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S V K, Newton's Laws of Motion, Point Mass, (1) An object can be considered as a point object if during motion in a given time, it covers, distance much greater than its own size., (2) Object with zero dimension considered as a point mass., , (3) Point mass is a mathematical concept to simplify the problems., , Inertia, , (1) Inherent property of all the bodies by virtue of which they cannot change their state of, rest or uniform motion along a straight line by their own is called inertia., , (2) Inertia is not a physical quantity, it is only a property of the body which depends on mass, of the body., (3) Inertia has no units and no dimensions, , (4) Two bodies of equal mass, one in motion and another is at rest, possess same inertia, because it is a factor of mass only and does not depend upon the velocity., does not depend upon the velocity., , Linear Momentum, , (1) Linear momentum of a body is the quantity of motion contained in the body., (2) It is measured in terms of the force required to stop the body in unit time., , (3) It is also measured as the product of the mass of the body and its velocity i.e., Momentum, = mass × velocity., If a body of mass m is moving with velocity → then its linear momentum →is given by → =, →, , (4) It is a vector quantity and it’s direction is the same as the direction of velocity of the, body., (5) Units : kg-m/sec [S.I.], g-cm/sec [C.G.S.], (6) Dimension : [, ], , Newton’s First Law, , A body continue to be in its state of rest or of uniform motion along a straight line, unless it, is acted upon by some external force to change the state., (1) If no net force acts on a body, then the velocity of the body cannot change i.e. the body, cannot accelerate., (2) Newton’s first law defines inertia and is rightly called the law of inertia. Inertia are of, three types :
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S V K, Inertia of rest, Inertia of motion and Inertia of direction., , Inertia of rest : It is the inability of a body to change by itself, its state of rest. This means a, , body at rest remains at rest and cannot start moving by its own., Example : (i) A person who is standing freely in bus, thrown backward, when bus starts, suddenly., When a bus suddenly starts, the force responsible for bringing bus in motion is also, transmitted to lower part of body, so this part of the body comes in motion along with the bus., While the upper half of body (say above the waist) receives no force to overcome inertia of rest, and so it stays in its original position. Thus there is a relative displacement between the two parts, of the body and it appears as if the upper part of the body has been thrown backward., , Inertia of motion : It is the inability of a body to change by itself its state of uniform motion, i.e., a body in uniform motion can neither accelerate nor retard by its own., , Example : (i) When a bus or train stops suddenly, a passenger sitting inside tends to fall, forward. This is because the lower part of his body comes to rest with the bus or train but the, upper part tends to continue its motion due to inertia of motion., , Inertia of direction : It is the inability of a body to change by itself it's direction of motion., , Example : (i) When a stone tied to one end of a string is whirled and the string breaks, suddenly, the stone flies off along the tangent to the circle. This is because the pull in the string, was forcing the stone to move in a circle. As soon as the string breaks, the pull vanishes. The, stone in a bid to move along the straight line flies off tangentially., Newton’s Second Law, , (1) The rate of change of linear momentum of a body is directly proportional to the, external force applied on the body and this change takes place always in the direction of the, applied force., , (2) If a body of mass m, moves with velocity ⃗ then its linear momentum can be given by ⃗ =, , ⃗ and if force, ⃗∝, , or, or, , ⃗ =, , ⃗, , ⇒, , →, , is applied on a body, then, , =, , ⃗=, ⃗=, , ⃗, , ⃗, , ⃗, , (, , (K = 1 in C.G.S. and S.I. units), , ⃗) =, , ⃗, , =, , ⃗, , (As, , =, , ⃗, , =acceleration produced in the body)
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S V K, Force, (1) Force is an external effect in the form of a push or pull which, (i) Produces or tries to produce motion in a body at rest., (ii) Stops or tries to stop a moving body., , (iii) Changes or tries to change the direction of motion of the body., (2) Dimension : Force = mass acceleration, (3) Units :, , [ ] = [ ][, , ]=[, , ], , Absolute units : (i) Newton (S.I.) (ii) Dyne (C.G.S), , Gravitational units : (i) Kilogram-force (M.K.S.) (ii) Gram-force (C.G.S), , Newton : One Newton is that force which produces an acceleration of 1 / in a body, of mass 1 Kilogram., ∴ 1Newton = 1 ⥂ −⥂ /, Dyne : One dyne is that force which produces an acceleration of 1 / in a body of, mass 1 gram., 1 Dyne= 1, /, Relation between absolute units of force 1 Newton = 10 Dyne, Kilogram-force : It is that force