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Energy conservation in a mass-spring system

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A block of mass M slides along a horizontal table with speed Vo. At x=0 it hits a spring with spring constant k and begins to experience a friction force. The coefficient of friction is variable and is given by Mu=b*x, where b is a constant. Find the loss in mechanical energy when the block has first come momentarily to rest

Details about the drawing ;
The drawing shows at the left a block M with a velocity vector Vo horizontal going to the right.
To the the right there is this horizontal spring (at rest) whose right end is attached to a wall.
The drawing shows that the x axis is directed toward the right (the wall) and the origin of this axis (x=0) is at the left end of the horizontal spring (at rest in the given drawing) .

This is a Energy chapter problem

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Solution Summary

The solution is a detailed step by step process that shows how to use the conservation of energy principles. The solution is 3 pages long including full derivatios and an illustration.

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