Find the velocity

1. Sep 13, 2012

utkarshakash

1. The problem statement, all variables and given/known data
I have attached a picture. The question is in the diagram itself.

2. Relevant equations

3. The attempt at a solution
I tried to solve it by drawing free body diagrams and writing the equations but that seemed enormous and complex too and it seems that it will take a lot of time to solve it by that method. I know that this problem requires me to apply conservation of momentum and energy conservation principle but how? No doubt it can be solved by the traditional method but it would be too long and calculations will be extremely complex. There must be some easier way to do this.

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2. Sep 13, 2012

cmmcnamara

Can you write the equations for energy at the two states of the system, before and after the slide?

3. Sep 13, 2012

utkarshakash

If I assume the final velocity of wedge to be v$_{w}$ and of block to be v$_{b}$ wrt ground then using conservation of energy

mgh=(Mv$_{w}$$^{2}$)/2+(mv$_{b}$$^{2}$)/2

Now what to do next?

4. Sep 13, 2012

Saitama

5. Sep 14, 2012

utkarshakash

I know that I have to apply conservation of momentum. But I don't even know the velocities. I have only assumed them according to my convenience. Nevertheless if you want me to try using that here's it

Along X-axis(taking left direction as -ve)
$\vec{P}_{initial}$=0
$\vec{P}_{final}$=-Mv$_{w}$+???????????

Here the problem arises. I don't know what is the velocity of block in the x-direction. How do i proceed?

6. Sep 14, 2012

azizlwl

The work done by gravity equal to MgSinθ°d
This energy is tranlated to final kinetic energy at the bottom.
Since both objects experience same force(Newton's 3rd Law), the momentum of for each object is equal and opposite.

7. Sep 15, 2012

Saitama

Assume that the velocity of block when it reaches the bottom is vb. Equate the initial and final momentum. You will get a relation between vb and vw. Use that relation in the energy equation.