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CHAPTER ONE, INTRODUCTION TO PHYSICS, CONTENT, Definition of Physics, The Importance of Physics, Aspects/Careers in Physics, Branches of Physics, Definition of Physics, The word ‘’PHYSICS’’ originates from the Greek word, ‘’PHYSIS’’, which means nature and natural characteristics., Physics as a body of scientific knowledge, deals with the study of events in the universe, both remote and immediate universe., In actual sense, Physics deals with the behaviour of matter as well as the interaction of matter and natural forces., Physics is the study of matter in relation to energy., The Importance of Physics, Physics is important for the following reasons:, Physics is constantly striving to make sense of the universe. This is seen in the development of theories and new theories used for better understanding of the universe., When we study physics, we acquire the knowledge and skills to understand how and why natural things happen the way they do, and to make reliable predictions about their future occurrences. (e.g mirage, eclipse, earthquake, thunder,…), The knowledge of physics gives us a better understanding of our immediate and natural environment., The study of physics has enhanced the communication and the transportation world, thus, making the world a ‘’global village’’., Human health has been improved from the study of physics through the invention of modern medical equipment., EVALUATION, What Greek word is physics derived from?, Define physics., State five importance of physics., Aspects/Careers in Physics, Physics has several applications on health, technology & engineering, agriculture and applied sciences. As a result, below are some of the aspects/careers related to Physics., A: In Health, We have:, Human medicine and surgery, Nursing & midwives, Radiotherapy, Pharmacology, Physiology, Anaesthesia, Veterinary etc., B: In Engineering, We have:, Electrical engineering, Electronic engineering, Mechanical engineering, Aeronautic engineering, Petroleum engineering etc., C: In Agriculture, We have:, Agricultural engineering, Agricultural production engineering, Horticulture etc., D: In Basic/Applied Sciences, We have:, Geophysics, Applied physics, Biophysics, Medical physics, Space physics, Astronomical physics, Engineering physics, etc., EVALUATION, Mention any four (4) careers related to physics in:, Health, Basic science, Engineering., Branches of Physics, The following are the branches of physics., Mechanics, Heat, Electricity, Optics, Sound, Magnetism, Atomic physics, Nuclear physics, NOTE: No. 7 & 8 above had been combined and addressed with the current name, ‘’NUCLEAR PHYSICS’’, since the energy comes from the nucleus of the atom. The OLD NAME is ATOMIC PHYSICS., EVALUATION, Develop a mnemonic for branches of physics., Mention the branches of physics., What is the recent name for atomic physics?, What do you understand by the term, ‘Physics’?, How has physics made the world, ‘a global village’?, State five importance of physics., Mention five careers each related to Physics in the following areas. i. Engineering ii. Health iii. Applied sciences, Mention the branches of physics., CHAPTER TWO, FUNDAMENTAL AND DERIVED QUANTITIES AND UNITS, CONTENT, Fundamental Quantities, The Concept of Fundamental Quantities, Other Fundamental Quantities, Derived Quantities, The Concept of Derived Quantities, Dimensions and Units of Derived Quantities, Fundamental Quantities, The Concept of Fundamental Quantities, Fundamental quantities are physical quantities whose dimensions and units are not usually derived from other physical quantities. Basically, there are three fundamental quantities in mechanics. They include:, (i) Mass, (ii) Length and, (iii) Time, (i) Mass: This is a fundamental quantity with dimension ‘M’, usually written in capital letter. The S.I. unit of mass is kilogramme (kg). Mass can also be measured in gramme (g), tonne (t), etc., (ii) Length: This is another fundamental quantity with dimension ‘L’, written in capital letter. The S.I. unit of length is metre (m). Length can also be measured in kilometre (km), centimetre (cm), inches (inch), feet (ft), etc., (iii) Time: Time is a fundamental quantity with dimension ‘T’, also written in capital letter. The S.I. unit of time is second (s). Time can also be measured in minutes and hours., The below table summarized the dimensions and units of the basic fundamental quantities., EVALUATION, List the three basic fundamental quantities., What are their dimensions and SI units?, Other Fundamental Quantities, NB: The Physics teacher should carry out activities on simple measurement of current and temperature with the students., ACTIVITY: PRACTICAL, Measuring the temperature of boiled water in a specific interval of time say, 2mins as it cools down., Measuring the current value in a simple electric circuit., EVALUATION, Mention the three most fundamental quantities and their SI units., How many fundamental quantities are there altogether?, Enumerate all the fundamental quantities with their SI units., Write down the dimension of the three basic fundamental quantities., Why are the above quantities called fundamental quantities?, Derived Quantities, The Concept of Derived Quantities, Derived quantities are physical quantities whose dimensions and units are usually derived from the fundamental quantities. E.g force, speed, etc., Other physical quantities apart from the fundamental quantities are derived quantities. This is because their dimensions and units are usually derived from the fundamental ones., Derived quantities include:, Work, Energy, Momentum, Impulse, Volume, Area, Pressure, Power, Density, Moment, Torque, etc., EVALUATION, What are derived quantities?, Mention five examples of derived quantities., Dimensions and Units of Derived Quantities, 1. Derive the dimensions and the S.I. units of (i) speed (ii) acceleration (iii) Force., SOLUTION, (i) =LT = LT−1, ∴ The dimension for speed is LT−1, The S.I. unit of length is ‘m’ and that of time is ‘s’, ∴ The S.I. unit of speed is m/s ms−1, NB: Speed and velocity have the same dimension and S.I.unit., Also,, (ii) = LT−1 T = LT-2=LT−2, ∴ The S.I. unit of acceleration = =ms−2 ms−2, (iii) Force =mass×acceleration=M×LT-2 =MLT-2=MLT−2, ∴ The unit of force is kgms2, But the S.I. unit of force is Newton (N). This is the unit used in all calculations, 2. Show that the dimension of pressure is ML−1T−2. Hence, derive the S.I. unit., SOLUTION, Now, pressure =, ∴ Pressure =MLT−2L2=MT−2L=ML−1T−2, The S.I. unit of force is Newton, N; while that of area is metresquare, m2, Hence, the S.I. unit of pressure =Nm2orNm−2, 3. Derive the dimension for work. What is the S.I. unit of work?, SOLUTION, Work =force×distance, ∴ work =MLT−2×L=ML2T−2, Unit of work =Nm, But the S.I. unit of work is Joule (J). This is the unit used in all calculations., In summary, the table below shows the dimensions and S.I. units of some derived quantities., EVALUATION, 1. Derive the dimensions and the units of the following quantities:, (i) Volume (ii) Power (iii) Density., 2. Differentiate between fundamental and derived quantities., 3. List ten examples of derived quantities and explain why they are called derived quantities., 4. Write down the SI unit of (i) acceleration (ii) force (iii) momentum (iv) density, OBJECTIVE QUESTIONS, Which of the following is a derived unit?, Second, Ampere, Kilogramme, Ohm, Which of the following unit is equivalent to the Watt?, kgms-1, kgm2s-3, kgm2s-1, kgm2s-2, Which of the following are NOT fundamental units?, I. Kelvin II. Newton III. Second IV. Radian, I and II only, I and III only, I, II and IV only, II and IV only, Which of the following physical quantities is correctly paired with its corresponding SI unit?, Specific latent heat (Jkg-1K-1), Power (Js-1), Pressure (Nm-1), Density (kgm3), In which of the following physical quantities are the units correctly indicated?, I. Weight [N] II. Energy [J] III. Momentum [NKg-1], II and III only, I, II and III, III and I only, I and II only, DIMENSIONS AND MEASUREMENT OF PHYSICAL QUANTITIES, CONTENT, Measurement of Length/Distance, Measurement of Mass/Weight, Measurement of Volume, Measurement of Area, Measurement of Time, Units of Measurement in Industries, Measurement of Length/Distance, Length is measured using the following instruments., (a) Metre Rule: A metre rule is a measuring device calibrated in centimetres (cm) with a range of 0 – 100cm. In using the metre rule, the eye must be fixed vertically on the calibration to avoid parallax errors.The smallest reading that can be obtained on a metre rule is 0.1cm (0.01cm)., (b) Callipers: These are used in conjunction with metre rule for measuring diameter of tubes, thickness of sheet, etc. The callipers are of two types –, (i) The external calliper and, (ii) The internal calliper., The external calliper is used to measure the external diameters of solid objects; while the internal calliper is used to measure the internal diameters of solid objects., (c) Vernier calliper, The vernier calliper can be used for measuring smalllinear length and diameters of objects within the range of 0-12cm at least. It is calibrated in centimetres (cm). It has a reading accuracy of 0.1mm (0.01cm), (d) The micrometer screw gauge: It is used to measure the thickness of a round objects E.g, the diameter of a wire. The micrometer screw guage gives a more accurate reading than the vernier calliper. It is calibrated in millimetre (mm). It has a reading accuracy of 0.01mm (0.001cm), Other instruments for measuring length include: measuring tape, ruler, etc. The S.I. unit of length is metre (m)., EVALUATION, Mention any three instrument used in measuring length., Which of the above instrument could give the highest degree of accuracy?, Measurement of Mass/Weight, Mass is defined as the quantity of matter a body contains; while Weight is the amount of gravitational force acting on a body or the force with which a body is attracted towards the centre of the earth. The weight of a substance varies from place to place due to variation in acceleration due to gravity,‘g’ over places but mass remains constant from place to place., Mass and weight of objects are measured using instrument such as spring balance, beam balance, chemical balance, scale balance, etc., However, the differences between mass and weight are shown below., EVALUATION, State three instruments used in measuring mass and weight., Differentiate between mass and weight in four ways., Why is weight a vector quantity?, Measurement of Volume, Volume of liquid objects is measured using instruments such as cylinder, burette, pipette, eureka can, etc. For regular solid objects, their volume could be determined using their mathematical formula., The S.I. unit of volume is metre cube m3, Measurement of Area, The area of a solid object could be determined using mathematical formulae after determining the two dimensions of the object., The S.I. unit of volume is metre square m2, WORKED EXAMPLES, 1. Find the volume of a cylinder of diameter 12cm and height 15cm., SOLUTION, d =12cm, ∴ r =12cm2=6cm, h =15cm,π=227, Now, v =πr2h, ∴ v =227×62×15, ∴ v =22×36×157=118807, ∴ v =1697.14cm3, 2. What is the area of a triangular card board of base 6cm and height 4cm?, SOLUTION, b =6cm and h =4cm, Now, A =12bh, ∴ A =6×42=242, ∴ A =12cm2, EVALUATION, 1. Calculate the volume of a rectangular prism of dimension 7cm by 3.5cm by 1.5cm., 2. A cube has an edge of 0.8cm. Find its volume., Measurement of Time, The Concept of Time, You must have heard the following statements made about time:, “Time and tide waits for no man”, “Time is business”, “There is time for everything: time to sow and time to reap, time to laugh and time to cry, time to go to bed and time to wake up” and so on, Time is very important in our daily activities. Many people have failed in one area or the other because of mismanagement of time. In Physics time is very important. Wrong timing can lead to wrong observations, results and wrong conclusions., What then is time? Time may be considered as the interval between two successive events. It is a fundamental quantity. Its S.I unit is seconds., Ways of Measuring Time, Time as mentioned earlier is very important. That is why early men developed various means of measuring time. They used the sun to tell time. Even today people still use the position of the sun to determine time. Other devices they developed and used are:, The water clock or hourglass, The sand clock, The primitive Sundials, Today, we have better time-measuring devices that measure time more accurately than the above mentioned devices. Some of them are:, The stop watch which is the standard instrument for measuring time in the laboratory, The wrist watch, The modern pendulum clock, The wall clock, It is worthy of note that:, 60 seconds makes one minute, 60 minutes makes one hour, 24 hours makes one day, 365 ¼days makes one year, 10 years makes a decade, 100 years makes a century/centenary, 1000 years makes a millennium, Calculations on Time, Example 1: How many seconds are there in 2 hours 15 minutes?, Since 60 seconds makes 1 minute and 60 minutes makes 1 hour, 1 hour will have 60 x 60 seconds. 2 hours will have 60 x 60 x 2 seconds = 7200 seconds., 15 minutes will have 60 x 15 seconds = 900 seconds, Therefore 2 hours 15 minutes will have (7200 + 900) seconds = 8100 seconds, Example 2: If it takes a pendulum bob 32 seconds to complete 20 oscillations, what is the period of oscillation of the bob?, Period ( T ) is time ( t ) taken for the bob to complete an oscillation., i.e. T =timenumber of oscillations, =3220=1.6seconds, EVALUATION, What are the standard instruments for measuring time in the laboratory?, Mention 2 examples each of modern and olden days time-measuring devices you know., Units of Measurement in Industries, Measurement of Length, Length was considered earlier as a fundamental quantity whose S.I unit is metre. We also learnt that other units of length are centimeter, millimitre,, and kilometer., Units of Length, Class Activity, Mention the unit for measuring the following quantitiesby the following person, Classify these units under S.I units and other units., Example 1, Convert 3550km to miles, The length of an iron rod is given as 66 inches. What is its length in metres?, Solution, 1. 