# Friction between two blocks on top of each other

I am a little bit confused to the concept of friction between two blocks on top of each other. there could be two situations: the first situation is when all surfaces are frictionless including that one between the two blocks. if one force $$F$$ pulls the lower block, then I read somewhere that we should consider both blocks as one block and the upper block will remain at rest and so they have the same acceleration. but still, i don't get why it will remains at rest? second situation: if there is a friction between the two blocks, then applying an F force will make the upper block slide with it's own acceleration. Is this right? and regarding the force needed to make the upper block slide, is there any specifications?

• I don't know where you read that, but I think it actually should be the opposite. If there's friction between the blocks and you start moving the bottom one, both will move as one block as long as friction force is able to "hold together" the two-block system (i.e. until it begins to slide, which you can calculate given $Fr=\mu_sN$). On the other hand, if there's no friction, when you start moving the bottom block there's no force to keep the upper one on place, so it will immediatly start to slide. Do you remember where did you read the opposite? Oct 4, 2018 at 20:51
• Condition for a slide is $$F_{l} > \mu_{s} m_{u} g$$, here l denotes lower block and u - upper block Sep 4, 2019 at 15:17

Most of the confusion that arises in friction problems like this due to not drawing free body diagrams (FBD) showing all forces acting on the blocks.

The FBD below show the two scenarios you posed.

The left figure shows that the only horizontal force acting on the two blocks is the force $$F$$ applied to the lower block. There is no horizontal force acting on the upper block and therefore it does not move. There are no forces resisting motion of the lower block and therefore it moves with acceleration $$a_Y=\frac {F}{M_Y}$$ and slides underneath the stationary upper block and over the ground. The blocks will never move together.

The right figure shows equal and opposite friction forces acting on the upper and lower block. To make things simpler, we are assuming no friction between the lower block and ground.

You need to keep in mind that the friction force always opposes the applied force. Consequently, the friction force varies from zero, when the applied force is zero, to the maximum static friction force shown in the diagram, at which point the applied force causes impending sliding between the two blocks. Up until the maximum friction force is reached, the two blocks move together with the same acceleration ($$a_X=a_Y$$) with respect to the ground. So yes, the upper block will continue to have an acceleration equal to that of the lower block. However, once the applied force, $$F$$, reaches a level such that the static friction force reaches the maximum possible, slippage occurs between the blocks and the friction becomes sliding, or kinetic friction. The kinetic friction force is generally lower than the static friction. If the force $$F$$ is maintained, the acceleration of the lower block will be greater than the upper block.

Hope this helps. • that was a Great explanation, Thanks! but I have a question. it's about the FBD of the upper block when there is a Friction between the two blocks. assuming that the Force applied on the lower body has just reached a magnitude similar to the Fsmax and its direction is right, so for the upper block FBD i will be drawing only the Applied F to right and vertically (Fn& (my+mx)g). I will not draw any friction forces here right!?. and for the upper block, what i don't get when seeing FBDs is that why the Fsmax dircted to right?, even if it was a kinetic friction i see people drawing (continue)..... Oct 5, 2018 at 12:06
• even when drawing the direction of the kinetic friction that draw it (parallel to the applied force in the lower block) why? it's supposed to be opposite to the direction of motion. and i see that the upper block will be moving to the right (relative acceleration) but it appers only that it moves backwards the lower block. but i believe that it moves just the same direction as the lower except that its acceleration is lower so it's slower. that why i don't get why Fk is directed right where is should be directed left! please tell how to think about it Oct 5, 2018 at 12:10
• @SakuReema. Many good questions. Since it is difficult to answer them in the comments format which is very limited, especially regarding math, I will be updating my answer. When I do, please look it over and if it doesn't fully answer your questions, we can follow up with more exchange of comments. Thanks. Oct 5, 2018 at 17:31
• thanks a lot for that. i do appreciate your helping. But I glad to say that I got the idea after studying the situation more and more. i concluded that the friction force also follow the 3rd newton's law, so the lower block will also have friction force to the left( incase moving to right) and the upper one will have friction force to the right. and I learned to decide the dirction of the friction force for the upper one according the movement with RESPECT TO THE LOWER BLOCK. so the lower one moves to right and the upper to left and friction on upper is to right. i hope it's right.thanks again Oct 5, 2018 at 17:37
• @DavidLeonardoRamos See corrections on diagram. Thanks for bringing to my attention. Sep 30, 2019 at 19:49