which produces an acceleration of 9.8 /, of mass 1 kg., 1 kg-f = 9.80 Newton, Gram-force : It is that force which produces an acceleration of 980, mass 1gm., 1 gm-f = 980 Dyne, , /, , in a body, in a body of, , Common forces in mechanics :, , (i) Weight : Weight of an object is the force with which earth attracts it. It is also called the, force of gravity or the gravitational force., (ii) Reaction or Normal force : When a body is placed on a rigid surface, the body, experiences a force which is perpendicular to the surfaces in contact. Then force is called ‘Normal, force’ or ‘Reaction’., R, , R, , , mg, , mg, , mg cos, , (iii) Tension : The force exerted by the end of taut string, rope or chain against pulling, (applied) force is called the tension. The direction of tension is so as to pull the body., T=F
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S V K, (iv) Spring force : Every spring resists any attempt to change its length. This resistive force, increases with change in length. Spring force is given by, = − ; where x is the change in, length and K is the spring constant (unit N/m)., F = – Kx, , x, , Newton’s Third Law, To every action, there is always an equal (in magnitude) and opposite (in direction), reaction., , (1) When a body exerts a force on any other body, the second body also exerts an equal and, opposite force on the first., (2) Forces in nature always occurs in pairs. A single isolated force is not possible., , (3) Any agent, applying a force also experiences a force of equal magnitude but in opposite, direction. The force applied by the agent is called ‘Action’ and the counter force experienced by, it is called ‘Reaction’., , (4) Action and reaction never act on the same body. If it were so, the total force on a body, would have always been zero i.e. the body will always remain in equilibrium., →, →, (5) If, = force exerted on body A by body B (Action) and, = force exerted on body B by, body A (Reaction), →, →, Then according to Newton’s third law of motion, =−, , Frame of Reference, , (1) A frame in which an observer is situated and makes his observations is known as his, ‘Frame of reference’., (2) The reference frame is associated with a co-ordinate system and a clock to measure the, position and time of events happening in space. We can describe all the physical quantities like, position, velocity, acceleration etc. of an object in this coordinate system., (3) Frame of reference are of two types : (i) Inertial frame of reference (ii) Non-inertial, frame of reference., Inertial frame of reference :, , (a) A frame of reference which is at rest or which is moving with a uniform velocity along a, straight line is called an inertial frame of reference., (b) In inertial frame of reference Newton’s laws of motion holds good., (c) Inertial frame of reference are also called unaccelerated frame of reference or, Newtonian or Galilean frame of reference.
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S V K, (d) Ideally no inertial frame exist in universe. For practical purpose a frame of reference, may be considered as inertial if it’s acceleration is negligible with respect to the acceleration of, the object to be observed., (e) To measure the acceleration of a falling apple, earth can be considered as an inertial, frame., (f) To observe the motion of planets, earth can not be considered as an inertial frame but, for this purpose the sun may be assumed to be an inertial frame., Example : The lift at rest, lift moving (up or down) with constant velocity, car moving with, constant velocity on a straight road., Non-inertial frame of reference, , (a) Accelerated frame of references are called non-inertial frame of reference., (b) Newton’s laws of motion are not applicable in non-inertial frame of reference., Example : Car moving in uniform circular motion, lift which is moving upward or downward, with some acceleration, plane which is taking off., Impulse, , (1) When a large force works on a body for very small time interval, it is called impulsive, force., An impulsive force does not remain constant, but changes first from zero to maximum and, then from maximum to zero. In such case we measure the total effect of force., (i) In hitting or kicking a ball we decrease the time of contact so that large force acts on the, ball producing greater acceleration., (ii) In catching a ball a player by drawing his hands backwards increases the time of contact, and so, lesser force acts on his hands and his hands are saved from getting hurt., , (iii) In jumping on sand (or water) the time of contact is increased due to yielding of sand, or water so force is decreased and we are not injured. However if we jump on cemented floor the, motion stops in a very short interval of time resulting in a large force due to which we are, seriously injured., (iv) An athlete is advised to come to stop slowly after finishing a fast race, so that time of, stop increases and hence force experienced by him decreases., (v) China wares are wrapped in straw or paper before packing.
