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Force and Laws of Motion, , Force, Here we will learn about the cause of motion. This, study about the cause of motion is called Dynamics., It is that physical quantity which we can neither see, not touch, but its effect can be felt on the objects on, which it is applied. Some effort is required to move a, stationary toy-cart or a ball or box or anything lying at, rest on ground. On the other hand we can stop a, stroller rushing down the road by pulling it., The effort required to bring such changes in the state, of an object is called force., , Though balanced forces do not produce any, acceleration, they can change the shape or size of the, body. They are deforming forces., When two or more forces acting simultaneously on a, body produce a non-zero acceleration it i.e. produce a, change in its state of rest or of uniform motion in a, straight line, the forces are said to be unbalanced. The, resultant force is not zero., Example:, 1., In tug of war, the team applying greater pull, will pull the rope and hence the opposite, team towards itself,, 2., While pushing a heavy box lying on the floor,, it starts moving when force of push is greater, than or overcomes the force of friction., , A force can bring following changes., 1. It can move a stationary A soccer player kicks, body., the ball forward., 2. It can stop a by A fielder stops the ball, batsman, hit moving body., 3. It can change the speed While cycling against, of a moving body., the blowing wind, wind, exerts force which, slows down speed., 4. It can change the Cricket ball hit by the, direction of a moving bats man., body., 5. It can change the shape A spring pushed at, and size of a body., either or both its ends, gets elongated., , Types of Forces, There are mainly two kinds, upward, (a) Contact force, (b) Field force or non-contact forces., , Thus we observe that a force is a push or a pull that, produces or tends to produce above mentioned, effects. It has both direction and magnitude. So it is a, vector quantity., , , , Resultant Force, If a single force acting on a body produces the same, acceleration as produced by a number of forces acting, simultaneously, that single force is called the resultant, force of all these forces acting simultaneously. The, resultant force is also called the net force., Balanced and Unbalanced Forces, When two or more forces acting simultaneously on an, object produce no acceleration in it, i.e. do not bring, about any change in its state of rest or of uniform, motion in a straight line, the forces are said to be, balanced forces. or we can say that the net force, acting on the object is zero., Example: In the game of tug of war, the two teams, apply force of pull on the rope in opposite directions., If both teams pull with equal force, rope remains at, rest and the forces are balanced., 2, , of, , forces:, , Contact Force, The force exerted by an object on another object, only when they are in contact with each other is, called contact force., For example:, We push a door to close it, load carried by porter, on his head exerts a downward force on him due, to its weight., Mentioned below are some important contact, forces.

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, , , , 1., Sol., , (i) Normal Force:, If contact forces between the bodies are, perpendicular to the surfaces in contact, the, forces are known as normal forces., For example a wooden block kept on a table is in, equilibrium. Block applies a downward force on, table due to its weight and table pushes the block, upwards. Thus both table and block apply a, normal force on each other., (ii) Frictional Force:, When we try to slide a heavy box on a rough floor, by pushing it, a force acts parallel to the surface in, contact with the floor and opposes the pushing, force. This parallel force is called the frictional, force., Field Force, These may also be referred as non-contact forces., If an object attracts or repels another object from, a distance i.e. without being in contact we say it, applies a field force on the other., , If two forces F1 and F2 act on an object in, perpendicular direction to each other then,, from vector addition, their resultant comes, out to be equal to F, F  F12  F22  2 F1F2 cos90o,  F12  F22 which is non-zero., , 2., , Sol., , A block of weight 5 units is placed on a, horizontal table. A person pushes the block, from top by exerting a downward force of 3, units on it. Find the force exerted by the table, on the block, There are three forces acting on the body:, (i) 5 units, downward by earth, (ii) 3 units, downward by the person, (iii) F, upward by the table, As the block is at rest, the resultant force on it, must be zero., The total downward force in 5 units + 3 units, = 8 units. Hence the upward force F should be, 8 units. So the force exerted by the table on, the block is 