# two block problem in friction [duplicate]

This is a seemingly basic mechanics problem but I'm having a dilemma in understanding what happens. You start with two blocks, one on top of the other (the bottom block has a larger mass than the top block). There is friction between the blocks, so they stick together. These two blocks rest on a frictionless surface. If I apply a force F to the top block, what happens?

Drawing the free body diagram, the force F I apply is counter acted by a frictional force f because of the friction between the two blocks. Additionally, this frictional force will be opposed by another frictional force on the bottom block that forces it in the direction I applied the force. Thus, we see that the blocks will move in the direction I have pushed.

HOWEVER, I can't understand why the top block will move forward as well. The force I have applied should be negated by the frictional force, but this is not the case. Clearly, the block accelerates forward despite the friction. Why is this paradox created???