What is the Critical Value of Friction for a System of Blocks to Move Together?

[rwx1606]

Homework Statement

So I have a system with 3 blocks, one small block is on top of the bigger block and another small block is on the left side of the bigger block. You apply an external force to the block on the side such that the system accelerates together. Assuming there is a friction force between the blocks and no friction between floor and the bigger block, the question asks if the coefficient of static friction is less than some critical value, then no matter how hard how you push the system the blocks will not move together. Why?

Homework Equations

F=Ma

The Attempt at a Solution

I know the harder you push, the greater the normal force will be between the small block on the side and the bigger block. I also know that it's friction that allows the block on top to accelerate with the big block. But looking at the questions, I can't see why if you decrease the coeff. of static friction you can't increase the force? Is it because if the coeff. of friction is so small, it would required an infinite force to keep the block on the side from sliding down and to keep the block on top stationary with respect to the bigger block?

 

[tiny-tim]

… to keep the block on the side from sliding down …

uh? sliding down what?

 

[rwx1606]

sliding down the side of the bigger block.

 

[tiny-tim]

sliding down the side of the bigger block.

what shape is this block?

 

[rwx1606]

square.