The coefficient of friction by spring compression

[Teacup_in_space]

Homework Statement

A box has the mas 50.0Kg. The box slides on a horizontal surface that has friction. The box has the velocity 3.00m/s when its 0.600m away from a spring with negligible mass and the force coefficent 20Kn/m. The box hits the spring and comes to a momentary rest after compressing the spring 0.120m before shooting off into the opposite direction.

A ) [solved] What is the work that the spring exerts on the box as it slows down?
Assuming I did this correctly: Then the spring exerts 144J of energy onto the box.

B ) [Unsolved] What is the coefficent of kinetic friction that acts on the box?Relevent equations include (I assume) Hooks law and the equations of conservation of energy and motion.

W = F * S
F = MA
F_k = MGμ
E = -KΔx
E = 0.5*m*v²What I've done:

Now, I started by trying to evaluate at what speed the box hits the spring based on the compression. I started thinking that I could just use the conversation of energy to connect 0.5*m*v² = -KΔx and solve for v. But then I thought that this wouldn't be accurate since a small amount of the energy must have gone into the friction over those 0.120m and thus the velocity would be incorrect. I was thinking that maybe I'd use the force that the spring exerted on the box from A) but I'm not quite sure how I should approach this problem correctly.

So to sum up:

Given the compression of a spring hit by a box of mass m how can I calculate the kinetic friction?

 

[Doc Al]

First figure out how much work must have been done by friction.