# Inelastic collision for equal masses

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1. Nov 11, 2015

### Mr Davis 97

Assume that we have two equal masses that collide horizontally, where one is initially at rest. From the conservation of linear momentum, we have
$P_0 = P$
$mv_{10} = mv_{1} + mv_{2}$
$v_{10} = v_{1} + v_{2}$

Assuming we have an initial velocity, it would seem as though the final velocity of mass 1 could add with the final velocity of mass 2 in order to equal the initial velocity. However, this is not the case because collisions don't act randomly like that. Therefore, what am I missing? I know that in elastic collisions, $v_{10} = v_{2}$ because of the additional constraint posed by the conservation of mechanical energy, but I claimed that this was an inelastic collision. Is there some constraint that I am missing?

2. Nov 11, 2015

### jbriggs444

Equivocating on the variable $m$ ?

3. Nov 11, 2015

### Mr Davis 97

You might need to elaborate...

4. Nov 11, 2015

### Chandra Prayaga

The problem is not fully specified. There are two unknowns, v1 and v2, and only one equation. One more condition comes from either stating that it is a completely inelastic collision,or stating the percentage of kinetic energy lost. Either one will give the necessary second condition.

5. Nov 11, 2015

### Mr Davis 97

6. Nov 12, 2015

### Svein

In a completely inelastic collision, the objects "stick together", which means that their velocities are equal after the collision.

7. Nov 12, 2015

### mathman

One way to get a clear picture is to change coordinates to a center of mass system. In that case, after collision, neither object will be moving when the collision is completely inelastic.