1 mile = 1.609km, Hence, 3550km = (3550 x 1.609) miles = 5,712 miles, 2. 1 inch = 2.54cm, Therefore 66 inches = (66 x 2.54) cm = 167.64cm., But 100cm = 1m,, Thus 167.64cm = =167.64100m = 1.6764m, Therefore the length of the iron rod in metres is 1.676.4m, EVALUATION, The height of a girl is 7.5 feet. Estimate her height in metres, Convert 30km to miles, Measurement of Volume, Volume is a measure of the space contained in an object. A barrel of oil is equivalent to 158.987 litres., Example 2, The table below is a statistics of oil exportation to the United States for three years by NNPC, (i) What volume of oil in litres was exported in 1994?, (ii) What is the highest amount gotten and in what year was it gotten?, Solution, (i) In 1994, 1.5 million barrels of oil was exported., Since 1 barrel = 158.987 litres, 1.05 million barrels = (1.5million x 158.987) litres = 238.4805million litres, (ii) In 1993, volume of oil exported = 1.05 million barrels. Price per barrel = N140, Amount realized = 1.05million × 140 = N147,000000, In 1994, volume of oil exported = 1.5million, price per barrel = N135, Amount realized = 1.5million × N135 = N202.5 million, In 1995, volume of oil exported = 0.9 million barrels. Price per barrel = N162, Amount realized = 0.9 million × N162 = N145.8 million, Therefore, the highest amount of money gotten is N202.5 million and it was gotten in 1994, Measurement of Temperature, The S.I unit of temperature is Kelvin. Other units for temperature include degree Celsius and degree Fahrenheit. In the U.S.A, degree Fahrenheit is still in use. On the Celsius scale, the freezing point and the boiling point of water are measured as 00C and 1000C respectively. But on the Fahrenhiet scale, the freezing point and the boiling point of water are measured as 320F and 2120F respectively., The Celsius Scale is related to the Fahrenheit scale by the equation:, F is temperature in Fahrenheit scale, C is temperature in Celsius scale, F–329=C100orC5=F–329, Example: (a) Convert 77 degrees Fahrenheit to Celsius scale (b) Convert 105 degrees Celsius to degrees Fahrenheit, Solution, (a) Considering the equation:, C5=F–329C=5(F–32)9=5(77–32)9=5×459=25, (b) C5=F–329F=9C5+32=9×1055+32=9×21+32=189+32=221oF, EVALUATION, Discuss the significance of time to the study of science., Highlight the various instrument for measuring time., State four differences between mass and weight., Draw the following measuring instruments: (i) Beam balance (ii) Spring balance, An object moves from point A to point B to point C, then back to point B and then to point C along the line shown in the figure below. Calculate the distance covered by the moving object., 17km, 9km, 14km, 13km, What is the volume of a rectangular box whose length = 5cm, width = 4cm, and height = 2cm?, 40cm3, 22cm3, 10cm3, 11cm3, The right instrument for measuring weight is the, scale balance., lever balance., chemical balance., spring balance., Which of the following instruments is the best for measuring the diameter of a thin constantan wire?, Callipers, Metre rule, Vernier callipers, Micrometre screw gauge, Which of the following properties of a steel bar can be measured in terms of the dimension of length?, Density, Weight, Volume, Pressure, POSITION, DISTANCE AND DISPLACEMENT, CONTENT, The Concept of Position, The Concept of Distance and Measurement, The Concept of Displacement, Distinction between Distance and Displacement, The Concept of Position, The position of an object is its location in space. It is usually expressed in relation to a reference point. To locate an object in space, a co-ordinate system is needed. It is usually a mathematical construct with co-ordinates., A coordinate system could be two-dimensional as in P(x,y) or three dimensional as in P(x,y,z)., The Concept of Distance and Measurement, Distance can be defined as a physical measurement of length between two points. It does not take into consideration the direction between the two points it measures; hence, it is a scalar quantity. This therefore means that distance has only magnitude but no direction. E.g, 10km., Distance could be measured using instruments like measuring tape, ruler, venier calliper, micrometer screw gauge, etc., The Concept of Displacement, Displacement is defined as the distance travelled or moved in a specific direction. It takes into consideration the direction between the different points it seeks to measure; hence, displacement is a vector quantity. Thus, it has both magnitude and direction. E.g, 10km due east. The ‘10km’ is the magnitude (or value), while ‘due east’ is the direction., Both distance and displacement have the same S.I. unit, metre (m). They could also be expressed in kilometre (km), miles, etc., Distinction between Distance and Displacement, We need to understand the concepts of distance and displacement. Distance is the gap between two points with no regard to direction. On the other hand, displacement is distance covered in a particular direction. Therefore distance is a scalar quantity while displacement is a vector quantity. The only similarity between distance and displacement is that they have the same unit. Let us consider a girl who walked and covered a distance of 20m between two points A and B as shown in fig 1 and fig 2 below, The two activities of the girl are not exactly the same. In both figs. 1 and 2, she covered a distance of 20m. If we are only interested in the distance covered, we can conclude that she did the same thing in fig. 1 and 2 i.e she covered the same distance (20m). If we are interested in both distance and direction, then her displacement in fig. 1 and 2 are not the same. In fig.1 she covered a distance of 20m due east while in fig.2, she covered a distance of 20m due west. From these, we see that distance is a scalar quantity because it has magnitude only while displacement is a vector quantity because it has both magnitude and direction., Summarily, the table below shows the difference between distance and displacement, EVALUATION, Define distance., What is displacement?, State the SI unit of distance., Differentiate between distance and displacement., Why is 5km due east a displacement?, Enumerate the measuring devices for distance., One of the following is not a measuring device for distance., Micrometer screw gauge, Rule, Vernier calliper, Spring balance, Which of the following is displacement?, 88km, 52mm due south, 25cm, 43inches, A boy travels 8km eastward to a point B and then 6km northward to another point C. Determine the difference between the magnitude of the displacement of the boy and distance traveled by him., 10.0km, 14.0km, 4.0km, 2.0km, The slope of a straight line displacement time graph indicates the, uniform acceleration, distance travelled, uniform velocity, uniform speed, MOTION, CONTENT, Definition of Motion, Types of Motion, Causes and Effects of Motion, Definition of Motion, Motion by definition is a change in the position of a body with time with respect to a reference point. Motion exists in various forms and occurs in all the three states of matter (solids, liquids and gases). These various forms are; random, translational, rotational and oscillatory motion., Some examples of motion are;, The movement of the earth round the sun, The rotation of the earth about its axis, An aeroplane flying in the sky, A boy walking or running, Types of Motion, A. Random motion, Random motion is the movement of a body in a zigzag or disorderly manner with no specific direction as shown in the diagram below. Some examples of this kind of motion are; the motion of dust particles in the air, the motion of smoke particles, the motion of butterfly e.t.c., Random Motion, B. Translational motion, This is motion performed by a body in a straight line from point ‘P’ to another point ‘Q’. if you walk from one end of the classroom to the other, you have performed translational motion. Translational motion can also be called rectilinear motion. Another example of translational motion is the dropping of a fruit from a tree to the ground., Translational Motion, C. Rotational motion, When a body moves in a circular path about an axis, it has performed rotational motion. In other words, rotational motion is the motion a body performs in a circular path about an axis. The rotation of the blades of a fan, the rotation of a wheel about an axis, the rotation of the earth about its axis, the motion of a moving vehicle wheel are all examples of rotational motion. See diagrams below., Rotational Motion, D. Oscillatory motion, This is the motion of a body in a to and fro manner about a fixed point. When a body moves to and fro about a fixed point, we say, the body is oscillating. One complete oscillation is a circle. Examples of oscillatory motion include, the motion of the balanced wheel of a wrist watch, the motion of a simple pendulum, the motion of a loaded test tube inside water, e.t.c., Note: It is possible for a body to perform two types of motion at the same time. For example a rolling football performs both rotational and translational motion at the same time., Class activity, Set up a simple pendulum as shown above, For a length (L) of the pendulum say, 80.0cm, push the bob through a small angle to oscillate to and fro, Using a stop watch, determine and record down the time (t) it will take the bob to complete 20 oscillations, Calculate the period (T) of oscillation of the bob i.e t/20, Repeat the experiment for four other values of L= 70.0cm, 60.0cm, 50.0cm and 40.0cm. in each case determine the period (T) and its square., Tabulate your results. Plot a graph of T2 on the vertical axis against L on the horizontal axis, Determine the slope S of the graph, Given that 4π2/g = S, calculate the value of g., E. Relative motion, Relative motion is the motion of a body with respect to another. Put in another way, it is the motion of a body with respect to a reference point. All motions are relative., EVALUATION, Mention 2 other examples each of random motion, translational motion, rotational motion and oscillatory motion apart from the ones in this e-note., Mention two examples of bodies that perform two motions at the same time. State the two motions. Do not include the example given in the e-note., Causes and Effects of Motion, Sir Isaac Newton’s works on motion reveals that an object will remain in its state of rest (inertia) unless an external force acts on it. This means that if an object is kept on a table, the object will remain in that state of rest or on the table unless something touches it. This leads to the conclusion that the cause of motion is force which can either be a push or a pull. Consider the diagram below., A pull or push will make the object to move to point B from point A. this means that force is a vector quantity because it has both magnitude and direction., Class activity, Tap a stationary ball on the table or ask your classmate to hold your hand and pull you towards his or her side. What is your observation? What can you conclude from this?, OBJECTIVE QUESTIONS, Which of the following types of motion will be produced when a pair of equal and opposite non-collinear parallel forces acts on a body?, Translational motion, Rotational motion, Vibrational motion, Random motion, The motion of the bob of a swinging pendulum is, oscillatory., circular., translational., rotational., The motion of the prongs of a sounding turning fork is, rotational., random., vibratory., translational., An object is said to undergo oscillatory motion when it moves, in a circular path, to and fro about a fixed point, in an erratic manner, along a continuous path from the starting point, A loaded test tube in water is carefully and slightly depressed and then released. Which of the following best describes the subsequent motion of the test tube?, Random, Oscillatory, Circular, Linear, MOTION: FORCE AND FRICTION, CONTENT, Force, Definition of Force, Types of Forces, Friction, Definition of Friction, Types of Friction, The Laws of Solid Friction, Coefficient of friction, Advantages and Disadvantages of Friction, Methods of Reducing Friction, Force, Definition of Force, Force can be defined as that which changes or tends to change the state of rest or uniform motion of a body. Force is a vector quantity and the S.I unit is Newton., Force can cause a body at rest to move, it causes a moving object to accelerate, change direction, move in a curved path e.t.c., Types of Forces, There are two types of forces, namely contact force and force field. Contact force is a force that exists between bodies by virtue of their contact. They are push, pull, normal reaction, tension in strings, wires or frictional force., Force field/Non-contact force is the force that exists within a vector field such as gravitational field, magnetic field, Electric field, nuclear field. The forces are gravitational force, magnetic force, electrostatic force and nuclear force., Gravitational force, This is the force of attraction with which a planet attracts any object towards its centre or the force of attraction between any two masses. The earth is a gravitational field., Electrostatic force, This is a force that exist round a charged body. The charged body could be positively charged or negatively charged., Magnetic force, This is a force that exist around a magnet. A magnet always have the North pole and the South pole, Influence of Magnetic Force, Nuclear force: This is the force of attraction which holds the protons and neutrons in the nucleus of an atom., Friction, Definition of Friction, Friction can be defined as the force that opposes the relative motion between any two surfaces in contact. There can be solid friction or fluid friction. Fluid friction is also called viscosity., It acts whenever there is motion or tendency for something to move. i.e friction (or frictional force) is absent if there is no motion or if there is no force intending to cause motion.It stops your car when the brake is applied. It prevents your foot from slipping backward when you walk., friction is preventing this box from moving., Types of Friction, There are two types of frictional force, Static friction: This is the frictional force that exists between two surfaces relatively at rest and preventing the motion of one surface over the other., Dynamic/kinetic friction: This is the frictional force that exists between the two objects that are in relative motion to each other., EVALUATION, What is force?, List the two types of forces and differentiate between the two., What is friction?, Differentiate between static friction and dynamic friction., The Laws of Solid Friction, It always opposes motion, It depends on the nature of surfaces in contact. Friction between rough surfaces is greater than the frictional force between smooth surfaces., It does not depend on the relative speed between the two surfaces., It does not depend on the area of the surface in contact., It is directly proportional to the perpendicular force (normal reaction) between the two surfaces.