8 units in the upward direction., Galileo's Experiments, , Field Force, For example:, (i) Gravitational pull:, It is the downward force acting on an object due, to gravitational pull of earth. Now even if the, object is not m contact with the earth, the earth, pulls it. If we release an apple or a stone or, anything from a height, it falls to the ground., (ii)Magnetic force and Electrostatic force:, We know that a magnet can pull an iron piece, from distance. Also when we rub a comb with hair, and bring it near bits of paper, it attracts them, from a distance. These are all examples of field, force., , , , Can two forces acting in perpendicular, directions be balanced?, For two forces to balance each other they, should have zero resultant force. They should, act in opposite directions and should have, equal magnitude., , 3, , Unbalanced Force Accelerates or Decelerates a, Body, Before Galileo's observations, there was a general, m is belief that a force is necessary to keep a body, moving with uniform velocity. But through a, series of experiments and observations, Galileo, reached the correct, conclusion that a body, continues to move with uniform velocity if no, force acts on it., He observed that when a marble rolls down a, smooth inclined plane, its velocity increases. Its, velocity decreases when it climbs up., He argued that if a marble, kept on one side of a, smooth plane inclined at both sides, is released, from rest. It would roll down the slope and go up, on the opposite side to the same height above, bottom line, from which it was released, If the, angle of inclination of the right side plane were, gradually decreased, the marble would travel, further distances till it reach the original height., If the right side plane were ultimately made, horizontal the marble would continue to travel, forever trying to reach the same height that it was, released from., Thus it suggest that an unbalanced force (Gravity, in this example) is required to change the motion, (i.e. speed up or slow down) of the marble, but no

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net force is needed to sustain the uniform motion, of the marble., , Newton's First Law, Newton further studied Galileo's ideas and, formulated three fundamental laws of motion., These are as follows:,  An object remains in a state of rest or of uniform, motion in a straight line unless compelled to, change that state by an applied unbalanced force., In other words, if a body is in a state of rest, it will, remain so and if it is in the state of motion, it will, keep moving in same direction with same speed, unless an external unbalanced force is applied on, it., , When we push a ball forward, after moving some, distance it comes to rest. It seems as if some, unbalanced force is required continuously to keep it, moving. But actually it is not so., An equal and opposite force is required continuously, to cancel or to balance the force of friction acting on, the ball to keep it moving with constant velocity., Practically, every surface has got some friction. So, in, practice marble would stop after travelling some, distance due to frictional force., , , , , Take a small ball and tie it with a string. Fix the other, end of the string from a nail on a wall. Make a mark, on the wall just behind the ball. Pull the ball to one, side, again mark the new position of the ball on the, wall. Note the difference in height between these two, marks. Let it be h. Release the ball from this position, and observe its motion on the other side., On carefully marking the position of the ball where it, just, momentarily comes to rest on the other side, we, find the difference in height of this position with the, centre position is same as h. Thus the ball reaches the, same height on the other side. This is very similar to, Galileo’s experiments., , , , 4, , Thus an unbalanced force is required to change, speed or direction of an object. And if this, unbalanced force is removed completely, the, object would continue to move with a velocity it, has acquired till then., The tendency of undisturbed objects to stay at, rest or to keep moving with same velocity is called, inertia. Therefore, Newton's first law is also, known as law of inertia. In general a heavier body, has greater inertia than a lighter body., Thus we can say that mass of a body is the, measure of its inertia. It is difficult to push a, heavy box than to push a light book. Similarly it is, easier to stop moving ball with our hand than to, stop a moving bicycle. Thus a heavier object has, greater inertia., Common examples to verify Newton's First Law, Inertia of rest, Example: (i) Jerks while travelling: When we stand, in a bus and the bus start moving suddenly, we, tend to fall backward. This is because our feet are, in contact with the floor of the bus and the, friction at the contact is high. This force does not, allow the feet to slip on the floor. The feet,, therefore, move forward with the floor. The, upper part of the body does not feel the forward

