N), and nucleon number (A), and use the equation A = Z + N,, • explain the terms isotope and nuclide and use symbols to, 35Cl ,, represent them, e.g. 17, • write equations for radioactive decay and interpret them,, • connect the release of energy in a nuclear reaction with a, change of mass according to the equation E = mc2,, • outline the process of fission,, • outline the process of fusion., , 244, , 9781444176421_Section_05.indd 244, , 20/06/14 7:42 AM
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evision questions, R, 6, , General physics, Measurements and motion, 1, , 2, , 3, , Which are the basic SI units of mass, length and, time?, A kilogram, kilometre, second, B gram, centimetre, minute, C kilogram, centimetre, second, D gram, centimetre, second, E kilogram, metre, second, Density can be calculated from the expression, A mass/volume, B mass × volume, C volume/mass, D weight/area, E area × weight, Which of the following properties are the same, for an object on Earth and on the Moon?, 1 weight 2 mass 3 density, Use the answer code:, A 1, 2, 3 B 1, 2 C 2, 3 D 1 E 3, , 4 a The smallest division marked on a metre rule, is 1 mm. A student measures a length with the, ruler and records it as 0.835 m. Is he justified in, giving three significant figures?, b The SI unit of density is, A kg m B kg/m2 C kg m3, D kg/m E kg/m3, , ball, 4, , A 3 kg mass falls with its terminal velocity., Which of the combinations A to E gives its, weight, the air resistance and the resultant force, acting on it?, , A, , Weight, , Air resistance, , Resultant force, , 0.3 N down, , zero, , zero, , B, , 3 N down, , 3 N up, , 3 N up, , C, , 10 N down, , 10 N up, , 10 N down, , D, , 30 N down, , 30 N up, , zero, , E, , 300 N down, , zero, , 300 N down, , 3, , O, , X, , 2, 5, , 1, , Energy, work, power and pressure, 7, , The work done by a force is, 1 calculated by multiplying the force by the, distance moved in the direction of the force, 2 measured in joules, 3 the amount of the energy changed., Which statement(s) is (are) correct?, A 1, 2, 3 B 1, 2 C 2, 3 D 1 E 3, , 8, , The main energy change occurring in the device, named is, 1 electric lamp, electrical to heat and light, 2 battery, chemical to electrical, 3 pile driver, k.e. to p.e., Which statement(s) is (are) correct?, A 1, 2, 3 B 1, 2 C 2, 3 D 1 E 3, , 9, , The efficiency of a machine which raises a load, of 200 N through 2 m when an effort of 100 N, moves 8 m is, A 0.5% B 5% C 50%, D 60% , E 80% , , Forces and momentum, 5, , A boy whirls a ball at the end of a string round, his head in a horizontal circle, centre O. He, lets go of the string when the ball is at X in the, diagram. In which direction does the ball fly off?, A 1 B 2 , C 3 D 4 E 5, , 10 Which one of the following statements is not true?, A Pressure is the force acting on unit area., B Pressure is calculated from force/area., C The SI unit of pressure is the pascal (Pa) which, equals 1 newton per square metre (1 N/m2)., D The greater the area over which a force acts, the greater is the pressure., E Force = pressure × area., , 245, , 9781444176421_BM_06.indd 245, , 20/06/14 7:28 AM
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Revision questions, , 11 A stone of mass 2 kg is dropped from a height of 4 m., Neglecting air resistance, the kinetic energy (k.e.) of, the stone in joules just before it hits the ground is, A 6 B 8 C 16 D 80 E 160, 12 An object of mass 2 kg is fired vertically upwards, with a k.e. of 100 J. Neglecting air resistance,, which of the numbers in A to E below is, a the velocity in m/s with which it is fired,, b the height in m to which it will rise?, A 5 B 10 C 20 D 100 E 200, 13 An object has k.e. of 10 J at a certain instant. If, it is acted on by an opposing force of 5 N, which, of the numbers A to E below is the furthest, distance it travels in metres before coming to rest?, A 2 B 5 C 10 D 20 E 50, , 2 Thermal physics, Thermal properties and temperature, 14 If the piston in the diagram is pulled out of the, cylinder from position X to position Y, without, changing the temperature of the air enclosed, the, air pressure in the cylinder is, A reduced to a quarter, B reduced to a third, C the same, D trebled, E quadrupled., 30 cm, , piston, , Y, , 10 cm, , X, , cylinder, , 15 Which one of the following statements is not true?, A Temperature tells us how hot an object is., B Temperature is measured by a thermometer, which uses some property of matter (e.g., the expansion of mercury) that changes, continuously with temperature., , C Heat flows naturally from an object at a lower, temperature to one at a higher temperature., D The molecules of an object move faster when, its temperature rises., E Temperature is measured in °C, heat is, measured in joules., 16 The pressure exerted by a gas in a container, 1 is due to the molecules of the gas bombarding, the walls of the container, 2 decreases if the gas is cooled, 3 increases if the volume of the container, increases., Which statement(s) is (are) correct?, A 1, 2, 3 B 1, 2 C 2, 3 D 1 E 3, 17 A drink is cooled more by ice at 0 °C than by the, same mass of water at 0 °C because ice, A floats on the drink, B has a smaller specific heat capacity, C gives out latent heat to the drink as it melts, D absorbs latent heat from the drink to melt, E is a solid., , Thermal processes, 18 Which of the following statements is/are true?, 1 In cold weather the wooden handle of a, saucepan feels warmer than the metal pan, because wood is a better conductor of heat., 2 Convection occurs when there is a change of, density in parts of a fluid., 3 Conduction and convection cannot occur in a, vacuum., A 1, 2, 3 B 1, 2 C 2, 3 D 1 E 3, 19 Which one of the following statements is not true?, A Energy from the Sun reaches the Earth by, radiation only., B A dull black surface is a good absorber of, radiation., C A shiny white surface is a good emitter of, radiation., D The best heat insulation is provided by a vacuum., E A vacuum flask is designed to reduce heat, loss or gain by conduction, convection and, radiation., , 246, , 9781444176421_BM_06.indd 246, , 20/06/14 7:28 AM
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Revision questions, , 23 The diagram below shows the complete, electromagnetic spectrum., , 3 Properties of waves, General wave properties, 20 In the transverse wave shown below distances are, in centimetres. Which pair of entries A to E is, correct?, A, , B, , C, , D, , E, , Amplitude, , 2, , 4, , 4, , 8, , 8, , Wavelength, , 4, , 4, , 8, , 8, , 12, , 8, 6, 4, 2, , 0, , 2, , 4, , 6, , 8, , 10, , 12, , 21 When a water wave goes from deep to shallow, water, the changes (if any) in its speed,, wavelength and frequency are, Speed, , Wavelength, , Frequency, , A, , greater, , greater, , the same, , B, , greater, , less, , less, , C, , the same, , less, , greater, , D, , less, , the same, , less, , E, , less, , less, , the same, , 22 When the straight water waves in the diagram, pass through the narrow gap in the barrier they, are diffracted. What changes (if any) occur in, a the shape of the waves,, b the speed of the waves,, c the wavelength?, , radio, waves, , microwaves, , A, , visible, ultraviolet, light, , B, , , rays, , a Name the radiation found at, (i) A,, (ii) B., b State which of the radiations marked on the, diagram would have, (i) the lowest frequency,, (ii) the shortest wavelength., 24 The wave travelling along the spring in the, diagram is produced by someone moving end X, of the spring to and fro in the directions shown, by the arrows., a Is the wave longitudinal or transverse?, b What is the region called where the coils of, the spring are (i) closer together, (ii) further, apart, than normal?, X, , Light, 25 In the diagram a ray of light is shown reflected at, a plane mirror. What is, a the angle of incidence,, b the angle the reflected ray makes with the mirror?, incident ray, , 30°, , reflected ray, , 247, , 9781444176421_BM_06.indd 247, , 20/06/14 7:28 AM
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Revision questions, , 26 In the diagram below a ray of light IO changes, direction as it enters glass from air., a What name is given to this effect?, b Which line is the normal?, c Is the ray bent towards or away from the, normal in the glass?, d What is the value of the angle of incidence in air?, e What is the value of the angle of refraction in, glass?, P, I, , air, 40°, O, , X, , 29 When using a magnifying glass to see a small object, 1 an upright image is seen, 2 the object should be less than one focal length, away, 3 a real image is seen., Which statement(s) is (are) correct?, A 1, 2, 3 B 1, 2 C 2, 3 D 1 E 3, , Sound, 30 If a note played on a piano has the same pitch as, one played on a guitar, they have the same, A frequency, B amplitude, C quality, D loudness, E harmonics., 31 The waveforms of two notes P and Q are shown, below. Which one of the statements A to E is true?, , Y, , 65°, glass, R, Q, , 27 In the diagram, which of the rays A to E is most, likely to represent the ray emerging from the, parallel-sided sheet of glass?, D, , C, , B, , A, air, , E, , P, , A, B, C, D, E, , Q, , P has a higher pitch than Q and is not so loud., P has a higher pitch than Q and is louder., P and Q have the same pitch and loudness., P has a lower pitch than Q and is not so loud., P has a lower pitch than Q and is louder., , 32 Examples of transverse waves are, 1 water waves in a ripple tank, 2 all electromagnetic waves, 3 sound waves., Which statement(s) is (are) correct?, A 1, 2, 3 B 1, 2 C 2, 3 D 1 E 3, , glass, , air, ray of light, , 28 A narrow beam of white light is shown passing, through a glass prism and forming a spectrum on, a screen., a What is the effect called?, b Which colour of light appears at (i) A, (ii) B?, , screen, , te, whi, , A, , t, , ligh, , prism, , B, , 248, , 9781444176421_BM_06.indd 248, , 20/06/14 7:28 AM
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Revision questions, , 4 Electricity and magnetism, Simple phenomena of magnetism, 33 Which one of the following statements about the, diagram below is not true?, Y, , S, , N, , N, , P, , Q, , S, , X, , S, , coil, , N, , A If a current is passed through the wire XY, a, vertically upwards force acts on it., B If a current is passed through the wire PQ, it, does not experience a force., C If a current is passed through the coil, it, rotates clockwise., D If the coil had more turns and carried a larger, current, the turning effect would be greater., E In a moving-coil loudspeaker a coil moves, between the poles of a strong magnet., , 36 An electric kettle for use on a 230 V supply, is rated at 3000 W. For safe working, the cable, supplying it should be able to carry at least, A 2 A B 5 A C 10 A D 15 A E 30 A, 37 Which one of the following statements is not true?, A In a house circuit, lamps are wired in parallel., B Switches, fuses and circuit breakers should be, placed in the neutral wire., C An electric fire has its earth wire connected to, the metal case to prevent the user receiving, a shock., D When connecting a three-core cable to a, 13 A three-pin plug the brown wire goes to, the live pin., E The cost of operating three 100 W lamps for, 10 hours at 10p per unit is 30p., 38 Which of the units A to E could be used to measure, a electric charge,, b electric current,, c p.d.,, d energy,, e power?, A ampere B joule C volt D watt, E coulomb, 39 Which one of the following statements about the, transistor circuit shown below is not true?, lC, , Electrical quantities and circuits, 34 For the circuit below calculate, a the total resistance,, b the current in each resistor,, c the p.d. across each resistor., , X, B, , 6V, , lB, , Y, VBE, , E, , 2Ω, , 2Ω, , 35 Repeat question 33 for the circuit below., 6V, , 2Ω, , C, , A The collector current IC is zero until base, current IB flows., B IB is zero until the base–emitter p.d. VBE is, +0.6 V., C A small IB can switch on and control a large IC., D When used as an amplifier the input is, connected across B and E., E X must be connected to supply the – terminal, and Y to the + terminal., , 1Ω, , 249, , 9781444176421_BM_06.indd 249, , 20/06/14 7:28 AM
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Revision questions, , 40 A magnet is pushed, N pole first, into a coil as in, the diagram below. Which one of the following, statements A to E is not true?, A A p.d. is induced in the coil and causes a, current through the galvanometer., B The induced p.d. increases if the magnet is, pushed in faster and/or the coil has more turns., C Mechanical energy is changed to electrical, energy., D The coil tends to move to the right, because the induced current makes face X a, N pole which is repelled by the N pole of the, magnet., E The effect produced is called electrostatic, induction., S, , N, , coil, , X, , magnet, 0, galvanometer, , 5 Atomic physics, 41 The diagram shows three types of radiation, X, Y, and Z., , 42 The graph shows the decay curve of a radioactive, substance., count rate/counts per s, , Electromagnetic effects, , 120, 90, 60, 30, 0, , 1, , 2, 3, 4, time/min, , 5, , What is its half-life in minutes?, A 1 B 2 C 3 D 4 E 5, 43 A radioactive source which has a half-life of, 1 hour gives a count-rate of 100 counts per, second at the start of an experiment and, 25 counts per second at the end. The time taken, by the experiment was, in hours,, A 1 B 2 C 3 D 4 E 5, 44 Which symbol A to E below is used in equations, for nuclear reactions to represent, a an alpha particle,, b a beta particle,, c a neutron,, d an electron?, A −10e B 01 n C 42 He D −11e E 11 n, 45 a Radon 220, 86 Rn decays by emitting an alpha, particle to form an element whose symbol is, 218Po, 216, A 216, 85 At B 86 Rn C 84, , X, Y, Z, , D, paper, , aluminium, , lead, , Which of the columns A to E correctly names, the radiations X, Y and Z?, A, , B, , C, , D, , E, , X, , alpha, , beta, , gamma, , gamma, , beta, , Y, , beta, , alpha, , alpha, , beta, , gamma, , Z, , gamma, , gamma, , beta, , alpha, , alpha, , 216 Po, 84, , E, , 217 At, 85, , b Thorium 234, 90Th decays by emitting a beta, particle to form an element whose symbol is, A, , 235 Th, 90, , B, , 230 Ac, 89, , D, , 232 Ra, 88, , E, , 234 Pa, 91, , C, , 234 Ac, 89, , 250, , 9781444176421_BM_06.indd 250, , 20/06/14 7:29 AM
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Cambridge IGCSE exam questions, 1 General physics, , block, , Measurements and motion, 1 a (i) The two diagrams show the dimensions of, a rectangular block being measured using, a ruler. They are not shown full size., Use the scales shown to find the length, and the width of the block, giving your, answers in cm., [2], , 40, , 50, 60, grams, , 70, , Find the density of this block., , [4], [Total: 8], , (Cambridge IGCSE Physics 0625 Paper 21 Q1, November 2010), , 140 150 160 170 180 190 200 210 220 230 240 250, millimetres, 50, , 60, , 70, , 80, , 90 100 110 120 130 140 150 160, 80, 70, 60, 50, 40, 30, 20, 10, 140, , 140 210 220 230 240 250 260 270 280 290 300 250, millimetres, , 90 250, , 2, , (ii) When the block was made, it was cut from, a piece of metal 2.0 cm thick., Calculate the volume of the block., [2], b Another block has a volume of 20 cm3., The diagram shows the reading when the, block is placed on a balance., , An engineering machine has a piston which is, going up and down approximately 75 times per, minute., Describe carefully how a stopwatch may be used, to find accurately the time for one up-and-down, cycle of the piston., [4], [Total: 4], (Cambridge IGCSE Physics 0625 Paper 31 Q1 June 2009), , 3, , Imagine that you live beside a busy road. One of, your neighbours thinks that many of the vehicles, are travelling faster than the speed limit for the, road., You decide to check this by measuring the speeds, of some of the vehicles., a Which two quantities will you need to, measure in order to find the speed of a vehicle,, and which instruments would you use to, measure them?, , Quantity measured, , Instrument used, , [4], b State the equation you would use to calculate, the speed of the vehicle. If you use symbols,, state what your symbols mean., [1], 251, , 9781444176421_BM_06.indd 251, , 20/06/14 7:29 AM
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Cambridge IGCSE exam questions, , c One lorry travels from your town to another, town. The lorry reaches a top speed of, 90 km/h, but its average speed between the, towns is only 66 km/h., (i) Why is the average speed less than, the top speed?, [1], (ii) The journey between the towns takes, 20 minutes., Calculate the distance between, the towns., [3], , (ii) On a copy of the speed/time axes on the, bottom graph, draw a thick line that could, show the speed during AB., [1], b On your copy of the speed/time axes, (i) draw a thick line that could show the, speed during BC,, [1], (ii) draw a thick line that could show the, speed during CD., [2], c How far from her starting point is the girl, when she has finished her ride?, [1], , [Total: 9], , [Total: 8], , (Cambridge IGCSE Physics 0625 Paper 21 Q1 June 2010), , (Cambridge IGCSE Physics 0625 Paper 02 Q3, November 2009), , distance from, starting point, , 4 The top graph shows the distance/time graph for, a girl’s bicycle ride and the bottom graph gives, the axes for the corresponding speed/time graph., , 5 In a training session, a racing cyclist’s journey is, in three stages., Stage 1 He accelerates uniformly from rest to, 12 m/s in 20 s., Stage 2 He cycles at 12 m/s for a distance of 4800 m., Stage 3 He decelerates uniformly to rest., The whole journey takes 500 s., a Calculate the time taken for stage 2., [2], b On a copy of the grid below, draw a, speed/time graph of the cyclist’s ride., [3], 14, 12, , 0, A, , B, , C, , D, , time, , speed/m/s, , 10, 8, 6, 4, 2, , speed, , 0, , 0, A, , B, , C, , D, , time, , a Look at the distance/time graph that has been, drawn for you., (i) Answer the following questions for the, time interval AB., 1 What is happening to the distance, from the starting point?, [2], 2 What can you say about the speed of, the bicycle?, [1], , 0, , 100, , 200, , 300, time/s, , 400, , 500, , c Show that the total distance travelled by the, cyclist is 5400 m., [4], d Calculate the average speed of the cyclist. [2], [Total: 11], (Cambridge IGCSE Physics 0625 Paper 02 Q2 June 2007), , 252, , 9781444176421_BM_06.indd 252, , 20/06/14 7:29 AM
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Cambridge IGCSE exam questions, , 6 A large plastic ball is dropped from the top of, a tall building. The diagram shows the speed/, time graph for the falling ball until it hits the, ground., , 120, , extension/mm, , 100, , 20, , speed/m/s, , 15, 10, , 80, , 60, , 40, 5, 20, , 0, 0, , 1, , 2, , 3, time/s, , 4, , 5, , 6, 0, 0, , a From the graph estimate,, (i) the time during which the ball is, travelling with terminal velocity,, (ii) the time during which the ball is, accelerating,, (iii) the distance fallen while the ball is, travelling with terminal velocity,, (iv) the height of the building., b Explain, in terms of the forces acting, on the ball, why, (i) the acceleration of the ball decreases,, (ii) the ball reaches terminal velocity., , [1], [1], [2], [2], [3], [2], , [Total: 11], (Cambridge IGCSE Physics 0625 Paper 03 Q1, November 2007), , Forces and momentum, 7 A student investigated the stretching of a, spring by hanging various weights from it and, measuring the corresponding extensions. The, results are shown in the table below., Weight/N, , 0, , 1, , 2, , 3, , 4, , 5, , Extension/mm, , 0, , 21, , 40, , 51, , 82, , 103, , 1, , 2, , 3, weight/N, , 4, , 5, , 6, , b The student appears to have made an error in, recording one of the results. Which result is, this?, [1], c Ignoring the incorrect result, draw the, best straight line through the remaining, points., [1], d State and explain whether this spring is, obeying Hooke’s law., [2], e Describe how the graph might be shaped, if the student continued to add several, more weights to the spring., [1], f The student estimates that if he hangs, a 45 N load on the spring, the extension, will be 920 mm., Explain why this estimate may be, unrealistic., [1], [Total: 8], (Cambridge IGCSE Physics 0625 Paper 31 Q3, November 2009), , a On a copy of the grid, plot the points from, these results. Do not draw a line through, the points yet., [2], , 253, , 9781444176421_BM_06.indd 253, , 20/06/14 7:29 AM
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Cambridge IGCSE exam questions, , 8, , In an experiment, forces are applied to a spring, as shown in the diagram. The results of this, experiment are shown on the graph., 16.0, Q, , R, , 12.0, force/N, , spring, , P, , 8.0, , [Total: 6], 4.0, , (Cambridge IGCSE Physics 0625 Paper 31 Q1, November 2010), , weights, 0, , ruler, , 0, , 2.0, 4.0, 6.0, extension/mm, , a, , b, , a What is the name given to the point marked Q, on the graph?, [1], b For the part OP of the graph, the spring obeys, Hooke’s law. State what this means., [1], c The spring is stretched until the force and, extension are shown by the point R on the, graph. Compare how the spring stretches, as, shown by the part of the graph OQ, with that, shown by QR., [1], d The part OP of the graph shows the spring, stretching according to the expression, F = kx, Use values from the graph to calculate the, value of k., [2], [Total: 5], (Cambridge IGCSE Physics 0625 Paper 03 Q2, November 2006), , 9, , An object of weight W is suspended by two ropes, from a beam, as shown in the diagram. The tensions, in the ropes are 50.0 N and 86.6 N, as shown., , 50.0 N, , a On graph paper, draw a scale diagram to find, the resultant of the two tensions., Use a scale of 1.0 cm = 10 N., Clearly label the resultant., [3], b From your diagram, find the value of the, resultant., [1], c State the direction in which the resultant is, acting., [1], d State the value of W., [1], , 60°, , 30°, , W, , 86.6 N, , 10 The diagram shows a circular metal disc of mass, 200 g, freely pivoted at its centre., pivot, , Masses of 100 g, 200 g, 300 g, 400 g, 500 g and, 600 g are available, but only one of each value., These may be hung with string from any of the, holes. There are three small holes on each side of, the centre, one at 4.0 cm from the pivot, one at, 8.0 cm from the pivot and one at 12.0 cm from, the pivot., The apparatus is to be used to show that there is, no net moment of force acting on a body when it, is in equilibrium., a On a copy of the diagram, draw in two, different value masses hanging from, appropriate holes. The values of the masses, should be chosen so that there is no net, moment. Alongside the masses chosen, write, down their values., [2], b Explain how you would test that your, chosen masses give no net moment to, the disc., [1], c Calculate the moments about the pivot, due to the two masses chosen., [2], , 254, , 9781444176421_BM_06.indd 254, , 20/06/14 7:29 AM
