Distance of box pushed up incline by spring

[anothertangent]

Homework Statement

A block of mass m=1.5kg is attached to a spring of constant k=590N/m. It is initially at rest on inclined plane of 21 degrees, and coefficient of kinetic friction between block and plane is MUk=.19. In initial position, where spring is compressed by d=.18m, mass is at lowest position and spring is compressed maximum amount. Take initial gravitational energy of block as 0. If spring pushes the block up the incline, what distance L will the block travel, in m?

Homework Equations

W=Fd
KE=.5mv^2
PE=mgh
PE of spring=.5kx^2
Fkinetic friction= MUk(mgcos(theta))
KE0+PE0+Wfriction=KE+PE

The Attempt at a Solution

I assume the basic formula to be KE0+PE0+Wfriction=KE+PE. I have solved for the initial mechanical energy in the first part of the problem, and it equals 9.558J. The equation then becomes 9.558+Wf=KE+PE. Because it's a spring, the PE=.5kx^2, so the equation becomes 9.558+Wf=.5mV^2+.5kx^2, and because the block's final speed is 0, the equation is 9.558+Wf=.5kx^2. Substituting for the spring constant becomes 9.558J+Wf=.5(590N/m)x^2. I assume that if I could solve for x, I could calculate the total distance traveled, as the spring started at being compressed 18m. Wf should equal Ffriction times L, and I calculated 2.607N for Ffriction, from Fk=MUk(mgcos(theta)). I'm a bit unsure of where to go next, as I seem to have hit a wall; I don't know Wf, x (which equals L-.18), or L (which I'm trying to solve for). Any help is greatly appreciated.

 

[kuruman]

You have correctly found that the block starts with 9.558 J worth of energy. It spends these Joules (a) to buy potential energy and (b) to overcome friction until it stops. Both quantities involve the distance L up the incline. Can you write (a) expressions for each and (b) the energy balance equation?