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force immediately and remains at rest for a while., So the upper part of our body gets jerked, backward., (ii) Make a pile of similar carom coins on a table., Attempt a sharp horizontal hit at the bottom of, the pile using another carom, coin or the, striker. If the hit is strong enough, the bottom, coin moves out quickly. Once the lowest coin is, removed, the inertia of rest of the other coins, makes them 'fall' vertically on the table., , Take an iron weight and rest the weight on empty, can, Strike the weight with the hammer as hard as, possible with. Remove the weight and strike the can, directly with the same force, crushing the can. The, weight stay at rest, so the blow does not move it, downwards to crush the can., Show that a similar weight does not significantly, accelerate it., , Inertia of Motion, The tendency of the body to maintain its motion, in a straight line is called inertia of motion., Example:, (i) A man carelessly getting down a moving bus, falls forward, the reason being that his feet come, to rest suddenly, whereas the upper part of his, body retains the forward motion., (ii) An athlete runs through certain distance, before taking a leap so that the inertia of motion, of his body at the time of leaping may help him in, his muscular efforts., (iii) We remove snow or mud from our shoes by, striking them against wall. On striking the wall,, the feet comes to rest whereas the snow which is, still in motion separates from the shoes., Inertia of Direction, The tendency of the body to maintain its direction, of motion is called inertia of direction., Example:, (i) If a car takes a sudden turn along a curved, track, it appear as the passengers are pushed, sideways. This is the result of tendency of the, passenger to continue moving along a straight, path., (ii) Tie a stone to one end of a string and then, holding other end of the string in hand rotate the, stone in a horizontal circle., If during rotation, the string breaks at certain, stage, the stone is found to fly off tangentially at, that point of the circle., (iii) The water drops sticking of cycle tyre are, found to fly off tangentially while rotating., (iv) The sparks produced during the sharpening of, a knife or a razor against a grinding wheel leave, the rim of the wheel tangentially., , Linear Momentum, The product of mass of a body and its velocity is called, the linear momentum or simply momentum of the, body., It is a very important physical quantity which, measures the quantity of motion in a body For, example let us take a plastic ball and an iron ball both, of same size. If we push them one by one to strike a, sand hill with same velocity and from same distance,, it can be observed that plastic ball (lesser mass), causes no damage or little damage to the sand hill., But the iron ball (greater mass) causes greater, damage to the sand hill. So though both the balls have, same velocity, heavier ball has greater impact or, strikes the sand hill with a greater force., Similarly if two identical plastic balls are made to, strike a sand hill, one with a greater velocity than the, other i.e. the faster ball causes greater damage to the, sand hill than the slower one., So the impact produced is directly proportional to, both the mass and the velocity thus mass and, velocity, simultaneously give the idea about, magnitude of impact produced by the object., Momentum (m x v) was introduced by Newton. It is a, vector quantity and directs in the direction of velocity., It is denoted by symbol p., Thus p = mv., Its S.I. unit is kg m/s., , 5

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S.I. unit of force is kg m s 2 or new ton which has, the symbol N., 3., , Sol., , A ball of mass 10 g is initially moving with a, velocity of 50 m s 1 .On applying a constant, force on ball for 2.0 s, it acquires a velocity of, 70 m s 1 . Calculate:, (i) the initial momentum of ball, (ii) the final momentum of ball, Given: m = 10 g = 0.01 kg,, u  50 ms 1 , t  2.0s,  70ms 1, (i) Initial momentum of ball = x initial, Velocity = mu,  0.01kg  50ms1  0.5kg ms1, (ii) Final momentum of ball = mass x final, velocity, = mv,  0.01kg  70ms 1, , 4., , Sol., , A hammer of mass 500 g, moving at 50 m s 1 ,, strikes a nail. The nail stops the hammer in a, very short time of 0.01 s. What is the force of, the nail on the hammer?, Force = Rate of change of momentum, m  mu, , t, Here m  500 g  0.5kg ,  0m / s,, , u  50m / s, t  0.01s, 0.5  50,  F,  2500 N, 0.01, Negative sign shows that the force of the nail, on hammer is in opposite to the direction of, motion of hammer., ,  0.70kg m s 1., Newton's Second Law, , Impulse, , Force applied on an object not only depend on its, momentum, but