# Homework Help: Cons. of momentum and cons. of energy

1. Oct 28, 2008

### musicfairy

Particle A and particle B are held together with a compressed spring between them. When they are released, the spring pushes them apart, and they then fly off in opposite directions, free of the spring. The mass of A is 5.00 times the mass of B, and the energy stored in the spring was 63 J. Assume that the spring has negligible mass and that all its stored energy is transferred to the particles. Once that transfer is complete, what are the kinetic energies of each particle?

What I did:

0 = m1v1 + m2v2

m1 = 5m2

v1 = .2v2

U = K1 + K2

I got stuck here. I'm not given v or m. What am I supposed to do?

2. Oct 28, 2008

### LowlyPion

You are given PE and you know the relationship between the velocities basically from Newton's Third Law - action = reaction and from that you figured the Velocity of the heavier is 1/5 that of the the lighter one. (Though I note that it's really v1 = -1/5*v2.)

So you know that the KE of the system is 63 J after the spring unloads.

You also know that

0 = m1v1 + m2v2

m1v1 = - m2v2

Multiply both sides by the identity that v1 = - 1/5 V2

m1v12 = 1/5 * m2v22

Now look at your PE = KE1 + KE2 = 1/2 * m1v12 + 1/2 * m2v22

But we can substitute using the previous relationship and get:

PE = 1/2 * 1/5 * m2v22 + 1/2 * m2v22

63 J = 6/5 * 1/2 * m2v22

Last edited: Oct 28, 2008
3. Oct 28, 2008

### musicfairy

Thanks for the explanation.

Using the final equation you gave me, I was able to get the correct answer.

Earlier I substituted into U = K1 + K2 and got the right answer, except I switched the kinetic energies of A and B. Problem solved.

Once again, thanks a lot for the explanation. I understand the concepts better now.

4. Nov 1, 2008

### p21bass

Just wanted to thank you both. I was having a heck of a time with a problem that was very similar to this. I had tried to use the principles of energy, but was getting stuck. Pion's explanation was very helpful.

5. Nov 1, 2008

### LowlyPion

Welcome to PF.

Glad you found it of value.

Cheers.