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**1. Homework Statement**

Consider the following situation:

http://img206.imageshack.us/img206/9739/fbdow8.th.jpg [Broken]

**The height of the incline is 'h'.**

a) Find the net acceleration of the centre of mass of the combined system (of the incline and the block) relative to ground.

b) Find the speed of the incline when the block slides down to the bottom of the incline.

**[tex]g=10 m s^{-2}[/tex]**

And all the surfaces are assumed to be frictionless.

And all the surfaces are assumed to be frictionless.

**3. The Attempt at a Solution**

First I would list all the external forces acting upon the system.

1. Mg on the incline due to earth's pull.

2. mg on the block due to earth's pull.

3. The normal provided by the ground to the Incline (M+m)g

As these forces cancel out to zero, the accleeration of th centre of mass of the mentioned system is zero as there is no net external force on the system.

As the block falls down the incline the incline will also move in order to conserve the momentum (which is zero).

The velocity of the block as it reaches the bottom is = [tex]\sqrt{2gh}[/tex] relative to the incline and along the incline. The velocity can be written as [tex]\sqrt{2gh} cos \theta \hat{i}+\sqrt{2gh} sin \theta \hat{j}[/tex]

relative to the incline.

On writing the velocity relative to ground, I get=[tex]\sqrt{2gh} cos \theta - V \hat{i}+\sqrt{2gh} sin \theta \hat{j}[/tex]

Let V be the velocity of the incline in X direction.

Conserving momentum

[tex]m (\sqrt{2gh} cos \theta - V \hat{i}+\sqrt{2gh} sin \theta \hat{j})+MV\hat{i}=0[/tex]

I am confuse now, where does the j component come from. How will I conserve momentum????

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