(R is the perpendicular force between the two surfaces in contact), F α R, F = µR, F – Frictional force, R – normal reaction, µ – coefficient of static friction, Note that R = W for bodies on horizontal surfaces, Coefficient of friction, It is defined as the ratio of the frictional force to the normal reaction force between two surfaces. A high coefficient of friction implies that a large force is required to cause movement., Question: A crate solid down an inclined plane such that the frictional force opposing its motion is 40N. If the normal reaction of the plane on the crate is 50N, calculate the coefficient of dynamic friction., Solution: Frictional force F = 40N, Normal reaction R = 50N, Coefficient of friction µ= ?, F = µR, 40 = µ × 50 (dividing both sides by 50), 4050 = µ, µ = 0.8, Question B. A block of mass 12kg rests on a horizontal floor, coefficient of friction is 0.35. Determine the minimum force required to move the block when pulling horizontally. (g = 10m/s2), Solution, W = mg = 12 × 10 = 120N, W = R = 120N, Where W – weight of the body, m – mass of the body, g is acceleration due to gravity and R is the normal reaction, F = µR, F = P = µR = 120 × 0.35 = 42.0N, Question C. A metal block of mass 5kg lies on a rough horizontal platform. If a horizontal force of 8N applied to the block through its center of mass just slides the block on the platform. Calculate the coefficient of limiting friction between the block and the platform. ( g = 10m/s2)., Question D. A wooden block whose weight is 50N rests on a rough horizontal plane surface. If the limiting friction is 20N. Calculate the coefficient of static friction., EVALUATION, Mention at least four characteristics/laws of solid friction., A body of mass 40kg is given an acceleration of 10ms-2 on a horizontal ground for which coefficient of friction is 0.5. Calculate the force required to accelerate the body. ( g = 10m/s2)., Advantages and Disadvantages of Friction, Advantages of Friction (or Desirable Effects of Friction), Locomotion: when we walk, friction between our shoes and the ground prevents our shoes from slipping backward., Enhances fastening: friction between the bolt and the nut enhances their fastening ability. The friction between nails and wood also help the nail to hold woods together in firm position., Blending: friction between the grinding stones helps in grinding pepper, tomatoes,this is also true of the friction between the two rough discs of the grinding machine., Stops motion: friction between the car tyre and the road helps to stop the motion of a moving car when the brake is applied., Production of electric charge: when certain materials are robbed against each other, static electric charges is produced. This principle is applied in the Van de Graff generator., Ladder: when a ladder to be used to climb over a wall rest on the wall, friction between the foot of the ladder and floor prevent the foot of the ladder from slipping., Making of fire: matches sticks are ignited when they are robbed against the side of the matches’ box.Fire can also be made by striking two stones together., Disadvantages of Friction (or Undesirable Effects of Friction), Wearing: The thread pattern under your footwear soon wear out after a prolong use due to friction. This is also true of the thread on the tyre of cars and other automobile., Tearing/cutting: you can easily cut a piece of rope or cloth by robbing it repeatedly against the edge of the wall., Reduces efficiency of machines: all machines have efficiency less than 100% due to friction between their moving parts. Friction causes waste of useful energy, therefore it reduces the output of the machine., Generation of undesirable heat and noise: moving machine parts/machine itself soon becomes hot due friction and this may necessitate cooling of machine parts., Methods of Reducing Friction, Due to the disadvantages of friction mentioned above, it is often necessary to reduce friction in machines. This is possible through any of the following methods:, Lubrication: this is the use of certain substances (called lubricants) to reduce the effects of friction. Examples of lubricants includes, grease, oil,… many of which are petroleum products., Streamlining: This involves shaping an object in such a way that when the object is moving against direction of the wind or liquid, the surface in contact is minimal. That is the reason why ships, aircraft and submarines are made or designed after that of fish., Use of rollers/ball bearings: This involves the use of rollers , ball bearings, wheels to reduce the surface area in contact between two surfaces., Use of belt/chain drive: This can also be used to prevent two surfaces in contact., Smoothing/polishing: This reduces projections on the surface thus reducing friction., GENERAL EVALUATION, 1. State three: (i) laws of solid friction (ii) advantages of friction (iii) disadvantages of friction (iv) methods of reducing friction, 2. Explain the following terms (i) Force (ii) contact force (iii) force field, 3. A 5kg mass on a horizontal platform accelerated at the rate of 0.1m/s2, when a horizontal force of 10N is applied to it. Calculate the coefficient of friction between it and the platform (g = 10m/s2)., 4. A metal box of mass 4kg rests on the top of a metal surface. What force applied parallel to the surface is required to (i) just move the box? (ii) move the box with an acceleration of 2m/s2?, Take the coefficient of friction between the box and the surface as 0.25 and g = 10m/s2., 5. A force of 20N applied parallel to the surface of a horizontal table is just sufficient to make a block of mass 4kg move on the table, calculate the coefficient of friction between the block and the table (g = 10m/s2)., OBJECTIVE QUESTIONS, Which of the following statements about static friction is correct? It, is independent of the nature of the surfaces in contact, depends on the relative motion between the surfaces in contact., depends on the weight of the moving body, depends on the area of surfaces in contact, Which of the following substances lowers the surface tension of water?, Metal, Sand, Paper, Detergent, A moving car of mass 800kg experiences a frictional force of 200N. If it accelerates 2ms-2, calculate the magnitude of the force applied to the car., 600N, 1600N, 1800N, 1000N, A ball falling through a viscous liquid is acted upon by, upthrust, the ball's weight and viscous force, upthrust only, the ball's weight and viscous force, upthrust and the ball's weight, An agent that changes or tends to change the state of rest or of uniform motion in the straight line of a body is called, force., friction., velocity., acceleration., SPEED AND VELOCITY, CONTENT, The Concepts of Distance, Speed, Velocity and Uniform Speed/Velocity, Calculations on Speed and Velocity, Distance-Time Graph, Displacement-time Graph, The Concepts of Distance, Speed, Velocity and Uniform Speed/Velocity, 1. Distance (s), This is the separation or space between two points. It is measured in meters and it is a scalar quantity., 2. Displacement (s), It is distance in a specified direction. It is a vector quantity and it is measured in meters., 3. Speed (v), It is the rate of change of distance moved with time. The unit is m/ and it is a scalar quantity., Speed=distancetimev=st, (a) Uniform speed, It is obtained if the rate of change of distance with time is constant or when a body travels equal distances in equal time intervals., (b) Average speed, Average speed is the total distance travelled divided by the total time taken. The average speed is a better representation of the motion of a body not moving at a constant or uniform speed., Average speed=Total distance coveredTotal time taken, (c) Instantaneous speed, It is the actual speed of a body at any instant during the course of motion., 4. Velocity, It is the rate of change of displacement with time. The unit is m/s. It is avector quantity., Velocity=displacementtime, Uniform Velocity, It occurs when the rate of change of displacement with, time is constant or when a body travels equal displacement in equal time interval., EVALUATION, Define speed, velocity and uniform velocity., Differentiate between velocity and speed., Calculations on Speed and Velocity, 1. A car covers a distance of 60km in half an hour. What is the average speed of the car in (a) km/hr (b) m/s, Solution:, (a) Time = ½ hour = 0.5 hour =12hour=0.5hour, Average speed=Total distance coveredTotal time taken=600.5=120km/h, (b) Convert km/hr to m/s, 1km/h=100060×60m/s1km=1000m1hr=3600s120km/h=120×100060×60=33.33m/s, 2. A car travelled to Lagos a distance of 150m in 100 seconds. Calculate his average speed., Solution:, Average speed=Total distance coveredTotal time taken=150100=1.5m/s, 3. A car covers 1500m in 10 secs. What is the speed in km/hr?, Solution:, Speed=distancetime=150010=150m/s, Convert to km/hr, 1km/h=100060×60m/s1m/s=60×601000km/h150m/s=150×60×601000=540km/h, EVALUATION:, Convert 144km/h to m/s., A car covers a distance of 40m in 2 sec. What is his speed in km/h?, Distance-Time Graph, Displacement-time Graph, It is the graphical representation of the motion of a body. There are Distance-time graph, Displacement-time graph and Velocity-time graph., (a) Distance-Time Graph for Uniform Motion, Slope of distance–time graph = speed, Speed=distancetime=MNON, (b) Distance-Time Graph for Non-uniform Motion, Instantaneous speed at p = slope or gradient at p =distance MNtime interval QN, (c) Displacement-Time Graph for Uniform Velocity, Velocity=displacementtime=MNON, (d) Displacement-Time Graph for Non-uniform Velocity, QM is a tangant drawn to the curve at point p, Instantaneous velocity at p = slope or gradient at p =displacement MNtime interval (t), GENERAL EVALUATION, A boy moved continuously for 40secs and covered the following distances in the times stated below:, (i) Draw the distance-time graph and calculate the speed., (ii) State whether or not the speed is uniform. Give reason(s) for your answer., (iii) A Car is travelling with a uniform velocity of 72km/h. What distance does he cover in 20s?, (iv) A car travels with a constant velocity of 45km/h for 10s. What distance does it cover in this time?, OBJECTIVES QUESTIONS, The diagram below represents the speed-time graph of a car. If the car covered a total distance of 600m in 25s, calculate the maximum speed., 30m/s, 25m/s, 20m/s, 15m/s, Uniform speed occurs when there is equal change of, acceleration in equal times, displacement in equal times, distance in equal times, velocity in equal times, A car moves with a speed of 30ms-1. Calculate the distance travelled in 30s., 60m, 450m, 900m, 30m, The rate of change of displacement is known as, impulse, velocity, acceleration, speed, A car travels with a velocity of 20m/s in 5s at a rate of 4m/s2. What is the car’s final velocity?, 40 m/s, 60 m/s, 80 m/s, 100 m/s, RECTILINEAR ACCELERATION, CONTENT, The Concept of Acceleration, Uniform and Non-uniform Acceleration, Deceleration, Worked Examples on Acceleration and Deceleration, Velocity-Time (V – T) Graph, Worked Examples on V-T Graph, The Concept of Acceleration, When an object increases or changes its velocity within a set time, the object is said to undergo acceleration (or to accelerate). We therefore define acceleration as the rate of change of velocity with time., Acceleration=Change in VelocityTime takena=v–ut, Where a: acceleration, v: final velocity, u: initial velocity, Acceleration is a vector quantity and its SI unit is m/s2, However, be reminded that:, (i) When a body starts from rest, its initial velocity, ‘u’ is zero., (ii) When a body comes to rest, its final velocity, ‘v’ is zero., Uniform and Non-uniform Acceleration, Acceleration is said to be uniform if the velocity increases by equal amounts in equal intervals of time. That is, the time rate of change of velocity is constant. If the rate of change of velocity with time is not constant, then, the acceleration is non-uniform., Deceleration, Deceleration is defined as a negative change in