How Do You Calculate Forces and Accelerations in a Two-Block System?

[Dweirdo]

Homework Statement

A triangle shaped moving block of mass M2 is pushed by force F , a block of mass M1 is on the other block, a)what should be the F force so that the block will be in rest relative to M2?
b)what should be the Acceleration of M1 so that the block M2 will move up on the block M1 in an acceleration of A2?
c)what should be the Acceleration of M1 so that the block M2 will move down on the block M1 in an acceleration of A2?

Homework Equations

F=ma... etc
equivalence principle can help here as well...

The Attempt at a Solution

K, a) is done for me, easy, solved it in two ways 1)equivalence principle(elegant way),
2)using D'Alembert's principle and some Newton's laws.

now b) ffs! I hate it, nothing that I do works! nothing that I could think off,damnit!
the main thing that bothers me is that they don;t have the same acceleration now!

So If some 1 can point me in the right direction/hints or W\E that will help me finish this problem.
this is an epic sketch> I will add a normal one if it is needed.
| \
| \
| \M2
|M1\ pushed to the right-------->>>

so thank You!

 

[diazona]

I think we need that in monospace

| \
|  \
|   \M2
|M1  \       pushed to the right-------->>>

Anyway: the straightforward way is probably just plain old free-body diagrams. You know the force on the smaller block has to be $$m_2 a_2$$ directed upward and to the left, so just draw the diagram and instead of making the forces balance, let there be a difference of $$m_2 a_2$$ in that upward direction. Then I guess you could figure out what the excess force on the larger block is and divide by its mass to get its acceleration.

Alternatively, since you mentioned D'Alembert's principle: if you're familiar with the Euler-Lagrange equation, you could try using that with the displacement of the smaller block along the ramp as one generalized coordinate. I'm not sure offhand whether this or the free-body diagrams would be easier to work out.

 

[Dweirdo]

"if you're familiar with the Euler-Lagrange equation"
Nope,Haven't studied it yet :<
do the bodies have the same acceleration in the X direction(right direction)??

 

[Dweirdo]

OK It's done, thank You for your hep.
but there are more questions on this problem , ill write them later :D
so thanks