also on how fast it changes., Newton's second law says that:, The rate of change of momentum of an object is, proportional to the net force applied on the object., The direction of the change of momentum is the same, as the direction of the net force.,  Mathematical formulation, Suppose an object of mass, m is moving along a, straight line with an initial velocity u. It is, uniformly accelerated to velocity v in time t by the, application of a constant force F throughout the, time t. The initial and final momentum of the, object will be, p1  mu and p2  mu respectively., The change in momentum  p2  p1,  m  mu,  m  (  u)., m    u , The rate of change of momentum , t, m    u , F, Or, the applied force,, t, km  (  u ), F,  kma, t, Here a ,    u  / t  is the acceleration, which is, , When a cricketer smashes a ball, a large force acts on, the ball for a very short time. Even in this short time, the force varies, as shown in the figure, such a large, variable force acting for a short interval of time is, called impulsive force. As the impulsive force varies,, its measurement is difficult. But we can measure the, impact of the impulsive force with the help of change, in momentum it produces in the body on which it, acts. The impact produced by impulsive force is called, impulse and is measured by change in momentum, produced in the body., , Impulse (I) = Change in momentum = Final, momentum - Initial momentum = mv - mu, where u and v are initial and final velocities of the, body and m is the mass of the body, , , the rate of change of velocity., k is the constant of proportionality. The unit of, force is so chosen that the value of k becomes, one., 6, , Impulse in terms of average force and time of, impact,    u  m  mu, We know that F  ma  m , , t,  t ,  m  mu  F  t From (1) and (2), we have,, Impulse (I) = mv - mu = F x t

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, ,  I  F t, Thus impulse is equal to the product of the, average force and the time for which it acts., Units of impulse: S.I. unit is kg m s 1 (or) new ton, second, i.e. N s C.G.S. units is g m s 1 (or) dyne, second, Reducing the impact of impulsive force :, Impulse (I) = F x t = mv - mu, m(  u ), Average impulsive force  F , , t, Change in momentum, Time for which force acts, , , , To reduce the impact of impulsive force, the time, for which it acts should be increased. Otherwise, we can say, lesser the time of impact more is the, damage caused., , 5., , Sol., , Explain why a person falling on a cemented, floor gets injured but a person falling on a, heap of sand is not., For a person falling on a cemented floor, the, rate of change of momentum is very large as, he is stopped abruptly i.e. in a very small, interval of time. But a person falling on a heap, of sand comes to rest in longer period of time, as the sand yields under his weight. Increase, in time decreases the impact force and hence,, he does not get injured,, , The two opposing forces are also known as action, and reaction forces and they always act on, different objects and never on the same object., Thus Newton's third law cannot be applied to a, single body., For example when a bullet is fired, the gun recoils, with equal force. When we walk, our feet push, the ground backward and the reaction acts in the, opposite direction. This reaction makes us to, move forward., It is important to note that even though action, and reaction forces are always equal, they do not, produce acceleration of same magnitude. This is, because these forces may act on the bodies of, different masses. For example, when a bullet is, fired from a gun, the gases produced due to the, burning of explosive powder, exerts same force, on the bullet as well as the gun. However, the, bullet leaves the gun with a very large, acceleration due to its smaller mass whereas the, gun jerks back with a very small acceleration due, to its larger mass., , Newton's Third Law, Newton's third law deals with the relationship, between the forces that objects exert on each other., If we push on a wall it pushes back. This doesn't hurt if, you push gently, but if you punch a wall hard it hurts, very much. Newton hypothesized that at any time two, objects interact in such a way that when a force is, exerted on one of them, there is always a force that is, equal in magnitude exerted in the opposite direction, on the other object. This hypothesis is called Newton's, third law. Newton's third law of motion states that 'if, a body A exerts a force +F on a body B, then body B, exerts a force -F on A, that is a force of the same size, and along the same line of interaction but in the, opposite direction'. This law says that forces always, occur in pairs as the result of the interaction between, two objects., , Take two identical (similar in all respects) spring, balances P and Q. Attach the spring balance Q to a, fixed hook in the wall., Now join these spring balances in such a way that, their hooks at the free ends are interlocked as shown, in figure., , When the spring balance P is pulled to the left side,, the pointers of both the spring balances show the, same readings. The reading shown by a pointer of a, spring balance indicates the force acting on the spring, of the balance., 7

