Suppose you have a rail with two springs on the sides, both with the same constant K. The length of the rail is L, and the length of each spring is D (when not contracted or elongated). On that rail you have an object of mass M (which may be treated as a point particle), and the coefficient of friction between that object and the rail is μ. You take the object, and give it an initial potential energy of KD(adsbygoogle = window.adsbygoogle || []).push({}); ^{2}/2, by forcing it against one of the springs until it is fully contracted and releasing the object.

Where will the object be brought to a halt? Assume that once it stops, it does not start moving again (i.e infinite static friction).

Obviously the beginning of the answer should be:

[tex]F_{friction}x = \Delta {E_p}_{els}[/tex]

But where do we go from there? We don't know where the object stops, so we don't know if it still has potential energy. Furthermore, how do we find the final location of the object from x?

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# Homework Help: Friction, energies and variable distance

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