# Compressed spring between two particles

1. Apr 11, 2015

### AlephNumbers

1. The problem statement, all variables and given/known data
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 2.00 times the mass of B, and the energy stored in the spring was 60 J. Assume 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 (a) particle A and (b) particle B?

2. Relevant equations
Us = (1/2)kx2
K = (1/2)mv2
∑pi = ∑pi

3. The attempt at a solution

Using conservation of mechanical energy, I get
mbva2 + (1/2)mbvb2 = 60 J

Setting the initial momentum equal to the final momentum, I get
2mbva + mbvb = 0

Solving for vb I get
vb = -2va

Substituting that into the energy equation
mbva2 + 2mbvb2 = 60 J

Substituting k for mbva2
k + 2k = 60 J
Particle A has one third of the kinetic energy and particle B has two thirds of the kinetic energy. This seems to make sense since particle B has less mass than A.

2. Apr 11, 2015

### haruspex

Looks right. The body with half the mass will have twice the velocity so twice the energy.

3. Apr 11, 2015

### AlephNumbers

That is what my intuition told me, but I just wanted to make sure. Thank you!