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LAWS OF MOTION 53 astronaut, once he is out of the spaceship, is act. One reason is that the cricketer allows a zero. By the first law of motion the acceleration longer time for his hands to stop the ball. As of the astronaut is zero. ⊳ you may have noticed, he draws in the hands backward in the act of catching the ball 4.5 NEWTON’S SECOND LAW OF MOTION The first law refers to the simple case when the (Fig. 4.3). The novice, on the other hand, net external force on a body is zero. The second keeps his hands fixed and tries to catch the ball almost instantly. He needs to provide a law of motion refers to the general situation when much greater force to stop the ball instantly, there is a net external force acting on the body. and this hurts.The conclusion is clear: force It relates the net external force to the acceleration of the body. notonlydependsonthechangeinmomentum, but also on how fast the change is brought Momentum about. The same change in momentum Momentum of a body is defined to be the product brought about in a shorter time needs a of its mass m and velocity v, and is denoted greater applied force. In short, the greater the by p: rate of change of momentum, the greater is p = m v (4.1) the force. Momentum is clearly a vector quantity. The following common experiences indicate the importance of this quantity for considering the effect of force on motion. • Suppose a light-weight vehicle (say a small car) and a heavy weight vehicle (say a loaded truck) are parked on a horizontal road. We all know that a much greater force is needed to push the truck than the car to bring them to the same speed in same time. Similarly, a greater opposing force is needed to stop a heavy body than a light body in the same time, if they are moving with the same speed. • If two stones, one light and the other heavy, are dropped from the top of a building, a Fig. 4.3 Force not only depends on the change in momentum but also on how fast the change person on the ground will find it easier to catch isbroughtabout.Aseasonedcricketerdraws the light stone than the heavy stone. The mass of a body is thus an important inhishandsduringacatch,allowinggreater parameter that determines the effect of force timefortheballtostopand hencerequiresa on its motion. smallerforce. • Speed is another important parameter to consider. A bullet fired by a gun can easily • Observations confirm that the product of pierce human tissue before it stops, resulting mass and velocity (i.e. momentum) is basic to in casualty. The same bullet fired with the effect of force on motion. Suppose a fixed moderate speed will not cause much damage. force is applied for a certain interval of time Thus for a given mass, the greater the speed, on two bodies of different masses, initially at thegreateristheopposingforceneededtostop rest, the lighter body picks up a greater speed the body in a certain time. Taken together, than the heavier body. However, at the end of the product of mass and velocity, that is momentum, is evidently a relevant variable the time interval, observations show that each body acquires the same momentum. Thus of motion. The greater the change in the the same force for the same time causes momentum in a given time, the greater is the the same change in momentum for force that needs to be applied. • A seasoned cricketer catches a cricket ball different bodies. This is a crucial clue to the coming in with great speed far more easily second law of motion. • In the preceding observations, the vector than a novice, who can hurt his hands in the Reprint 2026-27