# Center of mass

1. Dec 16, 2007

### supercali

[SOLVED] center of mass

1. The problem statement, all variables and given/known data
2 bodies m1 and m2 are hanged from the ceiling with a thread with lenght L. the bodies are also connected to one another with a thread which length is equal to the lenght 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
2. Relevant equations

3. The attempt at a solution
i thought of using the concept to center of mass and say that the center went up....but i dont really know how to implement this...

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Last edited: Dec 16, 2007
2. Dec 16, 2007

### Staff: Mentor

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

3. Dec 16, 2007

### supercali

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

4. Dec 16, 2007

### Staff: Mentor

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

5. Dec 16, 2007

### supercali

according to the laws of energy the equation should be
$$h=\frac{U}{g(m_1+m_2)}$$
i dont think this is the answer though

6. Dec 16, 2007

### Staff: Mentor

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

7. Dec 16, 2007

### supercali

I did energy coservation....
again i find it hard with this m2 cause i dont 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

8. Dec 16, 2007

### Staff: Mentor

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

9. Dec 16, 2007

### supercali

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