This preview shows page 1. Sign up to view the full content.
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
T
0
=0
, while its initial potential energy is
V
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 12/16/2010 for the course AME 301 at USC.
 '06
 Shiflett

Click to edit the document details