A ball falls vertically onto a floor, with momentum p, and then bounce

1.	A ball falls vertically onto a floor, with momentum p, and then bounces repeatedly. The coefficient of restitution is e. The total momentum imparted by the ball to the floor is(a) p(1 + e)(b) p/1-e(c) p (1 + 1/e)(d) p (1 + e / 1- e)
Answer» Correct answer is: (d) p (1 + e / 1 - e) When a particle undergoes normal collision with a floor or a wall, with coefficient of restitution e, the speed after collision is e times the speed before collision. Thus, in this case, the change in momentum for the first impact is ep - (-p) = p(1 + e), for the second impact it is e(ep) - (-ep) = ep(1 + e) and so on. The total change in momentum is p(1 + e)[1 + e + e² + ...].

A ball falls vertically onto a floor, with momentum p, and then bounces repeatedly. The coefficient of restitution is e. The total momentum imparted by the ball to the floor is(a) p(1 + e)(b) p/1-e(c) p (1 + 1/e)(d) p (1 + e / 1- e)

Answer»

Correct answer is: (d) p (1 + e / 1 - e)

When a particle undergoes normal collision with a floor or a wall, with coefficient of restitution e, the speed after collision is e times the speed before collision. Thus, in this case, the change in momentum for the first impact is ep - (-p) = p(1 + e), for the second impact it is e(ep) - (-ep) = ep(1 + e) and so on. The total change in momentum is p(1 + e)[1 + e + e² + ...].

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A ball falls vertically onto a floor, with momentum p, and then bounces repeatedly. The coefficient of restitution is e. The total momentum imparted by the ball to the floor is(a) p(1 + e)(b) p/1-e(c) p (1 + 1/e)(d) p (1 + e / 1- e)

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