velocity with time. When such happens, the body’s velocity is said to be reducing or coming to rest., Deceleration is said to be uniform if the velocity decreases by equal amounts in equal intervals of time. That is, the negative change in velocity with time is constant., Also, Deceleration=Change in VelocityTime taken=v–ut, Deceleration is also called retardation and its SI unit is m/s2. It is also a vector quantity., EVALUATION, Define acceleration., Differentiate between acceleration and deceleration., Quote the formula for acceleration and its SI unit., Worked Examples on Acceleration and Deceleration, Example 1: A body experienced a change in velocity of 10m/s in 15s. What is the acceleration of the body?, Solution:, Data: ∆v = 10m/s, t = 15s, a = ?, Now, a=ΔvΔt=1015=0.67m/s2, Example 2: A car accelerated uniformly at 6m/s2 in 20s. What was the change in velocity?, Solution:, Data: a = 6m/s2, t = 20s, ∆v = ?, Now, a=ΔvΔtΔv=a×ΔtΔv=6×20Δv=120m/s, Example 3: The velocity of a lorry decreased from 60km/h to 35km/h within 0.5mins. Find the deceleration., Solution:, Data: u=60kmh=60×100060×60=60003600=16.67m/s,v=35km/h=9.72m/s,t=0.5mins=30s,d=?, Now, d=ΔvΔt=v–ut=9.72–16.6730=−6.9530d=−0.23m/s2, The negative sign shows that it is decelerating thus coming to rest., ( NOTE: you can convert velocity in km/h to m/s by simply dividing by 3.6 ), EVALUATION, Find the deceleration of a car whose change in velocity within a time interval of 10s is -30m/s., A car started from rest and accelerates uniformly until it reaches a maximum velocity of 80km/h in 20s. It is then brought to rest in further 12s. Find the deceleration of the car., GENERAL EVALUATION, What is the similarity between acceleration and deceleration?, Differentiate between acceleration and deceleration., Write down the formula for acceleration., Velocity-Time (V – T) Graph, When the velocity of a body moving uniformly is plotted against the time, a straight line is obtained and the slope gives the acceleration or deceleration depending on the ascending or descending nature of the graph. This is shown below., The slope of line OA gives the acceleration., ∴ a=ΔvΔt, It is a positive value because the graph ascends from left to right., The slope of line BC gives the deceleration., ∴ d=−ΔvΔt, It is a negative value because the graph descends from left to right., Supposing a body accelerates from rest until it attains a final velocity v in time and then brought to rest in time , the v-t graph is shown below., Slope of line OA gives acceleration., Slope of line AB gives deceleration., Area of OAC gives the distance travelled during the acceleration., Area of ABC gives the distance travelled during the deceleration., Area of the whole shape, OAB gives the total distance travelled. You can equally add up the distances in (iii) and (iv) above to give the total distance travelled., Supposing another body accelerates uniformly from rest until it reaches a final velocity V in time,, and continues with uniform speed at this velocity in time, then brought to rest in a further time ,, the v-t graph is shown below:, Slope of line OA gives the acceleration., Slope of line BC gives the retardation., Area of OAE gives the distance covered during the acceleration., Area of rectangle ABDE gives the distance travelled during the uniform speed., Area of BCD gives the distance travelled during the deceleration., Area of the whole shape (trapezium OABC) gives the total distance travelled during the entire journey., You can also add up the distances in (iii), (iv) & (v) to get the total distance travelled during the entire journey., EVALUATION, Examine the below v-t graph and answer the questions that follows., Area of rectangle OVAC will give —, Area of triangle ABC will give —, How would you find the total distance travelled?, Did the body accelerate?, The slope of line AB will give —, Did the body start from rest?, Briefly discuss the motion of the body., Worked Examples on V-T Graph, 1. A body starts from rest and accelerates at until it gets to a final velocity in 20s. It is then brought to rest in another 10s. With the aid of a v-t graph, find the final velocity attained and the total distance travelled., Solution:, i) Slope of line OA = acceleration, ∴ a=ΔyΔx=A–CC–0=V–020–0, ∴ a=V20, ∴ V=2×20, Hence, V=40m/s, ii) Total distance travelled is the area of the whole shape =area of ΔOAB=12bh=12(0B)(AC), Note that VO = AC, ∴ Total distance covered =12(30)(40)=30×402, Hence, total distance travelled = 600m, 2. A car starts from rest and accelerates uniformly at until it reaches a final velocity of in 23s. It is then brought to rest for further 15s., Sketch the v-t graph., Find the value of x, Find the distance travelled during the acceleration and the deceleration., Find the total distance travelled., Solution:, ii) Acceleration = slope of line 0P =ΔyΔx, ∴ x=P–RR–0=60–023–0, ∴ x=6023, ∴ x=2.6m/s2, Hence, the acceleration of that car is 2.6m/s2, iii) Distance travelled during the acceleration is the area of ∆0PR =12bh=12(0R)(PR), Note that PR=60, ∴ Distance travelled =12(23)(60)=23×602=690m, Hence, the distance covered during the acceleration = 690m, For the distance covered during the deceleration, it is area of ∆PQR =12bh=12(QR)(PR), Note that PR = 60, Distance travelled during the acceleration =12(15)(60)=15×602=450m, Hence, the distance covered during the acceleration = 450m, iii) Total distance travelled = 690m + 450m = 1,140m, Alternatively, total distance travelled is the area of the whole shape = area of ∆0PQ =12bh=12(0Q)(PR), Note that PR = 60, Total distance travelled =12(38)(60)=38×602=1,140m, EVALUATION, A car starts from rest and accelerates uniformly at until it attains a maximum velocity of in 10s. It continues with this speed for further 100s until it is brought to rest for another 25s. Using a v-t graph, find the total distance travelled., A body moves with a constant speed of 10m/s for 10 s then decelerate uniform to rest in another 5 s. (i) Draw a velocity–time graph to illustrate this motion. (ii) calculate the deceleration of the body (iii) calculate the total distance travelled by the body., N.B: for bodies moving with constant or uniform acceleration, the following formulas could be used., v=u+at… … … (i), s=ut+12at2… … … (ii), s=(v+u2)t… … … (iii), v2=u2+2as … … … (iv), Worked Examples, 1. A body starts from rest and accelerates at until it gets to a final velocity in 20s. It is then brought to rest in another 10s. Using equations, find the final velocity attained and the total distance travelled., Solution:, 1st stage data: u = 0 (because it started fron rest); a = 2m/s2, t = 20s; v = ?, 2nd stage data: u = value of ‘v’ above; v = 0 (because it came to rest); t = 10s, i) Using v = u + at v=u+at, ∴ v=0+2×20=0+40, ∴ v=40m/s, ii) To get the total distance covered, let’s get the distance covered in each stage., In the first stage, using v2=u2+2as, ∴ s =v2–u22a=402–02×2=16004=400m, In the second stage, using v2=u2+2as, Here, “a” is deceleration and not acceleration. We need to find it., Deceleration =v–ut=0–4010=−4m/s2, ∴ s=v2–u22a=0–4022×−4=−1600−8=200m, ∴ Total distance travelled =400m+200m=600m, (NB: You can also use s=ut+12at2 for each stage), 2. A car starts from rest and accelerates uniformly at until it reaches a final velocity of in 23s. It is then brought to rest for further 15s. Using equations,, Find the value of x, Find the distance travelled during the acceleration and the deceleration., Find the total distance travelled., Solution:, 1st stage data: u = 0 (Because it started from rest); a = xm/s2; v = 60m/s, t = 23s., 2nd stage data: u = 60m/s; v = 0 (because it came to rest); t = 15s, i) Using a=v–ut=60–0232.61m/s2, ∴ x=2.61m/s2, ii) Distance covered during the acceleration, using v2=u2+2as, s=v2–u22a=602–02×2.61=36005.22=689.6m=690m, Now, the deceleration =v–ut=0–6015=−4m/s2, Now, s=v2–u22a=0–6022×−4=−3600−8=450m, Total distance travelled =690m+450m=1,140m., OBJECTIVE QUESTIONS, A particle starts from rest and moves with a constant acceleration of 0.5ms-2. Calculate the time taken by the particle to cover a distance of 25m., 2.5s, 50.0s, 7.1s, 10.0s, For a body thrown upward, its acceleration is usually, neutral., positive., valueless., negative., Which of the following velocity-time graphs does NOT represent an accelerated motion?, A, B, C, D, When velocity is plotted against the time taken, the gradient of the uniform graph obtained gives, acceleration., speed., deceleration., uniform speed., A particle accelerates uniformly from rest at 6.0ms-2 for 8s and then decelerates uniformly to rest in the next 5s. Determine the magnitude of the deceleration., 24.0ms-2, 9.6ms-2, 30.0ms-2, 48.0ms-2, CIRCULAR MOTION, CONTENT, Meaning of Circular Motion, Definition of Terms Used in Circular Motion, Calculations on Circular Motion, Meaning of Circular Motion, Circular motion is the motion of a body around a circle. The simplest form of circular motion is the uniform circular motion, where the speed is constant but the direction is changing., Consider a body moving in a circular path center O with a constant speed., 1. The direction at different points are not the same i.e. the direction at A is different from the direction at B. This leads to a change in velocity., 2. This difference in velocity produces an acceleration directed towards the center of the circle. This acceleration is called centripetal acceleration., 3. Since there is an acceleration, there is a force directed towards the center of the circle called centripetal force., 4. In addition to the centripetal force, there is an equal but opposite force which acts outwards from the centerof the circle. This force is called the centrifugal force. The centripeal and the centrifugal forces enable the object to move in the orbit., Definition of Terms Used in Circular Motion, 1. Angular velocity (ω):, The ratio of the angle turned through to the elapsed time., ω= Angular velocity, ω=angular displacementtime=θt, The S.l unit is rad/sec, 2. Tangential velocity (V):, This is the linear velocity whose direction is along the tangent to the circumference of the circle., V=displacement(s)time(t)=st=rθt, But ω=θt, Then V=rω, The unit is m/s, 3. Centripetal acceleration (a):, This can be defined as the acceleration of a body in uniform circular motion whose direction is towards the centre of the circle. It is given as:, a=V2r, The unit is m/s2, But V=rω, Then a=rω2, 4. Centripetal force (F):, It is defined as that inward force that is always directed towards the centre of the circle required to keep an object moving with a constant speed in a circular path., Centripetal force =mass×centripetal acceleration, F=mv2ror, F=rω2=ωVr=ma, The unit is Newton, 5. Centrifugal force:, This force is equal in magnitude to the centripetal force but opposite in direction. (it is always directed away from the centre of the circle), F=−mv2rorF=−rω2, 6. Period (T):, This is the time taken for a body to complete one revolution round the circle., Displacement = 2, Time = T, Velocity = v, v=displacementtime=2πrTT=2πrv, 7. Frequency (f):, It is the number of revolutions in one second., f=1TT=v2πr, The unit is Hertz or per seconds. (i.e Hz or s-1), Calculations on Circular Motion, Question 1:, A stone of mass 2kg is attached to the end of an inelastic string and whirled round two times in a horizontal circular path of radius 3m in 3 sec, find:, (i) Angular velocity, (ii) Linear velocity, (iii) Centripetal acceleration, (iv) Centripetal force, (v) Centrifugal force, Solution, (i) ω=angular displacementtime=θt, Where is the angular displacement and ω is the angular velocity, θ=360×2=720o (ie two times), π=180oθ=4πradω=4π3=1.33πrad/sec, (ii) v=rω=3×1.33π=3.99πm/s, (iii) a=v2ra=(3.99π)23a=5.31π2m/s2, (iv) F=ma=2×5.31π2=10.62π2N, (v) F=−mv2r=−10.62π2N, GENERAL EVALUATION, 1. Explain the following terms (i) Angular velocity (ii) Tangential velocity (iii) Centripetal acceleration, 2. A body of mass 10kg is attached to the end of an inelastic thread and whirled round in a circular path of radius 0.3m, if the body makes a complete revolution in 3 sec find, (i) angular velocity, (ii) linear velocity, (iii) centripetal acceleration, (iv) centripetal force, (v) centrifugal force, OBJECTIVE QUESTIONS, A displaced pendulum bulb made 20 oscillations in 2s. Calculate the frequency., 20 Hertz, 10 Hertz, 30 Hertz, 40 Hertz, The mass on a loaded spiral spring oscillates vertically between two extreme positions P and R equidistant from the equilibrium position Q. Which of the following statements about the system is NOT correct?, The total energy of the system is always constant., The elastic potential energy of the spring is maximum at Q., The momentum of the mass is maximum at Q., The kinetic energy of the mass is maximum at P., A stone tied to a string is made to revolve in a horizontal circle of radius 4m with an angular speed for 2 radians per second. With what tangential velocity will the stone move off the circle if the string cuts?, 16m/s, 0.5m/s, 6.0m/s, 8.0m/s, The number of revolutions covered by a body in one second is called, period., amplitude., wavelength., frequency., Score: 1, The number of revolutions made per second is known as, frequency., period., vibration., gyration., ENERGY, CONTENT, The Concept of Energy, Types of Energy, The Law of Conservation of Energy, Sources of Energy, Classification of the Sources of Energy, Uses of Energy, Energy and Social Environment, The Impact of Energy Usage on the Environment, Energy Crises, Oil Spillage, The Concept of Energy, Energy is the ability or capacity to do work. Its unit is Joules., Types of Energy, Energy exists in various forms some of which are;, Mechanical energy, Chemical energy, Solar energy, Heat energy, Sound energy, Electrical energy, Nuclear energy, Mechanical