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Cambridge IGCSE exam questions, , d Calculate the force on the pivot when, the two masses chosen are hanging from, the disc., , stiff, cardboard, , [2], , [Total: 7], , sticky-tape, ‘hinge’, SUPER, MATCH, ES, , plank, of wood, , (Cambridge IGCSE Physics 0625 Paper 31 Q2, November 2008), , 11 A piece of stiff cardboard is stuck to a plank of, wood by means of two sticky-tape ‘hinges’. This, is shown in the diagram., , (i) Copy and complete the sentence below,, using either the words ‘greater than’ or, ‘the same as’ or ‘less than’., , stiff, cardboard, , When the box of matches is open, the, angle through which the cardboard can, be lifted before the box of matches falls is, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . the angle, before the closed box of matches falls. [1], (ii) Give a reason for your answer to c(i). [1], , sticky-tape, ‘hinge’, , plank, of wood, A, , B, , C, , [Total: 7], , a The cardboard is lifted as shown, using a force, applied either at A or B or C., (i) On a copy of the diagram, draw the force, in the position where its value will be as, small as possible., [2], (ii) Explain why the position you have chosen, in a(i) results in the smallest force., [1], b Initially, the cardboard is flat on the plank of, wood. A box of matches is placed on it. The, cardboard is then slowly raised at the left-hand, edge, as shown in the diagram below., stiff, cardboard, sticky-tape, ‘hinge’, SUPER, MATCH, ES, , plank, of wood, , State the condition for the box of, matches to fall over., [2], c The box of matches is opened, as shown in, the diagram below. The procedure in b is, repeated., , (Cambridge IGCSE Physics 0625 Paper 02 Q3 June 07), , 12 a State the two factors on which the turning, effect of a force depends., [2], b Forces F1 and F2 are applied vertically, downwards at the ends of a beam resting on a, pivot P. The beam has weight W., F, , F1, , P, , W, , F2, , (i) Copy and complete the statements about, the two requirements for the beam to be, in equilibrium., 1 There must be no resultant . . ., 2 There must be no resultant . . ., [2], (ii) The beam is in equilibrium. F is the force, exerted on the beam by the pivot P. Copy, and complete the following equation, about the forces on the beam., F=, [1], (iii) Which one of the four forces on the beam, does not exert a moment about P?, [1], [Total: 6], (Cambridge IGCSE Physics 0625 Paper 02 Q5, November 2006), 255, , 9781444176421_BM_06.indd 255, , 20/06/14 7:29 AM
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Cambridge IGCSE exam questions, , 13 Two students make the statements about, acceleration that are given below., Student A: For a given mass the acceleration of, an object is proportional to the resultant force, applied to the object., Student B: For a given force the acceleration of, an object is proportional to the mass of the object., a One statement is correct and one is incorrect., Rewrite the incorrect statement, making, changes so that it is now correct., [1], b State the equation which links acceleration, a, resultant force F and mass m., [1], c Describe what happens to the motion of a, moving object when, (i) there is no resultant force acting on it, [1], (ii) a resultant force is applied to it in the, opposite direction to the motion,, [1], (iii) a resultant force is applied to it in a, perpendicular direction to the motion. [1], [Total: 5], (Cambridge IGCSE Physics 0625 Paper 31 Q3 June 2010), , 14 A car travels around a circular track at constant speed., a Why is it incorrect to describe the circular, motion as having constant velocity?, [1], b A force is required to maintain the circular, motion., (i) Explain why a force is required., [2], (ii) In which direction does this force act? [1], (iii) Suggest what provides this force., [1], , Weight of the hanging, mass/N, , Acceleration of the, trolley/m/s2, , 0.20, , 0.25, , 0.40, , 0.50, , 0.70, 0.80, , 1.0, , a (i) Explain why the trolley accelerates., [2], (ii) Suggest why the runway has a slight, slope as shown., [1], b Calculate the mass of the trolley, assuming, that the accelerating force is equal to the, weight of the hanging mass., [2], c Calculate the value missing from the table., Show your working., [2], d In one experiment, the hanging mass has a, weight of 0.4 N and the trolley starts from rest., Use data from the table to calculate, (i) the speed of the trolley after 1.2 s,, [2], (ii) the distance travelled by the trolley, in 1.2 s., [2], [Total: 11], (Cambridge IGCSE Physics 0625 Paper 31 Q1, November 2008), , 16 The diagram shows a model car moving, clockwise around a horizontal circular track., direction, of movement, , [Total: 5], (Cambridge IGCSE Physics 0625 Paper 31 Q2, November 2010), , model, car, , P, , 15 The diagram shows apparatus used to find a, relationship between the force applied to a trolley, and the acceleration caused by the force., string, , hanging, mass, , trolley, , tickertape, , ticker-tape, timer, , roll of, tape, , circular, track, , runway, , For each mass, hung as shown, the acceleration, of the trolley is determined from the tape. Some, of the results are given in the table below., , a A force acts on the car to keep it moving in, a circle., (i) Draw an arrow on a copy of the diagram, to show the direction of this force., [1], , 256, , 9781444176421_BM_06.indd 256, , 20/06/14 7:29 AM
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Cambridge IGCSE exam questions, , (ii) The speed of the car increases. State, what happens to the magnitude, of this force., [1], b (i) The car travels too quickly and leaves the, track at P. On your copy of the diagram,, draw an arrow to show the direction of, travel after it has left the track., [1], (ii) In terms of the forces acting on the car,, suggest why it left the track at P., [2], c The car, starting from rest, completes one, lap of the track in 10 s. Its motion is shown, graphically in the graph below., , b An electric motor and a pulley in a warehouse, are being used to lift a packing case of goods, from the ground up to a higher level. This is, shown in the diagram., , electric, motor, , pulley, , 30, cable, , speed/cm/s, , 25, 20, 15, , chains, , 10, , packing, case, , 5, pallet, 0, , 0, , 1, , 2, , 3, , 4, , 5, 6, time/s, , 7, , 8, , 9, , 10, , (i) Describe the motion between 3.0 s and, 10.0 s after the car has started., [1], (ii) Use the graph to calculate the, circumference of the track., [2], (iii) Calculate the increase in speed per second, during the time 0 to 3.0 s., [2], [Total: 10], (Cambridge IGCSE Physics 0625 Paper 03 Q1, June 2007), , Energy, work, power and pressure, 17 a The diagram represents the energy into and, out of a machine., useful, output, energy U, , input, energy I, , wasted, energy W, , Write down the equation linking I, U, and W., , ground, , The packing case of goods, the chains and the, pallet together weigh 850 N., (i) State the value of the tension force in the, cable when the load is being lifted at a, steady speed., [1], (ii) When the load is just leaving the, floor, why is the force larger than your, answer to b(i)?, [1], (iii) The warehouse manager wishes to, calculate the useful work done when, the load is lifted from the ground, to the higher level. Which quantity,, other than the weight, does he need to, measure?, [1], (iv) Which further quantity does the, manager need to know, in order to, calculate the power required to lift, the load?, [1], , [1], 257, , 9781444176421_BM_06.indd 257, , 20/06/14 7:29 AM
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Cambridge IGCSE exam questions, , c How does the electrical energy supplied to, the electric motor compare with the increase, in energy of the load? Answer by copying and, completing the sentence., , 20 The diagram shows a manometer, containing, mercury, being used to monitor the pressure of a, gas supply., mm, , The electrical energy supplied to the motor is, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . the increase, in energy of the load., [1], , 300, , [Total: 6], , 250, , (Cambridge IGCSE Physics 0625 Paper 21 Q3 June 2010), 200, , from a, gas supply, , 18 A car of mass 900 kg is travelling at a steady, speed of 30 m/s against a resistive force of, 2000 N, as illustrated in the diagram., , 150, , 30 m/s, 100, 2000 N, resistive, force, , 50, mercury, , a Calculate the kinetic energy of the car., b Calculate the energy used in 1.0 s against, the resistive force., c What is the minimum power that the car, engine has to deliver to the wheels?, d What form of energy is in the fuel, used, by the engine to drive the car?, e State why the energy in the fuel is, converted at a greater rate than you have, calculated in c., , [2], , 0, , [2], [1], [1], [1], , [Total: 7], (Cambridge IGCSE Physics 0625 Paper 31 Q2 June 2010), , 19 a Name three different energy resources, used to obtain energy directly from water, (not steam)., [3], b Choose one of the energy resources you have, named in a and write a brief description of, how the energy is converted to electrical, energy., [3], , a Using the scale on the diagram, find the, vertical difference between the two, mercury levels., [1], b What is the value of the excess pressure of, the gas supply, measured in millimetres of, mercury?, [1], c The atmospheric pressure is 750 mm of, mercury., Calculate the actual pressure of the gas, supply., [1], d The gas pressure now decreases by, 20 mm of mercury. On a copy of the diagram,, mark the new positions of the two, mercury levels., [2], [Total: 5], (Cambridge IGCSE Physics 0625 Paper 02 Q4 June 2009), , [Total: 6], (Cambridge IGCSE Physics 0625 Paper 21 Q3, November 2010), , 258, , 9781444176421_BM_06.indd 258, , 20/06/14 7:29 AM
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Cambridge IGCSE exam questions, , 21 The diagram shows a design for remotely, operating an electrical switch using air pressure., electrical switch, operated by, air pressure, , flexible rubber, box cover, , 22 The diagram shows two mercury barometers, standing side-by-side. The right-hand diagram is, incomplete. The space labelled X is a vacuum., X, glass, tube, , connecting pipe, , metal, box, , The metal box and the pipe contain air at normal, atmospheric pressure and the switch is off. When, the pressure in the metal box and pipe is raised to, 1.5 times atmospheric pressure by pressing down on, the flexible rubber box cover, the switch comes on., a Explain in terms of pressure and volume, how the switch is made to come on., [2], 5, b Normal atmospheric pressure is 1.0 × 10 Pa., At this pressure, the volume of the box and, pipe is 60 cm3., Calculate the reduction in volume that must, occur for the switch to be on., [3], c Explain, in terms of air particles, why the, switch may operate, without the rubber cover, being squashed, when there is a large rise in, temperature., [2], [Total: 7], (Cambridge IGCSE Physics 0625 Paper 31, Q4 June 2008), , dish, , mercury, , a On a copy of the left-hand barometer,, carefully mark the distance that would have to, be measured in order to find the value of, the atmospheric pressure., [2], b A small quantity of air is introduced into X., (i) State what happens to the mercury, level in the tube., [1], (ii) In terms of the behaviour of the air, molecules, explain your answer to b(i). [2], c The space above the mercury in the righthand barometer is a vacuum., On a copy of the right-hand diagram, mark, the level of the mercury surface in the tube., , [1], d The left-hand tube now has air above the, mercury; the right-hand tube has a vacuum., complete the table below, using words chosen, from the following list, to indicate the effect, of changing the external conditions., rises falls stays the same, effect on the level of, the mercury in the, left-hand tube, , change, , effect on the level of, the mercury in the, right-hand tube, , atmospheric pressure, rises, temperature rises, , , , [4], [Total: 10], (Cambridge IGCSE Physics 0625 Paper 02 Q6, November 2008), 259, , 9781444176421_BM_06.indd 259, , 20/06/14 7:29 AM
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Cambridge IGCSE exam questions, , 23 A wind turbine has blades, which sweep out an, area of diameter 25 m as shown in the diagram., 25 m, , blades, , a The wind is blowing directly towards the wind, turbine at a speed of 12 m/s. At this wind speed,, 7500 kg of air passes every second through the, circular area swept out by the blades., (i) Calculate the kinetic energy of the air, travelling at 12 m/s, which passes, through the circular area in 1 second. [3], (ii) The turbine converts 10% of the kinetic, energy of the wind to electrical energy., Calculate the electrical power output, of the turbine. State any equation, that you use., [3], b On another day, the wind speed is half that in a., (i) Calculate the mass of air passing through, the circular area per second on this day. [1], (ii) Calculate the power output of the, wind turbine on the second day as a, fraction of that on the first day., [3], , 2 Thermal physics, Simple kinetic molecular model of matter, 24 The whole of a sealed, empty, dusty room is kept, at a constant temperature of 15 °C. Light shines, into the room through a small outside window., An observer points a TV camera with a, magnifying lens into the room through a second, small window, set in an inside wall at right angles, to the outside wall., Dust particles in the room show up on the TV, monitor screen as tiny specks of light., a Draw a diagram to show the motion of, one of the specks of light over a short, period of time., [1], b After a period of one hour the specks are, still observed, showing that the dust, particles have not fallen to the floor., Explain why the dust particles have not, fallen to the floor. You may draw a labelled, diagram to help your explanation., [2], c On another day, the temperature of the room, is only 5 °C. All other conditions are the same, and the specks of light are again observed., Suggest any differences that you would expect, in the movement of the specks when the, temperature is 5 °C, compared to before. [1], [Total: 4], (Cambridge IGCSE Physics 0625 Paper 31 Q4, November 2008), , [Total: 10], (Cambridge IGCSE Physics 0625 Paper 31 Q5 June 2009), , 260, , 9781444176421_BM_06.indd 260, , 20/06/14 7:29 AM
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Cambridge IGCSE exam questions, , 25 a Here is a list of descriptions of molecules in, matter., Description, , Solid, , (ii) The specific heat capacity of the, substance is 1760 J/(kg°C). Use the, information in the table for the period, 18–22 minutes to calculate the mass, of the substance being heated., [3], , Gas, , free to move around from place to place, , [Total: 10], , can only vibrate about a fixed position, , (Cambridge IGCSE Physics 0625 Paper 31 Q5, June 2010), , closely packed, relatively far apart, almost no force between molecules, strong forces are involved between, molecules, , Copy the table and in the columns alongside, the descriptions, put ticks next to those which, apply to the molecules in, (i) a solid, (ii) a gas., [4], b The water in a puddle of rainwater is, evaporating., Describe what happens to the molecules, when the water evaporates., [2], , 27 Three wires and a meter are used to construct, a thermocouple for measuring the surface, temperature of a pipe carrying hot liquid, as, shown in the diagram., meter, , wire 2, , wire 1, , cold junction, , wire 3, , [Total: 6], , hot junction, , (Cambridge IGCSE Physics 0625 Paper 02 Q5, June 2007), , hot liquid in pipe, , a Copper wire and constantan wire are used in, the construction of the thermocouple., State which metal might be used for, wire 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ., wire 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ., wire 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ., [1], b State what type of meter is used., [1], c State one particular advantage of, thermocouples for measuring temperature. [1], , Thermal properties and temperature, 26 A certain substance is in the solid state at a, temperature of −36 °C. It is heated at a constant, rate for 32 minutes. The record of its temperature, is given in the table at the bottom of the page., a State what is meant by the term latent heat. [2], b State a time at which the energy is being, supplied as latent heat of fusion., [1], c Explain the energy changes undergone by the, molecules of a substance during the period when, latent heat of vaporisation is being supplied. [2], d (i) The rate of heating is 2.0 kW., Calculate how much energy is supplied, to the substance during the period, 18–22 minutes., [2], , [Total: 3], (Cambridge IGCSE Physics 0625 Paper 31 Q7, November 2009), , Time/min, , 0, , 1, , 2, , 6, , 10, , 14, , 18, , 22, , 24, , 26, , 28, , 30, , 32, , Temperature/°C, , −36, , −16, , −9, , −9, , −9, , −9, , 32, , 75, , 101, , 121, , 121, , 121, , 121, , 261, , 9781444176421_BM_06.indd 261, , 20/06/14 7:30 AM
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Cambridge IGCSE exam questions, , 28 a State what is meant by specific heat capacity. [2], b Water has a very high specific heat capacity., Suggest why this might be a disadvantage, when using water for cooking., [1], c The diagram illustrates an experiment to, measure the specific heat capacity of some, metal., stirrer, , thermometer, , lid, boiling, water, metal, heater, , cup, thread, water, , insulation, , The piece of metal is heated in boiling water, until it has reached the temperature of the, water. It is then transferred rapidly to some, water in a well-insulated cup. A very sensitive, thermometer is used to measure the initial and, final temperatures of the water in the cup., specific heat capacity of water = 4200 J/(kg K), The readings from the experiment are as follows., mass of metal = 0.050 kg, mass of water in cup = 0.200 kg, initial temperature of water in cup = 21.1 °C, final temperature of water in cup = 22.9 °C, (i) Calculate the temperature rise of the, water in the cup and the temperature fall, of the piece of metal., [1], (ii) Calculate the thermal energy gained by, the water in the cup. State the equation, that you use., [3], (iii) Assume that only the water gained, thermal energy from the piece of metal., Making use of your answers to c(i), and c(ii), calculate the value of the specific, heat capacity of the metal. Give your, answer to three significant figures., [2], (iv) Suggest one reason why the experiment, might not have given a correct value for, the specific heat capacity of the metal. [1], , 29 a The thermometer shown below is calibrated at, two fixed points, and the space between these, is divided into equal divisions., –10, , 0, , 10, , 20, , 30, , 40, , 50, , 60, , 70, , 80, , 90, , 100, , 110, , A thermometer is being calibrated with the, Celsius scale., (i) 1 Write down another name for the, lower fixed point., [1], 2 How is this temperature, achieved?[2], 3 What is the temperature of this, fixed point?, [1], (ii) 1 Write down another name for, the upper fixed point., [1], 2 How is this temperature, achieved?[2], 3 What is the temperature of, this fixed point?, [2], b A block of copper and a block of aluminium, have identical masses. They both start at room, temperature and are given equal quantities, of heat. When the heating is stopped, the, aluminium has a lower temperature than the, copper., Fill in the missing words in the sentence, below, to explain this temperature difference., The aluminium block has a smaller, temperature rise than the copper block, because the aluminium block has a larger, ......................................., than the copper block., , [1], , [Total: 10], (Cambridge IGCSE Physics 0625 Paper 02 Q8, June 2008), , [Total: 10], (Cambridge IGCSE Physics 0625 Paper 31 Q9, November 2009), , 262, , 9781444176421_BM_06.indd 262, , 20/06/14 7:30 AM
