# Spring in between two masses

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1. Jan 24, 2016

### kyrillos

Let's say there are two masses, attached together by a string, and there's a compressed spring in between them. When the string in between is cut off, the spring unloads, pushing both masses in opposite directions.

My thinking:
1. Their momentums will be equal to each other.
Their momentum before the string is cut is equal to zero (because they were not moving). So the sum of their final momentums should be also zero.
2. Their kinetic energies will be equal to each other.
The spring unloads in both direction at equal rates, so I assume that their kinetic energies must also be equal. (I couldn't find a mathematical evidence in my Giancoli book to see if I am actually right)

Are my conclusions right?

2. Jan 24, 2016

### Staff: Mentor

Yes, that is correct.

This is only correct if the masses are equal. Can you think what will happen if the masses are not equal?

3. Jan 24, 2016

### kyrillos

Well:
0 = m1v1 + m2v2
v1 = -m2v2/m1

And:
0.5m1v12 + 0.5m2v22 = 0.5kx2

I don't know what to do next, since I also don't know the value of the elastic potential energy. Could you help me?

4. Jan 24, 2016

### Staff: Mentor

You can just leave the elastic potential energy as you have written it. So the next step is just to substitute

into
and then solve for the velocity.

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