A ball falls vertically onto a floor, with momentum p, and then bounces repeatedly. The coefficient of restitution is e. What is the total momentum imparted by the ball to the floor?
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When a ball falls vertically onto a floor with momentum p, and then bounces continuously the total momentum imparted by the ball to the floor is
P * [ (1 + e) / (1 - e)].
1) when a ball hits the ground with momentum p, it bounces back from the floor with a momentum of Pe. ( e is Coefficient of restitution ).
2) So, again when the ball falls on the ground its momentum goes to be P*e^2. And this continues.
3) So, on adding all these momentum, which will ultimately form an infinite Geometric progression series, we fing the total work done on the ground.
4) On adding all the terms of the g.p. series it comes to be P * [ (1 + e) / (1 - e)].
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