What Is the Velocity of an Inclined Plane as a Block Slides Down?

[varunKanpur]

Hello Friends, I am not able to solve a problem of my textbook
A block of mass m slides on a inclined plane of mass M, then What is the velocity of inclined plane when mass m reaches the ground ? ("All surfaces are friction less and the height of inline plane is H and the angle of inclination from ground is a.")

I am am to solve this problem by using force concept but its very long.
I am trying to find a way to solve this problem by using conservation of momentum as there is no force acting in x-axis.

Thanx in Advance

 

[nasu]

Have you seen this thread? It's the same problem, isn't it?
https://www.physicsforums.com/showthread.php?t=717478&highlight=inclined+plane

 

[Chestermiller]

Hello Friends, I am not able to solve a problem of my textbook
A block of mass m slides on a inclined plane of mass M, then What is the velocity of inclined plane when mass m reaches the ground ? ("All surfaces are friction less and the height of inline plane is H and the angle of inclination from ground is a.")

I am am to solve this problem by using force concept but its very long.
I am trying to find a way to solve this problem by using conservation of momentum as there is no force acting in x-axis.

Thanx in Advance

Let N₁ represent the (normal) force that the mass M exerts on m, and Let N₂ represent the (normal) force that the ground exerts on the inclined plane. Now draw free body diagrams for both m and M that show the forces acting on these masses. Write force balances in the horizontal and vertical directions for each of the masses.