Compressed spring with frictional forces problem

[offbeatjumi]

Homework Statement

A book (mass 2.50 kg) is forced against horizontal spring (negligible mass) with force constant 250 N/m, the spring is compressed 0.250m. When it's released the textbook slides horizontally across a surface with kinetic friction coeff = 0.30. How far does the book move from its original position before stopping?

Homework Equations

W = 1/2kX^2... F(s) = kx. U(s) = 1/2kx^2

The Attempt at a Solution

I know I need to use the work energy theorem here.
I was trying to use E2 + W(non-cons) = E1 since there is a nonconservative force in this problem. But isn't the initial and final kinetic energy both zero? I tried using Newton's 2nd law as well... F(net,x) = F(s) - f(k). But at the time when its released, it is not static equillibrium and I can't solve that equation. Unless... does f(k) = (mu)k*n (normal force?) where n = mg.
If anyone can help me set a foot in the correct direction I'd really appreciate it. Thanks!

 

[rock.freak667]

The Attempt at a Solution

I know I need to use the work energy theorem here.
I was trying to use E2 + W(non-cons) = E1 since there is a nonconservative force in this problem. But isn't the initial and final kinetic energy both zero? I tried using Newton's 2nd law as well... F(net,x) = F(s) - f(k). But at the time when its released, it is not static equillibrium and I can't solve that equation. Unless... does f(k) = (mu)k*n (normal force?) where n = mg.
If anyone can help me set a foot in the correct direction I'd really appreciate it. Thanks!

Right good, this is correct. If frictional force F_R= μN = μmg, and the initial energy is 1/2kx², what is this converted into during the motion in general?