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Cambridge IGCSE exam questions, , 30 The diagram shows apparatus that could be, used to determine the specific latent heat of, fusion of ice., , thermometer, , glass rod, stirrer, , ice, , finely, crushed ice, 40 W electric, heater, , glass, beaker, , water, , glass, funnel, , stand with, clamps to, hold funnel, and heater, , a In order to obtain as accurate a result as, possible, state why it is necessary to, (i) wait until water is dripping into the, beaker at a constant rate before, taking readings,, [1], (ii) use finely crushed ice rather than large, pieces., [1], b The power of the heater and the time for, which water is collected are known. Write, down all the other readings that are needed, to obtain a value for the specific latent heat of, fusion of ice., [2], c Using a 40 W heater, 16.3 g of ice is melted in, 2.0 minutes. The heater is then switched off., In a further 2.0 minutes, 2.1 g of ice is melted., Calculate the value of the specific latent heat, of fusion of ice from these results., [4], , top-pan, balance, , a Three mass readings are taken. A description, of the first reading is given., Write down descriptions of the other two., reading 1: the mass of the beaker + stirrer, , + thermometer, reading 2: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .., reading 3: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . [2], b Write down word equations which the student, could use to find, (i) the heat lost by the water as it cools, from 20 °C to 0 °C,, [1], (ii) the heat gained by the melting ice., [1], c The student calculates that the water loses, 12 800 J and that the mass of ice melted is 30 g., Calculate a value for the specific latent, heat of fusion of ice., [2], d Suggest two reasons why this value is, only an approximate value., [2], [Total: 8], (Cambridge IGCSE Physics 0625 Paper 03 Q4, June 2007), , [Total: 8], (Cambridge IGCSE Physics 0625 Paper 31 Q5, November 2008), , 31 The diagram shows a student’s attempt, to estimate the specific latent heat of fusion, of ice by adding ice at 0 °C to water at, 20 °C. The water is stirred continuously as, ice is slowly added until the temperature, of the water is 0 °C and all the added ice has, melted., , 32 The diagram shows a liquid-in-glass, thermometer., capillary tube, , –10, , 0, , 10, , 20, , 30, , 40, , 50, , 60, , 70, , 80, , 90, , 100 110 120 130 140 150, , liquid, , 263, , 9781444176421_BM_06.indd 263, , 20/06/14 7:30 AM
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Cambridge IGCSE exam questions, , a The thermometer is used for measuring, temperatures in school laboratory, experiments. State the units in which the, temperatures are measured., [1], b On a copy of the diagram, mark where the, liquid thread will reach when the thermometer, is placed in, (i) pure melting ice (label this point ICE), [1], (ii) steam above boiling water (label this, point STEAM)., [1], c A liquid-in-glass thermometer makes use, of the expansion of a liquid to measure, temperature. Other thermometers make use of, other properties that vary with temperature., In a copy of the table below, write in two, properties, other than expansion of a liquid,, that can be used to measure temperature., example, , expansion, , OF, , 1., , OF, , 2., , OF, , (ii) On a copy of the diagram, draw the ray, from the top of the object which passes, through F2. Continue your ray until it, meets the image., [4], [Total: 8], (Cambridge IGCSE Physics 0625 Paper 21 Q8 June 2010), , 34 In an optics lesson, a Physics student traces the, paths of three rays of light near the boundary, between medium A and air. The student uses a, protractor to measure the various angles., The diagrams below illustrate the three, measurements., , air, medium, air, A, medium, A, , a liquid, , [2], [Total: 5], , 02802702602502, , 0029, , Light, , 3503435034, 033 033, 032 032, 0, 0, , 3 Properties of waves, , 402, 30, , 02802702602502, 0029, , 402, 30, , 03, , 31, , 90 90, 02001 02001, 021 2021, 2, , ray, 1, ray, 1, , 22, , (Cambridge IGCSE Physics 0625 Paper 02 Q5, November 2007), , 03, 31, , 33 The diagram shows how an image is formed by a, converging lens., 10 cm, , 8 cm, , F2, , F1, , a State the value of the focal length of the, lens., [1], b The object O is moved a small distance to, the left., State two things that happen to the image I. [2], c Points F1 and F2 are marked on the diagram., (i) State the name we give to these two, points., [1], , ray, 3, ray, 3, , 03, , 31, , 402, 30, , 02802702602502, 0029, , 402, 30, , 90 90, 02001 02001, 021 2021, 2, , I, O, , 02802702602502, , 0029, , 03, 31, , 22, , ray, 2, ray, 2, , 3503435034, 033 033, 032 032, 0, 0, , 24 cm, , air, medium, air, A, medium, A, , air, medium, air, A, medium, A, , a State which is the optically denser medium,, A or air, and how you can tell this., [1], , 264, , 9781444176421_BM_06.indd 264, , 20/06/14 7:30 AM
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Cambridge IGCSE exam questions, , b State in which medium the light travels, the faster, and how you know this., [1], c State the critical angle of medium A., [1], d State the full name for what is happening, to ray 3 in the third diagram., [1], e The refractive index of medium A is 1.49., Calculate the value of the angle of refraction, of ray 1, showing all your working., [2], f The speed of light in air is 3.0 × 108 m/s., Calculate the speed of light in medium A,, showing all your working., [2], [Total: 8], , e In the experiment, the plane mirror is, perpendicular to the beam of light. State what,, if anything, happens to the image on the card if, (i) the plane mirror is moved slightly to, the left,, [1], (ii) the lens is moved slightly to the left. [1], [Total: 7], (Cambridge IGCSE Physics 0625 Paper 02 Q7, November 2009), , 36 A woman stands so that she is 1.0 m from a, mirror mounted on a wall, as shown below., , (Cambridge IGCSE Physics 0625 Paper 31 Q8 June 2009), , 35 The diagram shows an experiment in which an, image is being formed on a card by a lens and a, plane mirror., , mirror, , image, lens, r, , plane, mirror, , p, , torch, , q, hole cut, in card, , The card and the mirror are shown angled, so, that you can see what is happening. In a real, experiment they are each roughly perpendicular, to the line joining the torch bulb and the centre, of the lens., a State which of the three marked distances,, p, q and r, is the focal length of the lens. [1], b On a copy of the diagram clearly mark a, principal focus of the lens, using the, letter F., [1], c Which two features describe the image, formed on the card?, erect, inverted, real, , 1.0 m, , a Copy the diagram and carefully draw, (i) a clear dot to show the position of the, image of her eye,, (ii) the normal to the mirror at the bottom, edge of the mirror,, (iii) a ray from her toes to the bottom edge, of the mirror and then reflected from the, mirror., [5], b Explain why the woman cannot see the, reflection of her toes., [1], c (i) How far is the woman from her image?, (ii) How far must the woman walk, and, in what direction, before the distance, between her and her image is 6.0 m? [4], , [2], , [Total: 10], , d What can be said about the size of the image,, compared with the size of the object?, [1], , (Cambridge IGCSE Physics 0625 Paper 02 Q6, November 2006), , virtual , , 265, , 9781444176421_BM_06.indd 265, , 20/06/14 7:30 AM
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Cambridge IGCSE exam questions, , 37 The diagram shows a ray of light, from the top of, an object PQ, passing through two glass prisms., P, , A, , B, , (i) Copy the diagram and continue the paths, of the two rays after they reach the mirror., Hence locate the image of the object O., Label the image I., (ii) Describe the nature of the image I., [4], b The diagram below is drawn to scale. It shows, an object PQ and a convex lens., , Q, C, , position of, convex lens, , P, D, F, principal focus, F, , F, Q, , principal focus, , principal, axis, , E, , a Copy the sketch and complete the path, through the two prisms of the ray shown, leaving Q., [1], b A person looking into the lower prism, at the, position indicated by the eye symbol, sees, an image of PQ. State the properties of this, image., [2], c Explain why there is no change in direction of, the ray from P at points A, C, D and F., [1], d The speed of light as it travels from P to A is, 3 × 108 m/s and the refractive index of the, prism glass is 1.5. Calculate the speed of light, in the prism., [2], e Explain why the ray AB reflects through 90° at, B and does not pass out of the prism at B. [2], [Total: 8], , (i) Copy the diagram and draw two rays from, the top of the object P that pass through, the lens. Use these rays to locate the top, of the image. Label this point T., (ii) Draw an eye symbol to show the position, from which the image T should be, viewed., [4], [Total: 8], (Cambridge IGCSE Physics 0625 Paper 03 Q7, November 2005), , Sound, 39 The diagram shows a workman hammering a, metal post into the ground. Some distance away, is a vertical cliff., , (Cambridge IGCSE Physics 0625 Paper 03 Q6, November 2006), , 38 a The sketch shows two rays of light from a, point O on an object. These rays are incident, on a plane mirror., , cliff, workman, boy, , O, , girl, , a A boy is standing at the foot of the cliff. The, speed of sound in air is 330 m/s. It takes 1.5 s, for the sound of the hammer hitting the post, to reach the boy., , 266, , 9781444176421_BM_06.indd 266, , 20/06/14 7:30 AM
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Cambridge IGCSE exam questions, , (i) What does the boy hear after he sees each, strike of the hammer on the post?, [1], (ii) Calculate the distance between the, post and the boy., [3], b A girl is also watching the workman. She, is standing the same distance behind the, post as the boy is in front of it. She hears, two separate sounds after each strike of the, hammer on the post., (i) Why does she hear two sounds?, [2], (ii) How long after the hammer strike does, the girl hear each of these sounds?, girl hears first sound after . . . . . . . . . . . .s, girl hears second sound after . . . . . . . . s, [2], [Total: 8], (Cambridge IGCSE Physics 0625 Paper 21 Q8, November 2010), , 40 The trace shows the waveform of the note, from a bell. A grid is given to help you take, measurements., , 3 How long does it take for the, amplitude to decrease to half its, initial value?, [2], d A student says that the sound waves, which, travelled through the air from the bell, were, longitudinal waves, and that the air molecules, moved repeatedly closer together and then, further apart., (i) Is the student correct in saying that the, sound waves are longitudinal?, (ii) Is the student correct about the, movement of the air molecules?, (iii) The student gives light as another, example of longitudinal waves., Is this correct?, [2], [Total: 11], (Cambridge IGCSE Physics 0625 Paper 02 Q6 June 2009), , 41 The diagram shows a student standing midway, between a bell tower and a steep mountainside., , bell tower, and bell, steep, mountainside, , student, time, , a (i) State what, if anything, is happening to, the loudness of the note., [1], (ii) State how you deduced your answer, to a(i)., [1], b (i) State what, if anything, is happening to, the frequency of the note., [1], (ii) State how you deduced your answer, to b(i)., [1], c (i) How many oscillations does it take for, the amplitude of the wave to decrease, to half its initial value?, [1], (ii) The wave has a frequency of 300 Hz., 1 What is meant by a frequency of, 300 Hz?, [1], 2 How long does 1 cycle of the wave, take?[1], , 990 m, , 990 m, , The bell rings once, but the student hears two, rings separated by a short time interval., a Explain why the student hears two rings. [2], b State which of the sounds is louder,, and why., [2], c Sound in that region travels at 330 m/s., (i) Calculate the time interval between, the bell ringing and the student, hearing it for the first time., [2], (ii) Calculate the time interval between, the bell ringing and the student, hearing it for the second time., [1], (iii) Calculate the time interval between, the two sounds., [1], [Total: 8], (Cambridge IGCSE Physics 0625 Paper 02 Q8, November 2009), , 267, , 9781444176421_BM_06.indd 267, , 20/06/14 7:30 AM
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Cambridge IGCSE exam questions, , 4 Electricity and magnetism, , N, , brass rod, , Simple phenomena of magnetism, 42 a Four rods are shown in the diagram., plotting, compass, , plotting, compass, , On a copy of the diagram, mark the position, of the pointer on each of the two plotting, compasses., [2], plastic, rod, , iron, rod, , wooden, rod, , [Total: 6], , brass, rod, , (Cambridge IGCSE Physics 0625 Paper 02 Q8 June 2009), , State which of these could be held in the hand, at one end and be, (i) magnetised by stroking it with a, magnet,, [1], (ii) charged by stroking it with a dry cloth. [1], b Magnets A and B below are repelling each other., , 43 a An iron rod is placed next to a bar magnet, as, shown in the diagram., N, , iron rod, , N, magnet A, , S, , (i) On a copy of the diagram above, mark, clearly the north pole and the south pole, that are induced in the iron rod., [1], (ii) What happens to the magnet and the, rod? Tick the correct option below., nothing, , magnet B, , The north pole has been labelled on magnet A., On a copy of the diagram, label the other three, poles., [1], c Charged rods C and D below are attracting, each other., , they attract, they repel, , [1], , b A second bar magnet is now placed next to, the iron rod, as shown below., , ++, rod C, , rod D, , On a copy of the diagram, show the charge on, rod D., [1], d A plotting compass with its needle pointing, north is shown below., , N, , N, , S, , N, , S, , iron rod, , (i) On a copy of the diagram above, mark, clearly the magnetic poles induced in the, iron rod., [1], (ii) What happens to the iron rod and the, second magnet?, nothing, they attract, they repel , , [1], , A brass rod is positioned in an east–west, direction. A plotting compass is put at each, end of the brass rod, as shown below., , 268, , 9781444176421_BM_06.indd 268, , 20/06/14 7:30 AM
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Cambridge IGCSE exam questions, , c The iron rod is removed, leaving the two, magnets, as shown below., N, , S, , N, , S, , What happens to the two magnets?, nothing, , c The cable for connecting an electric cooker is, much thicker than the cable on a table lamp., (i) Why do cookers need a much thicker, cable?, [1], (ii) What would happen if a thin cable were, used for wiring a cooker to the supply? [1], [Total: 6], (Cambridge IGCSE Physics 0625 Paper 21 Q9, June 2010), , they attract, they repel , , [1], , d The second magnet is removed and, replaced by a charged plastic rod, as, shown below., N, , S, , 45 In the diagram, A and B are two conductors on, insulating stands. Both A and B were initially, uncharged., , +, , –, charged, plastic rod, , What happens to the magnet and the plastic, rod?, nothing, , +, +, +, +, , +, , + + +, , +, , A, +, , +, , +, , +, , X, +, +, +, +, , Y, , B, , they attract, they repel , , [1], [Total: 6], , (Cambridge IGCSE Physics 0625 Paper 02 Q8, November 2008), , Electrical quantities and circuits, 44 a A warning on the packaging of a light switch, purchased from an electrical store reads, Safety warning, This push-button switch is not suitable for use in a washroom., Lights in washrooms should be operated by pull-cord switches., , (i) Explain why it might be dangerous to use, a push-button switch in a washroom. [2], (ii) Why is it safe to use a pull-cord switch in, a washroom?, [1], b An electric heater, sold in the electrical store,, has a current of 8 A when it is working normally., The cable fitted to the heater has a maximum, safe current of 12 A., Which of the following fuses would be most, suitable to use in the plug fitted to the cable of, the heater?, 5 A, , , 9781444176421_BM_06.indd 269, , 10 A, , 13 A, , a Conductor A is given the positive charge, shown on the diagram., (i) On a copy of the diagram, mark the signs, of the charges induced at end X and at, end Y of conductor B., [1], (ii) Explain how these charges are induced. [3], (iii) Explain why the charges at X and at, Y are equal in magnitude., [1], b B is now connected to earth by a length of, wire. Explain what happens, if anything, to, (i) the charge at X,, [1], (ii) the charge at Y., [2], [Total: 8], (Cambridge IGCSE Physics 0625 Paper 31 Q9, November 2010), , 20 A, [1], , 269, , 20/06/14 7:30 AM
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Cambridge IGCSE exam questions, , 46 The diagram shows a simple circuit., 6V, , reading, 50 mA, , A, , R, , a What is the value of, (i) the e.m.f. of the battery,, (ii) the current in the circuit?, [2], b Calculate the resistance R of the resistor. [3], c State how the circuit could be changed to, (i) halve the current in the circuit,, [2], (ii) reduce the current to zero., [1], d A student wishes to include a switch in the, circuit, but mistakenly connects it as shown, below., , a Calculate the combined resistance of, [2], R1 and R2., b On a copy of the diagram, use the correct, circuit symbol to draw a voltmeter connected, to measure the potential difference between, X and Y., [1], c The variable resistor is set to zero resistance., The voltmeter reads 1.5 V., (i) Calculate the current in the circuit., [4], (ii) State the value of the potential, difference across the cell., [1], d The resistance of the variable resistor is increased., (i) What happens to the current in the, circuit? Tick the correct option below., increases, stays the same, decreases, , [1], , (ii) What happens to the voltmeter reading?, increases, stays the same, , 6V, , decreases , student’s, incorrect, connection, , A, , [1], , (iii) State the resistance of the variable resistor, when the voltmeter reads 0.75 V., [1], [Total: 11], , R, , (Cambridge IGCSE Physics 0625 Paper 02 Q10 June 2008), , (i) Comment on the size of the current in, the circuit if the student closes the, switch., [1], (ii) What effect would this current have, on the circuit?, [2], [Total: 11], (Cambridge IGCSE Physics 0625 Paper 02 Q9 June 2009), , 47 The diagram shows a series circuit., , X, , R1, , R2, , Y, , Resistance R1 = 25 Ω and resistance R2 = 35 Ω., The cell has zero resistance., , 48 a Draw the symbol for a NOR gate., [1], b Describe the action of a NOR gate in, terms of its inputs and output., [2], c A chemical process requires heating at low, pressure to work correctly., When the heater is working, the output of a, temperature sensor is high. When the pressure is, low enough, a pressure sensor has a low output., Both outputs are fed into a NOR gate. A, high output from the gate switches on an, indicator lamp., (i) Explain why the indicator lamp is off, when the process is working correctly. [1], (ii) State whether the lamp is on or off, in the following situations., 1 The pressure is low enough, but the, heater stops working., 2 The heater is working, but the, pressure rises too high., [2], [Total: 6], (Cambridge IGCSE Physics 0625 Paper 31 Q10 June 2008), , 270, , 9781444176421_BM_06.indd 270, , 20/06/14 7:30 AM
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Cambridge IGCSE exam questions, , 49 a The circuit shows two resistors connected to a, 6 V battery., , 50 The diagram shows part of a low-voltage lighting, circuit containing five identical lamps., 12 V d.c., supply, , 2 , A, 6V, , B, , X, C, 10 , D, Y, , (i) What name do we use to describe, this way of connecting resistors?, [1], (ii) Calculate the combined resistance, of the two resistors., [1], (iii) Calculate the current in the circuit., [4], (iv) Use your answer to a(iii) to calculate, the potential difference across the, 10 Ω resistor., [2], (v) State the potential difference between, terminals X and Y., [1], b The circuit shown is similar to the circuit above,, but it uses a resistor AB with a sliding contact., A, sliding, contact, , X, , 6V, , B, Y, , (i) State the potential difference between X, and Y when the sliding contact is at, 1 end A of the resistor, .............. V, 2 end B of the resistor. .............. V [2], (ii) The sliding contact of the resistor AB is, moved so that the potential difference, between X and Y is 5 V. On a copy of the, circuit mark with the letter C the position, of the sliding contact., [1], , E, , a Copy and complete the circuit, by the, addition of components as necessary, so that, (i) the total current from the supply can be, measured,, (ii) the brightness of lamp E only can be varied,, (iii) lamps C and D may be switched on and, off together whilst lamps A, B and E, remain on., [4], b All five lamps are marked 12 V, 36 W. Assume, that the resistance of each lamp is the same fixed, value regardless of how it is connected in the, circuit., Calculate, (i) the current in one lamp when, operating at normal brightness,, [1], (ii) the resistance of one lamp when, operating at normal brightness,, [1], (iii) the combined resistance of two lamps, connected in parallel with the 12 V, supply,, [1], (iv) the energy used by one lamp in 30 s, when operating at normal brightness. [1], c The whole circuit is switched on. Explain, why the brightness of lamps A and B is, much less than that of one lamp operating, at normal brightness., [2], [Total: 10], (Cambridge IGCSE Physics 0625 Paper 03 Q8 June 2007), , [Total: 12], (Cambridge IGCSE Physics 0625 Paper 02 Q9 June 2007), 271, , 9781444176421_BM_06.indd 271, , 20/06/14 7:30 AM
