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2–117.
Determine the magnitudes of the projected components of
the force F = [60i + 12j - 40k] N along the cables AB
and AC.
0.75 m
B
1m
z
1m
C
1.5 m
u
A
Solution
y
F
F = {60 i + 12 j - 40 k} N
uAB =
3m
x
- 3 i - 0.75 j + 1 k
1( - 3)2 + ( - 0.75)2 + (1)2
= -0.9231 i - 0.2308 j + 0.3077 k
uAC =
- 3 i + 1 j + 1.5 k
1( - 3)2 + (1)2 + (1.5)2
= -0.8571 i + 0.2857 j + 0.4286 k
Proj FAB = F # uAB = (60)( - 0.9231) + (12)( -0.2308) + ( - 40)(0.3077)
= -70.46 N
Ans.
|Proj FAB| = 70.5 N
Proj FAC = F # uAC = (60)( - 0.8571) + (12)(0.2857) + ( - 40)(0.4286)
= -65.14 N
Ans.
|Proj FAC| = 65.1 N
Ans:
|Proj FAB| = 70.5 N
|Proj FAC| = 65.1 N
138