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Mechanics: Work done against friction

The problem is: The light horizontal spring has a force constant of k=100 N/m. A 2.00 kg block is pressed against one end of the spring (compressing it 0.100 m). The block is released and moves from rest 0.250 m to the right of the release position. Show that the coefficient of kinetic friction between the block and the horizontal surface is 0.102.

I can understand and do problems that say for example have the mass on a decline and then I can use the W nc = W f =-uk(mg cos theta)x = delta KE + delta PEg _ delta PEs. And I understand how to show what the coefficient of kinetic friction is in that type of formula, but for some reason I can't show how to do it with this problem.

{What I came up with was: -uk (19.6 N Cos theta)(0.250m) = 0 + (19.6 N)(-.250 m sin theta) + 1/2 (100N/m)(0.250m)2} It doesn't seem to work or show that the coefficient is 0.102.

I've attached a drawing for the problem.

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Solution Preview

1. What is theta you have written in your sol. The spring is horizontal and obviously the surface is horizontal. So here theta is 0.
2. The compression in the spring is 0.100 m and not ...

Solution Summary

The block attached with a compressed spring is released. The block comes to rest at some distance. The coefficient of kinetic friction is calculated.