Can I figure out the force exerted on an object if i know

[grandpa2390]

Homework Statement

a block is sliding down an inclined plane that is resting on a frictionless terrain. so as the block slides down the ramp, the ramp also moves. Calculate the force exerted by the block on the plane.

I have the mass of both the object and the plane as variable m and M, the angle of contact theta, and using Lagrangians (or is it Hamiltonians... I am not quite sure at this point of the difference. feel free to explain that to me for extra credit lol :) but using L = T-U I have found the equation for the acceleration of x and X.

Homework Equations

f=ma

The Attempt at a Solution

I am thinking that I just need to say F=ma. the force required to accelerate the the inclined plane to the left is its mass M times its acceleration. That will give me the x component of the Normal Force acting on the Inclined plane by the block. Then using trigonometry, I can solve for the Normal Force. and I believe that is what the problem is looking for.
I am not entirely sure though. a little voice in my head is telling me that that is too easy. that maybe the mass of the little block should also be a factor in calculating the required force. (the mass is present in the equation of acceleration btw, but I am not sure if it should be part of the m in the F=ma equation.).

What do you think? is my first impulse a very wrong oversimplification... or is it fine?

 

[Jazz]

To be sure, you can draw a free body diagram. The Normal Force acts perpendicular to the incline, but the ramp does not slip in the direction of the Normal Force.

 

[grandpa2390]

To be sure, you can draw a free body diagram. The Normal Force acts perpendicular to the incline, but the ramp does not slip in the direction of the Normal Force.

what do you mean? it does slip in the direction of the normal force doesn't it? if the block slides down to the right and the ramp slides to the left.

 

[Jazz]

what do you mean? it does slip in the direction of the normal force doesn't it? if the block slides down to the right and the ramp slides to the left.

The ramp does not slide down to the left, but straight to the left instead (the Normal Force is not straight to the left). There must be a (component) net force toward that direction that is being supplied by the block.

 

[grandpa2390]

what do you mean? it does slip in the direction of the normal force doesn't it? if the block slides down to the right and the ramp slides to the left.

well of course. hence why I said it would be the x component of the normal force. but is that all I need to do. I don't have to factor in the mass of the small block or do another lagrangian or anything?

 

[Jazz]

As far as I understand the problem, nope. You don't need to do anything else.

As long as the box is on the incline, only the horizontal component of the normal force will make the ramp to move to the left (until the lower right edge of the box reaches level ground).

 

[haruspex]

well of course. hence why I said it would be the x component of the normal force. but is that all I need to do. I don't have to factor in the mass of the small block or do another lagrangian or anything?

As a check, how about you post your answer as an algebraic expression?