Page 207 - Dynamics of Mechanical Systems

0593_C06_fm Page 188 Monday, May 6, 2002 2:28 PM

188 Dynamics of Mechanical Systems

Z
P(1,2,4)
n
z
Q(2,5,3)
F
L
O B(0,3,0)
Y
A(2,0,0) n
y
FIGURE P6.2.1 n
A force F acting along a line L. X x

P6.2.2: See Problem P6.2.1. Find the moment of F about points O, A, and B of Figure P6.2.1.
Express the results in terms of n , n , and n .
z
x
y
P6.2.3: A force F with magnitude 52 N acts along diagonal OA of a box with dimensions
as represented in Figure P6.2.3. Express F in terms of the unit vectors n , n , and n , which
2
1
3
are parallel to the edges of the box as shown.
n
1
C D

B A 3m
F
O H
n
2
E 4m
12m G
FIGURE P6.2.3 n
A force F acting along a box diagonal. 3

P6.2.4: See Problem P6.2.3. Find the moment of F about the corners A, B, C, D, E, G, and
H of the box. Express the results in terms of n , n , and n .
3
2
1
Section 6.3 Systems of Forces
P6.3.1: Consider the force system exerted on the box as represented in Figure P6.3.1. The
force system consists of ten forces with lines of action and magnitudes as listed in Table
P6.3.1. Let the dimensions of the box be 12 m, 4 m, and 3 m, as shown.

a. Express the forces F ,…, F in terms of the unit vectors n , n , and n shown in
10
1
1
3
2
Figure P6.3.1.
b. Find the resultant of the force system expressed in terms of n , n , and n .
3
1
2
c. Find the moment of the force system about O (expressed in terms of n , n ,
1
2
and n ).
3