A wrench with a length of 24 cm24cm is being used to unscrew a 3 cm3cm bolt. If a torque of 7 Nm7Nm 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(blue)(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(red)(F=tau/(rsinphi))F=τrsinϕ
We are provided the following information:
"r"=24"cm"=0.24"m"r=24cm=0.24m
tau=7"Nm"τ=7Nm
And it is implied that
Note that I am not including the radius of the bolt in the measurement of the total radius because I am assuming that this is the radius of the body of the screw and not the head of the screw.
Therefore, we have:
F=(7"Nm")/(0.24"m")F=7Nm0.24m
=29.1bar6"N"=29.1¯6N
~~29"N"≈29N