Tricky Collision Problem: Solving for Block Masses and Heights

[jj2443]

1. Homework Statement
A small hard block of mass 3m is suspended from a thread of length L. A second block of mass m is located on an incline, originally at rest, a height y above the level of the large mass. When the smaller block is released it slides, without friction, down the ramp, and then collides elastically with the larger block. The large block swings around so that the tension in the string just barely drops to zero at the top of the loop. The small block slides back up the ramp, rising to a maximum vertical height h.


2. Homework Equations
conservation of momentum: pi=pf
p=mv


3. The Attempt at a Solution
...help to get started please!??

 

[AEM]

This is a nice problem --lots of good stuff in it! Start with conservation of energy to compute the velocity of the smaller block just before it hits the larger block. Then you can use your conservation of momentum and, since the collision is elastic, conservation of energy to calculate the velocities of the blocks after collision. Finally, the kinetic energy of the larger block goes into its potential energy at the top of its swing.

All good stuff. Just break the problem into pieces.

 

[jj2443]

So far I've come up with:

GPE=KE
m(10)y = (1/2)mv^2
v= sqrt(20y)

p1=m*sqrt(20y)
p2= 3mv+mv2

ehh something can't be right, anyone want to help me with the algebra?
thanks a lot!

 

[denverdoc]

First, you want to keep your velocities clear as the v in p2 is not the same as the v in p1. Let's call the velocity of the larger block v1 and the velocity of the small block as it strikes the bigger block v0.

You also know more about the velocity and energy of the big block by what happens subsequently.