A wrench with a length of $24 c m$ $24 cm$ is being used to unscrew a $3 c m$ $3 cm$ bolt. If a torque of $7 N m$ $7 Nm$ 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?

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A wrench with a length of $24 c m$ $24 cm$ is being used to unscrew a $3 c m$ $3 cm$ bolt. If a torque of $7 N m$ $7 Nm$ 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?

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Answer 1 · 2017-08-03T18:03:31

$F \approx 29 N$ $F~~29N$

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:

$τ = r F sin ϕ$ $color(blue)(tau=rFsinphi)$

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

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

$F = \frac{τ}{r sin ϕ}$ $color(red)(F=tau/(rsinphi))$

We are provided the following information:

$r = 24 cm = 0.24 m$ $"r"=24"cm"=0.24"m"$

$τ = 7 Nm$ $tau=7"Nm"$

And it is implied that $ϕ = 90^{o}$ $phi=90^o$ 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 screw and not the head of the screw.

Therefore, we have:

$F = \frac{7 Nm}{0.24 m}$ $F=(7"Nm")/(0.24"m")$

$= 29.1 ¯ 6 N$ $=29.1bar6"N"$

$\approx 29 N$ $~~29"N"$

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A wrench with a length of $24 c m$ $24 cm$ is being used to unscrew a $3 c m$ $3 cm$ bolt. If a torque of $7 N m$ $7 Nm$ 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?

1 Answer

Explanation:

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1 Answer

Explanation:

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A wrench with a length of $24 c m$ $24 cm$ is being used to unscrew a $3 c m$ $3 cm$ bolt. If a torque of $7 N m$ $7 Nm$ 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?