A mass M slides across a horizontal table. It collides with a spring, compresses the spring, and then the mass-spring system rebounds. This system can be used to find the spring constant k. When the mass first hits the spring at x = 0, it has speed v0. a.) Let the coefficient of kinetic friction be μk. Assume that the spring plus mass compresses to a distance l, rebounds, and stops when it returns to x = 0, having compressed the spring only once. Use the work-energy relation, Wnon-cons = ΔPE + ΔKE to find the required coefficient of friction μk in terms of l, v0 and g. b.) Next, consider just half the cycle, with the mass starting out with speed v0 at position x = 0, and stopping (for an instant) at x = l. Use the work-energy relation once again to find a relation between k, l, v0, μk, and g. c.) Use the results of parts (a) and (b) to solve for the spring constant k in terms of v0, μk, and g.