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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???

Pratyush Rohilla
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You seem to be assuming that the friction force f between the two blocks is equal in strength to the force F you push with. It won't be. f will be weaker than F and the top block will indeed accelerate forward.

I see two cases to consider: The two blocks may stay locked together by static friction and move together as a unit, or if you push hard enough the top block will slide forward on the lower block and both of them will travel forward but with different accelerations.

user55515
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