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 P4.47

Find μk such that the crate’s speed at the bottom of the chute (immediately before the crate’s trajectory becomes horizontal) is 15 ft/s.