A collision is completely inelastic when the loss of energy is the maximum loss compatible with the conservation of linear momentum. In the case of frontal collisions, this means that both particles end up stuck to one another.

Although there are no cases of completely elastic collisions, there are many cases of completely inelastic collisions.

This is what happens, for example, when a bullet is shot into a block of wood or when an atomic nucleus absorbs a particle in a nuclear reactor.

In the following visual we will assume that a collision of this kind takes place between two billiard balls.