Energy, Kinetic energy and potential energy constitutes mechanical energy. Kinetic energy is the energy a body possesses as a result of its motion. Potential energy on the other hand, is the energy possessed by a body because of its position. A body can also possess potential energy as a result of its nature. For example, an elastic material when stretched stores up energy (potential energy) which is given as ½ k e2 where k is what we call the elastic constant and e is extension in metres. Another form of potential energy is chemical potential energy which is energy stored up in a substance because of its chemical composition. Examples are; energy in the food we eat, electrolytes in cells or batteries., Mathematically, Kinetic energy K.E=12(mv2)., M is mass in kilogram, v is velocity in m/s., Examples of bodies that possess kinetic energy are, A rolling ball, An object falling under gravity, wind or air in motion, An athlete running a race, A bullet movement, A plane flying., If a body is raised to a height h, its potential energy is given as, P.E = mgh. Where m is mass in kilogram, h is height in metres and g is acceleration due to gravity., EVALUATION, Differentiate between potential energy and kinetic energy, What is the formula for calculating kinetic energy and potential energy, The Law of Conservation of Energy, Energy as we have treated earlier exists in various forms. Although energy can be converted from one form to the other, the total energy remains conserved., This is the law of conservation of energy. It states that energy can neither be created nor destroyed but can be converted from one form to the other. This law can be illustrated by mechanical systems as shown in the figures below., Energy Changes in a Simple Pendulum, For fig 1, As the pendulum bob approaches A, the velocityreduces until it becomes zero at point A where it momentarily comes to rest; thereby making the KE zero., Also at A, the bob attains its maximum height above the ground; thereby making the PE to be maximum., as the bob returns towards B, the velocity increases and the height decreases such that at B, velocity is maximum (since K.E=12(mv2), KE is also maximum)., At B, height is zero, PE is equal to zero., At the middle point either between A and B or B and C, energy is conserved. Hence, PE =KE, In fig. 2, as the body moves from the horizontal ground C to A, its velocity reduces and at point A, at height h, where the body is stationary, the velocity v is zero. Consequently its kinetic energy is zero but the potential energy is maximum. As the body drops to the ground, its velocity increases and the vertical height h reduces to zero. Therefore, potential energy just before it touches the ground is zero and the body has maximum kinetic energy. At point B, the body possesses both Kinetic energy and potential energy. From the two illustrations we see that although the energy changes from kinetic to potential energy and vice versa, the total energy of the system is conserved or remains unchanged., Another example where it is applied is for a falling body., Example 1, A ball of mass 8kg falls from rest from a height of 100m. Neglecting air resistance, calculate its kinetic energy after falling a distance of 30m. (take g as 10m/s2)., Solution, Initial velocity at height 100m, u = 0, Distance moved, s = 30m, a = 10ms-2, Velocity after falling 30m, v = ?, v2=u2+2asv2=02+2×10×30v=6–√00v=24.5m/sK.E=12mv2=12×8×600K.E=2400J, Alternative solution:, K.E = potential energy loss, KE. = mgΔh, K.E=8×10×30=2400J, Example 2, A body of mass 100kg is released from a height of 200m. With what energy does the body strike the ground? (g = 10 m/s2), Solution, Gravitational potential energy is given as P.E=mgh=100×10×200=200,000, Example 3, A stone of mass 50.0kg is moving with a velocity of 20 m/s. Calculate the kinetic energy, Solution, mass = 50.0kg, velocity = 20 m/s, K.E=12mv2=12×50.0×20.0=500J, EVALUATION, List eight forms of energy you know., State the law of conservation of energy and apply it to any mechanical system, State the principle of conservation of energy. Using this principle explain how energy is conserved for (i) objects falling under gravity (ii) swinging of a simple pendulum bob., A ball of mass 1kg is dropped from a height of 5m and bounces to a height of 10m. Calculate (i) its kinetic energy just before impact. (ii) its initial bouncing velocity and kinetic energy., Sources of Energy, The following are the sources of energy:, Energy from the sun (solar energy), Wood (fire wood), Coal, Electricity, Fossil fuels, Chemicals as in cells and batteries., Classification of the Sources of Energy, Sources of energy can be classified into:, Renewable sources of energy: These sources are not usually depleted as a result of usage. e.g, solar energy, tidal waves, wind, waterfalls and dams., Non renewable sources of energy: These sources are usually reduced as they are being used. E.g, fossil fuels-coal, oil, natural gas and wood., Uses of Energy, Solar energy is a universal source of light to planet earth. The plants also use it to manufacture their own food through photosynthesis., Fire wood gives heat for cooking our food., Energy from coal is used to boil water, then, produce steam used in steam engines., Energy from waterfalls is used in hydro-electric power stations like kanji dam to produce electricity., Natural gas, petroleum, diesel oil, etc are all derived from fossil fuels., Chemical energy from cells and batteries are used to power our electronics and phones., EVALUATION, State five source of energy discussed., What fuel can we derive from fossil fuels?, State three uses of energy., Energy and Social Environment, The availability of electricity and petrol is very essential to every society. In fact, all lives on earth depend on the availability of energy. This is because all our electrical gadgets at home and in offices, big machines and engines in the factories and manufacturing industries, our day to day activities, all depend on the availability of energy., In advanced countries like the USA, Japan, Canada, Russia, etc, the availability of electricity is everywhere. This has enhanced the economy of the countries and thus having a better Gross Domestic Products (GDP). The reverse is the case in the under-developing world like Nigeria, Liberia, Togo, etc where the availability of electricity is nothing to write home about. This has therefore jeopardized the economy, thus, giving rise to low GDP., Energy is indeed needed in every society for the production of food, efficient transport system, good health programmes, good educational system, etc., The need for energy availability in every society can never be over emphasized. In short, energy is a major factor to societal development., The Impact of Energy Usage on the Environment, The impact of energy usage on the environment could be friendly or unfriendly., The friendly impact is the display of light to give beauty to cities, at night and other significances; while the unfriendly impact include the hazardous radiations from nuclear reactors, gases from industries, etc which could be detrimental to human health., Global Warming, Global warming is the rise in the average temperature of Earth’s atmosphere and oceans.Since the early 20th century, Earth’s mean surface temperature has increased by about 0.8 °C (1.4 °F), with about two-thirds of the increase occurring since 1980., Warming of the climate system is unequivocal, and scientists are more than 90% certain that it is primarily caused by increasing concentrations of greenhouse gases( like carbon (iv) oxide, methane, etc) produced by human activities such as the burning of fossil fuels and deforestation., The Greenhouse Effect, The greenhouse effect is the process by which absorption and emission of infrared radiation by gases in the atmosphere warm a planet‘s lower atmosphere and surface. It was proposed by Joseph Fourier in 1824, discovered in 1860 by John Tyndall,was first investigated quantitatively by Svante Arrhenius in 1896,and was developed in the 1930s through 1960s by Guy Stewart Callendar., Human activity since the Industrial Revolution has increased the amount of greenhouse gases in the atmosphere, leading to increased radiation from CO2, methane, tropospheric ozone, CFCs and nitrous oxide. According to work published in 2007, the concentrations of CO2 and methane have increased by 36% and 148% respectively since 1750., EVALUATION, What is green house effect?, The concept of green house effect was developed by who?, Mention any four countries of the world that has high GDP, Why do you think that the mentioned countries above have high GDP?, Energy Crises, Meaning of Energy Crisis, An energy crisis is any great bottleneck (or price rise) in the supply of energy resources to an economy. It often refers to one of the energy sources used at a certain time and place, particularly those that supply national electricity grids or serve as fuel for vehicles., There has been an enormous increase in the global demand for energy in recent years as a result of industrial development and population growth. Since the early 2000s the demand for energy, especially from liquid fuels, and limits on the rate of fuel production has created such a bottleneck leading to the current energy crisis., Causes of Energy Crises, Market failure is possible when monopoly manipulation of markets occurs., Large fluctuations and manipulations in future derivatives can have a substantial impact on price., Pipeline failures and other accidents may cause minor interruptions to energy supplies, Oil Spillage, Meaning of Oil Spillage, Oil spillage is the release of a liquid petroleum hydrocarbon into the environment, especially marine areas, due to human activity, and is a form of pollution. The term is usually applied to marine oil spills, where oil is released into the ocean or coastal waters, but spills may also occur on land. Oil spills may be due to releases of crude oil from tankers, offshore platforms, drilling rigs and wells, as well as spills of refined petroleum products (such as gasoline, diesel) and their by-products, heavier fuels used by large ships such as bunker fuel, or the spill of any oily refuse or waste oil., Spilled oil penetrates into the structure of the plumage of birds and the fur of mammals, reducing its insulating ability, and making them more vulnerable to temperature fluctuations and much less buoyant in the water. Cleanup and recovery from an oil spill is difficult and depends upon many factors, including the type of oil spilled, the temperature of the water (affecting evaporation and biodegradation), and the types of shorelines and beaches involved.Spills may take weeks, months or even years to clean up., Causes of Oil Spillage, When oil tankers have equipment faults., From nature and human activities on land., Water Sports., Drilling works carried out in sea., EVALUATION, What are the causes of energy crises?, Define oil spill., State two causes of oil spillage., Define the concept of energy., Why do you think that energy is one of the vital factors to societal existence?, Discuss the impact of energy use on environment., Discuss the concept of global warming and the green house effect., Enumerate the factors to be considered in cleaning up the water bodies as a result of oil spillage., OBJECTIVE QUESTIONS, In which areas in Nigeria is oil spillage is commonly witnessed?, Bendel, Niger Delta, South West, Middle Belt, Which of the following sources of energy is renewable?, Uranium, Coal, The sun, Petroleum, A stone of mass 0.5kg is dropped from a height of 12m. Calculate its maximum kinetic energy., (g = 10m/s2), 30.0J, 60.0J, 6.0J, 3.0J, A ball of mass 8Kg falls from rest from a height of 100m. Neglecting air resistance, calculate the total energy after falling a distance of 40m., 5000J, 32000J, 4800J, 3800J, A stone of mass 2.0kg is thrown vertically upward with a velocity of 20.0m/s. Calculate the initial kinetic energy of the stone., 400J, 20J, 600J, 80J, WORK AND POWER, CONTENT, Work Done in a Force Field, Power, Interchangeability of Work and Energy, Calculations on Work and Power, Work Done in a Force Field, Definition of Work Done, Work done in Physics is simply defined as the product of force and distance moved in the direction of the force. If work done is w, distance covered is s and force is f, then mathematically,, Work done =force×distanceW=f×s, The S.I unit of work done is Joules ( J ). Since unit of force ‘F’ is Newton (N), unit of distance ‘s’ is metre, the unit of work done is also Newton-Metre (Nm). Other units are kilojoules and megajoules. Note: If no distance is covered, work done is zero. Work done is a scalar quantity., Every object on the earth’s surface is under the influence of the force of gravity. This force pulls the object towards its centre. The earth’s gravitational field is an example of force field. If a body is to be lifted vertically upwards, work has to be done against this force of gravity. The work done is given as, Work done =force×distance=m×g×h, Where m = mass of the body in kilogram, g = acceleration due to gravity and h is height in metres. If on the other hand, the body falls freely from a vertical height h to the ground, the work done is also mgh., Work is said to be done whenever a force moves a body over a distance in the direction of the force. i.e., work = force (F) × distance(d) moved in the direction of the force (f × d)., Mathematically,, Work done W(d)=F×d, The unit of work is joules with the symbol J.s, Work =F×dcosθ, Component of F along the direction of motion., WD=Fx×dcosθ=FxFFx=Fcosθ, ∴ WD=Fcosθ×d, Power, Definition of Power, Power can be defined in a number of ways:, Power is the time rate at which work is done., Power is energy expended with time., Power is work done in a given time interval. Its S.I unit is watt. Larger units are horse power (hp), kilowatt (kw) and megawatt (mw)., Mathematically, Power \((P) = {\text{work done(w) or energy expended} \over \text{, A 40kg girl climbing a flight of stairs expends energy at the rate of 50W. The time taken for her to reach a height of 20m is (t)}}\\ = \frac{w}{t}\\ =\frac{f \times s}{t} \\ = f \times v\), Where f is force and v is velocity (i.e s/ t). that means power can also be defined as the product of force and velocity. The instrument for measuring power is watt-metre., One horse power is equal to 746watts (1h.p = 746W)., Example, A machine is rated 2500watts. Calculate the power in horse power, Solution, 1 horse power = 746watts, Therefore 2500watts=2500746=3.35 horse power, The Interchangeability of Work and Energy, Energy and work can be used interchangeably because they are almost the same thing. They have the same unit which is Joule. For example, if someone has energy, it means he can do some work and if someone can do some work, it means he has some energy. Thus work and energy cannot be separated., EVALUATION, Define work, energy and power. State their S.I units., Can energy and work be used interchangeably? Explain., Calculations on Work and Power, Example 1., A body of weight 300N climbs to the top of a hill of height 20m. What is the work done by the body against the force of gravity?, Solution, Force F = 300N, distance s = 20m, Work done =force×distance=f×s=300N×20m=600J, Example 2., An object of mass 12kg is held at a height of 10m above the ground for 15 minutes. Calculate the work done within this period., Solution, Since the body is not falling freely under gravity, acceleration due to gravity is zero. Hence work done is also zero., Example 3., A bag of rice of mass 50kg was pushed through a distance of 5m for 10seconds by a force of 500N. Calculate the work done.