Solve Dynamics: Acceleration with F=52 N, µ=0.22, m1=4.3 kg, m2=1.1 kg

[PhysicsUSAAOK]

This question is tricky, but I would appreciate anyone who could actually solve it

The lower block, shown, is acted on by a force, F, which has a magnitude of 52 N. The coefficient of kinetic friction between the lower block and the surface is 0.22. The coefficient of kinetic friction between the lower block and the upper block is also 0.22. What is the acceleration of the lower block, if the mass of the lower block is 4.3 kg and the mass of the upper block is 1.1 kg?

(picture a wall with a pulley sticking out;
there are two blocks, a bigger one and a smaller one sitting beside the pully;
the smaller block rests on the bigger block
they are attached by rope, but the rope passes thru the pulley first; (so u can sense pulling one, makes other go the opposite way right)
umm that's about it, two blocks on each other, connected by sideways pully, and the bottom block is being pulled away from wall so top block slides towards wall on top of larger block)

 

[Fermat]

Basically you're just applying Newton's 2nd law to the two blocks.
Figure out the forces acting on the blocks, then set F=ma for the two blocks and solve for a.

The tricky bit is at the interface of the two blocks.
There is friction between the two blocks.
The friction force, from the botom block upon the top block, is directed away from the wall.
The friction force, from the top block upon the bottom block, is directed towards the wall.
Remember to include the tension(s) in the pulley rope.

I get the acceleration, a, a bit less than g.