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Cambridge IGCSE exam questions, , 51 The diagram shows two electrical circuits., The batteries in circuit 1 and circuit 2 are identical., V, , Calculate, (i) the current in resistor P,, (ii) the power supplied to resistor Q,, (iii) the energy transformed in resistor, Q in 300 s., , [1], [1], [1], , [Total: 10], (Cambridge IGCSE Physics 0625 Paper 03 Q8, November 2007), , 52 The diagram shows an electric circuit., 4.0 , , 6.0 , A, , P, , Q, ammeter, circuit 1, battery, , A, , ammeter, 1, , lamp, , 4.0 , P, ammeter, 2, , 15 Ω resistor, , A, 6.0 , Q, circuit 2, , a Put ticks in a copy of the table below to, describe the connections of the two resistors, P and Q., Series, , Parallel, , circuit 1, circuit 2, , [1], , b The resistors P and Q are used as small, electrical heaters. State two advantages of, connecting them as shown in circuit 2., [2], c In circuit 1, the ammeter reads 1.2 A, when the switch is closed. Calculate the, reading of the voltmeter in this circuit., [2], d The two switches in circuit 2 are closed., Calculate the combined resistance of the, two resistors in this circuit., [2], e When the switches are closed in circuit 2,, ammeter 1 reads 5 A and ammeter 2 reads 2 A., , a The lamp lights, but the ammeter needle, moves the wrong way. What change should be, made so that the ammeter works correctly? [1], b What does an ammeter measure?, [1], c Draw a circuit diagram of the circuit in the, diagram, using correct circuit symbols., [2], d (i) Name the instrument that would be, needed to measure the potential difference, (p.d.) across the 15 Ω resistor., (ii) Using the correct symbol, add this, instrument to your circuit diagram in c, in, a position to measure the p.d. across the, 15 Ω resistor., [2], e The potential difference across the 15 Ω, resistor is 6 V., Calculate the current in the resistor., [3], f Without any further calculation, state the, value of the current in the lamp., [1], g Another 15 Ω resistor is connected in parallel, with the 15 Ω resistor that is already in the, circuit., (i) What is the combined resistance of the, two 15 Ω resistors in parallel?, 30 Ω, 15 Ω, 7.5 Ω or zero?, , 272, , 9781444176421_BM_06.indd 272, , 20/06/14 7:30 AM
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Cambridge IGCSE exam questions, , (ii) State what effect, if any, adding this extra, resistor has on the current in the lamp. [2], , thumb, first finger, , motion/force, , [Total: 12], (Cambridge IGCSE Physics 0625 Paper 02 Q12, November 2006), , Electromagnetic effects, 53 Alternating current electricity is delivered at, 22 000 V to a pair of transmission lines. The, transmission lines carry the electricity to the, customer at the receiving end, where the potential, difference is V. This is shown in the diagram. Each, transmission line has a resistance of 3 Ω., 00, , 0, 22, , V, 3 , , V, , 3 , , a The a.c. generator actually generates at a, much lower voltage than 22 000 V., (i) Suggest how the voltage is increased, to 22 000 V., (ii) State one advantage of delivering, electrical energy at high voltage., b The power delivered by the generator, is 55 kW., Calculate the current in the transmission, lines., c Calculate the rate of loss of energy from, one of the 3 Ω transmission lines., d Calculate the voltage drop across one of, the transmission lines., e Calculate the potential difference V at the, receiving end of the transmission lines., , second finger, , One direction has been labelled for you., In each of the other two boxes, write, the name of the quantity that direction, represents., [1], b The diagram below shows a simple d.c. motor, connected to a battery and a switch., , [1], [1], , N, S, , [2], , X, , [2], [2], [2], , [Total: 10], (Cambridge IGCSE Physics 0625 Paper 31 Q10, November 2009), , 54 a The diagram illustrates the left-hand rule,, which helps when describing the force on a, current-carrying conductor in a magnetic field., , switch, , –, , +, battery, , (i) On a copy of the diagram, write in each, of the boxes the name of the part of the, motor to which the arrow is pointing. [2], (ii) State which way the coil of the motor, will rotate when the switch is closed,, when viewed from the position X., [1], (iii) State two things which could be done, to increase the speed of rotation of, the coil., [2], [Total: 6], (Cambridge IGCSE Physics 0625 Paper 31 Q9 June 2010), , 273, , 9781444176421_BM_06.indd 273, , 20/06/14 7:31 AM
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Cambridge IGCSE exam questions, , 55 The diagram shows a transformer., 30 turns, , 57 The diagram shows apparatus used to investigate, electromagnetic effects around straight wires., 300 turns, , 12 V, a.c., , a.c., V, voltmeter, , a (i) On a copy of the diagram, clearly label the, core of the transformer., [1], (ii) Name a suitable material from which the, core could be made., [1], (iii) State the purpose of the core., [1], b Calculate the reading on the voltmeter., [3], [Total: 6], (Cambridge IGCSE Physics 0625 Paper 02 Q10, November 2009), , thin flexible, wire, , T3, T1, , thick rigid, vertical wire, , large circular, hole in card, small circular, hole in card, , T4, , T2, , The diagram below is a view looking down on, the apparatus shown above., , 56 a An experimenter uses a length of wire, ABC in an attempt to demonstrate, electromagnetic induction. The wire is, connected to a sensitive millivoltmeter G as, shown in the diagram., , B, , N, , S, , A, C, , G, , Using the arrangement in the diagram,, the experimenter finds that she does not, obtain the expected deflection on G when, she moves the wire ABC down through the, magnetic field., (i) Explain why there is no deflection, shown on G., [2], (ii) What change should be made in order to, observe a deflection on G?, [1], b Name one device that makes use of, electromagnetic induction., [1], , a A battery is connected to T1 and T2 so that, there is a current vertically down the thick wire., On a copy of the diagram of the view looking, down, draw three magnetic field lines and, indicate, with arrows, the direction of all, three., [2], b Using a variable resistor, the p.d. between, terminals T1 and T2 is gradually reduced. State, the effect, if any, that this will have on, (i) the strength of the magnetic field,, [1], (ii) the direction of the magnetic field., [1], c The battery is now connected to terminals T3, and T4, as well as to terminals T1 and T2, so, that there is a current down both wires. This, causes the flexible wire to move., (i) Explain why the flexible wire moves. [2], (ii) State the direction of the movement of, the flexible wire., [1], , [Total: 4], (Cambridge IGCSE Physics 0625 Paper 02 Q11 June 2008), 274, , 9781444176421_BM_06.indd 274, , 20/06/14 7:31 AM
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Cambridge IGCSE exam questions, , (iii) The battery is replaced by one that, delivers a smaller current. State the effect, that this will have on the force acting on, the flexible wire., [1], [Total: 8], (Cambridge IGCSE Physics 0625 Paper 31 Q9 June 2008), , 58 The circuit in the diagram shows an, electromagnetic relay being used to switch an, electric motor on and off. The relay coil has a, much greater resistance than the potential divider., pivoted iron, armature, , 6V, , (i) On a copy of the diagram, draw the shape, of the magnetic field, both inside and, outside the coil., [4], (ii) A glass bar, an iron bar and a Perspex bar, are placed in turn inside the coil., Which one makes the field stronger? [1], b Two thin iron rods are placed inside the coil as, shown below. The switch is then closed., , power supply, for motor, , motor M, , switch, contacts, , The iron rods move apart. Suggest why this, happens., [3], , relay core, , a The relay operates when there is a potential, difference of 3 V across the coil. On a copy of, the diagram, mark the position of the slider, of the potential divider when the relay just, operates., [1], b Describe how the relay closes the contacts in, the motor circuit., [3], [Total: 4], (Cambridge IGCSE Physics 0625 Paper 02 Q10, November 2008), , 59 A coil of insulated wire is connected in series with, a battery, a resistor and a switch as shown below., , [Total: 8], (Cambridge IGCSE Physics 0625 Paper 02 Q10, November 2007), , 60 Electromagnetic induction may be demonstrated, using a magnet, a solenoid and other necessary, apparatus., a Explain what is meant by electromagnetic, induction., [2], b Draw a labelled diagram of the apparatus set, up so that electromagnetic induction may be, demonstrated., [2], c Describe how you would use the apparatus to, demonstrate electromagnetic induction., [2], d State two ways of increasing the magnitude of, the induced e.m.f. in this experiment., [2], [Total: 8], (Cambridge IGCSE Physics 0625 Paper 03 Q9, November 2007), , 5 Atomic physics, , a The switch is closed and the current in the coil, creates a magnetic field., , 61 Here is a list of different types of radiation., alpha (α), beta (β), gamma (γ), infra-red, radio,, ultra-violet, visible, X-rays, a List all those radiations in the list which are, not electromagnetic radiations., [2], 275, , 9781444176421_BM_06.indd 275, , 20/06/14 7:31 AM
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Cambridge IGCSE exam questions, , b Which radiation is the most penetrating? [1], c Which radiation has the longest, wavelength?, [1], d Which radiation consists of particles that are, [1], the same as 4He nuclei?, , , , , , , State the reasons for your answers., detector at A …………………........, detector at B …………………........, detector at C …………………........, , [Total: 10], , [Total: 5], (Cambridge IGCSE Physics 0625 Paper 21 Q5, November 2010), , 62 Emissions from a radioactive source pass through, a hole in a lead screen and into a magnetic field,, as shown in the diagram., magnetic field, into paper, , radioactive, source, , X, , X, , X, , X, , X, , X, , X, , X, , X, , X, , X, , X, , X, , X, , X, , X, , (Cambridge IGCSE Physics 0625 Paper 31 Q10, November 2010), , 63 A beam of ionising radiation, containing, α-particles, β-particles and γ-rays, is travelling, left to right across the page. A magnetic field acts, perpendicularly into the page., a In a copy of the table below, tick the boxes, that describe the deflection of each of, the types of radiation as it passes through, the magnetic field. One row has been, completed to help you., [3], , A, deflected, not, towards, deflected top of, page, , B, , lead, screen, , X, , X, , X, , X, , X, , X, , X, , X, , α-particles, , B, , C, , 543 counts/min, , 396 counts/min, , B, , C, , 33 counts/min, , 30 counts/min, , 31 counts/min, , ✓, , γ-rays, , The radioactive source is then completely, removed, and the readings become:, A, , ✓, , C, , Radiation detectors are placed at A, B and C., They give the following readings:, A, , deflected, towards large, small, bottom, deflection deflection, of page, , β-particles, , 3 cm, , 32 counts/min, , [2], [3], [3], , a Explain why there are still counts being recorded, at A, B and C, even when the radioactive source, has been removed, and give the reason for them, being slightly different., [2], b From the data given, deduce the type, of emission being detected, if any, at A, at, B and at C when the radiation source is, present., , b An electric field is now applied, in the same, region as the magnetic field and at the same, time as the magnetic field., What is the direction of the electric field, in order to cancel out the deflection of, [2], the α-particles?, [Total: 5], (Cambridge IGCSE Physics 0625 Paper 31 Q11 June 2009), , 64 a The table shows how the activity of a sample, of a radioactive substance changes with time., Time /minutes, , Activity /counts/s, , 0, , 128, , 30, , 58, , 60, , 25, , 90, , 11, , 120, , 5, , Use the data in the table to estimate the, half-life of the radioactive substance., , [2], , 276, , 9781444176421_BM_06.indd 276, , 20/06/14 7:31 AM
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Cambridge IGCSE exam questions, , b The half-lives of various substances are given, below., radon-220, 55 seconds, iodine-128, 25 minutes, radon-222, 3.8 days, strontium-90, 28 years, (i) If the radioactive substance in a is one of, these four, which one is it?, [1], (ii) A sample of each of these substances is, obtained. Which sample will have the, greatest proportion of decayed nuclei by, the end of one year, and why?, [2], [Total: 5], (Cambridge IGCSE Physics 0625 Paper 02 Q12, June 2008), , 65 a Chlorine has two isotopes, one of nucleon, number 35 and one of nucleon number 37., The proton number of chlorine is 17., The table refers to neutral atoms of chlorine., Copy and complete the table., Nucleon, number 35, , (i) State the proton number of the emitted, particle., [1], (ii) State the nucleon number of the emitted, particle., [1], (iii) Name the emitted particle. Choose from, the following:, α-particle, β-particle, neutron, proton, , [1], [Total: 5], , (Cambridge IGCSE Physics 0625 Paper 02 Q12, November 2008), , 67 The diagram shows the paths of three α-particles, moving towards a thin gold foil., gold foil, A, , Nucleon, number 37, , number of protons, , B, , number of neutrons, , [3], , number of electrons, , b Some isotopes are radioactive. State the three, types of radiation that may be emitted from, radioactive isotopes., [1], c (i) State one practical use of a radioactive, isotope., [1], (ii) Outline how it is used., [1], [Total: 6], (Cambridge IGCSE Physics 0625 Paper 31 Q11, June 2008), , 66 The nucleus of one of the different nuclides of, polonium can be represented by the symbol 218, 84 Po., a State the proton number of this nuclide. [1], b State the nucleon number of this nuclide. [1], c The nucleus decays according to the following, equation., 218Po, 84, , →, , 214 Pb, 82, , + emitted particle, , C, , Particle A is moving directly towards a gold, nucleus., Particle B is moving along a line which passes, close to a gold nucleus., Particle C is moving along a line which does not, pass close to a gold nucleus., a On a copy of the diagram, complete the paths, of the α-particles A, B and C., [3], b State how the results of such an experiment,, using large numbers of α-particles, provides, evidence for the existence of nuclei in, gold atoms., [3], [Total: 6], (Cambridge IGCSE Physics 0625 Paper 03 Q11, June 2007), , 277, , 9781444176421_BM_06.indd 277, , 20/06/14 7:31 AM
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Cambridge IGCSE exam questions, , 68 The activity of a sample of radioactive material, is determined every 10 minutes for an hour. The, results are shown in the table., Time /, minutes, , 0, , 10, , 20, , 30, , 40, , 50, , 60, , Activity /, counts/s, , 461, , 332, , 229, , 162, , 106, , 81, , 51, , a From the figures in the table, estimate the, half-life of the radioactive material., [1], b A second experiment is carried out with, another sample of the same material. At the, start of the experiment, this sample has twice, the number of atoms as the first sample., Suggest what values might be obtained for, (i) the activity at the start of the second, experiment,, [1], (ii) the half-life of the material in the second, experiment., [1], c Name one type of particle that the material might, be emitting in order to cause this activity., [1], , b A potential difference is applied between P1, and P3, with P1 positive with respect to P3., State what happens to the beam of, cathode rays., [2], c The potential difference in b is removed., Suggest how the beam of cathode rays can now, be deflected down the page towards Q., [2], d Cathode rays are invisible. State one way to, detect them., [1], [Total: 6], (Cambridge IGCSE Physics 0625 Paper 02 Q12, November 2007), , 70 The diagram shows an experiment to test the, absorption of β-particles by thin sheets of, aluminium., Ten sheets are available, each 0.5 mm thick., -particle source, , [Total: 4], (Cambridge IGCSE Physics 0625 Paper 02 Q11, November 2007), , 69 A beam of cathode rays is travelling in a direction, perpendicularly out of the page. The beam is, surrounded by four metal plates P1, P2, P3 and P4, as shown in the diagram., The beam is shown as the dot at the centre., , sheets of, aluminium, , detector, , counter, , a Describe how the experiment is carried out,, stating the readings that should be taken. [4], b State the results that you would expect to, obtain., [2], [Total: 6], (Cambridge IGCSE Physics 0625 Paper 03 Q11, November 2007), , P2, P1, , P3, , P4, , Q, , a Cathode rays are produced by thermionic, emission., What is the name of the particles which make, up cathode rays?, [1], , 278, , 9781444176421_BM_06.indd 278, , 20/06/14 7:31 AM
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Revision questions, Mathematics, for physics, USE THIS SECTION AS THE NEED ARISES, , ●● Solving physics problems, When tackling physics problems using mathematical, equations it is suggested that you do not substitute, numerical values until you have obtained the, expression in symbols which gives the answer., That is, work in symbols until you have solved the, problem and only then insert the numbers in the, expression to get the final result., This has two advantages. First, it reduces the, chance of errors in the arithmetic (and in copying, down). Second, you write less since a symbol is, usually a single letter whereas a numerical value is, often a string of figures., Adopting this ‘symbolic’ procedure frequently, requires you to change round an equation first. The, next two sections and the questions that follow them, are intended to give you practice in doing this and, then substituting numerical values to get the answer., , ●● Equations – type 1, In the equation x = a/b, the subject is x. To change it, we multiply or divide both sides of the equation by, the same quantity., To change the subject to a, We have, x = a, b, If we multiply both sides by b, the equation will still, be true., ∴, x ×b = a ×b, b, The b’s on the right-hand side cancel, ∴, , b ×x = a ×b = a, b, , and, a =b×x, To change the subject to b, We have, x = a, b, , Multiplying both sides by b as before, we get, a =b×x, Dividing both sides by x:, a = b×x = b×x =b, x, x, x, b = a, x, , ∴, , Note that the reciprocal of x is 1/x., Can you show that, 1 = b?, x, a, Now try the following questions using these ideas., , Questions, 1 What is the value of x if, a 2x = 6, b 3x = 15, x, =4, d x = 10, e, 3, 2, g 4 =2, h 9 =3, x, x, 2 Change the subject to, a f in v = fλ, c I in V = IR, m, e m in d =, V, g s in v = s, t, 3 Change the subject to, a I2 in P = I2R, c a in s =, e t in s =, , 1 2, at, 2, 1 2, at, 2, , c 3x = 8, 2x, =4, 3, x, 4, =, i, 6 3, f, , b λ in v = fλ, d R in V = IR, f V in d = m, V, h t in v =, , s, t, , b I in P = I2R, d t2 in s = 1 at2, 1, 2, , 2, , mv2 = mgh, ρl, g y in λ = ay, h ρ in R =, A, D, 4 By replacing (substituting) find the value of v = fλ if, a f = 5 and λ = 2, b f = 3.4 and λ = 10, c f = 1/4 and λ = 8/3, d f = 3/5 and λ = 1/6, e f = 100 and λ = 0.1, f f = 3 × 105 and λ = 103, 5 By changing the subject and replacing find, a f in v = fλ, if v = 3.0 × 108 and λ = 1.5 × 103, b h in p = 10hd, if p = 105 and d = 103, c a in n = a/b, if n = 4/3 and b = 6, d b in n = a/b, if n = 1.5 and a = 3.0 × 108, e F in p = F/A if p = 100 and A = 0.2, f s in v = s/t, if v = 1500 and t = 0.2, f v in, , 279, , 9781444176421_BM_06.indd 279, , 20/06/14 7:33 AM
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mathematiCs FoR phYsiCs, , ●● Equations – type 2, To change the subject in the equation x = a + by we, add or subtract the same quantity from each side., We may also have to divide or multiply as in type 1., Suppose we wish to change the subject to y in, x = a + by, Subtracting a from both sides,, , on. There is a one-to-one correspondence between, each value of x and the corresponding value of y., We say that y is directly proportional to x, or y, varies directly as x. In symbols, y∝x, Also, the ratio of one to the other, e.g. y to x, is, always the same, i.e. it has a constant value which in, this case is 2. Hence, y, = a constant = 2, x, , x − a = a + by − a = by, Dividing both sides by b,, , The constant, called the constant of proportionality, or constant of variation, is given a symbol, e.g. k,, and the relation (or law) between y and x is then, summed up by the equation, , x − a = by = y, b, b, y = x −a, b, , ∴, , y, = k or y = kx, x, , Questions, , Notes, , 6 What is the value of x if, a x+1=5, b 2x + 3 = 7, d 2 ( x − 3) = 10, , c x−2=3, f x + 1 =0, 3 4, , e x −1=0, 2 3, , x, 3, g 2x + 5 + 6, h 7 − = 11, i, +2=5, 4, x, 3, 7 By changing the subject and replacing, find the value of a, in v = u + at if, a v = 20, u = 10 and t = 2, b v = 50, u = 20 and t = 0.5, c v = 5/0.2, u = 2/0.2 and t = 0.2, 8 Change the subject in v2 = u2 + 2as to a., , 1 In practice, because of inevitable experimental, errors, the readings seldom show the relation so, clearly as here., 2 If instead of using numerical values for x and y we, use letters, e.g. x1, x2, x3, etc., and y1, y2, y3, etc.,, then we can also say, y1, y, y, = 2 = 3 = ... = k, x1, x2, x3, or, , ●● Proportion (or variation), One of the most important mathematical operations, in physics is finding the relation between two sets of, measurements., , a) Direct proportion, Suppose that in an experiment two sets of readings, are obtained for the quantities x and y as in Table M1, (units omitted)., Table M1, x, , 1, , 2, , 3, , 4, , y, , 2, , 4, , 6, , 8, , We see that when x is doubled, y doubles; when x is, trebled, y trebles; when x is halved, y halves; and so, , y1 = kx1, y2 = kx2, y3 = kx3,..., , b) Inverse proportion, Two sets of readings for the quantities p and V are, given in Table M2 (units omitted)., Table M2, p, , 3, , 4, , 6, , 12, , V, , 4, , 3, , 2, , 1, , There is again a one-to-one correspondence between, each value of p and the corresponding value of V, but, when p is doubled, V is halved, when p is trebled, V, has one-third its previous value, and so on., We say that V is inversely proportional to p, or V, varies inversely as p, i.e., V ∝ 1, p, , 280, , 9781444176421_BM_06.indd 280, , 20/06/14 7:34 AM
