Question

At an Amazon shipping center, a box of cups of mass 2.6 kg rests on top of a box of dishes of mass 5.5 kg. The boxes are stacked on a rolling conveyer system that is essentially frictionless. However, the coefficient of static friction between the boxes is μs=0.45μs=0.45.

What is the maximum horizontal force that can be applied to the upper box so that the boxes accelerate together, without the upper box sliding on the lower one?

Answer 1

Boxes accelerating together, means both boxes move with same acceleration.

Only horizontal force acting on the lower box is force of friction from the upper block. Force of friction between boxes can not exceed (mu s* mg), where m is mass of upper box. Hence maximum possible acceleration of lower box a(max)= (mu s*mg)/M, where M is mass of lower box.

a(max) = 0.45*2.6kg*9.8m/s^2 / 5.5kg = 2.08 m/s^2

As both box move together, a(max) is maximum acceleration of two boxes, without sliding of upper box over lower. Hence maximum external force on upper box without sliding = (m+M) (a(max) )

= (2.6kg + 5.5kg)*2.08m/s^2 = 16.8 N