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S V K, Law of Conservation of Linear Momentum, If no external force acts on a system (called isolated) of constant mass, the total momentum, of the system remains constant with time., →, →, (1) According to this law for a system of particles =, In the absence of external force ⃗ = 0 then ⃗ = constant, i.e., → = → + → + → +. . . . =constant., →, , →, , →, , or, +, +, +. . . . =constant, This equation shows that in absence of external force for a closed system the linear, momentum of individual particles may change but their sum remains unchanged with time., , (2) Law of conservation of linear momentum is independent of frame of reference, though, linear momentum depends on frame of reference., (3) Conservation of linear momentum is equivalent to Newton’s third law of motion., , For a system of two particles in absence of external force, by law of conservation of linear, momentum., → + → = constant., , , ⃗ +, , ⃗ = constant., , Differentiating above with respect to time, , , →, , ⃗, , +, , =−, , →, , ⃗, , =0, , , , ⃗ +, , ⃗ =0, , →, , +, , →, , =0, , i.e. for every action there is an equal and opposite reaction which is Newton’s third law of, motion., (4) Practical applications of the law of conservation of linear momentum, , (i) When a man jumps out of a boat on the shore, the boat is pushed slightly away from the, shore., (ii) A person left on a frictionless surface can get away from it by blowing air out of his, mouth or by throwing some object in a direction opposite to the direction in which he wants, to move., , Introduction, , Friction, , If we slide or try to slide a body over a surface, the motion is resisted by a bonding between, the body and the surface. This resistance is represented by a single force and is called friction force., The force of friction is parallel to the surface and opposite to the direction of intended, motion., , Types of Friction, , (1) Static friction :
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S V K, The opposing force that comes into play when one body tends to move over the surface, of another, but the actual motion has yet not started is called static friction., (i) If applied force is P, R, and the body remains at rest, P, F, then static friction F = P., (ii) If a body is at rest, mg, Fig., 5.1, and no pulling force is acting, on it, force of friction on it is zero., (iii) Static friction is a self-adjusting force because it changes itself in accordance with the, applied force and is always equal to net external force., (2) Limiting friction :, , If the applied force is increased, the force of static friction also increases. If the applied, force exceeds a certain (maximum) value, the body starts moving. This maximum value, of static friction upto which body does not move is called limiting friction., (i) The magnitude of limiting friction between any two bodies in contact is directly, proportional to the normal reaction between them., ∝ or =, (ii) Direction of the force of limiting friction is always opposite to the direction in which one, body is at the verge of moving over the other, (iii) Coefficient of static friction : (a), is called coefficient of static friction and is defined, as the ratio of force of limiting friction and normal reaction, , =, , (b) Dimension : [, ], (c) Unit : It has no unit., (d) Value of depends on material and nature of surfaces in contact that means whether, dry or wet ; rough or smooth polished or non-polished., (e) Value of does not depend upon apparent area of contact., (3) Kinetic or dynamic friction :, , If the applied force is increased further and sets the body in motion, the friction, opposing the motion is called kinetic friction., (i) Kinetic friction depends upon the normal reaction., ∝ or =, where is called the coefficient of kinetic friction, (ii) Value of depends upon the nature of surface in contact., , (iii) Kinetic friction is always lesser than limiting friction, < , <, i.e. coefficient of kinetic friction is always less than coefficient of static friction. Thus we, require more force to start a motion than to maintain it against friction. This is because once the, motion starts actually ; inertia of rest has been overcome. Also when motion has actually started,, irregularities of one surface have little time to get locked again into the irregularities of the other, surface., (iv) Kinetic friction does not depend upon the velocity of the body.
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S V K, (v) Types of kinetic friction, (a) Sliding friction : The opposing force that comes into play when one body is actually, sliding over the surface of the other body is called sliding friction. e.g. A flat block is moving over, a horizontal table., (b) Rolling friction : When objects such as a wheel (disc or ring), sphere or a cylinder rolls, over a surface, the force of friction that comes into play is called rolling friction., Rolling friction is directly proportional to the normal reaction (R) and inversely, proportional to the radius (r) of the rolling cylinder or wheel., =, , is called coefficient of rolling friction. It would have the dimensions of length and would be, measured in metre., Rolling friction is often quite small as compared to the sliding friction. That is why heavy, loads are transported by placing them on carts with wheels., In rolling the surfaces at contact do not rub each other., The velocity of point of contact with respect to the surface remains zero all the times, although the centre of the wheel moves forward., Advantages and Disadvantages of Friction, (1) Advantages of friction, , (i) Walking is possible due to friction., , (ii) Two body sticks together due to friction., (iii) Brake works on the basis of friction., , (iv) Writing is not possible without friction., , (v) The transfer of motion from one part of a machine to other part through belts is possible, by friction., , Disadvantages of friction, , (i) Friction always opposes the relative motion between any two bodies in contact., Therefore extra energy has to be spent in over coming friction. This reduces the efficiency of, machine., (ii) Friction causes wear and tear of the parts of machinery in contact. Thus their, lifetime reduces., , (iii) Frictional force result in the production of heat, which causes damage to the, machinery.
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S V K, Methods of Changing Friction, We can reduce friction, (1) By polishing., , (2) By lubrication., , (3) By proper selection of material., , (4) By streamlining the shape of the body., (5) By using ball bearing., , Also we can increase friction by throwing some sand on slippery ground. In the, manufacturing of tyres, synthetic rubber is preferred because its coefficient of friction with, the road is larger., Angle of Friction, , Angle of friction may be defined as the angle which the resultant of limiting friction and, normal reaction makes with, R, S, the normal reaction., , , F, , By definition angle is, called the angle of friction, , mg, , =, , tan = s, or, , [As we know, =, , (, , P, , =, , ), , ], , Hence coefficient of static friction is equal to tangent of the angle of friction., , Angle of Repose, , Angle of repose is defined as the angle of the inclined plane with horizontal such that a body, placed on it is just begins to slide., By definition, is called the angle of repose., In limiting condition, , =, , and, , R, , mg sin , , , F, , , mg, , mg cos , , =
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S V K, So, , , =, , =, , =, , =, , [As we know =, , =, , ], , Thus the coefficient of limiting friction is equal to the tangent of angle of repose., As well as = i.e. angle of repose = angle of friction.
