# Small block with velocity inside a large block at rest

1. Nov 2, 2015

### CoconutFred

1. The problem statement, all variables and given/known data

2. Relevant equations

(Conservation of momentum)
(Conservation of energy)

3. The attempt at a solution

I know linear momentum must be conserved on the X-axis, so

mvo=mv1x+Mv2

where v1 is the final velocity of the small mass and v2 is the final velocity of the large mass. Also, M=2m.

Energy is also conserved, so

(1/2)mvo2=(1/2)mv12+(1/2)Mv22+mgR

Since the problem stipulates that the 2 blocks never lose contact with each other, I'm guessing the momentum in the x direction would actually be

mvo=(m+M)v2

and v2=v1x

But I'm not sure if that is right, and so I'm not totally sure where to go from here.

2. Nov 2, 2015

### Mister T

It looks like you have all the physics in place to solve it. Keep going with the algebra ...

When I solved it I wrote everything in terms of the velocity $\vec{v}$ of the small block, so that

$v^{\ 2}=v_x^{\ 2}+v_y^{\ 2}.$

Last edited: Nov 2, 2015
3. Nov 5, 2015

### J Hann

I don't think that momentum is conserved in the x-direction.
What can one say about conservation of momentum in the y-direction?
Also, the two blocks do not form an isolated system because of the normal
force on the larger block by the frictionless surface.

4. Nov 5, 2015

### Mister T

There are no external forces in the x-direction.
There are external forces in the y-direction.

That normal force is one of the external forces in the y-direction.