Physics/Mechanics/Statics Wrench Problem?

  • Thread starter Thread starter Gary W
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Gary W

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You are asked to remove a screw with the most torque possible. You can either apply 2X Newtons to a normal wrench of length R or X Newtons to each arm of a double handle wrench of length 2R. All forces are applied directly perpendicular to the wrench. In the case of the second option, the forces are applied so they do not cancel one another out.

Can anyone explain why the second option gives the best mechanical advantage?

Many thanks!
 
The moment of each force is given by the position vector crossed by the force vector. In this case, we're only dealing with the moment along the axis of the screw, so consider correct for that by crossing with the unit vector of the direction of the screw's axis.

Now, in the two-force scenario:

Mo = (ra x Fa) + (rb x Fb)

Fb = -Fa

Mo = (ra - rb) x Fa,

In this case, the displacement vector is twice as long as in the single force scenario but the force is only one half, so unless there is some advantage to placing two forces over placing one stronger force, the two systems work about the same.
 
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