# Inelastic collision for equal masses

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
Homework Helper
Equivocating on the variable ##m## ?

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.

Svein