Chapter 6, Problem 17TE

Consider the swinging-balls apparatus. If two balls are lifted and released, momentum is conserved as two balls pop out the other side with same speed as the released balls at impact. But momentum would also be conserved if one ball popped out at twice the speed. Can you explain why this never happens? (Hint: If the collision is perfectly elastic, what besides momentum would have to be conserved? Can you see why this exercise is here rather than in the previous chapter on the momentum? )

To determine

The explanation of the momentum conservation of the balls in the swinging-ball apparatus.

Answer to Problem 17TE

The momentum of one ball does not remain conserve due to the absence of elastic collision.

Explanation of Solution

The momentum of the ball describes the effect of the mass and speed of the ball. If any quantities from the mass and speed vary, then the momentum of the ball also varies.

The momentum of the two balls moving with same speed is equal to the two times the momentum of a single ball. If one ball popped out at twice the speed of the two balls speed in the previous release, then the momentum of one ball should be same as the momentum of two balls.The momentum of a single ball does not conserve due to the absence of the collision for one ball.

Conclusion:

Therefore, The momentum of one ball does not remain conserve due to the absence of elastic collision.