Types of collision: elastic, inelastic, totally inelastic

A collision is a brief, intense interaction between two bodies. During the collision the internal contact forces are very large, while the external forces (weight, friction) are negligible: therefore momentum is conserved in every type of collision. What changes from one collision to another is the fate of the kinetic energy.

Depending on what happens to the kinetic energy, we distinguish three cases:

Type of collision	What is conserved
Elastic	$\vv{p}$ and $E_{\text{cin}}$
Inelastic	$\vv{p}$ (but not $E_{\text{cin}}$: part becomes $E_{\text{term}}$)
Totally inelastic	$\vv{p}$, and the bodies stay stuck together ($v_1' = v_2'$)

The elastic case is the ideal one: no energy is dissipated, the bodies bounce off without permanent deformation (steel balls, billiard balls, Newton’s cradle spheres). The inelastic case is the generic real one: part of the kinetic energy is turned into heat, sound, deformation. The totally inelastic case is the opposite extreme of the elastic one: the bodies lock together and continue with a single final velocity — it is the case in which the maximum kinetic energy compatible with conservation of $\vv{p}$ is lost.

Common mistake

“If energy is not conserved, then momentum isn’t conserved either.” False: in an inelastic collision the kinetic energy decreases (it becomes thermal), but $\vv{p}$ is still conserved, because it depends only on the external forces, not on how much energy is dissipated internally.

Links

Topics: Quantità di moto e urti Concepts: Urto elastico · Urto anelastico · Conservazione della quantità di moto · Energia cinetica

Related exercises: Urto elastico tra due biglie · Vero o falso sugli urti · Pendolo balistico (altezza)