Inelastic Collision and Kinetic Energy

In a classical frame, the total energy of a system $E$ is the sum kinetic $E_K$, potential $E_P$, and internal $U$. Any event rebalances the energies. In a frame with no potential energy, the loss of $E_K$ goes to $U$.

For example, a mass of water $m$ starts at the top of a water fall with no (vertical) $E_K$, a potential $E_P = m g Delta h$, and a certain internal energy $U$ as indicated primarily by its temperature. At the bottom of the water fall, just before the falling water $m$ hits the stagnant water at the bottom, $m$ has translated $E_p$ to $E_K$ (assuming that the fall is essentially an isothermal process so that $Delta U$ is zero). As $m$ now stops moving vertically, it translates $E_K$ to $U$. This causes an increase in the temperature of the water.

The above example is drawn from a common problem in engineering thermodynamic textbooks.

By further reference, an inelastic collision does not directly imply that we must consider friction. Picture two spheres at the same $mv$ and $E_K$ that collide, stick, and stay in one place. The collision is entirely inelastic. Friction at the macroscopic level does not need to be invoked to explain this event. It can be explained entirely by recognizing a permanent deformation for the spheres themselves.

Friction, when it does occur, is a source of irreversibility in a process. Friction is translated typically to be a heat loss from the system to the surroundings.