5.19. CHAPTER 5, PROBLEM 19 257 5.19 Chapter 5, Problem 19 Problem: A ball initially at rest falls from a height H above a flat surface. If the coefficient of restitution between the ball and the surface is e ,towha the igh t , h , does it rebound on the first, second and n th bounces? Compute the height reached on the tenth bounce for e =0 . 9 . Solution: We solve by first using energy conservation to determine the ball’s velocity just before it impacts the surface. Then, we use the impact relation to determine the ball’s velocity just after the impact. Finally, we use energy conservation to compute the height to which the ball rises after the impact. We then generalize to n bounces. Energy Conservation 1. Denote the ball’s mass by m and gravitational acceleration by g . Also, let the origin of the coordinate axis normal to the surface be z=0 . Because the ball is initially motionless, its initial kinetic energy is T0 =0 , while its initial potential energy is V
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This note was uploaded on 12/16/2010 for the course AME 301 at USC.