A bolt on a bicycle is tightened to a torque of 25 N*m. If a 20.0 cm long wrench is pulled at a 40 degree angle from the perpendicular. What is the length of the lever arm?

Question

A bolt on a bicycle is tightened to a torque of 25 N*m.  If a 20.0 cm long wrench is pulled at a 40 degree angle from the perpendicular.  What is the length of the lever arm?

theeric · Answer

Hi! Do you know any formulas for this sort of thing, @watermelon16 ?

anonymous · Answer

I know formulas but I am not sure which one to use for this one.

theeric · Answer

Okay! So, is this physics? I just want to know what you know before I continue...

anonymous · Answer

Yes it is physics

theeric · Answer

I think the formula you want is this formula, which is always you're go-to in a situation with a lever arm.

$\tau=F\ r\ \sin\theta$
Where $\tau$ is torque
$F$ is the force
$r$ is the "radius", or distance from the center of the turn to the place where you push
and $\theta$ is the angle between the force and the radius.

I'll draw a picture as to why.

anonymous · Answer

:) okay.

theeric · Answer

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theeric · Answer

|dw:1389988923281:dw|And we want only the component of the force that is perpendicular to the radius because that is the TORQUE part...

theeric · Answer

The toque is that part of the force, TIMES the radius!
So, you get more torque the further out you are, and that's why they make huge wrenches and crowbars.

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