A horizontal spring with spring constant 200 N/m is compressed 10 cm and is used

Question

A horizontal spring with spring constant 200 N/m is compressed 10 cm and is used to launch a 3 kg box across a frictionless, horizontal surface. After the box travels some distance, the surface becomes rough. The coefficient of kinetic friction of the box on the surface is 0.2. Use work and energy to find how far the box slides across the rough surface before stopping.

heres what i did so far

1/2kx^2 = 1 J

F = u * mg

where u is the coefficient of kinetic friction

FD = KE and need to solve for D

but I am not sure, if someone can please post the solution in detail will be greatly appreciated Thanks

Explanation / Answer

what u did was pretty right intial energy = 1/2*k*x^2 = 1j friction force = u*mg = 0.2*3*10 = 6 N work done f*d = 6*D work = change in energy 6*d = 1 d = 1/6 m

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