Perfectly inelastic collision
Also called Completely inelastic collision
A perfectly inelastic collision is one in which the objects stick together and move off with a single common velocity. It loses the most kinetic energy that any collision with that momentum can lose, which is not the same as losing all of it.
EK 4.4.A.5 gives the entire definition: in a perfectly inelastic collision the objects stick together and move with the same velocity after the collision. Coupling railcars, a bullet embedding in a block and a lump of clay landing on a cart are the standard set-ups.
Because there is one unknown final velocity instead of two, conservation of momentum alone fixes it:
That is why these are the first collisions taught and the easiest to solve.
Maximum loss is not total loss. This is the trap the name invites. The kinetic energy that disappears is the largest amount conservation of momentum permits, but the combined object keeps moving unless the total momentum was zero to start with, and anything moving has kinetic energy. Kinetic energy reaches zero only in the special case where the two momenta cancel exactly, such as identical carts meeting head-on at equal speeds.
The reverse case exists too. An explosion, a spring released between two carts, or a person jumping off a raft is the same algebra run backwards: one object at rest separating into pieces, with the total momentum still zero.
For the loss worked out with numbers, use what is conserved in a collision or the momentum collision calculator.