# Collision > Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Collision > Markdown URL: https://mediated.wiki/source/Collision.md > Source: https://en.wikipedia.org/wiki/Collision > Source revision: 1356356648 > License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) In physics, two bodies contacting each other This article is about physics models. For other uses, see [Collision (disambiguation)](/source/Collision_(disambiguation)). A 3D simulation demonstrating a collision with a ball knocking over a bunch of blocks In [physics](/source/Physics), a **collision** is any event in which two or more bodies exert [forces](/source/Force) on each other in a relatively short time. Although the most common use of the word *collision* refers to incidents in which two or more objects collide with great force, the scientific use of the term implies nothing about the magnitude of the force.[1] ## Types of collisions [Deflection](/source/Deflection_(physics)) happens when an object hits a plane surface. If the kinetic energy after impact is the same as before impact, it is an elastic collision. If kinetic energy is lost, it is an inelastic collision. The diagram does not show whether the illustrated collision was elastic or inelastic, because no velocities are provided. The most one can say is that the collision was not perfectly inelastic, because in that case the ball would have stuck to the wall. Collision is short-duration interaction between two or more bodies simultaneously, causing change in their [velocities](/source/Velocity) due to repelling forces exerted by their interactions. The magnitude of the velocity difference just before impact is called the **closing speed**. All collisions conserve the total [momentum](/source/Momentum) of the colliding objects. What distinguishes different types of collisions is whether they also conserve [kinetic energy](/source/Kinetic_energy) of the system before and after the collision. Collisions are of two types: 1. **[Elastic collision](/source/Elastic_collision)** If all of the total kinetic energy is conserved (i.e. no energy is released as sound, heat, etc.), the collision is said to be *perfectly elastic*. Such a system is an [idealization](/source/Idealization_(science_philosophy)) and cannot occur in reality, due to the [second law of thermodynamics](/source/Second_law_of_thermodynamics). 1. **[Inelastic collision](/source/Inelastic_collision)**. If most or all of the total kinetic energy is lost ([dissipated](/source/Dissipation) as heat, sound, etc. or absorbed by the objects themselves), the collision is said to be [*inelastic*](/source/Inelastic_collision); such collisions involve objects coming to a full stop. An example of this is a baseball bat hitting a baseball - the kinetic energy of the bat is transferred to the ball, greatly increasing the ball's velocity. The sound of the bat hitting the ball represents the loss of energy. A "perfectly inelastic" collision (also called a "perfectly plastic" collision) is a [limiting case](/source/Limiting_case_(mathematics)) of inelastic collision in which the two bodies [coalesce](/source/Coalescence_(physics)) after impact. An example of such a collision is a car crash, as cars crumple inward when crashing, rather than bouncing off of each other. This [is by design](/source/Crashworthiness), for the [safety of the occupants](/source/Automotive_safety) and bystanders should a crash occur - the frame of the car absorbs the energy of the crash instead. The degree to which a collision is elastic or inelastic is quantified by the [coefficient of restitution](/source/Coefficient_of_restitution), a value that generally ranges between zero and one. A perfectly elastic collision has a coefficient of restitution of one; a perfectly inelastic collision has a coefficient of restitution of zero. The line of impact is the line that is collinear to the common normal of the surfaces that are closest or in contact during impact. This is the line along which internal force of collision acts during impact, and Newton's [coefficient of restitution](/source/Coefficient_of_restitution) is defined only along this line. Collisions in [ideal gases](/source/Ideal_gases) approach perfectly elastic collisions, as do scattering interactions of [sub-atomic particles](/source/Sub-atomic_particles) which are deflected by the [electromagnetic force](/source/Electromagnetic_force). Some large-scale interactions like the slingshot type gravitational interactions between satellites and planets are almost perfectly elastic. ## Examples ### Billiards Collisions play an important role in [cue sports](/source/Cue_sports). Because the collisions between [billiard balls](/source/Billiard_balls) are nearly [elastic](/source/Elastic_collision), and the balls roll on a surface that produces low [rolling friction](/source/Rolling_friction), their behavior is often used to illustrate [Newton's laws of motion](/source/Newton's_laws_of_motion). After a zero-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 is an important fact that professional billiards players take into account,[2] although it assumes the ball is moving without any impact of friction across the table rather than rolling with friction. Consider an elastic collision in two dimensions of any two masses *m*a and *m*b, with respective initial velocities **v**a1 and **v**b1 where **v**b1 = **0**, and final velocities **v**a2 and **v**b2. Conservation of momentum gives *m*a**v**a1 = *m*a**v**a2 + *m*b**v**b2. Conservation of energy for an elastic collision gives (1/2)*m*a|**v**a1|2 = (1/2)*m*a|**v**a2|2 + (1/2)*m*b|**v**b2|2. Now consider the case *m*a = *m*b: we obtain **v**a1 = **v**a2 + **v**b2 and |**v**a1|2 = |**v**a2|2 + |**v**b2|2. Taking the [dot product](/source/Dot_product) of each side of the former equation with itself, |**v**a1|2 = **v**a1•**v**a1 = |**v**a2|2 + |**v**b2|2 + 2**v**a2•**v**b2. Comparing this with the latter equation gives **v**a2•**v**b2 = 0, so they are perpendicular unless **v**a2 is the zero vector (which occurs [if and only if](/source/If_and_only_if) the collision is head-on). ### Perfect inelastic collision In a perfect [inelastic collision](/source/Inelastic_collision), i.e., a zero [coefficient of restitution](/source/Coefficient_of_restitution), the colliding particles [coalesce](/source/Coalescence_(physics)). Using conservation of momentum: - - m a v a 1 + m b v b 1 = ( m a + m b ) v 2 , {\displaystyle m_{a}\mathbf {v} _{a1}+m_{b}\mathbf {v} _{b1}=\left(m_{a}+m_{b}\right)\mathbf {v} _{2},} the final velocity is given by - - v 2 = m a v a 1 + m b v b 1 m a + m b . {\displaystyle \mathbf {v} _{2}={\frac {m_{a}\mathbf {v} _{a1}+m_{b}\mathbf {v} _{b1}}{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](/source/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](/source/Projectile), or a [rocket](/source/Rocket) applying [thrust](/source/Thrust) (compare the [derivation of the Tsiolkovsky rocket equation](/source/Tsiolkovsky_rocket_equation#Derivation)). ### 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](/source/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](/source/Force_platform) (sometimes called a "force plate") as well as detailed [kinematic](/source/Kinematic) and [dynamic](/source/Dynamics_(mechanics)) (sometimes termed kinetic) analysis. ### Hypervelocity impacts Video of the hypervelocity impact of NASA’s [Deep Impact probe](/source/Deep_Impact_(spacecraft)) on comet [Tempel 1](/source/Tempel_1). Hypervelocity is very high [velocity](/source/Velocity), approximately over 3,000 [meters per second](/source/Metre_per_second) (11,000 km/h, 6,700 mph, 10,000 ft/s, or [Mach](/source/Mach_number) 8.8). In particular, hypervelocity is velocity so high that the strength of materials upon impact is very small compared to [inertial](/source/Inertia) stresses.[3] Thus, [metals](/source/Metal) and [fluids](/source/Fluid) behave alike under hypervelocity impact. An impact under extreme hypervelocity results in [vaporization](/source/Vaporize) of the [impactor](/source/Impact_force) and target. For structural metals, hypervelocity is generally considered to be over 2,500 m/s (5,600 mph, 9,000 km/h, 8,200 ft/s, or Mach 7.3). [Meteorite](/source/Meteorite) [craters](/source/Impact_crater) are also examples of hypervelocity impacts. ## See also - [Ballistic pendulum](/source/Ballistic_pendulum) - [Coefficient of restitution](/source/Coefficient_of_restitution) - [Collision detection](/source/Collision_detection) - [Contact mechanics](/source/Contact_mechanics) - [Elastic collision](/source/Elastic_collision) - [Friction](/source/Friction) - [Impact crater](/source/Impact_crater) - [Impact event](/source/Impact_event) - [Inelastic collision](/source/Inelastic_collision) - [Kinetic theory of gases](/source/Kinetic_theory_of_gases) - collisions between [molecules](/source/Molecule) - [Projectile](/source/Projectile) - [Coulomb collision](/source/Coulomb_collision) ## Notes 1. **[^](#cite_ref-1)** Schmidt, Paul W. (2019). ["Collision (physics)"](https://www.accessscience.com/content/collision-physics/149000). *Access Science*. [doi](/source/Doi_(identifier)):[10.1036/1097-8542.149000](https://doi.org/10.1036%2F1097-8542.149000). 1. **[^](#cite_ref-2)** Alciatore, David G. (January 2006). ["TP 3.1 90° rule"](http://billiards.colostate.edu/technical_proofs/TP_3-1.pdf) (PDF). [Archived](https://ghostarchive.org/archive/20221009/http://billiards.colostate.edu/technical_proofs/TP_3-1.pdf) (PDF) from the original on 2022-10-09. Retrieved 2008-03-08. 1. **[^](#cite_ref-AIAA_3-0)** Air Force Institute of Technology (1991). [*Critical technologies for national defense*](https://books.google.com/books?id=HsEorBWNGWwC&dq=Hypervelocity+3%2C00&pg=PA287). AIAA. p. 287. [ISBN](/source/ISBN_(identifier)) [1-56347-009-8](https://en.wikipedia.org/wiki/Special:BookSources/1-56347-009-8). ## References - Tolman, R. C. (1938). [*The Principles of Statistical Mechanics*](https://archive.org/details/in.ernet.dli.2015.74301). Oxford: Clarendon Press. Reissued (1979) New York: Dover [ISBN](/source/ISBN_(identifier)) [0-486-63896-0](https://en.wikipedia.org/wiki/Special:BookSources/0-486-63896-0). ## External links - [Three Dimensional Collision](https://archive.today/20130201232203/http://www.regispetit.com/bil_praa.htm) - Oblique inelastic collision between two homogeneous spheres. - [One Dimensional Collision](https://web.archive.org/web/20110724005555/http://www.physics-lab.net/applets/one-dimensional-collisions) - One Dimensional Collision Flash Applet. - [Two Dimensional Collision](https://web.archive.org/web/20170420214508/http://www.physics-lab.net/applets/two-dimensional-collisions) - Two Dimensional Collision Flash Applet. --- Adapted from the Wikipedia article [Collision](https://en.wikipedia.org/wiki/Collision) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Collision?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.