Page 93 - Dynamics of Mechanical Systems

0593_C03_fm Page 74 Monday, May 6, 2002 2:03 PM

74 Dynamics of Mechanical Systems

a. Determine the velocity of the pickup truck relative to the automobile. Express
the answer in both feet per second and miles per hour and in terms of unit
vectors i and j where i is directed east and j is directed north.
b. Determine the acceleration of the pickup truck relative to the automobile. Express
the answer in feet per second squared (ft/sec ) and in terms of the unit vectors
2
i and j defined in (a).

P3.4.3: Car A is traveling west at a constant speed of 30 mph. As car A crosses an
intersection (see Figure P3.4.3), car B starts from rest 120 feet south of the intersection and
moves north with a constant acceleration of 4.4 ft/sec . Determine the position, velocity,
2
and acceleration of B relative to A, 6 seconds after A crosses the intersection.

N
j
W E
S

A

i
FIGURE P3.4.3
Cars A and B passing through
an intersection. B

Section 3.5 Differentiation of Rotating Unit Vectors

P3.5.1: Consider a point P moving on a circle at constant speed V as represented in Figure
P3.5.1. Let the circle have radius r and let p locate P relative to the center O, as shown,
with θ being the angle between p and the X-axis.

a. Express p in terms of the unit vectors n and n shown in Figure P3.5.1.
x
y
b. Compute the velocity V of P. Show that V is perpendicular to p.
c. Express the speed V in terms of r and θ.
d. Compute the velocity V of P using Eq. (3.5.9).
e. Compute the acceleration a of P by differentiating the velocity V obtained in (b).
Show that a is directed opposite to p.
f. Compute a by differentiating V obtained in (d) by using Eq. (3.5.9).

Y V
n
r
P
n
y
r p
θ
X
O
n
x
FIGURE P3.5.1
A point P moving on a circle at
constant speed.