Page 337 - Dynamics of Mechanical Systems

0593_C09_fm Page 318 Monday, May 6, 2002 2:50 PM

318 Dynamics of Mechanical Systems

a. A perfectly plastic collision: e = 0
20 mph (stopped)
b. A semi-elastic collision: e = 0.5
c. A perfectly elastic collision: e = 1.0 A B
FIGURE P9.10.1
where e is the coefficient of restitution.
A rear-end collision.
P9.10.2: Repeat Problem P9.10.1 if B is moving to the right at 10 mph just before impact.
P9.10.3: See Problems 9.10.1 and 9.10.2. Repeat Problem P9.10.1 if B is moving to the left
at 10 mph (that is, B is backing).
P9.10.4: A basketball B is dropped from a height h onto a fixed horizontal surface S. It is
known that the speed v of B just before it strikes S is 2 gh (g is gravity acceleration). Also
it is known that if B is projected upward from S, after bouncing, with a speed it will
ˆ v
ˆ
2
h
reach a height given by ˆ v 2 . g Let e be the coefficient of restitution between B and
S. Let h be 7 ft and e be 0.9. Find v, ˆ v and h ˆ .
ˆ
P9.10.5: See Problem P9.10.4. If h is 7 ft and is 6.5 ft, what is e?
h
Section 9.11 Oblique Impact
P9.11.1: Two spheres, A and B, collide as in Figure P9.11.1. Let their masses be m = 0.5
A
kg and m = -.75 kg. Let the collision be nearly elastic so that the coefficient of restitution
B
e is 0.9. Determine the velocities (speeds and directions) of A and B immediately after
impact.

A B
(Impact)

3 m/s
4 m/sec
60° 30° B
FIGURE P9.11.1
Colliding spheres. A
P9.11.2: Repeat Problem P9.11.1 if m = 0.75 kg, m = 0.5 kg, and e = 0.85.
A
B
P9.11.3: A test car A collides with a fixed, angled barrier as in Figure P9.11.3. Let the barrier
surface S be smooth and rigid so that it does not resist motion in its tangential direction.
Determine the velocity (speed and direction) of A immediately after impact if the coeffi-
cient of restitution between A and C is (a) 0 (plastic), (b) 0.75 (semi-elastic), and (c) 1.0
(elastic).
P9.11.4: Repeat Problem P9.11.3 if the barrier angle is at 45°.
P9.11.5: Two cars A and B have an intersection collision at 45° to their pre-impact direction
of travel as in Figure P9.11.4. Determine the post-impact velocity of the cars for the
following conditions: m = 100 slug, m = 80 slug, V = 30 mph, V = 25 mph, and the
A
B
B
A
coefficient of restitution e = 0.75. Assume the colliding surfaces are smooth. (Express the
results in terms of the unit vectors n and n of Figure P9.11.4.)
e
n
P9.11.6: Repeat Problem P9.11.4 if the collision is (a) perfectly plastic (e = 0), and (b)
perfectly elastic (e = 1).