(g = 10ms-2), Solution, m = 50.0kg, F= 500 N, s = 5m and t = 10 seconds., Work done =force×distance=f×s=500N×5m=2500J, Example 4., Calculate the power of a pump which lifts 1000kg of water through a vertical height of 2m in 10 seconds. ( g = 10ms-2), Solution, Mass (m) = 1000kg, distance (s) = 2m, time (t) = 10s, Power =work donetime taken=force×distancetime=m×g×sT=1000×10×210=2000W, Example 5., An engine develops a power of 750W while moving a car at constant velocity of 3ms-s. Calculate the force exerted on the car by the engine., Solution, Power = 750W, velocity = 3m/s, F = ?, Power =force×velocityForce=PowerVelocity=7503=250N, Example 6., A stone of mass 10kg falls from a height of 2.0m. Calculate the work done. (take g = 10ms2), Solution, Mass (m) = 10kg, height (h) = 2.0m, Work done =mgh, =10×10×2=200J, EVALUATION, Differentiate between work done and power., What other unit is used in measuring work done?, A girl applied a force of 20N on an object for 5s. if the object remains stationary, calculate the work done, A boy lifted up a bag of yam of weight 5N through a height of 2m in 10s. Calculate his power, OBJECTIVE QUESTIONS, A car of mass 800kg attains a speed of 25m/s in 20s. The power developed in the engine is, 1.25 × 106W., 1.25 × 104W., 2.50 × 106W., 2.50 × 104W., What is the unit equivalent of joules?, Nm, kgm/s2, Nm2, kgm/s, Which of the following is the unit of work?, Watt, Kg, Nm, Nm-1, An object of mass 12kg is held at a height of 5m above the ground for 30sec. The work done within this period is, 600J., 60J., 0., 200J., A man of 50kg ascends a flight of stairs 5m high in 5s. If acceleration due to gravity is 10ms-2, calculate the power expended., 100W, 500W, 200W, 250W, HEAT ENERGY: THERMAL EXPANSIVITY, CONTENT, The Concept of Heat and Temperature, The Differences between Heat and Temperature, The Kinetic Theory of Matter, The Effects of Heat on Substances (Expansion, Vaporization), Using Kinetic Theory to Explain the Temperature of a Body, Linear Expansion, Coefficient of Linear Expansivity, Expansion in Liquids, Applications of Expansion, The Concept of Heat and Temperature, Heat is a form of energy that moves from one point to the other due to temperature difference. When you dip one end of an iron rod into fire and hold the other end with your hand, this other end soon becomes hot because energy has flowed from the point dipped into the fire to this other end. This energy flow is what is known as heat. Temperature is a measure of how cold or hot a body is., The Differences between Heat and Temperature, The Kinetic Theory of Matter, The kinetic theory of matter states that:, Matter is made up of atoms and molecules., The molecules are in a state of constant random motion., They possess kinetic energy because of their motion., The kinetic energy of the molecules is directly proportional to the temperature of the body., EVALUATION, Define temperature and state its unit., State three assumptions of the kinetic theory of matter., The Effects of Heat on Substances (Expansion, Vaporization), When heat is applied to a substance, it can lead to the following changes, Chemical changes., Temperature changes., Expansion/Contraction, Change of state (melting, vaporization, sublimation)., Change in pressure in gases at constant volume., Thermionic emission., Thermal Expansion, Most solid substances expand when heated. The rate of expansion varies from one solid to another. Expansion is more pronounced in gases followed by liquids and least in solids. A substance whether solid, liquid or gaseous consists of molecules. When the substance is heated, the molecules gain kinetic energy and move faster and hence the molecules take up more space in the substance. This leads to expansion., Ball and Ring Experiment, Experiment to demonstrate expansion of a solid., Apparatus: Bunsen burner, ball and ring apparatus, Solid Expansion, Procedure: Allow the metal ball to pass through the ring. Heat the metal ball for some time in the Bunsen burner and make it pass through the same ring. The metal ball will no longer pass through the same ring it passed through earlier as a result of expansion. When allowed to cool down for some time and allowed to pass through the ring once more, it will pass through because it has contracted and regained its original size., Using Kinetic Theory to Explain the Temperature of a Body, According to the kinetic theory of matter, the average kinetic energy of the molecules is directly proportional to the temperature. This means that as the kinetic energy of the molecules increases, the temperature also increases. When a body is subjected to heat, the velocities of the molecules increases and hence they gain more kinetic energy this of course will lead to increase in the temperature of the body. On the other hand, if we reduce or lower the heat, the velocities of the molecules will decrease leading to a decrease in the kinetic energy of the molecules. Hence the temperature falls or reduces., EVALUATION, Give three differences between heat and temperature, Explain the phenomenon of expansion using the kinetic theory of matter, Give four effects of heat on a substance, Linear Expansion, Coefficient of Linear Expansivity, Types of Expansion, Linear expansion, Area or Superficial Expansion, Volume or cubic Expansion, 1. Linear Expansion, Linear expansion is expansion in length of a body. Different solids expand at different rates, this is because they have different coefficient of linear expansivity., Coefficient of Linear Expansivity (α), It is defined as increase in length per unit length per degree rise in temperature. The unit is per Kelvin or 1/K or K–1, α=Increase in lengthoriginal length×temperature rise=L2–L1L1(θ2–θ1), L2 – L1 = Increase in length or expansion, θ2 – θ1 = Temperature rise or increase in temperature, θ2 is final temperature, θ1 is initial temperature, L2 is new length, L1 is original length, Question 1., What is meant by the statement, the linear expansivity of copper is 0.000017/k?, Solution:, It means that the increase in length per unit length per degree rise in temperature of copper is 0.000017m., Question 2., A brass is 2 meters long at a certain temperature. What is its length for a temperature rise of 100k, if expansivity of brass is 1.8 x 10-5/k, α =Increase in lengthoriginal length×temperature rise=L2–L1L1(θ2–θ1), L2–L1=αL1(θ2–θ1)L2=L1{α(θ2–θ1)+1}L2=2{1.8×10−5(100)+1}L2=2{0.0018+1}L2=0.0036+2=2.0036m, Question 3., A metal of length 15.01m is heated until its temperature rises to 600C. If its new length is 15.05m, calculate its linear expansivity., Solution:, L1 = 15.01m, L2 = 15.05, θ2 – θ1 = 60o, L2 – L1 = 0.04, α=Increase in lengthoriginal length×temperature rise=L2–L1L1(θ2–θ1)α=15.05–15.0115.01×60o=0.04900.6=0.000044=4.4×10−5/k, EVALUATION, What is meant by the statement that the linear expansivity of copper is 0.000017/k., Steel bars each of length 3m at 290c are to be used for constructing a rail line. If the linear expansivity of steel is 1.0 x 10-5/k. Calculate the safety gap that must be kept between successive bars, if the highest temperature expected is 400c., Experiment to Determine the Linear Expansivity of a Metal Block, Aim: Experiment to determine the linear expansivity of a metal block, Apparatus: Thermometer, Micrometer screw gauge, steam jacket, metal rod, meter rule, Method:, (i) Measure the length of the metal rod (L1)., (ii) Insert the metal rod in the steam jacket and take the initial temperature of the metal rod with thermometer (θ1)., (iii) Screw the micro-meter to touch the end of the rod and take the reading of micro-meter (xi)., (iv) Unscrew micro meter to make room for expansion of metal rod., (v) Introduce steam into the steam jacket for several minutes then the metal rod will expand., (vi) Screw the micrometer screw guage to touch the end of the metal rod again and take the reading again (x2)., (vii) Record the final temperature (θ2)., Calculation:, α=x2–x1x1(θ2–θ1), Conclusion: Since all parameters are known, α can be calculated., 2. Area or Superficial Expansivity (β), It is defined as the increase in area per unit area per degree rise in temperature, β=Increase in Areaoriginal area×temperature rise=A2–A1A1(θ2–θ1), A2 – A1 = Increase in area or expansion, θ2 – θ1 = Temperature rise or increase in temperature, θ2 is final temperature, θ1 is initial temperature, A2 is new area, A1 is original area, Relationship between Linear Expansivity and Area Expansivity: β = 2α, Question 1: A metal cube of cross sectional area 3.45m2 at 00C is heated at a temperature rise of 70K, when the final length of the cube is 3m. Find the:, (i) coefficient of superficial expansivity., (ii) coefficient of linear expansivity., Solution, (i) β=Increase in Areaoriginal area×temperature rise=A2–A1A1(θ2–θ1)A2=L2=3×3=9m2θ2–θ1=70kA1=3.45m2β=9–3.453.45×70=5.55241.5=0.023/k=2.3×10−2/k, (ii) β=2αα=β2α=2.3×10−22=1.15×10−2K−1, EVALUATION, The linear expansivity of a metal is 0.000019 per k. What will the area of 400mm2 be if its temperature is raised by 100C., 3. Cubic Expansivity, Experiment to Determine the Apparent Cubic Expansivity, Cubic or Volume Expansivity (γ), It is defined as the increase in volume per unit volume per degree rise in temperature, γ=Increase in Volumeoriginal volume×temperature rise=V2–V1V1(θ2–θ1), V2 – V1 = Increase in volume or expansion, θ2 – θ1 = Temperature rise or increase in temperature, θ2 is final temperature, θ1 is initial temperature, V2 is final volume, V1 is original volume, Relationship between Linear Expansivity and Cubic Expansivity: γ = 3α, Question 2: The increase in the volume of 10cm3 of mercury when the temperature rises by 1000C is 0.182cm3. What is cubic expansivity of mercury., γ=Increase in Volumeoriginal volume×temperature rise=V2–V1V1(θ2–θ1), V2 – V1 = Increase in volume = 0.182cm2, θ2 – θ1 = Temperature rise = 100oC, V1 = original volume = 10cm2, γ=0.18210×100=0.1821000=0.00082/k=1.82×10−4K−1, Expansion in Liquids, Expansion in liquid is complicated by the expansion of the container because while the liquid expands, the container equally expands. So it is important to differentiate between real and apparent cubic expansivity., Real or Absolute Cubic Expansivity (γr):, It is defined as the increase in volume per unit volume per degree rise in temperature., Apparent Cubic Expansivity (γa):, It is defined as the increase in volume per unit volume per degree rise in temperature when the liquid is heated in an expansible vessel., Question 3., A cube with side 100cm at 00C is heated to 1000C. If the side becomes 101cm long find,, (a) The linear expansivity, (b) The cubic expansivity, Solution, (a) L1 = 100cm = 1m, L2 = 101cm = 1.01m, θ2 = 100o, θ1 = 0o, γ=increase in volumeoriginal volume×temperature rise=V2–V1V1(θ2–θ1)γ=1.01–11×100=0.01100=0.0001/k=1.0×10−4/k, (b) γ=3αγ=3×1.0×10−4=3.0×10−4/k, Determination of the Apparent Cubic Expansivity of a Liquid, Apparent Cubic Expansion of a Liquid, Apparatus: Thermometer, Density bottle, Retort stand, Water, Source of heat, Beaker, Beam balance, Liquid, Stirrer., Method:, (i) Dry the density bottle and weigh it (M)., (ii) Fill the density bottle with the liquid that the apparent cubic expansivity is required and weigh it (M1), (iii) Immerse the density bottle into a beaker of water and suspend with a thread on the clamp of the retort stand., (iv) Take the original temperature of the water in the beaker (θ1)., (v) Heat the set up gently until the water boils., (vi) Some liquid are expelled through the orifice of the bottle cover, the heating continues until no liquid is seen expelled again., (vii) The final temperature of water is taken (θ2), (viii) The density bottle is removed and wiped dry and re-weighed (M2)., Calculation, Mass of empty density bottle = M, Mass of density bottle + liquid = M1, Original temperature of water = θ1, Final temperature of liquid = θ2, Mass of remaining liquid + density bottle = M2, γα=Mass of liquid expelledMass of liquid remaining×temperature rise=M1–M2M2–M(θ2–θ1), Conclusion, Since all the parameters are known, apparent cubic expansivity can be calculated., EVALUATION, Differentiate between Real cubic expansivity and Apparent cubic expansivity., A glass bottle full of mercury has mass 500g on being heated through 350C, 2.43g of mercury was expelled. Calculate the mass of mercury remaining in the bottle ( cubicexpansivity of mercury is 1.8 x 10-4/k and linear expansivity of glass is 8.0 x 10-6/k), Applications of Expansion, (A) Advantages of Expansion, 1. The use of the bimetallic strip in:, (i) Fire alarm, (ii) Bi-metallic thermometer, (iii) Temperature regulator in electric pressing iron, 2. Red hot rivet used in ship, 3. Fitting of wheels in rims, 4. Removal of tight glass stopper, A1. Bi-metallic Strip, It consists of two different metals joined together. They expand at different rates when heated e.g brass and iron., (i) Electric Fire Alarm, When a fire breaks out in a building, the resulting heat causes the bi-metallic strip to bend towards the contact, thus completing the circuit. This causes the bell to ring out a fire alarm., (ii) Bi-metallic Thermometer, It consists of a coiled bi-metallic strip which expands outwards when heated. As this happens, the pointer moves along the scale and the reading on the scale is taken as the temperature., (iii) Electric Pressing Iron, It has a device known as Thermostat, it is made of bi-metallic strip and it is used to regulate the temperature of the pressing iron, gas cooker, refrigerator, etc., Mode of Operation of Pressing Iron, When the current is switched on, current flows through the circuit and the bi-metallic strip is heated up. It expands and the strip bends away from the contact point thereby switching off the flow of current. The pressing iron cools down,straighten-out and contact is re-made and current begin to flows again and the process continues. This make-and-break device regulates the temperature of a pressing iron., A2. Red-hot Rivet Used in Ships, Steel plates and girders which are used in ship building and other constructional works are usually riveted together., A3. Fitting of Wheels in Rims, The large driving wheels of locomotive are fixed with steel tyre which are renewed from time to time as they wear out. In order to ensure a tight fitting, the tyre is made slightly smaller in diameter than the wheel. The tyre contracts on cooling thus ensuring tight fitting., A4. Removal of Tight Glass Stopper, A tight glass stopper can be removed by standing the bottle in hot water. The glass bottle expands and the stopper becomes loose., (B) Disadvantages of Expansion, Expansion of metal on steel bridges/galvanized iron sheets: Cracking sounds are heard when galvanized iron sheets used in the roof of buildings are being heated. This is due to the expansion of sheet when heated. Bridges made of steel equally expand during hot weather., Cracking of glass cup when hot water is poured into it: When hot water is poured into the glass tumbler, it often cracks due to uneven expansion of the interior walls and exterior walls of the glass cup., Expansion of balance wheel of a wrist watch. This makes the watch to give wrong reading, Sagging of overhead wires: Telegraph wires when laid in hot weather are allowed to sag so that in cold weather they can contract without snapping., Expansion of railway lines: Gaps are left between rails in railway lines to allow for free expansion and contraction of rails, without the gaps, there would be buckling of rails., GENERAL EVALUATION, Explain four advantages of expansion in solids., Explain three disadvantages of expansion in solids, WEEKEND ASSIGNMENT, Give three applications of expansion/contraction, What is a bimetallic strip? Give two applications of a bimetallic strip, Explain how a thermostat regulates the temperature of an electric iron, Mention three solids that undergoes sublimation, OBJECTIVE QUESTIONS, The unit of linear expansivity is, m/k, K– 1, k, k/m, The temperature 45oC is the same as, 113oF., 81oF., 25oF., 57oF., When a metal ball is heated through 30oC, its volume becomes 1.0018cm3. If the linear expansivity of the material of the ball is 2.0 × 10-5K-1, calculate its original volume., 2.00cm3, 1.20cm3, 2.20cm3, 1.00cm3, Which of the following devices is used to control temperature?, Thermostat, Thermocouple, Thermopile, Rheostat, Calculate the change in length of a wire of length 35m which is heated from a temperature of 10oc to 50oc., [Linear expansivity of the material of the wire = 2.0 × 10-61/k], 2.8 × 10-3m, 2.8 × 10-5m, 2.8 × 10-6m, 2.8 × 10-4m, HEAT ENERGY: TRANSFER OF HEAT, CONTENT, Conduction of Heat, Meaning of Heat Conduction, Using Kinetic Molecular Theory to Explain Conduction in Solids, Conduction of Heat in Liquids, Experiment to Show that Water is a Poor Conductor of Heat, Applications of Conductors and Insulators, Convection of Heat, Meaning of Convection of Heat, Using Kinetic Molecular Theory to Explain Convection in Liquids, Applications of Convection, Radiation, Emission and Radiation by Different Surfaces, Conduction of Heat, Meaning of Heat Conduction, Conduction of heat is the process by which heat is passed along a material from molecule to molecule while the heated particles remaining in mean position. Most metals are good conductors but their thermal conductivities differ from one metal to another. Experiment performed to compare the conductivity of solid showed that copper is a better conductor than brass, followed by iron, lead…, Using Kinetic Molecular Theory to Explain Conduction in Solids, When the end A is heated, molecule A vibrates about its mean position with a greater kinetic energy and pushes the molecule B to do the same. Molecule B’s increase in kinetic energy is transferred to C and so on until this effect reaches Z. Soon the kinetic energy of molecule at Z is also increased. As the kinetic energies of the molecules increase, temperature increases and heat is then tranferred from the hot part to the cold part., Conduction of Heat in Liquids, Liquids are poor conductors of heat except mercury and other molten metals. Experiment demonstrated below shows that water is a poor conductor of heat., Experiment to Show that Water is a Poor Conductor of Heat, Aim: To show that water is a bad conductor of heat., Apparatus: water, test tube, ice-block, Bunsen burner and wire guaze., Method: i. Wrap the ice block with wire guaze to prevent the ice from floating in water, and drop in the water in the test tube., ii. Heat the water near the top of the water with the Bunsen burner., Observation: It is observed that while the water was boiling on top, the ice at the bottom did not melt, Conclusion: The ice did not melt because water is a poor conductor of heat and was not able to conduct the heat to the ice., Applications of Conductors and Insulators, Cooking utensils: Bad conductors of heat are used as handles while the cooking pots are made ofmetals such as aluminium which are good conductors of heat., Lagging: Insulators are often used as lagging materials in hot water pipes, stem boilers, hot water storage tanks and ovens to prevent them from getting colder., Warmth: Woollen sweaters keep us warm during winter or cold weather to prevent conduction of heat from the body., Double walls: Houses built with double walls with space in between them have air trapped in the spaces that act as insulators, thus, keeping the house warm., EVALUATION, What is conduction?, Use the molecular theory to explain conduction., Explain three applications of conductors and insulators., Convection of Heat, Meaning of Convection of Heat, Convection is the process by which heat is transferred in a liquid or gas by the actual movement of the heated fluid from the hotter to the colder parts. Liquids and gases are poor conductors of heat but transfer heat by convection., Using Kinetic Molecular Theory to Explain Convection in Liquids, When a liquid is heated at the bottom of its container, the molecules there expand and becomes lighter. They therefore move to the top and are then replace by denser colder molecules from the top. The new dense molecules also get heated up and become lighter and hot then move to the upper part to be replaced by others. This action set up a convection flow of heat which continues until the water boils., Applications of Convection, 1. Land and sea breeze: This is convection current in nature. It happens in coastal area., (a) Sea breeze: In a hot day the sun warms the air near the land quickly than the sea because the earth has a lower specific heat capacity than the sea. This warm air rises. Cooler air from the sea moves to replace the risen air. This cool breeze from the sea is known as sea breeze., (b) Land breeze: at night, the air above the sea is hotter. There is a conventional flow of hot air from the sea rises up.They are replaced by cool air from the land. The flow of cool air from the land to the sea is called the land breeze., 2. Ventilation: Air heated by respiration and fires rises towards the ventilators placed near the ceiling. This is replaced by fresh air from windows and other openings., 3. Cooling of motor car engine: Car engines require cooling to prevent overheating. The heat generated by the engine is conducted by the metal to the water in the jacket. The water is cooled by the air circulating round the radiator as the vehicle moved and by the cool air from the fan, 4. The Domestic hot water system: Water is heated in the boiler by conduction through the metal. Hot water rises by convection to the cylinder, cold water flows in to take its place., EVALUATION, Describe an experiment to show Convection current in water., Radiation, Emission and Radiation by Different Surfaces, Meaning of Radiation, Radiation is the process by which heat is transferred from a hotter to a cooler place without heating of the intervening medium. Radiation is a mode of heat transfer that does not require a material medium for its transfer. Radiation can be detected by a radiometer and a thermopile. A thermopile detects and measures radiant energy., A black surface is a better radiator and absorber of heat than a polished/shining surface. This is why it is not advisable to wear a black cloth on a sunny day because one feels hot., Polished surface, white surface and silvered surface are good reflectors of heat., The Thermos Flask, This device is used to prevent loss of heat energy from its content, The three modes of heat transfer are prevented in the thermos flask in the following ways:, The vacuum between the double walled glass prevents loss of heat by conduction and convection., The silver colour of the inside of the double walls prevents heat loss by radiation, The cork support, or plastic prevents heat loss by conduction., The cork stopper prevents heat loss by conduction, evaporation and convection., GENERAL EVALUATION, Mention the features of the Thermo flask and explain how heat losses are prevented., OBJECTIVE QUESTIONS, The function of a silver wall in the vacuum flask is to minimize heat loss by, convection., conduction., radiation., evaporation., The heating element in an electric kettle is usually located near the bottom of the kettle because, heat can be more quickly radiated to all parts of the water., the convectional current which are set up can carry heat to all parts of the water., no heat can be lost to the surroundings., water is a good conductor of heat., Which of the following does NOT need a medium for heat transfer?, Evaporation, Conduction, Radiation, Convection, The heat from the sun reaches the earth mainly by the process of, reflection., radiation., convection., conduction., Some water is heated in a pot. The major mode(s) of heat transfer within the water is/are by, convection, conduction and radiation, conduction, radiation, ELECTROSTATICS, CONTENT, Definition of Electrostatics, Types of Charges, The Law of Electrostatics, Gold leaf Electroscope, Ways of Producing Charges, Charge Distribution in a Conductor, Lightning Conductors, Electrophorus, Definition of Electrostatics, Electrostatics is the study of charges at rest. It is electricity that does not move from one point to another in the substance in which it is produced., Types of Charges, Positive charge, A body becomes positively charged if it losses electron. This can be obtained in the Laboratory if glass rod is rubbed with silk and there is a net transfer of surface electrons from glass to the silk. The glass becomes positively charged and the silk becomes negatively charged., Negative charge, A body is negatively charged if it gains electron. This is obtained by rubbing ebonite rod with fur and there is a transfer of electrons from the atoms of fur to the ebonite rod. The fur becomes positively charged., The positively charged protons deep in the nucleus are not free to be transferred. Hence bodies do not become electrically charged by transfer of protons. They become charged by transfer of electrons, The Law of Electrostatics, Like or similar charges repel each other; unlike or opposite charges attract each other., Gold leaf Electroscope, An electroscope is an instrument used for the detection and testing of small electric charges. It consists of a flat brass disc or cap, a brass rod with a gold leaf. The metal case is made draught-proof and connected to the earth to prevent accumulation of charges due to external influence., Uses of the Gold Leaf Electroscope, To detect charges: If a charged body is placed on the cap of a charged electroscope an increase in divergence or collapse of the leaf shows the body is charged. If there is no change in the divergence, it means the body is not charged., To