A crate, initially traveling horizontally with a speed of 18 ft/s, is made to slide down a...

A crate, initially traveling horizontally with a speed of 18 ft/s, is made to slide down a 14 ft chute inclined at 35°. The surface of the chute has a coefficient of kinetic friction μk, and at its lower end, it smoothly lets the crate onto a horizontal trajectory. The horizontal surface at the end of the chute has a coefficient of kinetic friction μk2. Model the crate as a particle, and assume that gravity and the contact forces between the crate and the sliding surface are the only relevant forces.

Figure P4.48

Let μk = 0.5 and suppose that once the crate reaches the bottom of the chute and after sliding horizontally for 5 ft, the crate runs into a bumper. If the weight of the crate is W = 110 lb, μk2 = 0.33, and you model the bumper as a linear spring with constant k and neglect the mass of the bumper, determine the value of k so that the crate comes to a stop 2 ft after impacting with the bumper.