A wrench with a length of 20 cm20cm is used to unscrew a 5/2 cm52cm bolt. If a torque of 12 Nm12Nm is needed to overcome the friction keeping the bolt in place, what is the minimum torque that must be applied to the wrench to unscrew the bolt?
1 Answer
Explanation:
I assume the question is meant to ask what is the minimum force required to unscrew the bolt.
Torque is given by the equation:
color(darkblue)(tau=rFsinphi)τ=rFsinϕ where
FF is the applied force,rr is the distance from the pivot (axis of rotation) that the force is applied, andphiϕ is the angle at which the force is applied.
We can rearrange the equation for torque to find
color(crimson)(F=tau/(rsinphi))F=τrsinϕ
We are provided the following information:
-
|->"r"=20"cm"=0.20"m"↦r=20cm=0.20m -
|->tau=12"Nm"↦τ=12Nm
And it is implied that
Note that I am not including the radius of the bolt in the measurement of the total radius because it should not affect the distance from the applied force to the bolt itself.
Therefore, we have:
F=(12"Nm")/(0.20"m")F=12Nm0.20m
=color(crimson)(60"N")=60N