An object of mass m is traveling on a horizontal surface. There is a coefficient of kinetic friction μ 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.
a) Find k, the spring constant. Express k in terms of µ, m, g, and v.