A crate , initially traveling horizontally with a speed of 19 ft / s , is made t

Question

A crate, initially traveling horizontally with a speed of 19 ft/s, is made to slide down a 15 ft chute inclined at 35 degrees. The surface of the chute has a coeff. of kinetic friction uk, and at its lower end it smoothely lets the crate onto a horizontal trajectory. The horizontal surface at the end of the chute has a coeff. of kinetic friction of uk2. Model the crate as a particle and assume that gravity and the contact forces between the crate and the surface are the only relevant forces. Find uk so that the crates speed at the bottom of the chute is 13 ft/s.

Please help!!!

Explanation / Answer

At the top of the chute, the crate will have PE and KE

PE = mgh

KE = .5mv^2

At the bottom of the chute the crate will have KE and some energy lost due to friction

Frictional loss = uFnd = umgcos35d

Thus

mgh + .5mv^2 = umgcos35d + .5mv^2 (mass cancels)

(32)(15)(sin 35) + (.5)(19)^2 = u(32)(cos 35)(15) + (.5)(13)^2

u = .944

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