How Is Work Done by Friction Calculated in a Spring-Box System?

[deezy]

Homework Statement

A horizontal spring with spring constant 200 N/m is compressed 20 cm and used to launch a box across a rough horizontal surface. After traveling a distance it stops. What is the work done by friction force?

Homework Equations

$$W = F \cdot d$$
$$KE_{spring} = \frac{1}{2}k \Delta x^2$$

The Attempt at a Solution

I don't know where to start, because I'm not sure what other relevant equations I can use. I'm thinking that the friction has to do enough work to make the box stop (v = 0). But I don't know how to relate the work by friction to the energy of the spring.

 

[Delphi51]

Initially you have the spring energy. It gets converted into kinetic energy. That gets converted into heat by the work of friction. All your initial energy is equal to the work of friction.

 

[deezy]

Ah... so $$W_{friction} = KE_{spring} = \frac{1}{2}k \Delta x^2 = \frac{1}{2} \cdot 200 \cdot .2^2$$?

 

[Delphi51]

looks good!