Question

A wrench with a length of `42 cm` is being used to unscrew a `7/2 cm` bolt. If a torque of `32 Nm` 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?

Answer 1

`F~~76"N"`

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)`

where `F` is the applied force, `r` is the distance from the pivot (axis of rotation) that the force is applied, and `phi` is the angle at which the force is applied.

We can rearrange the equation for torque to find `F`.

`color(crimson)(F=tau/(rsinphi))`

We are provided the following information:

• `|->"r"=42"cm"=0.42"m"`

• `|->tau=32"Nm"`

And it is implied that `phi=90^o` since no angle—nor the necessary information to calculate one—is provided.

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 bolt and not the head of the bolt.

Therefore, we have:

`F=(32"Nm")/(0.42"m")`

`=76.19"N"`

`~~76"N"`