Physics help needed?

Question

A box of mass, m is on top of a box of mass M. There is friction between the surfaces of the two boxes, 
but no friction between the large box and the table. A force F is applied to the large box as shown.

a) You apply a force, F, so that the two boxes move together (i.e. the top box doesn’t slip). Draw a 
free body diagram of the forces acting on each box (i.e. you should have two FBDs, one for each 
box). (2 marks)

b) For the situation in (a), solve Newton’s equations for the acceleration of the system? (4 marks)

c) Now you want to apply a large enough force to just keep the top box from slipping. Solve for 
the maximum force you can apply, Fmax, before the top box just begins to slip? (4 marks) 
(The picture in the question is just a box on the ground with a small box on top with an arrow coming out of big box and going to the right titled F for force)

Dr. Zorro · Accepted Answer

(a) there are two (horizontal) forces acting on the bottom box: applied force F to the right and friction force from the top box to the left. On the top box only the force of friction (from the bottom box) acts to the right. Of course there are also the vertical forces from gravity (weight) and normal forces.

(b) no slip, so both boxes move with the same acceleration a. Total mass accelerating is (M+m), total (external) force F, so

a = F/(M+m)

(c) the maximum static friction force to accelerate m is μ m g, so the maximum acceleration for m is

a_max = μmg / m = μ g

The maximum force we can apply therefore is

Fmax = (M+m) μ g

Trending News

Physics help needed?

1 Answer