Solving the Acceleration of a Rectangular Block on a Triangular Block

[fireemblem13]

I would appreciate any help, even a nudge in the right direction.

Problem: A rectangular block of mass m was put on a triangular block of mass M. (There's a diagram for this, but imagine a right triangle, with a square on the hypotenuse, as it slides down.) Assume all friction forces can be neglected (including between the blocks and between the triangle and the surface.) What's the acceleration of the square block as it slides down, and what's the acceleration of the triangle as it slides away.

I'm thinking the acceleration of the square is gsin(theta). Let the bottom left angle be theta. I know the only force on the triangle is Ncos(theta). So is the acceleration gcos(theta)?

 

[fireemblem13]

I have another problem. These are both bonus problems for my physics class.

One block of mass m is stacked on another block of mass M. Coefficient of friction between table and block is u and between blocks is u. There is a force acting on the lower block. What is the minimum magnitude of force to be applied to the lower block to attain maximum acceleration of the upper block?

I'm not really sure at all. If the move together, then this equation models their movement.
F-f = a(M+m). I'm not sure what to do now.

 

[jegues]

For the second question you're looking for the minimum magnitude of force to which can be applied to the lower block to attain maximum acceleration of the upper block.

Since the 2 blocks move as a system what you're going to want to do is examine the friction between both blocks, and the lower block and the table. I think it's safe to assume that the friction they're referring to is static friction.