billiards provide an excellent example of momentum conservation. no matter how c

Question

billiards provide an excellent example of momentum conservation. no matter how complicated the collision, the total momentum of the system of interacting balls is always equal to the initial momentum of the cue ball. (if you want to develop some intuition about momentum, go shoot some pool! Conservation of linear momentum will be most readily observed if you dont put any back spin on the cue ball)

a) explain why the cue ball will always stop short when it collides head on wiht a ball at rest

b) explain why the cue ball will never come to a complete stop if it hits a ball off center, such that the struck balls moves off at an angle to the original path of the cue ball

c) explain why the cue ball could stop short if it simultaneously struck two balls which were very close together. How would the two bals have to move after the collison? would this be likely to occur?

Explanation / Answer

a) As the momentum carried by the cue ball is transfered (most of it ) in head on, as the mass of the cue ball and others are nearly same , the cue ball almost stops shorts and transfers its momentum to the other ball.

B) If the collsion is not head on then there is always a component of velocity in a direction other then the intial velocity, hence to conserve this momentum cue ball doesn;t stop.

c) Same thing happens with the cue ball and the first ball this is struck by the cue ball, as happened in case A. The second ball moves away woth the maximum momentum.

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