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The force indicated by the spring balance P is known, as the action (i.e. force exerted by the spring balance, P on the spring balance Q). The force indicated by the, spring balance Q is known as reaction (i.e., force, exerted by the spring balance Q on the spring balance, P). From this experiment, it is concluded that (i) action, (force) = reaction (force) and (ii) both action and, reaction act in opposite directions i.e., action to the, left side and reaction to the right side. This activity, shows that action and reaction are equal and, opposite., , force. But A is neither going down nor going up. This is, because m1 g and N 1 are equal in magnitude and, opposite in direction. These two forces balance each, other so that the total external force on A is equal to, zero. Similarly, the total external force on B is also, zero. Hence the net external force on the system is, zero., , , Law of Conservation of Linear Momentum, , The principle of conservation of linear momentum, follows from Newton's laws of motion. We will show, this through an example., Suppose two objects A and B of masses m1 and m 2, respectively are kept on a horizontal table, which is so, smooth that friction can be neglected., Suppose A is made to move with a velocity u 1 and B, is made to move with a velocity u 2 in the direction AB., Also, suppose that u1  u 2 . The linear momentum of, A is m1u 2 and that of B is m 2 u 2 . The total linear, momentum of the system is p1 = m1u1 +m 2 u 2, As u1 > u 2 the object A will collide with B at some point, of time. The two objects will remain in contact for a, short time t 0 and then they will separate. When they, separate, the velocities of the objects are different, from their velocities before the collision. Let the, velocity of A become 1 and that of B become  2, after the collision., During the collision, A will push B towards the right,, and B will push A towards the left. By Newton's third, law, the magnitudes of these forces will be equal. As, we are taking the direction towards AB as positive,, write the force on B by A as F, and the force on A by B, as -F. We assume that the force F remains constant, during the collision., If we consider A and B together to be a system, the, forces F and -F are internal forces. There are some, external forces also act on A and B. Consider the, object A. The earth is pulling it down by the force, m1 g . This is an external force. The table is pushing it, up by a normal force N1 . This is also an external, , The force -F acting on A (due to B) produces an, acceleration in it, which changes its velocity from, u1 to 1 Using Newton's second law, the,  F 1  u1  F, acceleration, is, or, or, a1 , , m1, t0, m1, …(1), m1v1  m1u1   Ft0 ., The force on B is F. This produces an acceleration, in B, changing its velocity from u2 to  2 in the, same time interval t0 . Again using Newton's, F, second law, the acceleration is a2 , or, m2,  2  u2 F, , t0, m2, or m2v2  m2u1  Ft0 ., …(2), , (i) Take a test tube having small quantity of water. Fit, a stop cork at the mouth of the tube., (ii) Now hang the test tube by two strings with the, help of a stand., (iii) Start heating the tube till water vaporizes., The mouth of the tube and tube moves in opposite, direction. This is because, the steam in the test tube, pushes the cork out of the mouth of the tube and the, tube recoils backward to conserve the linear, momentum of the system (i.e. the tube and the cork)., This activity demonstrates the law of conservation of, linear momentum., , Adding equations (1) and (2), m1v1  m1u1  m2v2  m2u2  0, 8

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or m1v1  m2v2  m1u1  m2u2 or, p2  p1, Where p 2 is the linear momentum, of the system after the time interval, t 0 and p1 before the collision. Thus, the linear momentum of the system, remained constant, although the, linear momentum of each of the two, particles got changed., Example:, Jet Engines and Rockets: - Just before the launching of, the rocket its momentum is zero as it is at rest. When, the jet of hot gases pass out in downward direction, with tremendous velocity, the rocket moves up with, such a velocity so as to make the momentum of the, system (rocket + emitted gases) zero again., , 6., , Sol., , 8., , Sol., , A 1.2 kilogram basketball travelling at 7.5, meters per second hits the back of a 12, kilogram wagon and bounces off at 3.8 meters, per second, sending the wagon off in the, original direction of travel of the ball. How, fast is