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.
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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.
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 subatomic particles which are deflected by the electromagnetic force. Some largescale 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 twobody collisions.
Let the linear, angular and internal momenta of a molecule be given by the set of r variables { p_{i} }. The state of a molecule may then be described by the range δw_{i} = δp_{1}δp_{2}δp_{3} ... δp_{r}. 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 Htheorem of statistical mechanics.
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 lowrolling friction, their behavior is often used to illustrate Newton's laws of motion. After a lowfriction 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 m_{1} and m_{2}, with respective initial velocities v_{1} in the xdirection, and v_{2} = 0, and final velocities V_{1} and V_{2}.
Conservation of momentum: m_{1}v_{1} = m_{1}V_{1}+ m_{2}V_{2}.
Conservation of energy for elastic collision: (1/2)m_{1}v_{1}^{2} = (1/2)m_{1}V_{1}^{2} + (1/2)m_{2}V_{2}^{2}
Now consider the case m_{1} = m_{2}, we then obtain v_{1}=V_{1}+ V_{2} and v_{1}^{2} = V_{1}^{2}+V_{2}^{ 2}
Using the dot product, v_{1}^{2} = v_{1}•v_{1} = V_{1}^{2}+V_{2}^{ 2}+2V_{1}•V_{2}
So V_{1}•V_{2} = 0, so they are perpendicular.
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.
An object may deliberately be made to crashland 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:

A collision occurs when two objects come in contact with each other. All collisions have the same momentum before and after a collision. Examples of collisions include car crashes, bouncing a ball, and playing pool. Collisions are made from two smaller sections called elastic and inelastic collisions.
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In the case of playing hard to get or bouncing your balls, an elastic collision occurs. An elastic collision generally occurs when an elastic or hard object experiences a collision that bounces off another elastic or hard object, where the kinetic energy and momentum are the same before and after the collision. In an experiment, a small amount of energy will still be lost because of the friction between the surface and the objects.
In the case of a car crash, an inelastic collision occurs. An inelastic collision generally occurs when a soft object experiences a collision that does not result in a bounce. Kinetic energy is lost during this type of collision because the energy is transformed into other forces. The momentum is the same before and after the collision.
In the case of a two dimensional collision, the rules in elastic and inelastic collision are still the same, but vectors are used to find the momentum before or after a collision.
Duncan, Tom. Advanced Physics for Hong Kong: Volume 1 Mechanics & Electricity. Bill Murray Ltd, 1995. Wai, Loo Kwok. Longman ALevel Course in Physics: Volume 1. Pearson Education South Asia Pte Ltd, 2003.
