Block colliding with movable ramp

[ionic_scream]

Homework Statement

http://img360.imageshack.us/img360/8953/ramppd7.png
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.

Homework Equations

m1v1i + m2v2i = v1(m1 + m2)

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

 

[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.

 

[thomate1]

.I would approach this problem by first analyzing the forces acting on the block and the ramp. The block has a normal force from the surface it is sliding on, as well as a gravitational force pulling it downward. The ramp also has a normal force from the ground, as well as a normal force from the block pushing against it.

Next, I would use the equations of motion to analyze the motion of the block and the ramp. Since the surface is frictionless, the only force acting on the block in the horizontal direction is the normal force. This means that the acceleration of the block in the horizontal direction is zero. In the vertical direction, the block will experience a constant acceleration due to the gravitational force.

For the ramp, since it is initially at rest, we can use the equations of motion to determine its velocity as it moves up the ramp. The normal force from the block will provide a force in the horizontal direction, causing the ramp to accelerate. Once the block reaches its maximum height, the normal force from the block will disappear and the ramp will continue to move with a constant velocity.

Using the equations of motion, we can determine the velocity of the ramp at the instant the block reaches its maximum height (part a), the maximum height the block will reach (part b), and the final velocities of both the ramp and the block (part c).

I would also consider the conservation of energy in this system. The block gains potential energy as it moves up the ramp, and this energy is transferred to the ramp as it moves up. When the block reaches its maximum height, all of its potential energy is transferred to the ramp, and the block will have no kinetic energy. This means that the final velocities of the ramp and the block will be determined by the conservation of energy equation.

In summary, as a scientist, I would approach this problem by analyzing the forces and using the equations of motion to determine the velocities and heights involved. I would also consider the conservation of energy in this system to confirm my results.