the wagon going?, The momentum of the ball before it hit has to, equal the sum of the moment of the two, objects after the collision. Let’s call the, original direction of travel of the ball positive., Then the equation becomes, (1.2)kg (7.5ms1 ), , , ,  (1.2kg )(3.8ms 1 )  (12kg )( ), 7., , Sol., , 1.1m s 1   ms 1 or   1.1ms 1, A hockey ball of mass 200 g travelling at 10, ms1 is struck by a hockey stick so as to return, it along its original path with a velocity at 5, ms1 . Calculate the change of momentum, occurred in the motion of the hockey ball by, the force applied by the hockey stick., Mass of hockey ball, m = 200 g = 0.2 kg, Velocity of hockey ball before force striking in, the hockey stick, 1 =10ms1 Velocity of, hockey ball after striking the hockey stick, 2 =-5ms1,  Change of momentum  m1  m2,  m(1  2 )  0.2(10  5), , , , , ,  0.2 15  3.0kg ms-1, 9, , A bullet of mass 100 g is fired from a gun of, mass 20 kg with a velocity of 100ms-1 ., Calculate the velocity of recoil of the gun., Mass of bullet, m = 100 g, 10, 1, , kg  kg, 100, 10, Velocity of bullet, υ  100ms1, Mass of gun, M = 20 g, Let recoil velocity of gun = V, Step 1: Before firing, the system (gun +, bullet) is at rest therefore, initial momentum, of the system = 0, Final momentum of the system = momentum, of bullet + momentum of gun, 1,  m  MV  100  20V  10  20V, 10, Step 2: Apply law of conservation of, momentum Final momentum = Initial, momentum i.e. 10+ 20 V = 0, 10, 20 V =- 10or V    0.5ms1, 10, Negative sign shows that the direction of, recoil velocity of the gun is opposite to the, direction of the velocity of the bullet., , Force :- It is a physical quantity, a push or pull, acting on an object which, - causes or tends to cause motion in an object, - change or tends to change the direction of, motion of a moving object., - or changes or tends to change the size and shape, of an object., - changes or tends to change speed of an object., Balanced forces: When two forces of equal, magnitude but act in opposite directions on an, object simultaneously, then the object continues, in its state of rest or of uniform motion in a, straight line. Such forces acting on the object are, known as balanced forces., Net force acting on an object on which balanced, forces act is zero., Unbalanced forces: When two forces of unequal, magnitudes and acting in opposite directions on, an object simultaneously, then the object moves, in the direction of a large force., These forces acting on the object are known as, unbalanced forces.

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, , , , , , , , , , , Net Force acting on an object on which, unbalanced forces act is non-zero., Newton's first law of motion: Everybody, continues in its state of rest or uniform motion in, a straight line unless compelled by some external, unbalanced force to change that state., Inertia. The tendency of a body to oppose any, change in its state of rest or uniform motion is, called inertia of the body., Inertia of a body is equal to the mass of the body., S.I. unit of inertia is same as that of mass i.e., kilogram (kg)., Types of inertia: (i) Inertia of rest (ii) Inertia of, motion and (Hi) Inertia of direction., Momentum of a body is defined as the product of, mass and velocity of the body., That is p = mv, Momentum is a vector quantity. S.I. unit is kg s 1, Law of conservation of momentum: The total, momentum of a system remains constant if no, external force acts on the system., Newton's second law of motion. The rate of, change of momentum of a body is directly, proportional to the force acting on the body and, the change in momentum of the body takes place, in the direction of applied force, dp, or F = ma, F, dt, Units of Force, , , , , , , , , , , 10, , Absolute units: S.I. unit of force is newton (N)., 1N=1kg×1ms-2 =1kgms-2, In CGS system, the unit of force is dyne., 1dyne=1g×1cms-2 =1gcms-2 1N=105 dyne, Newton's third law of motion: To every action,, there is an equal and opposite reaction., Action and reaction forces exist in pairs., Action and reaction act on two different bodies, and never cancel each other. Each force produces, its own effect., From Newton's second law of motion, we learn, that No force is required to move a body, uniformly along a straight line., When a-body is moving uniformly along a straight, line and there is no force of friction, acceleration, or retardation of the body, a = 0. According to, Newton's second law of motion,, F = ma = w x 0 = 0, Accelerated motion is always due to some, external force acting on the body., The magnitude of force acting on a body is the, product of mass of the body and acceleration of, the body. Thus, Newton's second law of motion, gives us a measure of force., Some examples of Newton's third law are:, recoiling of gun, firing of rockets, walking,, swimming etc.

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