# A bolt is to be tightened with a torque of 8.0 N*m. If you have a wrench that is 0.35 m long, what is the least amount of force you must exert?

Jun 13, 2014

23 N

$T = F d$ so $F = \frac{T}{d} = \frac{8.0}{0.35} = 23 N$

This is the minimum force because in a real situation friction will add to the required force.

Also:

1. This assumes a force acting at a point at the very end if the handle, in reality the force applied by a hand on the wrench will be a distributed load of finite width. So it will depend upon the actual positioning of the hand and how the force is applied to the handle through the the hand. The distance will be <0.35 m and so the required force will increase proportionately.

2. This ignores the recess in the wrench itself to accommodate the bolt/nut. That further reduces the perpendicular distance and thus will proportionately increase the required force.