Page 369 - Dynamics of Mechanical Systems

0593_C10_fm Page 350 Monday, May 6, 2002 2:57 PM

350 Dynamics of Mechanical Systems

B D
O

smooth Perfectly
rough
4 m 4 m

30° 30°

FIGURE P10.6.16 FIGURE P10.6.17
A block sliding down a smooth inclined A circular disk D rolling down an incline plane.
surface.
P10.6.17: See Problem P10.6.16. A 10-kg circular disk D with 0.25-m diameter is placed at
the top of an incline that has a perfectly rough surface as represented in Figure P10.6.17.
If D is released from rest and rolls down the incline, what will be the speed of the center
O of D when it reaches the bottom of the incline? Compare the result with that of Problem
P10.6.16.
P10.6.18: A solid half-cylinder C, with radius r and mass m, is placed on a horizontal
surface S and held with its flat side vertical as represented in Figure P10.6.18. Let C be
released from rest and let S be perfectly rough so that C rolls on S. Determine the angular
speed of C when its mass center G is in the lowest most position.

C
G

FIGURE P10.6.18 S
A half-cylinder (end view) on a Perfectly rough
horizontal surface.

P10.6.19: Repeat Problem P10.6.18 if S is smooth instead of rough.
P10.6.20: A 7-kg, 1.5-m-long rod AB has its end pinned to light blocks that are free to move
in frictionless horizontal and vertical slots as represented in Figure P10.6.20. If the pins
are also frictionless, and if AB is released from rest in the position shown, determine the
speed of the mass center G and the angular speed of AB when AB falls to a horizontal
position and when AB has fallen to a vertical position. Assume that the guide blocks at
A and B remain in their vertical and horizontal slots, respectively, throughout the motion.

A
1.5 m
G
B

FIGURE P10.6.20
A rod with ends moving in
frictionless guide slots.
P10.6.21: Repeat Problem P10.6.20 if the guide blocks at A and B are no longer light but
instead have masses of 1 kg each.