Conceptual Problem with Friction FBD.

[Sarin]

here is the scenario:

there are 2 blocks A & B, both have the same mass 'm'.
block A is kept on an endless surface.
there is no friction between the block A and the surface.
now the other block, B, is kept on top of the block A.
the coeff of friction between A & B is say 'u'.
the limiting friction between A & B is therefore = umg = 'f'.
now say i apply a force 'F', equal to 'f', on the block A, i.e F = f.

What will be the FBD's for A and B.

I did the FBD for B & A and i am getting f = 0 = F , which is not possible since f = umg.
So I think i have made some mistake.

And I am not saying that A and B are necessarily stationary initially, they could be moving with a uniform velocity.

Is this suggesting that since there is no relative motion between A & B therefore there is no friction existing. If this is the case then isn't this contradicting the fact that B moves with A
(with a relative velocity = 0) due to friction when a force is applied to A and that if friction was not present A would just slide past underneath B and B would just fall to the ground.
kindly help me out with this!

Thanks.

 

[Doc Al]

the limiting friction between A & B is therefore = um = 'f'.
now say i apply a force 'F', equal to 'f', on the block A, i.e F = f.

Realize that the limiting friction is not necessarily equal to the actual friction force.

If you push A with a force equal to μmg, then the friction acting between the masses will be only half that.

 

[Sarin]

Realize that the limiting friction is not necessarily equal to the actual friction force.

If you push A with a force equal to μmg, then the friction acting between the masses will be only half that.

not sure i understand what you're saying.

 

[Doc Al]

not sure i understand what you're saying.

Try this: Assume that you push block A with a force equal to μmg. What will be the acceleration of the two-block system? Use that to figure out the friction force.