Solve 100J Torque Problem with a 30cm Wrench and Force Vector

[munther]

A wrench 30cm long lies along the positive y-axis and grips a bolt in the origin. A force is applied in the
direction < 0; 3; -4 > at the end of the wrench. Find the magnitude of the force needed to supply 100J of
torque to the bolt.

how can i solve it?

r=<0,.3,0>
F=<0,3,4>
T= r X F =100
then i solved it by finding the det = 100

|i j k|
|0 .3 0| = 100
|0 3x -4x|

then x = 83.333 N

but the answer is wrong Why?

 

[Curious3141]

This is the wrong forum for the question, but no matter.

How do you find the magnitude of a vector from the components? What you've found (I didn't check your work, so I'll assume it's right) is a scalar multiplier x that satisfies the problem's constraints. Multiply the (0,3,4) vector by the scalar x to get the force vector (three orthogonal components), then find the magnitude using Pythagoras theorem in the usual way.

 

[m2003]

The answer is wrong because you did not include the unit for torque, which is Newton-meters (Nm). The correct equation should be T = r x F = 100 Nm. Therefore, the magnitude of the force needed to supply 100J of torque to the bolt is 100 Nm / 0.3 m = 333.33 N.