determine the nature of charge on the body: If a charged body is placed on a charged electroscope, increase in divergence means the charge on the electroscope and the body are the same. If there is collapse of the leaf, it means they have opposite charge or the body is uncharged., To determine the conducting properties of a body: If a good conductor is placed on the cap of an electroscope, the leaf collapses immediately. If it is a semi conductor, it collapses gradually and if an insulator, there is no alteration of the leaf, EVALUATION, What is electrostatics?, Explain three functions of a Gold leaf electroscope, Ways of Producing Charges, 1. Electrostatic Induction:, Electrostatic induction is the act of charging a neutral body by placing a charged body near it without any contact between the two., STEP 1: A negatively charged body is brought near the uncharged body, free electrons from the metal sphere are repelled by the excess electrons on the rod. They shift towards the right. They can not escape from the sphere because the stand and the surrounding air are insulated., STEP 2: These excess charges called induced charges are released to the earth by touching the right part of the sphere with a wire and the other part of the wire to the earth., STEP 3: The wire is disconnected., STEP 4: The negatively charged rod is removed. A net positive charge is left on the rod., 2. Friction:, Charges can also be produced by friction. By rubbing as in ebonite and fur, glass rod and silk, charges are transferred from one by either of the two bodies involved. Equal and opposite charges are produced by friction., Effects of Charging by Friction, Passengers stepping out of cars and buses complain of a slight electric shock as soon as their feet touch the ground.This is because friction between the air and the body of the fast moving car makes the body of the vehicle to be charged., A chain is often left hanging from the rear of a petrol tanker to discharge the charges acquired on the body during movement as this may cause a spark when inflammable vapour is present., Contact: This is done by bringing a charged body in contact with an uncharged body. Charges are transferred from the charged body to the uncharged body., Charge Distribution in a Conductor, Charges are usually concentrated at places where the surface is sharply curved. The charge density is highest at the sharpest point of the conductor. Because of this high charge density, air molecule close to this point get ionized ( i.e broken down into positive and negative ions). Those with charge opposite to the conductor will be attracted to the conductor. Those with charge opposite to that of the conductor will be repelled. As these ions move, they collide with other molecules and knock off electron from them thereby ionizing those molecules. This process could continue leading to a geometrical increase in the number of ions around the conductor., For a hollow conductor, charges reside only on its outside surface, no charges reside inside the conductor., EVALUATION, What is electrostatic induction?, Explain the three methods of charging., Lightning Conductors, Lightning conductors are used to prevent tall buildings from being damaged when being struck by lightning. They are made from a copper with a sharp point edge or spike at the top. It helps to conduct the charges generated harmlessly to the earth. When electrical charges in thunderclouds build up, attraction between unlike charges within a cloud increases steadily until a heavy spark and sound is produced as the charges approach one another. This spark is observed as lightning and the sound is thunder. The heat generated can set a building or tree on fire., The charge on the cloud induces electrical charges on the lightening conductor. This buildup at the sharp edge and cause ionization of air molecule around it. Some of the charge avalanche result from the ionization of air around the lightening conductor travels toward the cloud and help to neutralize some of the charge on the cloud thereby reducing the possibility of a lightening., Electrophorus, Electrophorus is used for storing and transferring electric charges. It consists of a metal disc fitted with an insulating handle and another flat disc made of insulating material such as ebonite, GENERAL EVALUATION, Explain the use of the following: (i) Lightning conductor (ii) Electrophorus, A short chain is usually attached to the rear side of a petrol tanker trailing behind it to ensure that the, charges generated by friction in the tanker are conducted to the earth., the petrol tanker is balanced on the road., chain vibrates in resonance with the tanker’s engine., heat generated by friction in the engine is conducted to the earth., A building can be adequately protected from lightning by, using asbestos for the roof the house, fixing a long copper strip from the ground along the outside wall to a sharp vertical spike, planting trees around the house, fixing a long wooden pole with sharp spikes to the outside wall, Which of the following substances is NOT an insulator?, Silver, Clay, Plastic, Glass, A gold leaf electroscope is to be charged by induction .Which of the following indicates the correct sequence of steps to be taken?, I. Touch the cap with a finger., II. Bring the charged rod near the cap., III. Remove the charge rod from the cap., IV. Remove the finger from the cap., II, III, I and IV, II, III, IV and I, I, II, III and IV, II, I, IV and III, The magnitude of charges on two bodies are to be compared. Which of the following instruments would be most suitable?, Gold leaf electroscope, Capacitor, The electrophorus, Ebonite rod, FIELD FORCE, CONTENT, The Concept of Fields, Types of Fields, Properties of a Force Field, Acceleration Due to Gravity, Determination of Acceleration Due to Gravity, The Shape and Dimension of the Earth, The Concept of Fields, A field is a region under the influence of some physical agencies such as gravitation, magnetism and electricity., Types of Fields, There are two types of field:, (i) Vector field, (ii) Scalar field., Vector Fields, A vector field is that field which is usually represented by lines of force; while a scalar field is that field that is not represented by lines of force., Examples of vector fields include gravitational field, magnetic field and electric field., Examples of scalar fields include regions with distribution of temperature, density, etc., (i) Gravitational Field, Gravitational field is a region of space or a force field surrounding a body that has the property of mass. In this region, any object that has mass will experience a force of attraction, called gravitational force., Gravitational force is responsible for the fact that any object thrown up must definitely fall back. This force of gravity pulls every object towards the centre of the earth. That is to say, gravitational force causes a body which is not in contact with the earth to fall to the ground. This therefore means that the earth exerts an attractive force on every object either on it or near it., Similarly, two objects of different masses exert equal and opposite forces of attraction on each other., The radial field near a planet (e.g, earth) is shown below:, (ii) Magnetic Field, Magnetic field is a region around a magnet where it exerts force on other magnets. It is also a region where magnetic force is felt., The patterns of the magnetic lines of force are shown below:, Magnetic Field Patterns, 1. Field of a bar magnet:, 2. Attraction between unlike poles:, 3. Repulsion between like poles:, NP means Neutral Point. In this point, no magnetic influence is felt, (iii) Electric Field, An electric field is a region around an electric charge where it exerts force on other charges. It is a field where an electric influence is felt., The patterns of the electric lines of force are shown below:, 1. Isolated positive and negative charge field lines:, 2. Attraction between unlike charges:, 3. Repulsion between like charges:, NP means Neutral Point. In this point, no electrical influence is felt., EVALUATION, What is a field?, State the two types of field., List the examples of vector field., What is neutral point?, Properties of a Force Field, (i) Properties of Gravitational Field, (a) The lines of force are directed towards the centre of the planet; hence, it is a radial field., (b) The gravitational force field (field strength) ‘g’ at a point is the force per unit mass placed at that point. i.e, g=Fm in N/kg but the S.I unit is m/s2, (c) Any force acting on a body falling towards the centre of the earth is given by F = mg, (d) Gravitational field is a vector quantity., (ii) Properties of Magnetic Field, (a) Direction: When a magnet is freely suspended, it comes to rest in the South-North direction of the earth., (b) Attraction: A magnet has the ability to attract magnetic materials e.g, steel, iron, etc., (c) Force: A magnet exerts force on other magnets in such a manner that like poles repel and unlike poles attract., (d) The inseparable nature of poles on the magnetic dipoles: If a magnet is broken into small pieces, however small it may be, it will still have a North and South Poles. The smallest bit of a magnet is a dipole., (e) Magnetic lines of force originate from the North pole and terminate at the South pole., (iii) Properties of Electric Field, (a) Electric lines of force originate from a positive charge and terminate in a negative charge., (b) Electric lines of force never cross each other., (c) They repel each other side ways., (c) They are in a state of tension which tends to shorten them., (d) The electric field at a point is defined as the force per unit charge placed at that point. i.e, ε=Fq measured in Newton per Coulomb N/C, EVALUATION, State two properties each of the three vector fields discussed., What is the direction of the magnetic lines of force?, What is the unit of electric field strength?, GENERAL EVALUATION, Discuss the properties of the magnetic flux., Define the electric field strength., Itemise the three vector fields., Why is electric When a field is represented by lines of force, it is then calledlines of force a vector quantity?, Acceleration Due to Gravity, When an object is dropped from the top of a hill or even a tree, the body moves and increases in velocity until it touches the ground with a velocity of finite value. Such movement is influenced by the earth’s gravitational field. The increase in velocity is therefore due to acceleration due to gravity which is usually represented by ‘g’. The motion of such body under gravity is always described as motion under free fall., However, when two bodies of different masses are released from a height above the ground level, they do hit the ground at the same time. This is because acceleration due to gravity at a location is the same for all bodies irrespective of their masses and thus reach the ground at the same time., This constant acceleration is called acceleration due to gravity and has a value of or ., When a body is released from a height so that it falls towards the centre of the earth, ‘g’ is positive; but when a body is thrown upward, it goes against ‘g’ thereby decreasing in velocity until it momentarily comes to rest at the maximum height. For upward movement, ‘g’ is negative., The equations connecting acceleration due to gravity, ‘g’ are as follows:, For downward movement, v2=u2+2gs and s=ut+12gt2, For upward movement, v2=u2–2gs and s=ut−12gt2, When a body is released from rest at a certain height so that it falls towards the centre of the earth,, For upward movement, s=ut+12gt2, Since, u = 0, 2s = gt2, ∴ t2=2sg, Hence, t=2sg−−√, This equation shows that the time to reach the ground does not depend on the mass of the object., Determination of Acceleration Due to Gravity, The value of ‘g’ could be determined using:, 1. Formula method: A body is released from a height ‘s’ and the time t is taken; then use s=12gt2 to get the value of ‘g’., 2. Simple Pendulum Experiment method: The value of ‘g’ could also be determined using this experiment., The period T for the oscillation is given by: T=2πlg−−√, By linearizing this formular, we have T2=4π2(lg), When T2 is plotted against l, the equation is T2=(4π2g)l, A. Hence, the slope for such graph is 4π2g, When l is plotted against T2, the equation is l=(g4π2)T2, And the slope for such graph is g4π2, In any case, from the slope, you get the value of ‘g’., (NB: Educator should carry out the two experiments with the students.), EVALUATION, What is the value of acceleration due to gravity?, What is the mathematical relationship between the period of oscillation T and the length of the string used l in a simple pendulum experiment?, The Shape and Dimension of the Earth, The earth is one of the nine planets in the solar system. It is spherical is shape. It is also divided into two hemispheres – the Northern and Southern hemispheres. There are two major types of lines that run through the earth. They include:, The latitude lines and, The longitude lines, The latitude lines are imaginary lines running from the east to the west, north or south of the equator. This means that they increase towards the North or South. Examples are:, Tropic of cancer, Tropic of capricon, Artic circle, Antartic circle., The equator line on zero degree., The longitude lines are imaginary lines running from the North pole to the South pole, east or west of the Greenwich meridian. They increase towards the east or west. E.g, the Greenwich meridian on zero degree running through Ghana and London., However, the earth has a radius of approximately 6400km., EVALUATION, State two differences between latitude lines and longitude lines., Mention two examples of the lines of latitude., What is the approximate radius of the earth?
