# Collisions: Wikis

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# Encyclopedia

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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

Deflection happens when an object hits a plane surface

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.

## 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 $\begin{pmatrix}i&j\\k&l\end{pmatrix}$, 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.

## Cue Sports

In cue sports, collisions play an important role. Because the collisions between billiard balls are nearly elastic, and the balls roll on a surface that produces low-rolling friction, their behavior is often used to illustrate Newton's laws of motion. After a low-friction collision of a moving ball with a stationary one of equal mass, the angle between the directions of the two balls is 90 degrees. This appears to be an important fact that many professional billiard players take into account.[1]

Consider an elastic collision in 2 dimensions of any 2 masses m1 and m2, with respective initial velocities v1 in the x-direction, and v2 = 0, and final velocities V1 and V2.

Conservation of momentum: m1v1 = m1V1+ m2V2.

Conservation of energy for elastic collision: (1/2)m1|v1|2 = (1/2)m1|V1|2 + (1/2)m2|V2|2

Now consider the case m1 = m2, we then obtain v1=V1+ V2 and |v1|2 = |V1|2+|V2| 2

Using the dot product, |v1|2 = v1•v1 = |V1|2+|V2| 2+2V1•V2

So V1•V2 = 0, so they are perpendicular.

## Attack

Types of attack by means of a deliberate collision include:

An attacking collision with a distant object can be achieved by throwing or launching a projectile.

## Space exploration

An object may deliberately be made to crash-land on another celestial body, to do measurements and send them to Earth before being destroyed, or to allow instruments elsewhere to observe the effect. See e.g:

## Notes

1. ^ Alciatore, David G. (January 2006). "TP 3.1 90° rule" (PDF). Retrieved 2008-03-08.

## References

• Tolman, R. C. (1938). The Principles of Statistical Mechanics. Oxford: Clarendon Press.   Reissued (1979) New York: Dover ISBN 0-486-63896-0.