Inelastic collision for equal masses

[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?

 

[jbriggs444]

Equivocating on the variable $m$ ?

 

[Mr Davis 97]

Equivocating on the variable $m$ ?

You might need to elaborate...

 

[Chandra Prayaga]

You might need to elaborate...

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.

 

[Mr Davis 97]

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.

That answers my question. Thanks.

 

[Svein]

I claimed that this was an inelastic collision. Is there some constraint that I am missing?

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

 

[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.