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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 left 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)

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    Solution Preview

    Note 1. I believe you meant that the right end, not the left end of the spring is attached to the wall.
    Note 2. let the total compression of the spring at first momentary stop be Xf.
    Note 3. The mass M ...

    Solution Summary

    The solution includes a step-by-step calculation for loss in mechanical energy for a block that is sliding along a horizontal table and comes to rest.