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I was trying to solve a problem, where we had two masses stacked on top of each other. A force was applied on the lower mass, towards the right side. If we assume, the surface between the ground and the system is smooth, and the surface between the two blocks is rough, I face a small confusion.

Note that my confusion is not related to how to solve the problem, it's regarding an intuitive understanding of how friction works.

If the net acceleration of the lower block is toward the right, then the lower block would experience some friction toward the left, opposing the motion.

The upper block will thus experience some friction toward the right, which will accelerate it toward the direction of the moving block. This second part is what confuses me the most.

First of all, why does the upper and lower blocks experience friction in opposite directions? Secondly, this system has been compared to the following: Imagine the lower block moving to the right. This is the same as the upper block moving to the left, and hence the friction on the upper block works towards the right, making it move in the direction of the lower block. But, if the upper block moves to the right now, shouldn't friction work to the left again, and cancel out this motion, keeping the upper box fixed in its place, until it falls down ?

How does friction create motion ? Isn't it supposed to oppose the motion ?

I've done the necessary FBD and convinced myself this is what happens, but intuitively, I'm unable to make sense of this. How does the two-block experience friction in opposite directions, and more importantly, how does friction make one of them move, if friction is supposed to oppose motion?

Are these opposing directions of friction for the two blocks, just mere consequences of the third law ?

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Friction doesn't oppose motion, exactly. Frictional forces oppose relative motion of two bodies that are in contact. If two bodies in contact are moving relative to each other, then each body will experience a force in the opposite direction of its relative velocity with respect to the other body.

Static friction works the same way. It will act in whatever direction is necessary to keep two bodies from moving relative to each other, so long as the magnitude of the force required to do so does not exceed a particular limit determined by the normal force and the coefficient of static friction. In your example, it is necessary for static friction to push the top block to the right in order to keep the surfaces from moving relative to each other, and so that's what the static friction does.

And yes, the fact that frictional forces are in opposite directions is just a consequence of Newton's Third Law.

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What would tend to happen if the surfaces were smooth and frictionless? The bottom block would accelerate while the top block stays static and just drops down. This is the tendency of the system: the impending motion of the top block relative to the bottom block is leftward relative to the bottom block.

Now if you have static friction, the blocks effectively behave as one rigid body together, with the friction force arising from an interfacial shear stress between blocks. You can consider the net effect of the shear stress as a constraint force, because the tendency of the top block is to stay in place relative to the bottom block due to its own inertia. Therefore, the constraint friction force enforces rigidity of the system and forces it to move as one.

Consider a rigid body at rest. All parts of the rigid body have inertia and therefore tend to stay at rest. When I supply a singular force at one material point in the rigid body, why doesn't just that material point accelerate? A system of constraint shear stresses develops throughout to enforce rigidity and pull forward other parts of the body.

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