Editing Collision

{{short description|Instance of two or more bodies physically contacting each other within a short period of time}}
{{About|physics models|accidents|}}
[[File:Collision 9 Block.gif|alt=A 3D simulation demonstrating collision with a ball knocking over some blocks.|thumb|A 3D simulation demonstrating a collision with a ball knocking over a bunch of blocks]]
In [[physics]], a '''collision''' is any event in which two or more bodies exert [[force]]s 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.<ref>{{Cite journal|last=Schmidt|first=Paul W.|date=2019|title=Collision (physics)|url=https://www.accessscience.com/content/collision-physics/149000|journal=Access Science|language=en|doi=10.1036/1097-8542.149000}}</ref>

== Types of collisions ==
[[File:Deflection.png|right|thumb|250px|[[Deflection (physics)|Deflection]] 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 bodies or more than two bodies simultaneously causing change in motion of bodies involved due to internal forces acted between them during this. Collisions involve forces (there is a change in [[velocity]]). The magnitude of the velocity difference just before impact is called the '''closing speed'''. All collisions conserve [[momentum]].  What distinguishes different types of collisions is whether they also conserve [[kinetic energy]] of the system before and after the collision. Collisions are of two types:
#'''[[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 (science philosophy)|idealization]] and cannot occur in reality, due to the [[second law of thermodynamics]].
#'''[[Inelastic collision]]'''. If most or all of the total kinetic energy is lost ([[Dissipation|dissipated]] as heat, sound, etc. or absorbed by the objects themselves), the collision is said to be [[Inelastic collision|''inelastic'']]; 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 (mathematics)|limiting case]] of inelastic collision in which the two bodies [[Coalescence (physics)|coalesce]] 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 [[Crashworthiness|is by design]], for the [[Automotive safety|safety of the occupants]] 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]], 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]] is defined only along this line.  

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 almost perfectly elastic.

==Examples==

===Billiards===
{{Anchor|Cue sports}}Collisions play an important role in [[cue sports]]. Because the collisions between [[billiard balls]] are nearly [[Elastic collision|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 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,<ref>{{cite web|last=Alciatore |first=David G. |date=January 2006 |url=http://billiards.colostate.edu/technical_proofs/TP_3-1.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://billiards.colostate.edu/technical_proofs/TP_3-1.pdf |archive-date=2022-10-09 |url-status=live |title=TP 3.1 90° rule |access-date=2008-03-08 }}</ref> 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''<sub>a</sub> and ''m''<sub>b</sub>, with respective initial velocities '''v'''<sub>a1</sub>  and '''v'''<sub>b1</sub> where '''v'''<sub>b1</sub> = '''0''', and final velocities '''v'''<sub>a2</sub> and '''v'''<sub>b2</sub>.
Conservation of momentum gives ''m''<sub>a</sub>'''v'''<sub>a1</sub> = ''m''<sub>a</sub>'''v'''<sub>a2</sub> + ''m''<sub>b</sub>'''v'''<sub>b2</sub>.
Conservation of energy for an elastic collision gives (1/2)''m''<sub>a</sub>|'''v'''<sub>a1</sub>|<sup>2</sup> = (1/2)''m''<sub>a</sub>|'''v'''<sub>a2</sub>|<sup>2</sup> + (1/2)''m''<sub>b</sub>|'''v'''<sub>b2</sub>|<sup>2</sup>.
Now consider the case ''m''<sub>a</sub> = ''m''<sub>b</sub>: we obtain '''v'''<sub>a1</sub> = '''v'''<sub>a2</sub> + '''v'''<sub>b2</sub> and |'''v'''<sub>a1</sub>|<sup>2</sup> = |'''v'''<sub>a2</sub>|<sup>2</sup> + |'''v'''<sub>b2</sub>|<sup>2</sup>.
Taking the [[dot product]] of each side of the former equation with itself, |'''v'''<sub>a1</sub>|<sup>2</sup> = '''v'''<sub>a1</sub>•'''v'''<sub>a1</sub> = |'''v'''<sub>a2</sub>|<sup>2</sup> + |'''v'''<sub>b2</sub>|<sup>2</sup> + 2'''v'''<sub>a2</sub>•'''v'''<sub>b2</sub>. Comparing this with the latter equation gives '''v'''<sub>a2</sub>•'''v'''<sub>b2</sub> = 0, so they are perpendicular unless '''v'''<sub>a2</sub> is the zero vector (which occurs [[if and only if]] the collision is head-on).

