Upload
rafe-strickland
View
216
Download
4
Embed Size (px)
Citation preview
Problem 3.149
The 15-ft boom AB has a fixedend A. A steel cable is stretchedfrom the free end B of the boomto a point C located on thevertical wall. If the tension in thecable is 570 lb, determine themoment about A of the forceexerted by the cable at B.
C
B
A
x
y
z
15 ft
6 ft10 ft
1. Determine the rectangular components of a force defined byits magnitude and direction. If the direction of the force isdefined by two points located on its line of action, the force canbe expressed by: F = F = (dx i + dy j + dz k)
Fd
C
B
A
x
y
z
15 ft
6 ft10 ft Solving Problems on Your Own
The 15-ft boom AB has a fixedend A. A steel cable is stretchedfrom the free end B of the boomto a point C located on thevertical wall. If the tension in thecable is 570 lb, determine themoment about A of the forceexerted by the cable at B.
Problem 3.149
2. Compute the moment of a force in three dimensions. If r is aposition vector and F is the force the moment M is given by:
M = r x F
C
B
A
x
y
z
15 ft
6 ft10 ft Solving Problems on Your Own
The 15-ft boom AB has a fixedend A. A steel cable is stretchedfrom the free end B of the boomto a point C located on thevertical wall. If the tension in thecable is 570 lb, determine themoment about A of the forceexerted by the cable at B.
Problem 3.149
Problem 3.149 Solution
Determine the rectangularcomponents of a force definedby its magnitude and direction.
First note:
dBC = (_15)2 + (6) 2 + (_10) 2
dBC = 19 ft
Then:
TBC = (_15 i + 6 j _ 10 k) = _ (450 lb) i + (180 lb) j _ (300 lb)k570 lb19
570 N
C
B
A
x
y
z
15 ft
6 ft10 ft
Problem 3.149 Solution
Compute the moment of aforce in three dimensions.
Have:
MA = rB/A x TBC
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
570 N
C
B
A
x
y
z
15 ft
6 ft10 ft