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y, 8, 6y, 4, 8, 2, 6, 40, , Also, the product p × V is always the same (= 12 in, this case) and we write, V = k, p, , 1, , 2, , 3, , 4, , x, , 1, , 2, , 3, , 4, , x, , 1, , 2, , 3, , 4, , V, , 1, , 2, , 3, , 4, , V, , 2p, 12, 0, 10, , or pV = k, , 8p, 6, 12, 4, 10, , where k is the constant of proportionality or variation, and equals 12 in this case., Using letters for values of p and V we can also say, p1V1 = p2V2 = p3V3 = .... = k, , 2, 8, , Figure M2, , ●● Graphs, Another useful way of finding the relation between, two quantities is by a graph., When the readings in Table M1 are used to plot, a graph of y against x, a continuous line joining, the points is a straight line passing through the, origin as in Figure M1. Such a graph shows there, is direct proportionality between the quantities, plotted, i.e. y ∝ x. But note that the line must go, through the origin., A graph of p against V using the readings in Table, M2 is a curve, as in Figure M2. However if we plot p, against 1/V (Table M3) (or V against 1/p) we get a, straight line through the origin, showing that p ∝ V,, as in Figure M3 (or V ∝ 1/p)., Table M3, V, , 1/V, , 3, , 4, , 0.25, , 4, , 3, , 0.33, , 6, , 2, , 0.50, , 12, , 1, , 1.00, , 6, 0, 4, 2p, 12, 0, 10, 8, p, 6, 12, 4, 10, , a) Straight line graphs, , p, , Graphs, , 2, 8, 6, 0, 4, , 0.50, , 1.0, , 1/V, , 0.50, , 1.0, , 1/V, , 2, 0, Figure M3, , b) Slope or gradient, The slope or gradient of a straight line graph equals, the constant of proportionality. In Figure M1, the, slope is y/x = 2; in Figure M3 it is p/(1/V) = 12., In practice, points plotted from actual, measurements may not lie exactly on a straight line, due to experimental errors. The ‘best straight line’ is, then drawn ‘through’ them so that they are equally, distributed about it. This automatically averages the, results. Any points that are well off the line stand out, and may be investigated further., , c) Variables, y, 8, 6, 4, 2, 0, Figure M1, , 1, , 2, , 3, , 4, , x, , p, 12, , As we have seen, graphs are used to show the, relationship between two physical quantities. In an, experiment to investigate how potential difference,, V, varies with the current, I, a graph can be drawn of, V/V values plotted against the values of I/A. This, will reveal how the potential difference depends upon, the current (see Figure M4)., In the experiment there are two variables. The, quantity I is varied and the value for V is dependent, upon the value for I. So V is called the dependent, variable and I is called the independent variable., , 10, 8, 6, , 281, , 4, 2, 9781444176421_BM_06.indd 281, , 0, , 1, , 2, , 3, , 4, , V, , 20/06/14 7:34 AM
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mathematiCs FoR phYsiCs, , Questions, , V/ V, 2, , 9 In an experiment different masses were hung from the end, of a spring held in a stand and the extensions produced, were as shown below., , 1, , Mass/g, 0, 0, , 0.1, , 0.2, , 0.3 I/A, , Figure M4, , Note that in Figure M4 each axis is labelled with the, quantity and the unit. Also note that there is a scale, along each axis. The statement V/V against I/A, means that V/V, the dependent variable, is plotted, along the y-axis and the independent variable I is, plotted along the x-axis (see Figure M5)., , y-axis, (dependent), , x-axis (independent), Figure M5, , 100, , 150, , 200, , 300, , 350, , 500, , 600, , Extension/cm 1.9, , 3.1, , 4.0, , 6.1, , 6.9, , 10.0, , 12.2, , a Plot a graph of extension along the vertical (y) axis, against mass along the horizontal (x) axis., b What is the relation between extension and mass? Give, a reason for your answer., 10 Pairs of readings of the quantities m and v are given, below., m, , 0.25, , 1.5, , 2.5, , 3.5, , v, , 20, , 40, , 56, , 72, , a Plot a graph of m along the vertical axis and v along the, horizontal axis., b Is m directly proportional to v? Explain your answer., c Use the graph to find v when m = 1., 11 The distances s (in metres) travelled by a car at various, times t (in seconds) are shown below., s/m, , 0, , 2, , 8, , 18, , 32, , 50, , t/m, , 0, , 1, , 2, , 3, , 4, , 5, , Draw graphs of, a s against t,, b s against t2., What can you conclude?, , d) Practical points, (i) The axes should be labelled giving the quantities, being plotted and their units, e.g. I/A meaning, current in amperes., (ii) If possible the origin of both scales should be, on the paper and the scales chosen so that the, points are spread out along the graph. It is good, practice to draw a large graph., (iii) The scale should be easy to use. A scale based on, multiples of 10 or 5 is ideal. Do not use a scale, based on a multiple of 3; such scales are very, difficult to use., (iv) Mark the points . or ×., , 282, , 9781444176421_BM_06.indd 282, , 20/06/14 7:34 AM
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Further experimental investigations, Stretching of a rubber band, Set up the equipment as shown in Chapter 6 (Figure, 6.3, p. 25) but replace the spring with a thick rubber, band. Draw up a table in which to record stretching, force/N, scale reading/mm and total extension/mm., Take readings for increasing loads on the hanger., Plot a graph with stretching force/N along the, x-axis and extension/mm along the y-axis. Draw, the best straight line through your points; are your, results consistent with Hooke’s law for all loads?, (If weights and a hanger are not available you, could use coins (all similar) in a paper cup instead; in, this case the stretching force would be proportional, to the number of coins used.), , (i) Attach a protractor to the bench with Blu-tack., Fill a carton with water and gently push it at the, top so that it tilts. Measure the maximum angle,, α, that the carton can be tilted through without, toppling; repeat your measurement several times, and obtain an average value for α., (ii) Draw a full-size diagram of the face of the, carton; mark the centre of mass on the face and, measure the angle β between the long side and a, diagonal as shown in Figure E1b; how do your, values for α and β compare?, (iii) Repeat part (i) with the carton half full, a quarter, full and empty. Draw up a table of your results as, shown below., , Toppling, , Liquid volume/litres, , The stability of a body can be investigated using a, 1 litre drinks carton or can as shown in Figure E1a., When the carton is tilted so that the centre of mass, moves outside the base, the carton will topple over., , 1.0, , α1/°, , α2/°, , α3/°, , Average α /°, , 0.5, 0.25, 0.0, , push here, , 0.5 (frozen), , Juice, 50, , 60, , 0 90 10011, 01, 70 8, 2, , 01, , 30, 016, , 5, 01, , 40, , 14, , α, , protractor, bench, , 0170, , 10 20, 30, , 1 litre carton, or can, , a, , centre of, mass, β, α, , bench, , Where is the centre of mass of an empty carton?, Plot a graph with volume/litres on the y-axis, and α/° on the x-axis. What angle of topple, would you expect if the carton was one third, full of water? How does changing the position, of the centre of mass affect the stability of the, carton?, (iv) Put a half-full carton in the freezer; when the, water is fully frozen repeat part (i); add your, results to the table., Will the carton be more or less stable when the, water has melted? How are the centre of mass, and the angle of topple changed by freezing the, water?, (v) Turn a full carton on its side and repeat steps (i), and (ii). Is the carton more or less stable than, when upright? Explain why., Summarise the factors that influence the stability of a, body., , Cooling and evaporation, b, Figure E1, , For this experiment you will need two heat sensors, connected to a datalogger and computer. Use some, cotton thread to tie a piece of tissue paper loosely, 283, , 9781444176421_BM_06.indd 283, , 20/06/14 7:34 AM
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Further experimental investigations, , over one of the heat sensors. Insert both heat sensors, into a beaker of hot water and wait until they reach a, constant temperature., Experiment 1: With the datalogger running,, remove the heat sensors from the water and quickly, dry the sensor that is not covered by tissue paper., Hang each sensor on a retort stand and allow each, to cool to room temperature. Use the computer to, record a graph of temperature (on the y-axis) versus, time (on the x-axis) for each sensor – these are, ‘cooling curves’., Discuss the general shape of the cooling curves –, when do the bulbs cool most rapidly? How do the, cooling curves differ for the ‘wet’ compared with the, ‘dry’ heat sensor? Which sensor reaches the lower, temperature – can you explain why?, Experiment 2: Repeat the first experiment but, this time hang the sensors in a draught to cool. An, artificial draught can be produced by an electric, cooling fan. Compare the cooling curves recorded, by the computer with those obtained when there was, no draught (Experiment 1). Comment on how the, rate of cooling and the lowest temperature reached, have changed for each sensor and try to explain, your results., From your findings, summarise the factors that, affect the rate at which an object cools., , (If dataloggers and computers are not available, this experiment could be done with mercury, thermometers and a ‘team’ of students to help record, temperatures manually every 15 seconds!), , Variation of the resistance of a wire, with length, Several different lengths of resistance wire, (constantan SWG 34 is suitable) are needed, in, addition to the equipment shown in Chapter 38, (Figure 38.6, p. 168)., Cut the following lengths (l ) of resistance wire:, 20 cm, 40 cm, 60 cm, 80 cm and 100 cm. Wind, each wire into a coil, ensuring that adjacent turns, do not touch if the wire is not insulated. Set up the, circuit shown in Figure 38.6 with the shortest coil, in position R. (Set the rheostat near the midway, position.) Draw up a table in which to record l, I, V, and R for each coil. Determine R (= V/I) from your, readings; repeat the measurements and calculation of, R for each coil., Draw a graph with average R values on the y-axis, and l values on the x-axis. Is it consistent with the, relation R = ρl ? Calculate the slope of the graph., Measure the diameter of the constantan wire with, a micrometer screw gauge and determine a value for, the resistivity, ρ, of the wire., , 284, , 9781444176421_BM_06.indd 284, , 20/06/14 7:34 AM
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RPevision, ractical questions, test questions, 1 In this experiment, you are to investigate the, stretching of springs. You have been provided, with the apparatus shown in Figure P1., , (i) Measure the new lengths of each of the, springs., (ii) Calculate the extension of each spring, using the appropriate equation from parts, a and b., (iii) Calculate the average of these two, [2], extensions eav. Show your working., d Theory suggests that, , clamp, , spring A, , (ea + eb ) = e, av, 2, , spring B, , State whether your results support this theory, and justify your answer with reference to the, results., [2], e Describe briefly one precaution that you took, to obtain accurate length measurements. [1], , Figure P1, , a (i) Measure the length lA of spring A., (ii) On a copy of Figure P1 show clearly, where you decided to start and end the, length measurement lA., (iii) Hang the 200 g mass on spring A., Measure the new length l of the spring., (iv) Calculate the extension eA of spring A, [3], using the equation eA = (l − lA)., b (i) Measure the length lB of spring B., (ii) Hang the 200 g mass on spring B., Measure the new length l of the spring., (iii) Calculate the extension eB of spring B, [2], using the equation eB = (l − lB)., c Use the small length of wooden rod provided, to hang the 400 g mass midway between the, springs as shown in Figure P2., , [Total 10], (Cambridge IGCSE Physics 0625 Paper 51 Q1, June 2010), , 2 In this experiment, you will investigate the effect, of the length of resistance wire in a circuit on the, potential difference across a lamp., The circuit has been set up for you., a Figure P3 shows the circuit without the, voltmeter., Draw on a copy of the circuit diagram the, voltmeter as it is connected in the circuit. [2], power, source, , l, A, spring A, , sliding, contact, C, , spring B, , B, , Figure P3, rod, , 400 g mass, Figure P2, , b (i) Switch on and place the sliding contact, C on the resistance wire at a distance, l = 0.150 m from end A. Record the value, of l and the potential difference V across, the lamp in the table. Switch off., 285, , 9781444176421_BM_06.indd 285, , 20/06/14 7:35 AM
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Practical test questions, , (ii) Repeat step (i) using the following, values of l:, 0.350 m, 0.550 m, 0.750 m and 0.950 m., Record all the values of l and V in a copy of, the table., l/m, , V/V, , V/ l, , (iii) For each pair of readings in the table calculate, and record in the table the value of V/l., (iv) Complete the table by writing in the unit, for V/l., [5], c A student suggests that the potential, difference V across the lamp is directly, proportional to the length l of resistance wire, in the circuit. State whether or not you agree, with this suggestion and justify your answer by, reference to your results., [2], d State one precaution that you would take, in order to obtain accurate readings in this, experiment., [1], , a Record the room temperature θr., [1], b (i) Place the thermometer into the water, as shown in Figure P4. When the, temperature shown on the thermometer, stops rising, record the temperature θ in a, copy of Table A at time t = 0 s., (ii) Remove the thermometer from the, beaker of water and immediately start, the stopclock. Record in Table A the, temperature shown on the thermometer, as it cools in the air. Take readings at 30 s, intervals from t = 30 s until you have a total, of seven values up to time t = 180 s., [2], c (i) Set the stopclock back to zero. With the, thermometer still out of the beaker, record, in a copy of Table B the temperature θ, shown on the thermometer at time t = 0 s., (ii) Replace the thermometer in the beaker, of hot water as shown in Figure P4 and, immediately start the stopclock. Record, in Table B the temperature shown by the, thermometer at 10 s intervals until you have, a total of seven values up to time t = 60 s., Table A, t/, , Table B, θ/, , t/, , θ/, , [Total 10], (Cambridge IGCSE Physics 0625 Paper 51 Q3 June 2010), , 3 In this experiment you will investigate the rate of, heating and cooling of a thermometer bulb., Carry out the following instructions referring to Figure, P4. You are provided with a beaker of hot water., , thermometer, , lid, , hot water, , [2], d Copy and complete the column headings in, both tables., [1], e Estimate the time that would be taken in, part b for the thermometer to cool from, the reading at time t = 0 s to room, [1], temperature θr., f State in which table the rate of temperature, change is the greater. Justify your answer by, reference to your readings., [1], g If this experiment were to be repeated in order, to determine an average temperature for each, time, it would be important to control the, conditions. Suggest two such conditions, that should be controlled., [2], [Total: 10], , Figure P4, , (Cambridge IGCSE Physics 0625 Paper 51 Q2, November 2010), , 286, , 9781444176421_BM_06.indd 286, , 20/06/14 7:35 AM
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Practical test questions, , 4 In this experiment you will investigate reflection, of light through a transparent block., Carry out the following instructions referring to, Figure P5., mirror, A, , B, N, , D, , E, P1, , C, , i, , P2, F, , Push two pins P3 and P4 into the surface,, between your eye and the block, so that P3,, P4 and the images of P1 and P2, seen through, the block, appear in line., Mark the positions of P1, P2, P3 and P4., Remove the block., g Continue the line joining the positions of P1, and P2 so that it crosses CD and extends as far, as side AB., h Draw a line joining the positions of P3 and, P4. Continue the line so that it crosses CD, and extends as far as side AB. Label the point, G where this line crosses the line from P1, and P2., i Remove the pins, block and mirror from the, ray trace sheet. Measure the acute angle θ, between the lines meeting at G., [1], j Calculate the difference (θ − 2i)., [1], k Repeat steps c to j using an angle of, incidence i = 30°., [1], l Theory suggests that θ = 2i. State whether, your result supports the theory and justify, your answer by reference to your results. [2], , [5], , N’, , [Total: 10], , eye, , (Cambridge IGCSE Physics 0625 Paper 51 Q4, November 2010), , Figure P5, , a Place the transparent block, largest face down,, on the ray-trace sheet supplied. The block, should be on the top half of the paper. Draw, the outline of the block and label it ABCD., b Remove the block and draw the normal, NN′ to side CD so that the normal is 2.0 cm, from D. Label the point E where NN′, crosses CD., c Draw the line EF at an angle of incidence, i = 20° as shown in Figure P5., d Place the paper on the pinboard. Stand the, plane mirror vertically and in contact with face, AB of the block as shown in Figure P5., e Push two pins P1 and P2 into line EF. Pin P1, should be about 1 cm from the block and pin, P2 some distance from the block., f Replace the block and observe the images of, P1 and P2 through side CD of the block from, the direction indicated by the eye in Figure, P5 so that the images of P1 and P2 appear one, behind the other., , 5 In this experiment, you are to make two sets of, measurements as accurately as you can in order, to determine the density of glass., Carry out the following instructions referring to, Figure P6., , h, , d, Figure P6, , 287, , 9781444176421_BM_06.indd 287, , 20/06/14 7:35 AM
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Practical test questions, , Method 1, a (i) Use the two blocks of wood and the rule, to measure the external diameter d of the, test tube in cm., (ii) Draw a labelled diagram to show how you, used the blocks of wood and the rule to, find, as accurately as possible, a value for, the external diameter of the test tube., (iii) Measure the height h of the test tube, in cm., (iv) Calculate the external volume Ve of the, test tube using the equation, Ve =, , πd 2h, 4, , , , [3], , b Use the balance provided to measure the mass, [1], m1 of the test tube., c (i) Completely fill the test tube with water., Pour the water into the measuring, cylinder and record the volume Vi of the, water., (ii) Calculate the density ρ of the glass using, the equation, [1], , ρ =, , m1, (Ve − Vi ), , Method 2, d (i) Pour water into the measuring cylinder up, to about the 175 cm3 mark. Record this, volume V1., (ii) Carefully lower the test tube, open, end uppermost, into the measuring, cylinder so that it floats. Record the new, volume reading V2 from the measuring, cylinder., (iii) Calculate the difference in volumes, (V2 − V1)., (iv) Calculate the mass m2 of the test tube, using the equation m2 = k(V2 − V1) where, [3], k = 1.0 g/cm3., e (i) Use the wooden rod to push the test tube,, open end uppermost, down to the bottom, of the measuring cylinder so that the test, tube is full of water and below the surface., Remove the wooden rod. Record the new, volume reading V3 from the measuring, cylinder., , (ii) Calculate the density ρ of the glass, using the equation, m1, (V3 − V1) [2], , ρ =, , [Total: 10], (Cambridge IGCSE Physics 0625 Paper 51 Q1 June 2009), , 6 In this experiment, you are to determine the, focal length of a converging lens., Carry out the following instructions referring to, Figure P7., illuminated, object, , u, , screen, , v, lens, , Figure P7, , a Place the lens so that its centre is a distance, u = 25.0 cm from the illuminated object., b In a copy of the table record the distance, u in cm from the centre of the lens to the, illuminated object, as shown in Figure P7., c Place the screen close to the lens. Move the, screen away from the lens until a focused, image of the object is seen on the screen., d Measure and record in your table the distance, v in cm from the centre of the lens to the, screen., u/cm, , v/cm, , f/cm, , e Calculate and record in your table the focal, length f of the lens using the equation, f =, , uv, (u + v ), , [5], , f Place the lens so that its centre is 45.0 cm, from the illuminated object., g Repeat steps b to e., h Calculate the average value of the focal length. [3], i State and briefly explain one precaution you took, in order to obtain reliable measurements., [2], [Total: 10], (Cambridge IGCSE Physics 0625 Paper 51 Q4 June 2009), , 288, , 9781444176421_BM_06.indd 288, , 20/06/14 7:35 AM
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Practical test questions, , 7 In this experiment, you are to investigate the, period of oscillation of a simple pendulum. Carry, out the following instructions referring to Figure, P8 and Figure P9., The pendulum has been set up for you. Do not, adjust the position of the clamp supporting the, pendulum., , f Plot a graph of T/s (y-axis) against d/cm, (x-axis)., [5], g State whether or not your graph shows that, T is directly proportional to d. Justify your, statement by reference to the graph., [1], [Total: 10], (Cambridge IGCSE Physics 0625 Paper 51 Q1, November 2009), , 8 In this experiment, you are to compare the, combined resistance of lamps arranged in series, and in parallel., Carry out the following instructions, referring to, Figure P10 and Figure P11., The circuit shown in Figure P10 has been set up, for you., power, source, , bob, d, , floor, one complete, oscillation, , Figure P8, , A, , Figure P9, , a Measure and record in a copy of the table, the vertical distance d from the floor to the, bottom of the pendulum bob., b Displace the pendulum bob slightly and, release it so that it swings. Measure and record, in your table the time t for 20 complete, oscillations of the pendulum (see Figure P9)., c Calculate the period T of the pendulum. The, period is the time for one complete oscillation., Record the value of T in the table., d Without changing the position of the clamp, supporting the pendulum, adjust the length, until the vertical distance d from the floor to the, bottom of the pendulum bob is about 20 cm., Measure and record in the table the actual value, of d to the nearest 0.1 cm. Repeat steps b and c., e Repeat step d using d values of about 30 cm,, 40 cm and 50 cm., d/cm, , t/s, , T/s, , V, Figure P10, , a Switch on. Measure and record in a copy of, the table the current I in the circuit and the, p.d. V across the two lamps. Switch off., b Calculate the combined resistance R of the, two lamps using the equation, R =V, I, Record this value of R in your table., V/, , l/, , R/, , Figure P10, , [4], , Figure P11, , [4], 289, , 9781444176421_BM_06.indd 289, , 20/06/14 7:35 AM
