Page 141 - Dynamics of Mechanical Systems

0593_C04*_fm Page 122 Monday, May 6, 2002 2:06 PM

122 Dynamics of Mechanical Systems

R
n 3

B 3 ft
x
A P
n
4 ft 2
12 ft
FIGURE P4.10.3
A box moving in a reference n
frame R. 1
where, as before, t is time, and n , n , and n are mutually perpendicular unit vectors fixed
1
3
2
relative to the box as shown. Also, as before, the velocity and acceleration of corner A of
the box in R are:
R A
V = 2 n + 5 n − 6 n ft sec
1 2 3
and

R A 2
a = 2 n − 8 n − 4 n ft sec
1 2 3
A particle P moves along the diagonal AB of the box with the distance x from corner A
given by:

−
x = 13 13sin π t ( ) 2 ft
Find at times t = 0 and t = 1:

a. The velocity of P relative to the box.
b. The velocity of P relative to R.
c. The acceleration of P relative to the box.
d. The acceleration of P relative to R.

Section 4.11 Rolling Bodies
P4.11.1: A circular disk D rolls at a constant speed on a straight line as indicated in Figure
P4.11.1. Let D roll to the right and remain in a vertical plane. Let the radius of D be 0.3
m, and let the velocity of the center O at D be 10 m/sec (a constant). For the instant shown
in the figure, find: (a) the angular speed ω of D, and (b) the velocity and acceleration of
points P, Q, and C of D. Express the velocities and accelerations in terms of unit vectors
n and n .
y
x
P4.11.2: See Problem P4.11.1. Let the disk D be slowing down so that the acceleration (or
deceleration) of O is to the left at 5 m/sec . For the configuration shown in Figure P4.11.2,
2
with V being 5 m/sec, find: a) the acceleration α of D, and (b) the acceleration of P, Q,
O
and C.