Gravitation & Conservation of Momentum and Energy

[blackheart]

1. Two spheres having masses M and 2M and radii R and 3R, respectively, are simultaneously released from rest when the distance between their centers is 12R. Assume the two spheres interact only with each other and we wish to find the speeds with which they collide. Write an equation from one of the models and solve it for v1, the velocity of the sphere of mass M at any time after release in terms of v2, the velocity of 2M.

2. Fg = Gm1m2/r^2

Change in E = E

3. Do I just use conservation of energy?

E = K + U

Ei = 0 + [G(M)(2M)]/(R^2)

Ef = 1/2Mv1^2 + 1/2(2M)v2^2 + 0

change in E = [1/2Mv1^2 + 1/2(2M)v2^2] - [G(M)(2M)]/(R^2)
This equals 0 since there are no nonconservation forces doing work.
change in E= Wnc = 0

My answer is sqrt(M/36R - 2v2^2)

This is confusing me because it asks for v1 in terms of v2 and I have R in the answer. How do I solve it without R?

 

[blackheart]

I also have to solve this using conservation of momentum.

Mv1i+2Mv2i = Mv1f + 2Mv2f

I don't get how to solve this for v1 in terms of v2 when I don't know initial or final velocities.