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Practical test questions, , c Complete the column headings in the table., d Disconnect the lamps and the voltmeter. Set, up the circuit shown in Figure P11., , ammeter, , power, source, , power, source, , A, motor A, , motor B, V, variable, resistor, , Figure P11, Figure P12a, , e Switch on. Measure and record in the table, the current I in the circuit and the p.d. V, across the two lamps. Switch off., f Calculate the combined resistance R of the, two lamps using the equation, R =V, I, Record this value of R in the table., g Using the values of resistance obtained in b, and f, calculate the ratio y of the resistances, using the equation, y =, , resistance of lamps in series, [3], resistance off lamps in parallel, , h (i) Figure P12a shows a circuit including two, motors A and B., Draw a diagram of the circuit using, standard circuit symbols. The circuit, symbol for a motor is shown in Figure, P12b., , M, Figure P12b, , (ii) An engineer wishes to measure the voltage, across motor A., On a copy of Figure P12a mark with the, letters X and Y where the engineer should, connect the voltmeter., (iii) State the purpose of the variable, resistor., [3], [Total: 10], (Cambridge IGCSE Physics 0625 Paper 51 Q3, November 2009), , 290, , 9781444176421_BM_06.indd 290, , 20/06/14 7:36 AM
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Alternative to practical test questions, 1, , (ii) Describe briefly how the graph line, shows this trend., , The IGCSE class is investigating the cooling, of water. Figure P13 shows the apparatus used., , [2], , [Total: 10], (Cambridge IGCSE Physics 0625 Paper 61 Q2 June 2010), thermometer, , 2, , The IGCSE class is investigating the current in a, circuit when different resistors are connected in, the circuit., The circuit is shown in Figure P14. The circuit, contains a resistor X, and there is a gap in the, circuit between points A and B that is used for, adding extra resistors to the circuit., X, , power source, , hot water, , A, , Figure P13, , Hot water is poured into the beaker and, temperature readings are taken as the water, cools., The table shows the readings taken by one, student., t/s, , θ /°C, , 0, , 85, , 30, , 78, , 60, , 74, , 90, , 71, , 120, , 69, , 150, , 67, , 300, , 63, , a (i) Using the information in the table,, calculate the temperature change T1 of the, water in the first 150 s., (ii) Using the information in the table,, calculate the temperature change T2 of, the water in the final 150 s., [3], b Plot a graph of θ/°C (y-axis) against t/s, (x-axis) for the first 150 s., [5], c During the experiment the rate of temperature, change decreases., (i) Describe briefly how the results that you, have calculated in part a show this trend., , A, , B, , Figure P14, , a A student connects points A and B together,, switches on and measures the current I0 in the, circuit., The reading is shown on the ammeter in, Figure P15., Write down the ammeter reading., [1], 0.4, , 0.6, , 0.2, 0, , 0.8, A, , 1.0, , Figure P15, , b The student connects a 3.3 Ω resistor, between points A and B, switches on, and records the current I. He repeats the, procedure with a 4.7 Ω resistor and then a, 6.8 Ω resistor., Finally he connects the 3.3 Ω resistor and the, 6.8 Ω resistor in series between points A and, B, and records the current I., 291, , 9781444176421_BM_06.indd 291, , 20/06/14 7:36 AM
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Alternative to practical test questions, , (i) Complete the column headings in a copy, of the table., [1], R/, , I/, , 3.3, , 0.23, , 4.7, , 0.21, , 6.8, , 0.18, 0.15, , (ii) Write the combined resistance of the, 3.3 Ω resistor and the 6.8 Ω resistor, in series in the space in the resistance, column of the table., [1], c Theory suggests that the current will be, 0.5 I0 when the total resistance in the circuit, is twice the value of the resistance of resistor, X. Use the readings in the table, and the, value of I0 from a, to estimate the resistance, of resistor X., [2], d On a copy of Figure P14 draw two resistors, in parallel connected between A and B and, also a voltmeter connected to measure the, potential difference across resistor X., [3], [Total: 8], (Cambridge IGCSE Physics 0625 Paper 61 Q3, November 2010), , 3 The IGCSE class is investigating the reflection of, light by a mirror as seen through a transparent block., Figure P16 shows a student’s ray-trace sheet., mirror, A, , B, , N, , transparent, block, , D, , E, , C, , P3, i, , [Total: 10], , P4, F, , N’, , a A student draws the outline of the transparent, block ABCD on the ray-trace sheet. He, draws the normal NN' to side CD. He draws, the incident ray EF at an angle of incidence, i = 20°. He pushes two pins P1 and P2 into, line EF and places the block on the sheet of, paper. He then observes the images of P1 and, P2 through side CD of the block from the, direction indicated by the eye in Figure P16, so that the images of P1 and P2 appear one, behind the other. He pushes two pins P3 and, P4 into the surface, between his eye and the, block, so that P3, P4 and the images of P1 and, P2, seen through the block, appear in line., (The plane mirror along side AB of the block, reflects the light.), The positions of P3 and P4 are marked on, Figure P16., (i) Make a copy of Figure P16. On line, EF, mark with neat crosses (×) suitable, positions for the pins P1 and P2., (ii) Continue the line EF so that it crosses, CD and extends as far as side AB., (iii) Draw a line joining the positions of P4, and P3. Continue the line so that it, crosses CD and extends as far as side AB., Label the point G where this line crosses, [4], the line from P1 and P2., (iv) Measure the acute angle θ between the, lines meeting at G., (v) Calculate the difference (θ − 2i)., [2], b The student repeats the procedure using an, angle of incidence i = 30° and records the, value of θ as 62°., (i) Calculate the difference (θ − 2i)., (ii) Theory suggests that θ = 2i. State, whether the results support the theory, and justify your answer by reference to, the results., [3], c To place the pins as accurately as possible,, the student views the bases of the pins., Explain briefly why viewing the bases of, the pins, rather than the tops of the pins,, improves the accuracy of the experiment. [1], (Cambridge IGCSE Physics 0625 Paper 61 Q4, November 2010), , eye, sheet of, paper, , Figure P16, 292, , 9781444176421_BM_06.indd 292, , 20/06/14 7:36 AM
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Alternative to practical test questions, , 4 An IGCSE student is investigating moments, using a simple balancing experiment., He uses a pivot on a bench as shown in Figure P17., First, the student balances the metre rule,, without loads, on the pivot. He finds that it does, not balance at the 50.0 cm mark, as he expects,, but it balances at the 49.7 cm mark., Load Q is a metal cylinder with diameter a little, larger than the width of the metre rule, so that, it covers the markings on the rule. Load Q is, placed carefully on the balanced metre rule with, its centre at the 84.2 cm mark. The rule does not, slip on the pivot., , a (i) On Figure P18, measure the vertical, distance d from the floor to the bottom of, the pendulum bob., (ii) Figure P18 is drawn one twentieth, actual size. Calculate the actual distance, x from the floor to the bottom of the, pendulum bob. Enter this value in the, top row of a copy of the table., The students displace the pendulum, bob slightly and release it so that it, swings. They measure and record in, the table the time t for 20 complete, oscillations of the pendulum, (see Figure P19)., x/cm, , t/s, , T/s, , T 2/s2, , 20.0, pivot, , bench, , Figure P17, , a Draw on a copy of Figure P17 the metre rule, with load Q on it., [2], b Explain, using a labelled diagram, how the, student would ensure that the metre rule, reading at the centre of Q is 84.2 cm., [2], c Calculate the distance between the pivot, and the centre of load Q., [1], [Total: 5], (Cambridge IGCSE Physics 0625 Paper 61 Q5 June 2009), , 5 The IGCSE class is investigating the period of, oscillation of a simple pendulum. Figure P18, shows the set-up., , 20.0, , 19.0, , 30.0, , 17.9, , 40.0, , 16.8, , 50.0, , 15.5, , [4], , b (i) Copy the table and calculate the period T, of the pendulum for each set of readings., The period is the time for one complete, oscillation. Enter the values in the table., (ii) Calculate the values of T 2. Enter the T 2, values in the table., c Use your values from the table to plot a graph, of T 2/s2 (y-axis) against x/cm (x-axis). Draw, the best-fit line., [5], d State whether or not your graph shows that, T 2 is directly proportional to x. Justify your, statement by reference to the graph., [1], [Total: 10], (Cambridge IGCSE Physics 0625 Paper 61 Q1, November 2009), , bob, d, , floor, one complete, oscillation, , Figure P18, , Figure P19, 293, , 9781444176421_BM_06.indd 293, , 20/06/14 7:36 AM
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Alternative to practical test questions, , 6, , An IGCSE student is carrying out an optics, experiment., The experiment involves using a lens to focus the, image of an illuminated object onto a screen., a Copy and complete Figure P20 to show the, apparatus you would use. Include a metre rule, to measure the distances between the object and, the lens and between the lens and the screen., The illuminated object is drawn for you., [3], , A, , B, Circuit 2, , Figure P22, A, , B, , Circuit 3, Figure P23, A, , illuminated, object, , B, Circuit 4, , lamp, , Figure P24, , card, , The voltage and current readings are, shown in the table., , Figure P20, , b State two precautions that you would take to, obtain accurate results in this experiment. [2], [Total: 5], (Cambridge IGCSE Physics 0625 Paper 61 Q5, November 2009), , 7, , The IGCSE class is comparing the combined, resistance of resistors in different circuit arrangements., The first circuit is shown in Figure P21., power, source, , A, , V, A, , B, , Circuit 1, , Figure P21, , a The current I in the circuit and the p.d. V, across the three resistors are measured and, recorded. Three more circuit arrangements, are used. For each arrangement, a student, disconnects the resistors and then reconnects, them between points A and B as shown in, Figures P22–24., , Circuit, , V/, , I/, , 1, , 1.87, , 1.68, , 2, , 1.84, , 0.84, , 3, , 1.87, , 0.37, , 4, , 1.91, , 0.20, , R/, , (i) Copy and complete the column headings, for each of the V, I and R columns of, the table., (ii) For each circuit, calculate the combined, resistance R of the three resistors using, the equation, R =V, I, Record these values of R in your table. [3], b Theory suggests that, if all three resistors, have the same resistance under all conditions,, the combined resistance in circuit 1 will, be one half of the combined resistance in, circuit 2., (i) State whether, within the limits of, experimental accuracy, your results, support this theory. Justify your answer by, reference to the results., (ii) Suggest one precaution you could, take to ensure that the readings are as, accurate as possible., [3], [Total: 6], (Cambridge IGCSE Physics 0625 Paper 61 Q2, June 2008), , 294, , 9781444176421_BM_06.indd 294, , 20/06/14 7:36 AM
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Alternative to practical test questions, , 8, , The IGCSE class is investigating the change in, temperature of hot water as cold water is added, to the hot water., A student measures and records the temperature, θ of the hot water before adding any of the cold, water available., He then pours 20 cm3 of the cold water into the, beaker containing the hot water. He measures, and records the temperature θ of the mixture of, hot and cold water., He repeats this procedure four times until he has, added a total of 100 cm3 of cold water., The temperature readings are shown in the table., V is the volume of cold water added., V/, , θ/, , 0, , 82, 68, 58, 50, 45, 42, , a (i) Copy and complete the column headings in, the table., (ii) Enter the values for the volume of cold, water added., [2], b Use the data in the table to plot a graph of, temperature (y-axis) against volume (x-axis)., Draw the best-fit curve., [4], c During this experiment, some heat is lost from, the hot water to the surroundings. Also, each, time the cold water is added, it is added in, quite large volumes and at random times., Suggest two improvements you could make to, the procedure to give a graph that more accurately, shows the pattern of temperature change of the, hot water, due to addition of cold water alone. [2], [Total: 8], (Cambridge IGCSE Physics 0625 Paper 61 Q3, November 2008), , 9, , a The table shows some measurements taken by, three IGCSE students. The second column, shows the values recorded by the three, students. For each quantity, underline the, value most likely to be correct., The first one is done for you., , Quantity measured, , Recorded values, , The mass of a wooden metre rule, , 0.112 kg, 1.12 kg, 11.2 kg, , The weight of an empty 250 cm3 glass, beaker, , 0.7 N, 7.0 N, 70 N, , The volume of one sheet of this paper, , 0.6 cm3, 6.0 cm3, 60 cm3, , The time taken for one swing of a simple, pendulum of length 0.5 m, , 0.14 s, 1.4 s, 14 s, , The pressure exerted on the ground by a, student standing on one foot, , 0.4 N/cm2, 4.0 N/cm2, 40 N/cm2, , [4], , b (i) A student is to find the value of the, resistance of a wire by experiment., Potential difference V and current, I can be recorded. The resistance is, then calculated using the equation, R =V, I, The student knows that an increase in, temperature will affect the resistance of, the wire., Assuming that variations in room, temperature will not have a significant, effect, suggest two ways by which the, student could minimise temperature, increases in the wire, during the experiment., [2], (ii) Name the circuit component that, the student could use to control, the current., [1], [Total: 7], (Cambridge IGCSE Physics 0625 Paper 61 Q5, November 2008), , 295, , 9781444176421_BM_06.indd 295, , 20/06/14 7:37 AM
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Alternative to practical test questions, , 10 The IGCSE class is investigating the resistance of, a wire. The circuit is as shown in Figure P25., power, source, , A, A, , B, , C, , D, , c Following this experiment, the student wishes, to investigate whether two lamps in parallel, with each other have a smaller combined, resistance than the two lamps in series. Draw, one circuit diagram showing, (i) two lamps in parallel with each other, connected to a power source,, (ii) an ammeter to measure the total current, in the circuit,, (iii) a voltmeter to measure the potential, difference across the two lamps., [3], , V, , [Total: 8], (Cambridge IGCSE Physics 0625 Paper 61 Q3, June 2007), , Figure P25, , a A student uses the switches to connect the, wire AB into the circuit and records the p.d., V across the wire between A and B. He also, records the current I in the wire., The student then repeats the measurements, using the wire CD in place of wire AB., The readings are shown in the table., Wire, , V/, , I/, , AB, , 1.9, , 0.24, , CD, , 1.9, , 0.96, , 11 a An IGCSE student is investigating the, differences in density of small pieces of, different rocks. She is using an electronic, balance to measure the mass of each sample, and using the ‘displacement method’ to, determine the volume of each sample. Figure, P26 shows the displacement method., , R/, cm3, , cm3, , [3], , (i) Calculate the resistance R of each wire,, using the equation R = V/I., Record the values in a copy of the table., (ii) Complete the column headings in your, table., b The two wires AB and CD are made of the same, material and are of the same length. The diameter, of wire CD is twice the diameter of wire AB., (i) Look at the results in the table. Below, are four possible relationships between, R and the diameter d of the wire. Which, relationship best matches the results?, R is proportional to d, R is proportional to 1/d, R is proportional to d2, R is proportional to 1/d2, (ii) Explain briefly how the results support, your answer in part b(i)., [2], , 100, , 100, , 80, , 80, , 60, , 60, , 40, , 40, , 20, , 20, , V1, , rock sample, , V2, , Figure P26, , (i) Write down the volume shown in each, measuring cylinder., (ii) Calculate the volume V of the rock, sample., (iii) Calculate the density of sample A using, the equation, density = m, V, where the mass m of the sample of, rock is 109 g., , [4], , 296, , 9781444176421_BM_06.indd 296, , 20/06/14 7:37 AM
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Alternative to practical test questions, , b The table shows the readings that the student, obtains for samples of rocks B and C. Copy, and complete the table by, (i) inserting the appropriate column headings, with units,, (ii) calculating the densities using the, equation, density = m, V, Sample, , m/g, , V/, , B, , 193, , 84, , 50, , 34, , C, , 130, , 93, , 50, , 43, , Density/, , [4], , c Explain briefly how you would determine the, density of sand grains., [1], [Total: 9], (Cambridge IGCSE Physics 0625 Paper 61 Q5, November 2007), , 297, , 9781444176421_BM_06.indd 297, , 20/06/14 7:37 AM
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Answers, Higher level questions are marked with *. The questions, example answers, marks awarded and/or comments, that appear in this book were written by the authors. In examination the way marks would be awarded to, answers like these may be different. Cambridge International Examinations bears no responsibility for the, example answers to questions taken from its past question papers which are contained in this publication., , General physics, Measurements and motion, 1 Measurements, 1 a 10, b 40, c 5, d 67, e 1000, 2 a 3.00, b 5.50, c 8.70, d 0.43, e 0.1, 3 a 1.0 × 105; 3.5 × 103;, 4.28 × 108; 5.04 × 102;, 2.7056 × 104, b 1000; 2 000 000; 69 200;, 134; 1 000 000 000, 4 a 1 × 103; 7 × 105;, 1 × 107; 5 × 105, b 5 × 101; 8.4 × 102;, 3.6 × 104; 1.04 × 103, 5 10 mm, 6 a Two, b Three, c Four, d Two, 7 24 cm3, 8 40 cm3; 5, 9 80, 10 a 250 cm3, b 72 cm3, 11 a 53.3 mm, b 95.8 mm, 12 a 2.31 mm, b 14.97 mm, 13 a Metre, kilogram,, second, b Different number of, significant figures, c (i) πr2, (ii) 4 πr3, 3, , (iii) πr2h, , 9781444176421_ANSWER_07.indd 299, , 2 Speed, velocity and, acceleration, 1 a 20 m/s, b 6.25 m/s, 2 a 15 m/s, b 900 m, 3 2 m/s2, 4 50 s, 5 a 6 m/s, b 14 m/s, 6 4s, 7 a Uniform acceleration, b 75 cm/s2, 8 a 1s, b (i) 10 cm/tentick2, (ii) 50 cm/s per tentick, (iii) 250 cm/s2, c 0, 9 A, 10 E, 3 Graphs of equations, 1 a 60 km, b 5 hours, c 12 km/h, d 2, e 1 12 hours, 1, f 60 km/3 2 h = 17 km/h, g Steepest line: EF, 2 a 100 m, b 20 m/s, c Slows down, 3 a 54 m/s2, b (i) 10 m, (ii) 45 m, c 22 s, 4 a (i) OA, BC: accelerating;, (ii) DE: decelerating;, (iii) AB, CD: uniform velocity, b OA: a = +80 km/h2;, AB: v = 80 km/h;, BC: a = +40 km/h2;, CD: v = 100 km/h;, DE: a = 200 km/h2, , c OA 40 km; AB 160 km;, BC (5 + 40) = 45 km;, CD 100 km; DE 25 km, d 370 km, e 74 km/h, 5 a Uniform velocity, b 600 m, c 20 m/s, 4 Falling bodies, 1 a (i) 10 m/s, (ii) 20 m/s, (iii) 30 m/s, (iv) 50 m/s, b (i) 5 m, (ii) 20 m, (iii) 45 m, (iv) 125 m, 2 3 s; 45 m, 5 Density, 1 a (i) 0.5 g, (ii) 1 g, (iii) 5 g, b (i) 10 g/cm3, (ii) 3 kg/m3, c (i) 2.0 cm3, (ii) 5.0 cm3, 2 a 8.0 g/cm3, b 8.0 × 103 kg/m3, 3 15 000 kg, 4 130 kg, 5 1.1 g/cm3, 6 Density of ice is less than density, of water, , Forces and momentum, 6 Weight and stretching, 1 a 1N, b 50 N, c 0.50 N, 2 a 120 N, b 20 N, 3 a 2000 N/m, b 50 N/m, 4A, , 299, , 20/06/14 7:27 AM
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Answers, , 7, 1, 2, 3, 4, , Adding forces, 40 N, 50 N, 25 N, 50 N at an angle of 53° to the, 30 N force, 5 a 7N, b 13 N, 8, 1, 2, 3, 4, 5, 6, 7, 8, , Force and acceleration, D, 20 N, a 5000 N, b 15 m/s2, a 4 m/s2, b 2N, a 0.5 m/s2, b 2.5 m/s, c 25 m, a 1000 N, b 160 N, a 5000 N, b 20 000 N; 40 m/s2, a (i) Weight, (ii) Air resistance, b Falls at constant velocity, (terminal velocity), , 9 Circular motion, 1 Force is greater than string can, bear, 2 a Sideways friction between, tyres and road, b (i) Larger, (ii) Smaller, (iii) Larger, 3 Slicks allow greater speed in dry, conditions but in wet conditions, treads provide frictional force to, prevent skidding, 4 5000 s (83 min), 10 Moments and levers, 1E, 2 (i) C, (ii) A, (iii) B, , 11 Centres of mass, 1aB, bA, c C, 2 Tips to right, 12 Momentum, 1 a 50 kg m/s, b 2 kg m/s, c 100 kg m/s, 2 2 m/s, 3 4 m/s, 4 0.5 m/s, 5 2.5 m/s, 6 a 40 kg m/s, b 80 kg m/s, c 20 kg m/s2, d 20 N, 7 2.5 m/s, , Energy, work, power and, pressure, 13 Energy transfer, 1 a Electrical to sound, b Sound to electrical, c k.e. to p.e., d Electrical to light (and heat), e Chemical to electrical to light, and heat, 2 A chemical; B heat; C kinetic; D, electrical, 3 180 J, 4 1.5 × 105 J, 5 a 150 J, b 150 J, c 10 W, 6 500 W, 7 a (300/1000) × 100 = 30%, b Heat, c Warms surroundings, 8 a Electricity transferred to k.e., and heat, b Electricity transferred, to heat, c Electricity transferred to, sound, 9 3.5 kW, , 14 Kinetic and potential energy, 1 a 2J, b 160 J, c 100 000 = 105 J, 2 a 20 m/s, b (i) 150 J, (ii) 300 J, 3 a 1.8 J, b 1.8 J, c 6 m/s, d 1.25 J, e 5 m/s, 4 3.5 × 109 W = 3500 MW, 15 Energy sources, 1 a 2%, b Water, c Cannot be used up, d Solar, wind, e All energy ends up as heat, which is difficult to use and, there is only a limited supply, of non-renewable sources, 2 Renewable, non-polluting (i.e. no, CO2, SO2 or dangerous waste),, low initial building cost of station, to house energy converters,, low running costs, high energy, density, reliable, allows output, to be readily adjusted to varying, energy demands, 16 Pressure and liquid pressure, 1 a (i) 25 Pa, (ii) 0.50 Pa, (iii) 100 Pa, b 30 N, 2 a 100 Pa, b 200 N, 3 a A liquid is nearly, incompressible, b A liquid transfers the pressure, applied to it, 4 1 150 000 Pa (1.15 × 106 Pa), (ignoring air pressure), 5 a Vacuum, b Atmospheric pressure, c 740 mmHg, d Becomes less; atmospheric, pressure lower, , 300, , 9781444176421_ANSWER_07.indd 300, , 20/06/14 7:27 AM
