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Problem 3.149
y
C
10 ft
The 15-ft boom AB has a fixed
end A. A steel cable is stretched
from the free end B of the boom
to a point C located on the
vertical wall. If the tension in the
cable is 570 lb, determine the
moment about A of the force
exerted by the cable at B.
6 ft
A
z
15 ft
B
x
y
Problem 3.149
C
10 ft
Solving Problems on Your Own
6 ft
A
z
15 ft
B
x
The 15-ft boom AB has a fixed
end A. A steel cable is stretched
from the free end B of the boom
to a point C located on the
vertical wall. If the tension in the
cable is 570 lb, determine the
moment about A of the force
exerted by the cable at B.
1. Determine the rectangular components of a force defined by
its magnitude and direction. If the direction of the force is
defined by two points located on its line of action, the force can
be expressed by:
F
F = Fl =
(dx i + dy j + dz k)
d
y
Problem 3.149
C
10 ft
Solving Problems on Your Own
6 ft
A
z
15 ft
B
x
The 15-ft boom AB has a fixed
end A. A steel cable is stretched
from the free end B of the boom
to a point C located on the
vertical wall. If the tension in the
cable is 570 lb, determine the
moment about A of the force
exerted by the cable at B.
2. Compute the moment of a force in three dimensions. If r is a
position vector and F is the force the moment M is given by:
M=rxF
y
Problem 3.149 Solution
C
10 ft
6 ft
Determine the rectangular
components of a force defined
by its magnitude and direction.
A
570 N
First note:
z
15 ft
B
dBC =
(_15)2 + (6) 2 + (_10) 2
x
dBC = 19 ft
Then:
TBC =
570 lb _
( 15 i + 6 j _ 10 k) = _ (450 lb) i + (180 lb) j _ (300 lb)k
19
y
Problem 3.149 Solution
C
10 ft
6 ft
Compute the moment of a
force in three dimensions.
A
570 N
Have:
z
MA = rB/A x TBC
B
15 ft
x
Where:
rB/A = (15 ft) i
Then:
MA = 15 i x (_ 450 i + 180 j _ 300 k)
MA = (4500 lb.ft) j + (2700 lb.ft) k