A crate of mass 38.0 kg is being transported on the flatbed of a pickup truck. T

Question

A crate of mass 38.0 kg is being transported on the flatbed of a pickup truck. The coefficient of static friction between the crate and the truck's flatbed is 0.280, and the coefficient of kinetic friction is 0.160. (a) The truck accelerates forward on level ground. What is the maximum acceleration the truck can have so that the crate does not slide relative to the truck's flatbed? (Give the magnitude of the acceleration.) m/s2 (b) The truck barely exceeds this acceleration and then moves with constant acceleration, with the crate sliding along its bed. What is the acceleration of the crate relative to the ground? (Give the magnitude of the acceleration.)

Explanation / Answer

Answer :

The crate will not move as long as the force exerted through the motion of the truck is less than the static friction between the crate and the flatbed. However, once this is overcome, the crate is no longer subject to static friction but to kinetic which is usually less than static. In other words it is more difficult to get something moving than it is to keep it moving.

(a) You need to balance the force from static friction with that provided on the crate by the forward motion of the truck.

Us = coefficient of static friction
Fs = static friction = (normal force)*Us = m*g*Us

Force pulling the crate = mass * acceleration = m*a

Equate the forces.
m*a = m*g*Us
a = g*Us = 9.81*0.28 = 2.7468 m/s^2

So the acceleration of the truck is 2.7468 m/s^2

(b) We now need to use the coefficient of kinetic friction in the above equation and then take the difference with the forward force to get the net acceleration. I will use the fact that the crate is still up to a maximu acceleration of g*Us (see above).

Uk = coefficient of kinetic friction
Fk = kinetic friction = m*g*Uk
g*Uk = acceleration due to friction

net acceleration = forward minus friction = g*Us - g*Uk = g(Us - Uk)
a = 9.81(0.289 - 0.160) = 9.81*0.129
a = 1.1772 m/s^2

So the acceleration of the crate relative to the ground is 1.772 m/s^2 and it is in the same direction as the truck is moving.

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