===Perfect inelastic collision===
[[Image:Inelastischer stoß.gif|a completely inelastic collision between equal masses]]

In a perfect [[inelastic collision]], i.e., a zero [[coefficient of restitution]], the colliding particles [[Coalescence (physics)|coalesce]]. Using conservation of momentum:
::<math>m_a \mathbf v_{a1} + m_b \mathbf v_{b1} = \left( m_a + m_b \right) \mathbf v_2,</math>
the final velocity is given by
::<math>\mathbf v_2 = \frac{m_a \mathbf v_{a1} + m_b \mathbf v_{b1}}{m_a + m_b}.</math>
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 [[Tsiolkovsky rocket equation#Derivation|derivation of the Tsiolkovsky rocket equation]]).

===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 [[Dynamics (mechanics)|dynamic]] (sometimes termed kinetic) analysis.

===Hypervelocity impacts===
[[File:HRIV Impact.gif|thumb|Video of the hypervelocity impact of NASA’s [[Deep Impact (spacecraft)|Deep Impact probe]] on comet [[Tempel 1]].]]
Hypervelocity is very high [[velocity]], approximately over 3,000 [[metre per second|meters per second]] (11,000&nbsp;km/h, 6,700&nbsp;mph, 10,000&nbsp;ft/s, or [[Mach number|Mach]] 8.8). In particular, hypervelocity is velocity so high that the strength of materials upon impact is very small compared to [[inertia]]l stresses.<ref Name="AIAA">{{cite book
|title= Critical technologies for national defense
|author= Air Force Institute of Technology
|year= 1991
|publisher= AIAA
|location= 
|isbn= 1-56347-009-8
|page= 287
|url= https://books.google.com/books?id=HsEorBWNGWwC&dq=Hypervelocity+3%2C000&pg=PA287}}</ref> Thus, [[metal]]s and [[fluid]]s behave alike under hypervelocity impact. An impact under extreme hypervelocity results in [[vaporize|vaporization]] of the [[impact force|impactor]] and target. For structural metals, hypervelocity is generally considered to be over 2,500&nbsp;m/s (5,600&nbsp;mph, 9,000&nbsp;km/h, 8,200&nbsp;ft/s, or Mach 7.3).  [[Meteorite]] [[impact crater|craters]] are also examples of hypervelocity impacts.

==See also==
{{colbegin}}
*[[Ballistic pendulum]]
*[[Coefficient of restitution]]
*[[Collision detection]]
*[[Contact mechanics]]
*[[Elastic collision]]
*[[Friction]]
*[[Impact crater]]
*[[Impact event]]
*[[Inelastic collision]]
*[[Kinetic theory of gases]] - collisions between [[molecule]]s
*[[Projectile]]
{{colend}}

==Notes==
{{Reflist}}

==References==
* {{cite book | author=Tolman, R. C. | title=The Principles of Statistical Mechanics | url=https://archive.org/details/in.ernet.dli.2015.74301 | publisher=Clarendon Press | year=1938 | location=Oxford}} Reissued (1979) New York: Dover {{ISBN|0-486-63896-0}}.

==External links==
*[https://archive.today/20130201232203/http://www.regispetit.com/bil_praa.htm Three Dimensional Collision] - Oblique inelastic collision between two homogeneous spheres.
*[https://web.archive.org/web/20110724005555/http://www.physics-lab.net/applets/one-dimensional-collisions One Dimensional Collision] - One Dimensional Collision Flash Applet.
*[https://web.archive.org/web/20170420214508/http://www.physics-lab.net/applets/two-dimensional-collisions Two Dimensional Collision] - Two Dimensional Collision Flash Applet.

[[Category:Collision| ]]
[[Category:Mechanics]]

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