Calculating Center of Mass: 2 Bodies, Unequal Masses

[supercali]

[SOLVED] center of mass

Homework Statement

2 bodies m1 and m2 are hanged from the ceiling with a thread with length L. the bodies are also connected to one another with a thread which length is equal to the length from the masses to the hanging point. around that thread there is a spring contracted and its mass can be neglected. the potential eng. of the spring is U. at a certain moment the thread between the mass m1 and m2 is being torn and the spring pushes the masses. what is the hightest height that m1 can go up to relatively to the first place it was
attched a scheme of the problem

Homework Equations

The Attempt at a Solution

i thought of using the concept to center of mass and say that the center went up...but i don't really know how to implement this...
please help if you can

 

[Doc Al]

Hint: When the thread is cut and the spring expands, what is conserved? Find the speed/energy of m1 just after the spring expands.

 

[supercali]

Hint: When the thread is cut and the spring expands, what is conserved? Find the speed/energy of m1 just after the spring expands.

the momntum is being conserved but my problem is kind of how to relate to m2 and its affect in the system

 

[Doc Al]

That's right: The total momentum of m1 and m2 is conserved. What's the total energy of m1 and m2 after the expansion?

 

[supercali]

according to the laws of energy the equation should be
$$h=\frac{U}{g(m_1+m_2)}$$
i don't think this is the answer though

 

[Doc Al]

It's not. How did you derive this answer?

 

[supercali]

I did energy coservation...
again i find it hard with this m2 cause i don't really know what to do with it
with the momentum equation i hve 2 different speeds one of m1 and another of m2
maybe i didnt understand this well

 

[Doc Al]

Show exactly how you did it. To do it correctly, you need both energy conservation and momentum conservation.

 

[supercali]

woowowowo
without too many hints i must say you really helped me
the answer is
$$h_1=\frac{m_2U}{gm_1(m_1+m_2)}$$

thanks