I had to solve a question regarding the maximum force that can be applied on the upper of two stacked blocks for the blocks to move together (there is friction between the two blocks). I managed to solve the question, but am a bit confused conceptually.
When we consider a block on the ground that is pulled with a force $F$ (not larger than the maximum static friction), we say that the static friction force equals $F$ and so the block does not move. In the case of the stacked blocks here, as I understand it, F on the upper block does not produce an equal static frictional force. It seems like the force of static friction between the blocks here adjusts according to the F and the masses of the two blocks to ensure that the blocks have the same acceleration. Therefore, until a maximum F (where static friction is max), the two blocks will always accelerate together as the friction between the blocks takes up values such that this happens. Below this F, there is no possibility for the blocks to slide with respect to each other.
Is this understanding correct? It confuses me to think of static friction adjusting in such a complex manner (according to masses of the blocks and F) to allow joint movement of the two blocks. It seems like friction is ensuring there is no relative movement, instead of us explaining no relative movement via friction (if that makes sense).