A COM, Linear Momentum Problem

[Avi1995]

Homework Statement

A Block of mass m is placed on a triangular block of mass M(as if Fig).Assuming Frictionless surfaces find the velocity of the triangular block when the smaller Block reaches the bottom end.

2. Relevant concepts

Centre of Mass,Linear Momentum and probably Conservation of energy concepts

The Attempt at a Solution

I confess , I am quite confused visualising this one. especially the velocity of Big and small black,as
small block is on top of big block so the big block's velocity will also effect the small block.
Any Hint to start, is appreciated.Also Please tell how to visualize these situations. :(

 

[Doc Al]

Rather than worry about the speed while the block is on the incline, just consider things after it slides off. Apply conservation of momentum and energy.

 

[Avi1995]

Rather than worry about the speed while the block is on the incline, just consider things after it slides off. Apply conservation of momentum and energy.

But the problem says when it reaches the bottom end, isn't it before it slides off?

 

[Doc Al]

But the problem says when it reaches the bottom end, isn't it before it slides off?

In that case it's a tad more complicated, but still the same basic idea. I would call the speed of the block with respect to the wedge v₁. Then consider conservation of momentum and energy. (Hint: How would you express the speed of the block with respect to the ground? Call the speed of the wedge with respect to the ground V₂.)

 

[Avi1995]

Thank you so much, Sir. I was finally able to solve the problem using your method.
Although I won't be able to post the solution as it is quite long but the method is same.

PS: Can anyone tell me some good FREE Mathematics Software, so that i am able to write equations easily and graph some functions. I have Microsoft Maths, but I don't quite like it.