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A .75kg block is going at a velocity of 1.5m/s and moves on a frictionless surface. Then all of a sudden, the block hits a rough patch. The rough patch is .5m long and has a coefficient of friction of .25. Then it slides onto the frictionless surface again. The mass then collides with a very long spring (spring coefficient is 12000N/m). Calculate how far the spring is compressed when the block just comes to rest?

How do I solve this?

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