# Completely inelastic collision

## Homework Statement

Is it true that a completely inelastic collision can be elastic (i.e. KE could be conserved) such as when you fire a gun at a metal ball at rest and the bullet and the metal ball stick togethor? Isn't completely inelastic somewhat of a misnomer since it implies that the collision is not elastic?

## The Attempt at a Solution

Doc Al
Mentor
Is it true that a completely inelastic collision can be elastic (i.e. KE could be conserved) such as when you fire a gun at a metal ball at rest and the bullet and the metal ball stick togethor?
No. What makes think KE is conserved in that situation? Do the calculation and find out for yourself.

Isn't completely inelastic somewhat of a misnomer since it implies that the collision is not elastic?
Well, it's not elastic--they stick together! KE is not conserved.

Why does the fact that they stick togethor require that KE is not conserved?

Doc Al
Mentor
Why does the fact that they stick togethor require that KE is not conserved?
Just do the calculation! Use conservation of momentum:

$$m_1\vec{v}_1 + m_2\vec{v}_2 = (m_1 + m_2)\vec{v}_f$$

Then compare initial and final KE. Keep it simple if you like, let v_2 = 0 and assume that all motion takes place along a single dimension.

OK. I did the calculation and I see that KE gets lost. But, in general, in a closed system, energy must be conserved, so that KE gets transformed to the energy in chemical bonds that holds the two units together, correct?

Doc Al
Mentor
When we say KE is "lost" we are talking about macroscopic translational KE. Of course, that energy isn't really lost--it's transformed mainly into thermal energy.