# Inelastic Collisions and ratio of their masses

1. Oct 14, 2011

### sleepingarmy

1. The problem statement, all variables and given/known data

Two objects moving in opposite directions with the same speed undergo a totally inelastic collision, and half the initial kinetic energy is lost. Find the ratio of their masses, m1/m2.

2. Relevant equations

m1v1+m2v2=(m1+m2)vf
The objects are moving in opposite directions with the same speed, so v1=-v2=v

3. The attempt at a solution

The part that gets me is the part that says half the kinetic energy is lost. Could someone explain how I factor that into the equations? If I just solve for m1/m2, plugging in 1/2v for vf(I don't know if that's right) I get 3, which is not the correct answer.

2. Oct 14, 2011

### LawrenceC

If the collision were perfectly elastic, kinetic energy is conserved. But it is totally inelastic and 1/2 of the energy is lost. Therefore you can say:

.5 * m1 * v1^2 + .5 * m2 * v2^2 = (.5 * (m1 + m2)* vf^2) * .5

Then start cranking on the algebra to get m1/m2.

3. Oct 14, 2011

### sleepingarmy

That makes sense. However, when I solve for m1/m2 I get (.5vf^2 + v^20/(v^2-.5vf^2) when I need an actual ratio.