# Collision

## Origin

Middle English, from Latin collision-, collisio, from collidere

## Definitions

- 1: an act or instance of colliding : clash
- 2: an encounter between particles (as atoms or molecules) resulting in exchange or transformation of energy

## Description

A **collision** is an isolated event in which two or more moving bodies (colliding bodies) exert relatively strong forces on each other for a relatively short time.

## Dynamics

Collisions involve forces (there is a change in velocity). Collisions can be elastic, meaning they conserve energy and momentum; inelastic, meaning they conserve momentum but not energy; or totally inelastic (or plastic), meaning they conserve momentum and the two objects stick together.

The magnitude of the velocity difference at impact is called the closing speed.

The field of dynamics is concerned with moving and colliding objects.

## Elastic and Inelastic Collisions

A perfectly elastic collision is defined as one in which there is no loss of kinetic energy in the collision. An inelastic collision is one in which part of the kinetic energy is changed to some other form of energy in the collision. Any macroscopic collision between objects will convert some of the kinetic energy into internal energy and other forms of energy, so no large scale impacts are perfectly elastic. Momentum is conserved in inelastic collisions, but one cannot track the kinetic energy through the collision since some of it is converted to other forms of energy. Collisions in ideal gases approach perfectly elastic collisions, as do scattering interactions of sub-atomic particles which are deflected by the electromagnetic force. Some large-scale interactions like the slingshot type gravitational interactions between satellites and planets are perfectly elastic. Collisions between hard spheres may be nearly elastic, so it is useful to calculate the limiting case of an elastic collision. The assumption of conservation of momentum as well as the conservation of kinetic energy makes possible the calculation of the final velocities in two-body collisions. [edit] Mathematical description

Let the linear, angular and internal momenta of a molecule be given by the set of r variables { pi }. The state of a molecule may then be described by the range δwi = δp1δp2δp3 ... δpr. There are many such ranges corresponding to different states; a specific state may be denoted by the index i. Two molecules undergoing a collision can thus be denoted by (i, j) (Such an ordered pair is sometimes known as a constellation.)

It is convenient to suppose that two molecules exert a negligible *effect* on each other unless their centre of gravities approach within a critical distance b. A collision therefore begins when the respective centres of gravity arrive at this critical distance, and is completed when they again reach this critical distance on their way apart. Under this model, a collision is completely described by the matrix , which refers to the constellation (i, j) before the collision, and the (in general different) constellation (k, l) after the collision.

This notation is convenient in proving Boltzmann's H-theorem of statistical mechanics.[1]