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 Sep 8th 2008, 06:46 AM #1 Senior Member   Join Date: Apr 2008 Location: HK Posts: 886 Difficult problem for me the choices are mgcos$\displaystyle \theta$ mgsin$\displaystyle \theta$ mg sin$\displaystyle \theta$cos$\displaystyle \theta$ mgsin$\displaystyle ^2\theta$ What is a systematic approach for the problem Attached Thumbnails
Sep 8th 2008, 07:38 AM   #2

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 Originally Posted by werehk the choices are mgcos$\displaystyle \theta$ mgsin$\displaystyle \theta$ mg sin$\displaystyle \theta$cos$\displaystyle \theta$ mgsin$\displaystyle ^2\theta$ What is a systematic approach for the problem
The most general approach to this would be to apply a force in an arbitrary direction, then use Calculus to find a minimum.

However we have a shortcut available. The minimum force is going to be in such a direction so as not to increase the tension, which would be "wasted" force, and also to not reduce the tension, which is helping hold the mass up. So we want the force to be directed perpendicular to the tension. The rest can be easily worked out from there.

-Dan
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 Sep 9th 2008, 08:44 AM #3 Senior Member   Join Date: Apr 2008 Location: HK Posts: 886 really good shortcut thanks

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