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Answers, , 6E, 7B, , Thermal physics, Simple kinetic molecular, model of matter, 17 Molecules, 1B, 2 a Air is readily compressed, b Steel is not easily, compressed, 18 The gas laws, 1 a 15 cm3, b 6 cm3, , Thermal properties and, temperature, 19 Expansion of solids, liquids, and gases, 2 Aluminium, 3B, 4A, 20 Thermometers, 1 a 1530 °C, b 19 °C, c 0 °C, d 12 °C, e 37 °C, 2C, 3 a Property must change, continuously with temperature, b Volume of a liquid, resistance,, pressure of a gas, c (i) Platinum resistance, (ii) Thermocouple, (iii) Alcohol, 21 Specific heat capacity, 1 15 000 J, 1500 J/°C, 2 A = 2000 J/(kg °C);, B = 200 J/(kg °C);, C = 1000 J/(kg °C), 3 Specific heat capacity of jam is, higher than that of pastry so it, cools more slowly, , 9781444176421_ANSWER_07.indd 301, , 22 Specific latent heat, 1 a 3400 J, b 6800 J, 2 a 5 × 340 + 5 × 4.2 × 50, = 2750 J, b 1700 J, 3 680 s, 4 a 0 °C, b 45 g, 5 a 9200 J, b 25 100 J, 6 157 g, 7 a Ice has a high specific latent, heat of fusion, b Water has a high specific, latent heat of vaporisation, 8 Heat drawn from the water, when it evaporates, 9 Heat drawn from the milk, when the water evaporates, 10 1200 J, , Thermal processes, 23 Conduction and, convection, 1 a Newspaper is a poor, conductor of heat, b The fur would trap more air,, which is a good insulator, and, so keep wearer warmer, c Holes in a string vest trap air,, which is a poor conductor,, next to the skin, 3 a If small amounts of hot, water are to be drawn, off frequently it may not, be necessary to heat the, whole tank, b If large amounts of hot, water are needed it will, be necessary to heat the, whole tank, 4 Metal is a better conductor of, heat than rubber, 24 Radiation, 1 Black surfaces absorb radiation, better than white ones so the, ice on the black sections of the, canopy melts faster than on the, white sections, , 2 a The Earth radiates energy, back into space, b Clouds reduce the amount, of energy radiated into space,, keeping the ground warmer, , Properties of waves, General wave properties, 25 Mechanical waves, 1 a 1 cm, b 1 Hz, c 1 cm/s, 2 A, C, 3 a Speed of ripple depends on, depth of water, b AB since ripples travel more, slowly towards it, therefore, water shallower in this direction, 4 a Trough, b (i) 3.0 mm, (ii) 15 mm/s, (iii) 5 Hz, , Light, 26 Light rays, 1 Larger, less bright, 2 a Four images, b Brighter but blurred, 3C, 4 Before; sound travels slower, than light, 27 Reflection of light, 1 a 40°, c 40°, 50°, 50, d Parallel, 2A, 3 Top half, 28 Plane mirrors, 1B, 2D, 3 4 m towards mirror, 4B, 29 Refraction of light, 3 250 000 km/s, 4C, 6E, 7A, , 301, , 20/06/14 7:27 AM
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Answers, , 30 Total internal reflection, 1 a Angle of incidence = 0, b Angle of incidence > critical, angle, 3 Periscope, binoculars, 4 a Ray passes into air and is, refracted away from the, normal, b Total internal reflection occurs, in water, 5 48.6°, 31 Lenses, 1 Parallel, 2 a Converging, c Image 9 cm from lens, 3 cm, high, 3 Distance from lens:, a beyond 2F, b 2F, c between F and 2F, d nearer than F, 4 Towards, 5 a 4 cm, b 8 cm behind lens, virtual,, m=2, 6 A: converging f = 10 cm, B: converging f = 5 cm, 32 Electromagnetic, radiation, 1 a 0.7 µm, b 0.4 µm, 2aB, bD, 3 a Ultraviolet, b Microwaves, c Gamma rays, d Infrared, e Infrared/microwaves, f X-rays, 4 a 3m, b 2 × 104 s, 5E, , Sound, 33 Sound waves, 1 1650 m (about 1 mile), 2 a 2 × 160 = 320 m/s, , b 240/(3/4) = 320 m/s, c 320 m, 3 a Reflection, refraction,, diffraction, interference, b Vibrations are perpendicular, to rather than along the, direction of travel of the wave;, longitudinal, 4 b (i) 1.0 m, (ii) 2.0 m, , Electricity and, magnetism, Simple phenomena of, magnetism, 34 Magnetic fields, 1C, , Electrical quantities and, circuits, 35 Static electricity, 1D, 2 Electrons are transferred from, the cloth to the polythene, 3C, 36 Electric current, 1 a 5C, b 50 C, c 1500 C, 2 a 5A, b 0.5 A, c 2A, 3B, 4C, 5 All read 0.25 A, 37 Potential difference, 1 a 12 J, b 60 J, c 240 J, 2 a 6V, b (i) 2 J, (ii) 6 J, 3B, 4 b Very bright, c Normal brightness, d No light, e Brighter than normal, , f Normal brightness, 5 a 6V, b 360 J, 6 x = 18, y = 2, z = 8, 38 Resistance, 1 3Ω, 2 20 V, 3C, 4 A = 3 V; B = 3 V; C = 6 V, 5 2Ω, 6 a 15 Ω, b 1.5 Ω, 7D, 8 a (i) ohm’s law, (ii) 2 Ω, 9B, 39 Capacitors, 2 a (i) Maximum, (ii) Zero, b (i) Maximum, (ii) Zero, 40 Electric power, 1 a 100 J, b 500 J, c 6000 J, 2 a 24 W, b 3 J/s, 3C, 4 2.99 kW, 5 Fuse is in live wire in a but not, in b, 7 a 3A, b 13 A, c 13 A, 8 40p, 9 a (i) 2 kW, (ii) 60 W, (iii) 850 W, b 4A, 41 Electronic systems, 1 b L1 lights, L2 does not, c L1 and L2 light, d L1 lights, L2 does not, 2 a V1 = V2 = 3 V, b V1 = 1 V, V2 = 5 V, c V1 = 4 V, V2 = 2 V, , 302, , 9781444176421_ANSWER_07.indd 302, , 20/06/14 7:27 AM
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Answers, , 42 Digital electronics, 1 A AND, B OR, C NAND, D NOR, 2 A OR, B NOT, C NAND, D NOR, E AND, , 46 Electric motors, 1E, 2 Clockwise, 3E, , Electromagnetic effects, , 48 Electrons, 1 a A ve, B +ve, b Down, 2 a 1.6 × 1016 J, b 1.9 × 107 m/s, , 43 Generators, 1 a A: slip rings, B: brushes, b Increase the number of turns, on the coil, the strength of, the magnet and the speed of, rotation of the coil., 2 The galvanometer needle swings, alternately in one direction, and then the other as the rod, vibrates. This is due to a p.d., being induced in the metal rod, when it cuts the magnetic field, lines; current flows in alternate, directions round the circuit as, the rod moves up or down, 44 Transformers, 2B, 3 a 24, b 1.9 A, 4B, 45 Electromagnets, 1 a North, b East, 2S, 3 a To complete the circuits to, the battery negative, b One contains the starter, switch and relay coil; the other, contains the relay contacts and, starter motor, c Carries much larger current to, starter motor, d Allows wires to starter switch, to be thin since they only, carry the small current needed, to energise the relay, , 47 Electric meters, 3 a 0–5 V, 0–10 V, b 0.1 V, c 0–5 V, d Above the 4, e Parallax error introduced, , Atomic physics, 49 Radioactivity, 1aα, bγ, c β, dγ, eα, f α, g β, hγ, 2 25 minutes, 3D, 50 Atomic structure, 1B, 2 C (symbol is 73Li ), , ●● Revision, questions, 1 E, 2 A, 3 C, 4* a Yes, 1 mm = 0.001 m, b E, 5 D, 6 E, 7 A, 8 B, 9 C, 10 D, 11 D, , 12 a B, b A, 13 A, 14 A, 15 C, 16 B, 17 D, 18 C, 19 C, 20 C, 21 E, 22 a Become circular, b No change, c No change, 23 a (i) Infrared, (ii) X-rays, b (i) Radio, (ii) γ-rays, 24 a Longitudinal, b (i) Compression, (ii) Rarefaction, 25 a 60°, b 30°, 26 a Refraction, b POQ, c Towards, d 40°, e 90 – 65 = 25°, 27 C, 28 a Dispersion, b (i) Red, (ii) Violet, 29 B, 30 A, 31 D, 32 B, 33 C, 34 a 1 Ω, b 3A, c 6V, 35 a 3 Ω, b 2A, c 4 V across 2; 2 V across 1, 36 D, 37 B, 38 a E, b A, c C, d B, e D, 39 E, 303, , 9781444176421_ANSWER_07.indd 303, , 20/06/14 7:27 AM
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Answers, , E, E, B, B, a, b, c, d, 45 a, b, 40, 41, 42, 43, 44, , C, A, B, A, D, E, , ●● Cambridge, IGCSE exam, questions, 1 General physics, Measurements and motion, , 1 a (i) 6 cm and 5 cm, (ii) 60 cm3, b 2.65 g/cm3, 2* Time 10 cycles and calculate, the average, 3 a, , Distance, , Tape measure, , Time, , Stopwatch, , b Speed = distance/time, c (i) Some distances at, slower speeds, (ii) 22 km, 4 a (i) 1 Increasing, 2 Constant, c Zero distance, 5 a 400 s, d 10.8 m/s, 6* a (i) 1.6 s, (ii) 4.2 s, (iii) 32 m, (iv) 7095 m (area under, graph), b (i) Weight of ball down,, air resistance up, (ii) Up force = down force, , Forces and momentum, , 7* b 3 N reading, d Straight line through the, origin shows Hooke’s law, e Graph curves, , f Exceeded elastic limit, 8* a Limit of proportionality, b Force proportional to, extension, c OQ extension proportional, to force, QR extension/unit force, greater, d 4.0 N/ mm, 9* b 98 N–102 N, c Vertically upwards, d 98 N–102 N, 10* c Mass × distance, 11 a (i) At A, (ii) Greatest distance from, the hinge, b When centre of mass is, outside base, c (i) Less than, (ii) Centre of mass of, matchbox has been, raised, 12 a Force, perpendicular, distance from pivot, b (i) Force, moment, (ii) F1 + F2 + W, (iii) F, 13* a Student B: force inversely, proportional to mass, b F = ma, c (i) Nothing or as before, (ii) Slows down, (iii) Moves in a circle, 14* a The direction is changing, b (i) Force needed to, change direction, (ii) Towards the centre, (iii) Friction between tyres, and the road, 15* a (i) Resultant force, (ii) To overcome friction, b 0.8 kg, c 0.875 m/s2, d (i) 0.6 m/s, (ii) 0.36 m, 16* a (ii) It gets larger, b (ii) Friction is too small, c (i) Constant speed, (ii) 212.5 cm, (iii) 8.33 cm/s, , Energy, work, power and, pressure, , 17 a I = U + W, b (i) 850 N, (ii) Force needed to get it, started, (iii) Height, (iv) Time, c Greater than, 18* a 405 000 J, b 60 000 J, c 60 000 W, d Chemical, e Energy lost as heat,, sound, etc., 19 a Tidal, wave, hydroelectric, 20 a 88–92, b 88–92 mm, c 840, 21* a Volume reduced, pressure, goes up, b 20 cm3, c Speed of particles greater at, higher temperature, 22 b (i) Falls, (ii) Air molecules cause, pressure on mercury, d, , rises, , rises, , falls, , stays the same, , 23* a (i), (ii), b (i), (ii), , 540 kJ, W = E/t, 54 kW, 3750 kg, 12.5%, , 2 Thermal physics, Simple kinetic and molecular, model of matter, 24* b Air molecules hit dust, particles, c Slower movement, 25 a Solid: 2, 3 and 6, Gas: 1, 4 and 5, b Molecules break free of, surface, , Thermal properties and, temperature, , 26* a Energy needed to change, state, , 304, , 9781444176421_ANSWER_07.indd 304, , 20/06/14 7:27 AM
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Answers, , b Any time between 1.6 min, and 18 min, c P.e of molecules increases, and they escape from the, liquid, d (i) 480 kJ, (ii) 6.65 kg, 27* a Copper or constantan, Copper or constantan, Constantan or copper, 28* a Heat required to produce, 1 °C rise in 1 kg, b Long time to heat up, c (i) 1.8 °C and 77.1°C, (ii) 1512 J, (iii) 392 J/kg K, 29* a (i) 1 Melting point of ice, 2 Pure melting ice, 3 0 °C, (ii) 1 Boiling point of, water, 2 Steam, 3 100 °C, b Thermal capacity, 30* a (i) Funnel no longer, giving heat to ice, (ii) Better contact between, heater and ice, b Mass of beaker, c 338 J/g, 31* a Total mass before ice added, Total mass after all ice, melted, b (i) Mass × sp. heat capacity, × change in temp, (ii) Mass × sp. latent heat, of fusion of ice, c 427 J/g, 32 a °C, , q, Inverted, real, Same, (i) Nothing, (ii) Blurred image, 36 c (i) 2 m, (ii) 2 m away from mirror, 37* b Virtual, inverted, same size, as object, c Ray strikes glass normally, d 2 × 108 m/s, e i is greater than c so total, internal reflection occurs, 38*a (ii) Virtual, upright, same, size, same distance from, mirror, , 3 Properties of waves, , 4 Electricity and, magnetism, , Light, 33 a, b, c, 34* a, b, c, d, e, f, , 10 cm, Gets smaller and closer to lens, (i) Principal focus, A, Air, 42°–43°, Total internal reflection, 58.7°, 2.01343 × 108, , 35 a, c, d, e, , Sound, , 39 a (i) One sound, (ii) 495 m, b (i) One sound plus echo, (ii) 1.5 s and 4.5 s, 40 a (i) Decreasing, (ii) Waves get smaller, b (i) Nothing, (ii) Wavelength the same, c (i) 12–14, (ii) 1 300 waves per, second, 2 1/300 s, 3 0.04 s, d (i) Yes, (ii) Yes, (iii) No, 41 a One sound plus echo, b First, c (i) 3 s, (ii) 9 s, (iii) 6 s, , Simple phenomen of, magnetism, 42 a (i), (ii), b S, 43 a (i), (ii), b (i), , Iron rod, Plastic rod, S N, N at left and S at right, They attract, N at left and S at right, , (ii) They attract, c They attract, d Nothing, , Electrical quantities and, circuits, , 44 a (i) Water conducts, electricity, (ii) Cord not a conductor, b 10 A, c (i) Larger current, (ii) Cable would melt, 45* a , (i) X negative; Y positive, (ii) +ve charge on A, attracts ve charge, on B, (iii) B is neutral, b (i) Nothing, (ii) +ve charge is, cancelled, 46 a (i) 6 V, (ii) 50 mA, b 120 Ω, 47 a 60 Ω, c (i) 0.025 A, (ii) 1.5 V, d (i) Decreases, (ii) Decreases, (iii) 60 Ω, 48* c (i) One input is high and, output is low, (ii) 1 On, 2 Off, 49 a (i) Series, (ii) 12 Ω, (iii) 0.5 A, (iv) 5 V, (v) 5 V, b (i) 1 6 V, 2 0 V, 50* b (i) 3 A, (ii) 4 Ω, (iii) 2 Ω, (iv) 1080 J, 51* a Circuit 1: series, Circuit 2: parallel, c 12 V, d 2.4 Ω, e (i) 3 A, (ii) 24 W, (iii) 7200 J, 305, , 9781444176421_ANSWER_07.indd 305, , 20/06/14 7:27 AM
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Answers, , 52 a Interchange, connections on, ammeter or battery, b Current, d (i) Voltmeter, e 0.4 A, f 0.4 A, g (i) 7.5 Ω, (ii) Increases, , Electromagnetic effects, , 53* a (i) Step-up transformer, (ii) Less heat/energy lost, b 2.5 A, c 18.75 W, d 7.5 V, e 21 985 V, 54* a First finger – field, Second finger – current, b (i) Contact, Commutator, (ii) Clockwise, 55 a (ii) Iron, (iii) Magnetic linkage, b 120 V, 56 a (i) e.m.f. induced in AB, cancelled by e.m.f., induced in BC, (ii) Straighten out ABC, b Transformer, generator,, dynamo, microphone,, alternator, 57* b (i) Reduced, (ii) Same or none, c (i) Thin wire is a currentcarrying conductor in a, magnetic field, (ii) Towards the thick, wire, (iii) Smaller force, 58 a Contact position at centre, of potential divider, b Current in coil magnetises, core, armature pivots, closing contacts, 59 a (ii) Iron bar, b Rods become magnetised, and repel, 60* a Magnetic field cut by, conductor induces a current, , c Move magnet in and out of, solenoid, d Move magnet faster,, stronger magnet, more, turns of solenoid, , 5, , Atomic physics, , 61 a Alpha and beta, b Gamma, c Radio, d Alpha, 62* a Background radiation, b A Only background as, reading constant, B Gamma as not affected, by magnetic field, C Beta as deflected by, magnetic field, 63* a Beta – third and fourth, column, Gamma – first column, 64 a Between 22 and 27 minutes, b (i) Iodine-128, (ii) Radon-220 as shortest, half-life, 65* a Protons: 17 and 17, Neutrons: 18 and 20, Electrons: 17 and 17, b Alpha, beta and gamma, 66 a 84, b 218, c (i) 2, (ii) 4, (iii) Alpha particle, 67* A rebounds, B carries on, slightly deflected, C carries straight on, 68 a Between 18 and 20 minutes, b (i) About 922, (ii) Between 18 and, 20 minutes, c Alpha or beta, 69 a Electrons, b Moves towards P1, c By making P3 or P4 positive, d Fluorescent screen, 70* a Measure background reading, No aluminium – take count, Aluminium – take count, Subtract background reading, , b Count decreases with more, aluminium, , ●● Mathematics, for physics, 1a3, b5, c 8/3, d 20, e 12, f 6, g2, h3, i 8, 2 a f = v/λ, b λ = v/f, c I = V/R, d R = V/I, e m=d×V, f V = m/d, g s = vt, h t = s/v, 3 a I 2 = P/R, b I = √(P/R), c a = 2s/t2, d t2 = 2s/a, e t = √(2s/a), f v = √(2gh), g y = Dλ/a, h ρ = AR/l, 4 a 10, b 34, c 2/3, d 1/10, e 10, f 3 × 108, 5 a 2.0 × 105, b 10, c 8, d 2.0 × 108, e 20, f 300, 6a4, b2, c 5, d8, e 2/3, f 3/4, , 306, , 9781444176421_ANSWER_07.indd 306, , 20/06/14 7:27 AM
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Answers, , g 13/6, h 16, i 1, 7 a = (v u)/t, a 5, b 60, c 75, 8 a = (v2 u2)/2s, 9 b Extension ∝ mass because, the graph is a straight line, through the origin, 10 b No: graph is a straight line, but does not pass through, the origin, c 32, 11 a Graph is a curve, b Graph is a straight line, through the origin,, therefore s ∝ t2 or s/t2 = a, constant = 2, , ●● Alternative to, practical test, questions, 1 a (i) T1 18 °C, (ii) T2 4 °C, c (i) , T1 is much greater, than T2, (ii) Graph has a decreasing, gradient, 2 a 0.3, b (i) Ω A, (ii) 10.1, c 10 Ω, 3 b (i) 2°, (ii) Yes, results are close, enough, c Doesn’t matter if pins not, vertical, , 4 c 34.5 cm, 5 a (i) 0.5 cm, (ii) 10 cm, b T/s, T 2/s 2, 1.0, 0.95, 0.9, 0.84, 0.78, , 1.0, 0.90, 0.81, 0.71, 0.61, , 7 a (i) V, A, Ω, (ii) 1.11, 2.19, 5.05, 9.55, b (i) Yes, as within 10%, 8 a (i) cm3, °C, (ii) 20, 40, 60, 80, 100, c Avoid heat loss to the, surroundings, 9 a 0.7 N, 6 cm3, 1.4 s,, 4.0 N/cm3, b (i) Minimum current,, switch off regularly,, turn down power, supply, (ii) Variable resistor or, rheostat, 10 a (i) 7.92 Ω, 1.98 Ω, (ii) V, A, Ω, b (i) , R is proportional, to 1/d2, (ii) The first R is about ¼, of the second, 11 a (i) 50 cm3, 75 cm3, (ii) 25 cm3, (iii) 4.36 g/cm3, b (i) , V2/cm3, V1/cm3, cm3,, g/cm3, (ii) 5.66 g/cm3, 3.02 g/cm3, c Same method but lots, of grains, , 307, , 9781444176421_ANSWER_07.indd 307, , 20/06/14 7:27 AM
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Index, A, , absolute zero 77, absorption of radiation 102, acceleration 9–10, equations of motion 14–15, force and 31–2, of free fall (g) 18–19, 32, from tape charts 10–11, from velocity-time graphs 13, mass and 31–2, uniform 10, 11, 13, 14–15, acid rain 60, action-at-a-distance forces 24, 32, 155, action at points 153, 154, activity, radioactive material 233, air, convection 99–100, density 22, as insulator 98, weight 76, air bags 58, air resistance 17, 18, 33, alcohol-in-glass thermometers 85, alpha particles 231–2, 240, alpha decay 240, particle tracks 232, scattering 238, alternating current (a.c.) 159–60, capacitors in a.c. circuits 176, frequency 160, 201, mutual induction 204, transmission of electrical power, 206–7, alternative energy sources ix, 60–2,, 63–4, alternators (a.c. generators) 200–1,, 201–2, aluminium, specific heat capacity 89, ammeters 158, 164, 219, ammeter-voltmeter method 168, ampere (A) 158, amplitude of a wave 107, 136, analogue circuits 193, analogue meters 193, AND gates 194, angle of incidence 108, 116, 126, angle of reflection 108, 116, 126, anode 187, 222, antineutrinos 240, area 3–4, armatures 216, atmospheric pressure 69, 76, atomic bombs 242, atomic (proton) number 239, atomic structure 151, 239, nuclear model 238, nuclear stability 240, ‘plum pudding’ model 238, , Rutherford-Bohr model 241, Schrödinger’s model 241–2, atoms 72, attraction forces, electrical charge 24,, 150, 152–3, audibility, limits of 141, average speed 9, , B, , background radiation 230, 235, balances 4–5, balancing tricks 45–6, banking of roads 36, barometers 69–70, base 188, base-emitter path 189, batteries 50, 158, 162, 163, beam balances 4, beams, balancing 39, beams, of light 113, Becquerel, Henri 230, beta particles 231–2, 240, beta decay 240, particle tracks 232, bicycle dynamos 202, bimetallic strips 82, biofuels 62, biogas 62, body heat 98, Bohr, Niels 241, boiling point 94, Bourdon gauges 69, 76, Boyle’s law 78, 79, 80, Brahe, Tycho xi, brakes, hydraulic 68, braking distances 58, Brownian motion 72, 73, brushes, in electric motors 216, 217, in generators 200, 201, bubble chambers 233, buildings, heat loss in 98, 100–1, burglar alarms 213, , C, , calibration, thermometers 85, capacitance 174, capacitors 174, charging and discharging 175, in d.c. and a.c. circuits 176, carbon dating 235, 236, carbon dioxide emissions 60, carbon microphones 213, cars, alternators 202, braking distances 58, hydraulic brakes 68, rounding bends 36, safety features 49, 58, , speedometers 207, cathode ray oscilloscopes (CRO) 224–5, musical note waveforms 142–3, uses 225–6, cathode rays 222, cathodes 187, 222, cells 158, 163, see also batteries, Celsius scale 85, relationship to Kelvin scale 77, centre of gravity see centre of mass, centre of mass 43–6, stability 44–5, 283, toppling 44, 283, centripetal force 35–6, chain reactions 242, changes of state 91, charge, electric see electric charge, Charles’ law 76, 79, chemical energy 50, 51, circuit breakers 181, 213, circuit diagrams 158, circuits, current in 158–9, household circuits 180–2, model of circuit 162, parallel 158, 159, 164, 170, 180, safety 181–2, series 158, 159, 164, 169–70, circular motion 35, centripetal force 35–6, satellites 36–8, clinical thermometers 86, cloud chambers 232, coastal breezes 100, coils, in electric motors 216, magnetic fields due to 210, in transformers 204–5, collector 188, collector-emitter path 189, collisions, elastic and inelastic 57–8, impulse and 48–9, momentum and 47, combustion of fuels 54, communication satellites 37, commutators, in dynamos 201, in electric motors 216, 217, compasses 146, 147, compressions 140, computers, static electricity and 154, condensation 94, conduction of heat 97–8, conductors (electrical) 151, 152, metallic 169, ohmic and non-ohmic 169, 188, , 308, , 9781444176421_Index_09.indd 308, , 20/06/14 7:29 AM
