Question

A mechanic can exert 113Nm of torque on his wrench. If the mechanic wants to create 2 times more torque with a wrench that is 3 times shorter, how does his force need to change?

Answer 1

It needs to increase by a factor of 6.

Explanation:

Torque is the cross product of the position vector and the force:

`tau=Fxxr`

This means that if `r` is decreased by a factor of 3 then the torque will decrease by this factor. To produce the same torque he would need to increase `F` by a factor of 3.

To double the force he would therefore need to increase `F` by a factor of 6.