A wrench with a length of $42 c m$ $42 cm$ is being used to unscrew a $\frac{7}{2} c m$ $7/2 cm$ bolt. If a torque of $18 N m$ $18 Nm$ 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?

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A wrench with a length of $42 c m$ $42 cm$ is being used to unscrew a $\frac{7}{2} c m$ $7/2 cm$ bolt. If a torque of $18 N m$ $18 Nm$ 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?

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Answer 1 · 2017-08-08T03:26:42

$F \approx 43 N$ $F~~43"N"$

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:

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

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:

$r = 42 cm = 0.42 m$ $"r"=42"cm"=0.42"m"$

$τ = 18 Nm$ $tau=18"Nm"$

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:

$F = \frac{18 Nm}{0.42 m}$ $F=(18"Nm")/(0.42"m")$

$= 42.86 N$ $=42.86"N"$

$\approx 43 N$ $~~43"N"$

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A wrench with a length of $42 c m$ $42 cm$ is being used to unscrew a $\frac{7}{2} c m$ $7/2 cm$ bolt. If a torque of $18 N m$ $18 Nm$ 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?

1 Answer

Explanation:

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1 Answer

Explanation:

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A wrench with a length of $42 c m$ $42 cm$ is being used to unscrew a $\frac{7}{2} c m$ $7/2 cm$ bolt. If a torque of $18 N m$ $18 Nm$ 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?