A 100 kg box of dimensions 50x50x50 cm is located on the center of a truck’s 2 m long flatbed. The coefficients of friction between the box and the bed of the truck: static=0.4 and kinetic=0.2.

Question

A 100 kg box of dimensions 50cm x 50 cm x 50 cm is located on the center of a truck’s 2 m long flatbed. The coefficients of friction between the box and the bed of the truck are static = 0.4 and kinetic = 0.2.

a. Draw a situational diagram and a free body diagram for the box.

b. What is the maximum acceleration the truck can have without the box slipping?

c. Find the time the box remains on the truck’s bed, if the truck starts accelerating from rest at twice the acceleration you found in part b.

Answer 1

b) The maximum acceleration of the truck will be determined by the max static friction that will allow the box to accelerate with the truck:

m_Ba = m_Bgμ_static or a = gμ

c) There could be some debate as whether the truck is off of the bed when it has gone 1.5 m, 1.75 m. or 2.0 m. Let's assume 1.75m, because, at that point, the box tilts and that changes the dynamics of the problem.

The acceleration of the box would equal would be F_{f ,k}/m = mgμ_k/m = gμ_k

d = v₀t + 1/2at² so t = sqrt(2d/a) where a is gμ_s-gμ_k , the acceleration with respect to the truck's acceleration. (It's actually negative of this, but we can make d positive and it will work out)