A mass-spring system with recoil and friction

[Trojanof01]

An object of mass m is traveling on a horizontal surface. There is a coefficient of kinetic friction, mu , between the object and the surface. The object has speed v when it reaches x=0 and encounters a spring. The object compresses the spring, stops, and then recoils and travels in the opposite direction. When the object reaches x=0 on its return trip, it stops.


Find k, the spring constant.
Express k in terms of mu, m, v, and g .

Any ideas how on setting this up? KE1 + SPE1 = KE2 + SPE2 is where I'm headed...

 

[Hootenanny]

Your on the right track with conservation of energy, however, don't forget the energy dissapated due to friction.

 

[Trojanof01]

This is what I've done so far

Work-energy theorem: E_f-E_i=W_fr:

0-(1/2)*m*v^2=- mu*m*g*2*x

x = .5v^2 / (2g(mu)) Max compression of spring

W=-mu*m*g*x

E_i=(1/2)*m*v^2 )

E_f=(1/2)*k*x^2

Work-energy theorem:

(1/2)*k*x^2-(1/2)*m*v^2=-mu*m*g*x

Plugged into x and solved for k and got 2m(mu)g...answer was incorrect. Any ideas?