Question
Asked Oct 9, 2019
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determine the magnitude of the force f given that its moment about the axis bc is 150 n·m

Determine the magnitude of the force F, given that its moment about axis BC is 150 N-m. Point C is located
on the x-y plane
y
m
Im
3 m
m
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Determine the magnitude of the force F, given that its moment about axis BC is 150 N-m. Point C is located on the x-y plane y m Im 3 m m

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Expert Answer

Step 1

Note down the coordinates:

O=(0,0,0)
B (0,0,3
C = (0,4.1)
A = (4,0,3
D (2,3,0)
Calculate the position vector AD
AD D A
=(2,3,0)-(4,0,3)
= -2i +3j 3k
Calculate the unit vector AD
AD
AD
AD
(-2.3,-3)
N-2+3(-3)
- 32 +(-3)
2
=-0.4264i 0.6936j - 0.6396k
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O=(0,0,0) B (0,0,3 C = (0,4.1) A = (4,0,3 D (2,3,0) Calculate the position vector AD AD D A =(2,3,0)-(4,0,3) = -2i +3j 3k Calculate the unit vector AD AD AD AD (-2.3,-3) N-2+3(-3) - 32 +(-3) 2 =-0.4264i 0.6936j - 0.6396k

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Step 2

Calculate the force vector...

F FAD
=150(-0.4264i +0.6936j- 0.6396k)
=-63.96i +95.94j - 95.94k
Calculate the position vector AB
AD B - A
(0,0,3)-(4,0,3)
=-4i
Calculate the moment about B
MBr F
=(-4i)x (-63.96i+95.94j- 95.94k)
= Oi - 383.76k - 383.76j
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F FAD =150(-0.4264i +0.6936j- 0.6396k) =-63.96i +95.94j - 95.94k Calculate the position vector AB AD B - A (0,0,3)-(4,0,3) =-4i Calculate the moment about B MBr F =(-4i)x (-63.96i+95.94j- 95.94k) = Oi - 383.76k - 383.76j

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Mechanical Engineering

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