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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???

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marked as duplicate by garyp, user36790, John Rennie newtonian-mechanics Sep 5 '16 at 6:33

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ this same ques have been asked before(2years ago) but no one was able to explain this $\endgroup$ – Pratyush Rohilla Sep 4 '16 at 20:05
  • $\begingroup$ Why do you assume that the force and friction should be equal? $\endgroup$ – Steeven Sep 4 '16 at 21:30
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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.

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  • $\begingroup$ Yes in this case both the blocks are not moving relative to each other but when we draw the F.B.D of upper block then force of friction is taken less than the applied force bu as in here there is static friction so frictions magnitude should be equal to force applied @user55515 $\endgroup$ – Pratyush Rohilla Sep 14 '16 at 20:23

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