# A wrench with a length of 10 cm is used to unscrew a 5/2 cm bolt. If a torque of 18 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?

Feb 24, 2018

18 Nm, same as the torque given in the question.

#### Explanation:

${F}_{m a n}$ = the force on the wrench.

${F}_{F r i c t i o n}$ = the force on the screw.

The formula for torque: $\tau$ = $F$ $\times$ $R$

$\tau$ = 18 $N m$ to overcome friction.

To unscrew the bolt at a constant angular velocity, once the desired angular velocity is attained, angular acceleration should be zero and therefore the net torque would be zero. Therefore

${\tau}_{w r e n c h} - {\tau}_{\text{friction}} = 0$

${\tau}_{w r e n c h}$ = ${F}_{m a n}$ $\times$ ${R}_{w r e n c h}$ Equation (1)

${\tau}_{\text{friction}}$ = ${F}_{F r i c t i o n}$ $\times$ ${R}_{s c r e w}$ Equation(2)

Therefore, ${F}_{m a n}$ $\times$ ${R}_{w r e n c h} = {F}_{F r i c t i o n}$ $\times$ ${R}_{s c r e w} = 18 N m$

So the torque applied to the wrench needs to be the torque that was given in the question $\rightarrow 18 N \cdot m$!

There are dozens of questions like this one on Socratic, with different data, but posing the same basic question. There have been other contributors answering the way I have here, that the applied torque has to be the torque that the question says was required "to overcome the friction keeping the bolt in place".

The author of the question is never (that I have seen) identified. They are nonsense questions and I suspect it is a troll asking them.