Page 371 - Dynamics of Mechanical Systems

0593_C10_fm Page 352 Monday, May 6, 2002 2:57 PM

352 Dynamics of Mechanical Systems

P10.10.8: Repeat Problem P10.10.6 if just before collision, instead of being stopped, the
automobile is moving toward the pickup truck at 10 mph (that is, a head-on collision).

Sections 10.11 and 10.12 Work, Energy, and Impact
P10.11.1: A 60-gauge bullet is fired into a 20-kg block suspended by a 7-m cable as depicted
in Figure P10.11.1. The impact causes the block pendulum to swing through an angle of
15°. Determine the speed v of the bullet.

7 m

60 g
20 kg
FIGURE P10.11.1
A bullet fired into a block. v
P10.11.2: A 14-in. diameter wheel W is rotating at 350 rpm when it is brought into contact
1
with a 10-in.-diameter wheel W , which is initially at rest, as represented in Figure P10.11.2.
2
After the wheels come into contact, they roll together without slipping. Although W is free
1
to rotate, with negligible friction, W is subjected to a frictional moment of 2 ft⋅lb in its
2
bearings. Let the weights of W and W be 28 lb and 20 lb, respectively. Let the radii of
1
2
gyration of W and W be 5 in. and 3.5 in., respectively. Determine the number of revolutions
1
2
N and N turned by each wheel after the meshing contact until they come to rest.
1
2
W (28 lb)
1
300 rpm
W (20 lb)
2
7 in.
5 in.
Initially at rest
FIGURE P10.11.2
Meshing wheels.
P10.11.3: A 1-m rod B with a mass of 1 kg is hanging
O
vertically and supported by a frictionless pin at O as
in Figure P10.11.3. A particle P with a mass of 0.25
kg moving horizontally with speed v collides with B
the rod as also indicated in Figure P10.11.3. If the x
1 m
collision is perfectly plastic (with coefficient of resti-
tution e = 0), determine v so that B completes exactly P
one half of a revolution and then comes to rest in a
vertically up position. Let the point of impact x be v
(a) 0.5 m; (b) 0.667 m; and (c) 1.0 m.
P10.11.4: Repeat Problem P10.11.3 for a perfectly FIGURE P10.11.3
A particle P colliding with a vertical pin
elastic collision (coefficient of restitution e = 1).
supported rod initially at rest.