A wrench 30 cm long lies along the positive x axis and grips the bolt at the ori

Question

A wrench 30 cm long lies along the positive x axis and grips the bolt at the origin. A force applied in the direction <0, 3,-4> at the end of the wrench. Find the magnitude of the force needed to supply 100 J of torque to the bolt . (Answer approx 333.33 N)
Please explain how to get this thank you. A wrench 30 cm long lies along the positive x axis and grips the bolt at the origin. A force applied in the direction <0, 3,-4> at the end of the wrench. Find the magnitude of the force needed to supply 100 J of torque to the bolt . (Answer approx 333.33 N)
Please explain how to get this thank you.
Please explain how to get this thank you.

Explanation / Answer

given

r = 30 cm = 0.3 m

means

= ( 0, 0.3 , 0 )

and F = 100 J or 100 N.m

v = <0, 3,-4>

using equation for the torque is

T = r X F

the force is F = | F | ( v / | v | )

so F = | F| X v / 5 ( because it is in same direction )

sonow substituting values

100 = ( 0, 0.3 , 0 ) X | F | X ( 0 , 3 , -4 ) / 5

| F | X ( -4 , 0 , 0 ) = 5000 / 3

| F | = 5000 / 12

| F | = 416.666 N

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