Mechanics: mass on moving slope. no friction

[sweep123]

1. Homework Statement
A wedge with mass M rests on a frictionless horizontal table top. A block with mass "m" is placed on the wedge. There is no friction between the block and the wedge. The system is released from rest.

A. Calculate the acceleration of the wedge.
B. Calculate the horizontal component of the acceleration of the block.
C. Calculate the vertical component of the acceleration of the block.
D. Do your answers to part A reduce to the correct result when M is very large?
E. Now, an additional horizontal force F is being applied as shown in part (b) of the figure. What must be the magnitude of F if the block is to remain at a constant height above the tabletop?


2. Homework Equations
F=ma


3. The Attempt at a Solution

I know that if wedge stayed stationary then acceleration of block would be gsin(theta). I know normal reaction must be related to the accelleration of the wedge. I should imagine that mg=M*(acceleration of wedge)+m*(acceleration of block). Does the normal reaction = mgsin(theta)-(M*acceleration of wedge)? I'm really struggling with this one. I think I will be able to manage it if i new how to calculate the acceleration of the wedge. Then I could use Newtons 3rd law to calculate acceleration of block and then continue from there. Any help would be appreciated. Thanks

 

[Bill Foster]

Interesting problem. Where do these people come up with this stuff?

Anyway, I'd begin with a free body diagram, draw force arrows and label them.

In the x-direction, there is the x-component of the Normal force the wedge exerts on the block, and there is an equal an opposite reactive force. Because the surface between the two is frictionless, that force doesn't have to include the mass of the block.

 

[Shooting Star]

Hi sweep123,

This looks like an interesting problem. What happened to the diagram?