# Block colliding with movable ramp

1. Oct 25, 2008

### ionic_scream

1. The problem statement, all variables and given/known data
http://img360.imageshack.us/img360/8953/ramppd7.png [Broken]
A block of mass m slides at velocity vo across a horizontal frictionless surface toward a large curved movable ramp of mass 3m as shown in Figure 1. The ramp, initially at rest, also can move without friction and has a smooth circular frictionless face up which the block can easily slide. When the block slides up the ramp, it momentarily reaches a maximum height as shown in Figure II and then slides back down the frictionless face to the horizontal surface as shown in Figure III.

a. Find the velocity v1 of the moving ramp at the instant the block reaches its maximum height.

b. To what maximum height h does the center of mass of the block rise above its original height?

c. Determine the final speed vf of the ramp and the final speed v' of the block after the block returns to the level surface. State whether the block is moving to the right or to the left.

2. Relevant equations
m1v1i + m2v2i = v1(m1 + m2)

3. The attempt at a solution
For part "a" i tried
m1v1i + m2v2i = v1(m1 + m2)
mVo = V1(m +3m)
Vo = 4mV1
V1=(Vo/3m)

But this just doesn't seem right to me. Since the block gains potential energy as it goes up the ramp. Does this mean that I need to use energy equations with conservation of momentum? I'm at a loss with this problem

Last edited by a moderator: May 3, 2017
2. Oct 26, 2008

### heth

Your solution to part a looks fine (apart from the typo in the final line, which is probably why you feel uneasy about the solution).

You're right that you'll need to use energy conservation. Is there anything in the question to indicate that there's anything other than mechanical energy (kinetic or potential) in play here?

If not, then you can play "spot the difference" between figure I and figure II to work out how the block's initial kinetic energy is transferred for part b.