A truck is traveling at 12 m/s down a hill when the brakes on all four wheels lock. The hill makes an angle θ = 15° with respect to the horizontal. The coefficient of kinetic friction between the tires and the road is 0.7. How far does the truck skid before coming to a stop?

Answer 1

Calculate the friction force using the kinetic coefficient of friction, Uk = .7. Call the friction force Ff

Ff = M*g*cos15*Uk

Let the distance it travels be X

When Ff*X equals the initial kinetic energy plus any gravitational potential energy decrease, all of the available energy will used up as frictional heating work, and the block stops.

Ff *X = M g*cos15*Uk*X
= (1/2) M V^2 + M g X sin 15

Solve for X

X = (1/2) (V^2/g)/[cos15*Uk + sin 15]