# A mass-spring system with recoil and friction

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

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?