Maximum Horizontal Force for Two Blocks to Accelerate Without Slipping?

[Patta1667]

Homework Statement

A block of mass $$M_1$$ rests on a block of mass $$M_2$$ which lies on a frictionless table. The coefficient of friction between the blocks is $$\mu$$. What is the maximum horizontal force which can be applied to the lower ($$M_2$$) block for the blocks to accelerate without slipping on one another?

Homework Equations

The Attempt at a Solution

The acceleration of the two blocks (assuming they're not slipping) is $$a = \frac{F}{M_1 + M_2}$$, and you want the upper block ($$M_1$$) to not slip, that is, the acceleration times $$M_1$$ must be less than or equal to the frictional force. When the blocks start slipping, $$M_1 a = \mu M_1 g$$ where the frictional force holding the upper block is $$f = \mu M_1 g$$. This means that $$a = \frac{F_{max}}{M_1 + M_2} = \mu g$$, or $$F_{max} = \mu g (M_1 + M_2)$$.

I'm not sure if this answer is right, but it makes intuitive sense when looking at the final equation. Thanks for any help!

[edit] Sorry, posted in wrong section. I can't find a delete button, but any help would still be appreciated

 

[dx]

Looks correct.