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INDEX, conservation of energy 53, 57, conservation of momentum 47–8, constant of proportionality 280, constant-volume gas thermometers 86, continuous ripples 107, continuous spectra 241–2, convection 99–100, convection currents 99, 100, convector heaters 179, conventional current 158, converging lenses 129, 130, 132, cooling, rate of 103–4, 283–4, Copernicus, Nicolaus xi, coulomb (C) 158, count-rate, GM tube 230, couples, electric motors 216, crests of waves 107, critical angle 126–7, critical temperatures of gases 94–5, critical value, chain reactions 242, crude oil 54, crumple zones 49, 58, crystals 74, current see electric current, , D, , dataloggers 5, 11, d.c. generators (dynamos) 201, 202, decay curves 233, deceleration 10, declination 148, deflection tubes 223, degrees, temperature scales 85, density 21–3, of water 83, dependent variables 281, depth, real and apparent 123, deuterium 239, 243, deviation of light rays 124, diaphragms, in steam turbines 63, dielectric 174, diffraction, of electromagnetic waves 137, of mechanical waves 108–9, 110, of sound waves 140, diffuse reflection 117–18, diffusion 74–5, diffusion cloud chambers 232, digital circuits 193, digital meters 193, diodes 169, 187–8, direct current (d.c.) 159, capacitors in d.c. circuits 176, direct proportionality 280, dispersion of light 124, 136, displacement 9, displacement-distance graphs 106, distance-time graphs 10, 14, 19, diverging lenses 129, 132, double insulation 181–2, , drop-off current 212, dynamic (sliding) friction 29, ‘dynamo rule’ 200, dynamos 201, 202, , E, , Earth, magnetic field 148, earthing 153, 181, echoes 141, ultrasonic 143, eddy currents 206, 207, efficiency 53, of electrical power transmission 207, of motors 178, of power stations 63, effort 40, Einstein, Albert xi, 242, elastic collisions 57–8, elastic limit 25, elastic potential energy 50, electrical energy 50, 182, production 61, 62, 63–4, transfer 51, 162, 163, 177, 207, electric bells 211–12, electric charge 150, 158, attraction forces 24, 150, 152–3, current and 157, electrons and 151, 152, see also static electricity, electric circuits see circuits, electric current 157, 158, alternating (a.c.) 159–60, 176, 201,, 204, 206–7, in circuits 158–9, direct (d.c.) 159, 176, effects of 157, electrons in 157, 158, 162, from electromagnetic induction 199, magnetic fields and 157, 209–10, 215, measurement 158–9, in transistors 189, electric fields 155–6, deflection of electron beams 223, deflection of radiation 232, electricity, dangers of 182–3, generation see power stations;, renewable energy sources, heating 179, lighting 178, paying for 182, transmission 206–7, see also static electricity, electricity meters 182, electric motors 178, 215–18, electric power 177–8, electric shock 182–3, electrolytic capacitors 174, electromagnetic induction 199, applications 202–3, , generators 200–2, mutual 204, electromagnetic radiation 51, 135–9, dual nature 227, gamma rays 135, 138, 231–2, 235,, 240, infrared 102, 135, 136, microwaves xii, 135, 137–8, properties 135, radio waves 135, 137, ultraviolet 102, 135, 136–7, X-rays xi, 135, 138, 226–7, see also light, electromagnetic spectrum 135, electromagnetism 209–10, electromagnet construction 210–11, magnetisation and demagnetisation, 210, uses 211–13, electromotive force (e.m.f.) 163, electronic systems 185, impact on society 196–8, input transducers 185, 186, output transducers 185, 186–7, electron microscopes viii, 72, electrons 151, 239, cathode rays 222, deflection of beams 222–3, electric current 157, 158, 162, energy levels 241, photoelectric emission 227, thermionic emission 222, see also atomic structure, electrostatic induction 152, elements, electric heating devices 179, emission of radiation 102–3, emitter 188, endoscopes 128, energy, conservation of 53, 57, of electromagnetic radiation 135, forms of 50–1, losses in buildings 98, 100–1, losses in transformers 205–6, sources see energy sources, transfer of see transfers of energy, see also specific types of energy e.g., kinetic energy; nuclear energy etc, energy density of fuels 60, energy levels, electrons 241, energy sources, alternative sources ix, 60–2, 63–4, consumption figures 64–5, economic, environmental and social, issues 64–5, food 50, 53–4, non-renewable 60, 62–3, renewable 60–2, 63–4, energy value of food 53–4, 309, , 9781444176421_Index_09.indd 309, , 20/06/14 7:29 AM
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INDEX, equations, changing the subject of 279–80, heat equation 88, of motion 14–15, wave equation 107, equilibrium, conditions for 39, 41, states of 44–5, errors, parallax 2–3, systematic 5–6, ethanamide, cooling curve 91, evaporation, conditions for 93–4, cooling by 94, 283–4, evidence xi–xii, expansion 81–2, expansion joints 81, explosions 48, extended sources of light 114, eyes 132–3, , F, , facts viii, falling bodies 17–20, terminal velocity of 33, Faraday’s law 199, farad (F) 174, ferro-magnetics 146, field lines 146–8, 209, filament lamps 169, 178, filaments 222, fire alarms 82, fission, nuclear 242, fixed points, temperature scales 85, Fleming’s left-hand rule 216, 218, 222, Fleming’s right-hand rule 200, floating 22–3, flue-ash precipitation 154, fluorescent lamps 178, focal length 130, food, energy from 50, 53–4, force 24, 27, acceleration and 31–2, action-at-a-distance forces 24, 32,, 155, addition of 27–8, of attraction 24, 150, 152–3, centripetal 35–6, on current-carrying wire 215, equilibrium 39, 41, friction 29, 36, moments 39–41, momentum and 48, Newton’s first law 30, Newton’s second law 31–2, 48, Newton’s third law 32–3, parallelogram law 27–8, force constant of a spring 25–6, force-extension graphs 25, , force multipliers 67, forward-biased diodes 187, fossil fuels 60, 64, ‘free’ electrons 98, free fall, acceleration of (g) 18–19, 32, freezing points 91, frequency, alternating current 160, 201, light waves 136, measurement by CRO 226, mechanical waves 106, 107, pendulum oscillations 5, sound waves 141, friction 29, 36, fuels 50, 54, 60, 64, see also energy sources, fulcrum 39, 40, full-scale deflection 220, fundamental frequency 142, fused plugs 181, fuses 179, 180, fusion, nuclear 243, specific latent heat of 91–2, 93, , G, , Galileo xi, 17, 30, galvanometers 219, gamma rays 135, 138, 231–2, 235, 240, gases, diffusion 74–5, effect of pressure on volume 78, 79, effect of temperature on pressure, 77, 79, effect of temperature on volume, 76, 79, kinetic theory 73, 79–80, liquefaction 94–5, pressure 76–80, gas laws 76–9, gas turbines 63, Geiger, Hans 238, Geiger-Müller (GM) tube 230, 232,, 233–4, generators 200–2, geostationary satellites 37, geothermal energy 62, glass, critical angle of 126, refraction of light 122, gliding 100, gold-leaf electroscope 151, 230, gradient of straight line graphs 281, graphs 281–2, gravitational fields 32, gravitational potential energy 50, 56, gravity 24, 32, centre of see centre of mass, greenhouse effect 60, 103, greenhouses 103, , H, , half-life 233–4, 236, hard magnetic materials 146, hard X-rays 226, head of liquid 69, head restraints 58, heat 50, 51, conduction 97–8, convection 99–100, expansion 81–2, from electric current 157, latent heat 91–3, loss from buildings 98, 100–1, radiation 102–4, specific heat capacity 88–90, temperature compared 87, heat equation 88, heaters, electrical 179, logic gate control of 195, heat exchangers, nuclear reactors 242,, 243, heating, electric 179, heating value of fuels 54, hertz (Hz) 106, 160, 201, Hooke’s law 25–6, 283, household electrical circuits 180–2, Hubble Space Telescope viii, xi, Huygens’ construction 109, hydraulic machines 67–8, hydroelectric energy 61, 64, hydrogen, atoms 151, isotopes of 239, hydrogen bombs 243, , I, , ice, specific latent heat of fusion 92, ice point 85, images 114, converging lenses 130, plane mirrors 119–20, impulse 48–9, incidence, angle of 108, 116, 126, independent variables 281, induced current see electromagnetic, induction, induction, electromagnetic 199–203, electrostatic 152, mutual 204, induction motors 216, inelastic collisions 57–8, inertia 30, infrared radiation 102, 135, 136, inkjet printers 154, 155, input transducers (sensors) 185, 186, insulators (electrical) 151, 152, insulators (heat) 98, integrated circuits 188, , 310, , 9781444176421_Index_09.indd 310, , 20/06/14 7:29 AM
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INDEX, intensity of light 136, interference, mechanical waves 110–11, sound waves 140, internal energy see heat, International Space Station ix, inverse proportionality 78, 280–1, inverter (NOT gate) 193–4, investigations x–xi, 283–4, ionisation 227, 230, ionisation energy 241, ionosphere 137, ions 230, iron, magnetisation of 146, irregular reflections 117–18, isotopes 239, I-V graphs 169, , J, , jacks, hydraulic 67, jet engines 48, joule (J) 52, joulemeters 180, , K, , kaleidoscopes 120–1, Kelvin scale of temperature 77, Kepler, Johannes xi, kilogram (kg) 4, kilowatt-hours (kWh) 182, kilowatts (kW) 177, kinetic energy (k.e.) 50, 51, 56, from potential energy 51, 57, kinetic theory of matter 72–3, behaviour of gases and 73, 79–80, conduction of heat and 98, expansion 81, latent heat and 93, temperature and 80, 85, 87, , L, , lagging 98, lamps 158, 178, lasers ix, 113, 187, latent heat 91–3, lateral inversion 118–19, law of the lever 39–40, law of moments 39–40, laws viii, length 2–3, 6–7, lenses 129–33, Lenz’s law 200, lever balances 4–5, levers 40–1, light 135, 136, colour 136, dispersion 124, 136, frequency 136, from electric current 157, lenses 129–33, rays and beams 113, , reflection 116–18, refraction 122–4, shadows 114, sources 113, 114, speed of 115, 135, total internal reflection 126, 127, light-beam galvanometers 219, light-dependent resistors (LDRs) 169, 186, light-emitting diodes (LEDs) 187, light energy 51, lighting, electric 178, lightning 150, 153, light-operated switches 190, limit of proportionality 25, linear expansivity 82, linear (ohmic) conductors 169, lines of force 146–8, 209, line spectra 241–2, liquefaction of gases and vapours 94–5, liquid-in-glass thermometers 85, liquids, convection 99, density 22, kinetic theory 73, pressure in 66–8, thermochromic 86, live wires 180, load 40, logic gates 193–4, uses 194–6, logic levels 193, longitudinal waves 106, 140, long sight 132–3, looping the loop 36, 37, loudness 142, loudspeakers 51, 140–1, 218, luminous sources 113, , M, , magnetic fields 146–8, deflection of electron beams 222–3, deflection of radiation 231, 232, due to a current-carrying wire 157,, 209–10, due to a solenoid 210, motor effect 215, magnetic recording 202–3, magnets, properties of 146, magnification 131, magnifying glasses 131–2, ‘Maltese cross tube’ 222, manometers 69, Marsden, Ernest 238, mass 2, 4–5, 29, acceleration and 31–2, centres of 43–6, 283, as measure of inertia 30, mass defects 242, matter, kinetic theory see kinetic, theory of matter, , measurements 2–8, degree of accuracy x, mechanical waves 106–12, diffraction 108–9, 110, frequency 106, 107, interference 110–11, polarisation 111, reflection 108, 109–10, refraction 108, 110, speed 107, 108, megawatt (MW) 177, melting points 91, meniscus 4, mercury barometers 69–70, mercury-in-glass thermometers 85, 86, metal detectors 207, metals, conduction of electrical current 169, conduction of heat 97, 98, metre (m) 2, micrometer screw gauges 6–7, microphones 51, 202, 213, microwaves xii, 135, 137–8, mirrors, multiple images in 127, plane 116, 119–21, mobile phones ix, xii, 37, 137, moderators, nuclear reactors 242, 243, molecules 72, in kinetic theory 72–3, moment of a force 39–41, moments, law of 39–40, momentum 47, collisions and 47, conservation of 47–8, force and 48, monitoring satellites 37, monochromatic light 136, motion, Brownian 72, 73, circular 35–8, equations of 14–15, falling bodies 18, projectiles 19–20, motion sensors 10, 11, 13, motor effect 215, motor rule 216, motors 215–18, efficiency 178, electric power 178, moving-coil galvanometers 219, moving-coil loudspeakers 218, moving-coil microphones 202, multiflash photography 9, 19, multimeters 220, multipliers, voltmeters 219–20, multiplying factors 67, muscles, energy transfers in 54, musical notes 142–3, mutual induction 204, 311, , 9781444176421_Index_09.indd 311, , 20/06/14 7:29 AM
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INDEX, , N, , NAND gates 194, National Grid 206–7, negative electric charge 150, neutral equilibrium 45, neutral points, magnetic fields 147, neutral wires 180, neutrinos 240, neutron number 239, neutrons 151, 239, Newton, Isaac xi, newton (N) 24–5, Newton’s cradle 58, Newton’s first law 30, Newton’s second law 31–2, 48, Newton’s third law 32–3, noise 142, non-luminous objects 113, non-ohmic conductors 169, 188, non-renewable energy sources 60,, 62–3, NOR gates 194, normal 108, 116, NOT gates (inverters) 193–4, nuclear energy 51, 60, 64, 242–3, nuclear reactors 60, 64, 242–3, nuclei 239, 240, see also atomic structure, nucleons 239, nuclides 239, 240, , O, , octaves 142, Oersted, Hans 209, ohm (Ω) 167, ohmic (linear) conductors 169, ohm-metre (Ωm) 171, Ohm’s law 169, opaque objects 114, open circuit 163, operating theatres, static electricity in, 153, optical centre of lens 129, optical density 122, optical fibres 128, orbits 36–7, OR gates 194, output transducers 185, 186–7, overtones 142, , P, , parallax errors 5–6, parallel circuits 158, 159, household circuits 180, resistors in 170, voltage in 164, parallelogram law 27–8, particle tracks 232–3, pascal (Pa) 66, , pendulums, energy interchanges 57, period of 5, penetrating power, radiation 231, penumbra 114, period, pendulums 5, periscopes 117, permanent magnetism 146, 211, petroleum 54, phase of waves 107, 110, photocopiers 154, photoelectric effect 135, photoelectric emission 227, photogate timers 11, photons 227, 241, pinhole cameras 114, pitch of a note 142, plane mirrors 116, 119–21, plane polarisation 111, planetary system xi, plotting compasses 147, plugs, electrical 181, plumb lines 43, ‘plum pudding’ model 238, pointer-type galvanometers 219, point sources of light 114, polarisation, of mechanical waves 111, poles, magnetic 146, pollution 60, 64, positive electric charge 150, positrons 240, potential difference (p.d.) 163, energy transfers and 162, measurement 164, 225, potential divider circuits 168, 172, 190, potential energy (p.e.) 50, 51, 56, change to kinetic energy 51, 57, potentiometers 168, power, in electric circuits 177–8, of a lens 131, mechanical 52, 53, power stations 62–4, alternators 201–2, economic, environmental and social, issues 64–5, geothermal 62, nuclear 242–3, thermal 62–3, 202, powers of ten 2, pressure 66, atmospheric 69, 76, effect on volume of gas 78, 79, of gases 76–80, in liquids 66–8, pressure gauges 69–70, Pressure law 77, 79, primary coils 204–5, principal axis of lens 129, principal focus of a lens 130, , prisms, refraction and dispersion of light, 124, total internal reflection 127, problem solving 279, processors 185, progressive (travelling) waves 106, 135, projectiles 19–20, proportions 280–1, proton number 239, protons 151, 239, pull-on current 212, pulses of ripples 107, pumped storage systems 63–4, , Q, , quality of a note 142–3, quartz crystal oscillators 143, , R, , radar 137, radiant electric fires 179, radiation, background 230, 235, electromagnetic see electromagnetic, radiation, of heat 102–4, nuclear see radioactivity, radioactive decay 233–4, 239–40, radioactivity 230, alpha, beta and gamma rays 231–2, dangers 235–6, detection 230, 232–3, ionising effect of radiation 230, particle tracks 232–3, safety precautions xi, 236, sources of radiation 235–6, uses 234–5, radioisotopes 234–5, 236, 239, radionuclides 239, radiotherapy 235, radio waves 135, 137, range of thermometers 86, rarefactions 140, ratemeters 230, ray diagrams 131, rays, of light 113, mechanical waves 107, real images 119, reciprocals 279, rectifiers 188, reed switches 212–13, reflection, angle of 108, 116, 126, heat radiation 102, light 116–18, mechanical waves 108, 109–10, radio waves 137, sound waves 141, total internal 126, 127, , 312, , 9781444176421_Index_09.indd 312, , 20/06/14 7:29 AM
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INDEX, refraction, light 122–4, mechanical waves 108, 110, refractive index 123–4, critical angle and 126–7, refuelling, static electricity and 153, regular reflection 117, relays 186–7, 212, renewable energy sources 60–2, 63–4, reports x–xi, residual current circuit breaker (RCCB), 181, residual current device (RCD) 181, resistance 167, measurement 168, in transformers 205, variation with length of wire 284, variation with temperature 169, resistance thermometers 86, resistivity 171–2, resistors 167–8, colour code 171, light dependent (LDRs) 169, 186, in series and in parallel 169–70, variable 168, 193, resultants 27, retardation 10, reverberation 141, reverse-biased diodes 187, rheostats 168, 190, right-hand grip rule 210, right-hand screw rule 209, ring main circuits 180, ripple tanks 107, rockets 48, rotors, in alternators 201–2, in steam turbines 63, Rutherford-Bohr model of the atom, 241, Rutherford, Ernest 238, 241, , S, , safety systems, logic gate control of, 195, satellites 36–8, scalars 9, 29, scale, temperature 85, scalers, radiation measurement 230, Schrödinger, Erwin 241, model of the atom 241–2, seat belts 49, 58, secondary coils 204–5, second (s) 5, security systems, logic gate control of, 194–5, seismic waves 144, semiconductor diodes 169, 187–8, sensitivity of thermometers 86, series circuits 158, 159, , resistors in 169–70, voltages 164, shadows 114, short sight 132, shrink-fitting 81, 95, shunts 219, significant figures 3, sinking 22, SI (Système International d’ Unités), system 2, sliding (dynamic) friction 29, slip rings 200, soft magnetic materials 146, soft X-rays 226, solar energy 60–1, 64, solar furnaces 61, solar panels 60, 61, solenoids 146, 210, solidification 94, solids, density 22, kinetic theory and 72–3, sonar 143, sound waves 51, 140–4, specific heat capacity 88–90, specific latent heat, of fusion 91–2, 93, of vaporisation 92–3, spectacles 132–3, spectra 124, 241–2, speed 9, braking distance and 58, from tape charts 10–11, of light 115, 135, of mechanical waves 107, 108, of sound 141–2, speedometers 207, spring balances 24, springs, longitudinal waves in 140, stretching 25–6, stability, mechanical 44–5, 283, nuclear 240, stable equilibrium 44–5, staircase circuits 180, standard notation 2, starting (static) friction 29, static electricity 150–2, dangers 153–4, uses 154, van de Graff generator 154–5, 157, static (starting) friction 29, stators, in alternators 201–2, in steam turbines 63, steam, specific latent heat of, vaporisation 93, steam point 85, steam turbines 62–3, , steel, magnetisation 146, step-down transformers 205, step-up transformers 205, sterilisation 235, stopping distance 58, storage heaters 179, straight line graphs 281, strain energy 50, street lights, logic gate control of 195, stroboscopes 107, sulphur dioxide 60, Sun 243, superconductors 77–8, 95, superfluids 77, superposition of waves 110, surface area, effect on evaporation 93, sweating 94, switches 158, 193, house circuits 180, reed switches 212–13, transistors as 189–91, systematic errors 5–6, , T, , tape charts 10–11, 13, telephones 213, temperature 85, absolute zero 77, effect on evaporation 93, effect on pressure of gas 77, 79, effect on resistance 169, effect on speed of sound 141, effect on volume of gas 76, 79, heat compared 87, kinetic theory and 80, 85, 87, temperature-operated switches 190–1, temporary magnetism 146, 211, tenticks 5, 10, terminal velocity 33, theories viii, thermal capacity 88, thermal energy see heat, thermal power stations 62–3, 202, thermals 100, thermionic emission 222, thermistors 86, 169, 186, 190–1, thermochromic liquids 86, thermocouple thermometers 86, thermometers 85–6, thermonuclear fusion 243, thermostats 82, thickness gauges 234, thinking distance 58, thoron, half-life of 233–4, three-heat switches 179, threshold energy, thermionic emission, 222, threshold frequency, photoelectric, emission 227, tickertape timers 5, 10–11, 313, , 9781444176421_Index_09.indd 313, , 20/06/14 7:29 AM
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INDEX, ticks 5, 10, tidal barrages 61, 62, tidal energy 61–2, 64, timbre 142–3, time 2, 5, measurement of 10–11, 226, time base 224–5, 226, timers 5, 10–11, toner 154, top-pan balances 5, toppling 44, 283, total internal reflection 126, 127, tracers 235, transfers of energy 50, 51, 57, 63, 177, efficiency 53, in electric circuits 162, 163–4, measurement 52, in muscles 54, potential difference and 162, in power stations 63, transformers 204–5, energy losses in 205–6, transistors 188–9, as switches 189–91, transverse waves 106, 135, polarisation 111, tritium 239, 243, truth tables 193, 194, tsunami waves 144, turning effect see moment of a force, , U, , ultrasonics 143–4, ultrasound imaging 143, ultraviolet radiation 102, 135, 136–7, umbra 114, uniform acceleration 10, 11, 13, 14–15, uniform speed 10, uniform velocity 13, 14, units 2, , unstable equilibrium 45, uranium 60, 242, U-tube manometers 69, , V, , vacuum 76, evaporation into 94, falling bodies in 17, sound in 140, vacuum flasks 103, van de Graff generator 154–5, 157, vaporisation, specific latent heat of, 92–3, vapours, liquefaction 94–5, variable resistors 168, 193, variables 281, variation (proportion) 280–1, vectors 9, 28, velocity 9, equations of motion 14–15, from distance-time graphs 14, terminal 33, uniform 13, 14, velocity-time graphs 10, 13, ventilation 101, vernier scales 6, vibration 140, virtual images 119, 130, voltage 162, see also potential difference, voltmeters 164, 219–20, 220–1, volt (V) 162, 163, volume 4, volume of a gas, effect of pressure 78, 79, effect of temperature 76, 79, , W, , water, conduction of heat 97, density 83, , expansion 83, refraction of light 123, specific heat capacity 89, water supply systems 67, watt (W) 52, wave energy 61, wave equation 107, waveforms, on CRO 225, musical notes 142–3, wavefronts 107, wavelength 106, 107, 141, waves, amplitude 107, 136, diffraction 108–9, 110, 137, 140, frequency 106, 107, 136, 141, interference 110–11, 140, longitudinal 106, 140, mechanical 106–12, phase 107, 110, polarisation 111, progressive 106, 135, reflection see reflection, refraction 108, 110, 122–4, seismic 144, sound 51, 140–4, superposition 110, transverse 106, 111, 135, see also electromagnetic radiation;, light, wave theory 109–10, weight 4, 24–5, gravity and 32, wet suits 98, wind turbines ix, 61, 64, work 52, power and 52, 177, , X, , X-rays xi, 135, 138, 226–7, , 314, , 9781444176421_Index_09.indd 314, , 20/06/14 7:29 AM
