# 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?

Nov 22, 2015

It needs to increase by a factor of 6.

#### Explanation:

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

$\tau = F \times r$

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.