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

Although the most common colloquial use of the word "collision" refers to accidents in which two or more objects collide, the scientific use of the word "collision" implies nothing about the magnitude of the forces.

Some examples of physical interactions that scientists would consider collisions:

• An insect touches its antenna to the leaf of a plant. The antenna is said to collide with leaf.
• A cat walks delicately through the grass. Each contact that its paws make with the ground is a collision. Each brush of its fur against --12.7.110.210 (talk) 16:17, 26 April 2014 (UTC)--12.7.110.210 (talk) 16:17, 26 April 2014 (UTC)--12.7.110.210 (talk) 16:17, 26 April 2014 (UTC)--12.7.110.210 (talk) 16:17, 26 April 2014 (UTC)--12.7.110.210 (talk) 16:17, 26 April 2014 (UTC)໔ັฝยวCite error: A <ref> tag is missing the closing </ref> (see the help page). although it assumes the ball is moving frictionlessly across the table rather than rolling with friction.

Consider an elastic collision in 2 dimensions of any 2 masses m₁ and m₂, with respective initial velocities u₁ and u₂ where u₂ = 0, and final velocities V₁ and V₂. Conservation of momentum gives m₁u₁ = m₁V₁+ m₂V₂. Conservation of energy for an elastic collision gives (1/2)m₁|u₁| = (1/2)m₁|V₁| + (1/2)m₂|V₂|. Now consider the case m₁ = m₂: we obtain u₁=V₁+V₂ and |u₁| = |V₁|+|V₂|. Taking the dot product of each side of the former equation with itself, |u₁| = u₁•u₁ = |V₁|+|V₂|+2V₁•V₂. Comparing this with the latter equation gives V₁•V₂ = 0, so they are perpendicular unless V₁ is the zero vector (which occurs if and only if the collision is head-on).

Perfectly inelastic collision

In a perfectly inelastic collision, i.e., a zero coefficient of restitution, the colliding particles stick together. It is necessary to consider conservation of momentum:

${\displaystyle m_{a}\mathbf {u} _{a}+m_{b}\mathbf {u} _{b}=\left(m_{a}+m_{b}\right)\mathbf {v} \,}$

where v is the final velocity, which is hence given by

${\displaystyle \mathbf {v} ={\frac {m_{a}\mathbf {u} _{a}+m_{b}\mathbf {u} _{b}}{m_{a}+m_{b}}}}$

The reduction of total kinetic energy is equal to the total kinetic energy before the collision in a center of momentum frame with respect to the system of two particles, because in such a frame the kinetic energy after the collision is zero. In this frame most of the kinetic energy before the collision is that of the particle with the smaller mass. In another frame, in addition to the reduction of kinetic energy there may be a transfer of kinetic energy from one particle to the other; the fact that this depends on the frame shows how relative this is. With time reversed we have the situation of two objects pushed away from each other, e.g. shooting a projectile, or a rocket applying thrust (compare the derivation of the Tsiolkovsky rocket equation).

Examples of collisions analyzed numerically

Animal locomotion

Collisions of an animal's foot or paw with the underlying substrate are generally termed ground reaction forces. These collisions are inelastic, as kinetic energy is not conserved. An important research topic in prosthetics is quantifying the forces generated during the foot-ground collisions associated with both disabled and non-disabled gait. This quantification typically requires subjects to walk across a force platform (sometimes called a "force plate") as well as detailed kinematic and dynamic (sometimes termed kinetic) analysis.

Collisions used as an experimental tool

Collisions can be used as an experimental technique to study material properties of objects and other physical phenomena.

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.:

• During Apollo 13, Apollo 14, Apollo 15, Apollo 16 and Apollo 17, the S-IVB (the rocket's third stage) was crashed into the Moon in order to perform seismic measurement used for characterizing the lunar core.
• Deep Impact
• SMART-1 - European Space Agency satellite
• Moon impact probe - ISRO probe

Mathematical description of molecular 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 = δp₁δp₂δp₃ ... 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 ${\displaystyle {\begin{pmatrix}i&j\\k&l\end{pmatrix}}}$, 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.

Attack by means of a deliberate collision

Types of attack by means of a deliberate collision include:

• striking with the body: unarmed striking, punching, kicking
• striking with a weapon, such as a sword, club or axe
• ramming with an object or vehicle, e.g.:
  • a car deliberately crashing into a building to break into it
  • a battering ram, medieval weapon used for breaking down large doors, also a modern version is used by police forces during raids

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

See also

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• Ballistic pendulum
• Car accident
• Coefficient of restitution
• Collision (telecommunications)
• Collision detection
• Elastic collision
• Friction
• Head-on collision
• Impact crater

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• Impact event
• Inelastic collision
• Kinetic theory
  - collisions between molecules
• Mid-air collision
• Projectile
• Satellite collision
• Space debris
• Train wreck

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Notes

References

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

External links

• Three Dimensional Collision - Oblique inelastic collision between two homogeneous spheres.
• Two Dimensional Collision - Java applet that simulates elastic collisions.
• One Dimensional Collision - One Dimensional Collision Flash Applet.
• Two Dimensional Collision - Two Dimensional Collision Flash Applet.

• Mechanics
• Collision