Page 335 - Dynamics of Mechanical Systems

0593_C09_fm Page 316 Monday, May 6, 2002 2:50 PM

316 Dynamics of Mechanical Systems

of B be 64 in. in front of the rear wheels. Finally, let the central moment of inertia of B
2
about a vertical axis be 1775 slug ft . Determine the angular velocity of B immediately
after impact. (Assume that A remains in contact with the right rear wheel of B for a brief
time after impact.)
P9.7.6: A body B modeled as a 36-in.-long bar PQ is moving to the right at 44 ft/sec as in
Figure P9.7.6a. Suppose end Q of the bar encounters and strikes a small ledge as in Figure
9.7.6b and begins to rotate about the ledge corner O. Determine (a) the angular speed of
B, (b) the velocity of P, and (c) the velocity of mass center G of B, immediately after impact.

P P

G
36 in G
44 ft/sec

O
Q Q
FIGURE P9.7.6 ledge
A moving bar striking a ledge at an
end of the bar. (a) (b)
P9.7.7: A ball B weighing 5 lb is held inside a rotating tube T by an 8-in. string as depicted
in Figure P9.7.7. In this position, B has a speed of 15 ft/sec. Let T have a smooth interior
surface, let T be light, and let T be free to rotate about a vertical axis as shown. Let the
restraining string be cut, allowing B to slide 19 in. to the end A of T. Determine the angular
velocities of T before and after the string is cut.

5 in B (5 lb) T
A
24 in

string
FIGURE P9.7.7
A ball inside a light, smooth rotating
tube.

P9.7.8: Repeat Problem P9.7.7 if B weighs 8 lb.
P9.7.9: A bullet of mass m is shot into a vertical hanging bar with length and mass M
at a distance h below a pin support O of the bar (Figure P9.7.9). If the speed of the bullet
just before impact is V, determine the angular speed of the bar just after impact. Assume
that the pin is frictionless and that m is small compared with M.
P9.7.10: Repeat Problem P9.7.9 if m = 28 g, M = 5.5 kg, V = 700 m/sec, = 1 m, and h = 0.8 m.
P9.7.11: See Problem P9.7.6. A plate ABCD with sides 3 m and 4 m is moving to the right
at 10 m/sec, as represented in Figure P9.7.11. Corner D of the plate encounters and strikes
a fixed ledge and begins to rotate about corner O of the ledge. Determine the n , n , and
1
2
n components of the angular velocity of the plate just after impact. (As before, the n are
i
3
mutually perpendicular unit vectors.)