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| | This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users. |
| {{redirect|Jostle|the racehorse|Jostle (horse)}}
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| A '''collision''' is an isolated event in which two or more moving bodies (colliding bodies) exert forces on each other for a relatively short time.
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| A collision is not constrained to only referring to moving bodies it can also refer to electronic transactions which share a common resource such as a bus interface. In this case a collision refers to two simultaneous requests for the shared resource being made.
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| Although the most common colloquial use of the word "collision" refers to [[accident]]s in which two or more objects collide, the scientific use of the word "collision" implies nothing about the magnitude of the forces.
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| Some examples of physical interactions that scientists would consider collisions:
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| * An insect touches its antenna to the leaf of a plant. The antenna is said to collide with leaf.
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| * 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 a blade of grass is a collision.
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| Some colloquial uses of the word collision are:
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| * [[automobile collision]], two cars colliding
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| * [[mid-air collision]], two planes colliding
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| * [[ship collision]], two ships colliding
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| ==Overview== | | '''source''' |
| [[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. It is not possible to determine from the diagram 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.]]
| | :<math forcemathmode="source">E=mc^2</math> --> |
| Collision is short duration interaction between two bodies or more than two bodies simultaneously causeng 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 at impact is called the closing speed. All collisions conserve [[momentum]]. What distinguishes different types of collisions is whether they also conserve [[kinetic energy]].Line of impact - It is the line which is common normal for surfaces 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.
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| Specifically, collisions can either be ''[[elastic collision|elastic]],'' meaning they conserve both momentum and kinetic energy, or ''[[inelastic collision|inelastic]],'' meaning they conserve momentum but not kinetic energy. An inelastic collision is sometimes also called a ''plastic collision.''
| | <span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples]. |
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| A “perfectly-inelastic” collision (also called a "perfectly-plastic" collision) is a limiting case of inelastic collision in which the two bodies stick together after impact.
| | ==Demos== |
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| 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.
| | Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]: |
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| ==Types of collisions==
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| There are two types of collision between two bodies- 1)head on collision or one dimensional collision - where nelocity of each just before impact is not alon line of impact. 2)non head on collision or oblique collision or two dimensional collision- where velocity of each is not long line of impact just before collision.
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| Though there are two special case of any collision as written below according to coefficient of restitution :
| | * accessibility: |
| | ** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]] |
| | ** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)] |
| | ** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)] |
| | ** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)] |
| | ** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]]. |
| | ** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]]. |
| | ** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode. |
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| 1)A perfectly [[elastic collision]] is defined as one in which there is no loss of [[kinetic energy]] in the collision. In reality, any macroscopic collision between objects will convert some kinetic energy to [[internal energy]] and other forms of energy, so no large scale impacts are perfectly elastic. However, some problems are sufficiently close to perfectly elastic that they can be approximated as such.Here coefficient of restitution is one.
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| 2)An [[inelastic collision]] is one in which part of the kinetic energy is changed to some other form of energy in the collision. [[Momentum]] is conserved in inelastic collisions (as it is for elastic collisions), but one cannot track the kinetic energy through the collision since some of it is converted to other forms of energy.Here coefficient of restitution is not one.
| | To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages: |
| In any type of collision there is a phase when for a moment colliding bodies have same velocity along line of impact then kinetic energy of bodies reduces to its minimum during this phase and may be called as maximum deformation phase for which momentarily coefficient of restitution become one.
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| 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.
| | *[[Styling]] |
| | *[[Linebreaking]] |
| | *[[Unique Ids]] |
| | *[[Help:Formula]] |
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| 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.
| | *[[Inputtypes|Inputtypes (private Wikis only)]] |
| | | *[[Url2Image|Url2Image (private Wikis only)]] |
| ==Analytical vs. numerical approaches towards resolving collisions ==
| | ==Bug reporting== |
| Relatively few problems involving collisions can be solved analytically; the remainder require [[numerical methods]]. An important problem in simulating collisions is determining whether two objects have in fact collided. This problem is called [[collision detection]].
| | If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de . |
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| {{cleanup|section|date=February 2011}}.
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| == Examples of collisions that can be solved analytically ==
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| ===Billiards===
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| {{Anchor|Cue sports}}Collisions play an important role in [[cue sports]]. 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 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 |title=TP 3.1 90° rule |format=PDF |accessdate=2008-03-08 }}</ref> although it assumes the ball is moving frictionlessly across the table rather than rolling with friction.
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| Consider an elastic collision in 2 dimensions of any 2 masses m<sub>1</sub> and m<sub>2</sub>, with respective initial velocities '''u<sub>1</sub>''' and '''u<sub>2</sub>''' = '''0''', and final velocities '''V<sub>1</sub>''' and '''V<sub>2</sub>'''.
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| Conservation of momentum gives m<sub>1</sub>'''u'''<sub>1</sub> = m<sub>1'''</sub>V<sub>1</sub>'''+ m<sub>2'''</sub>V<sub>2'''</sub>.
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| Conservation of energy for an elastic collision gives (1/2)m<sub>1</sub>|'''u<sub>1</sub>'''|<sup>2</sup> = (1/2)m<sub>1</sub>|'''V<sub>1</sub>'''|<sup>2</sup> + (1/2)m<sub>2</sub>|'''V<sub>2</sub>'''|<sup>2</sup>.
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| Now consider the case m<sub>1</sub> = m<sub>2</sub>: we obtain '''u<sub>1</sub>'''='''V<sub>1</sub>'''+'''V<sub>2</sub>''' and |'''u<sub>1</sub>'''|<sup>2</sup> = |'''V<sub>1</sub>'''|<sup>2</sup>+|'''V<sub>2</sub>'''|<sup>2</sup>.
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| Taking the [[dot product]] of each side of the former equation with itself, |'''u<sub>1</sub>'''|<sup>2</sup> = '''u<sub>1</sub>•u<sub>1</sub>''' = |'''V<sub>1</sub>'''|<sup>2</sup>+|'''V<sub>2</sub>'''|<sup>2</sup>+2'''V<sub>1</sub>•V<sub>2</sub>'''. Comparing this with the latter equation gives '''V<sub>1</sub>•V<sub>2</sub>''' = 0, so they are perpendicular unless '''V<sub>1</sub>''' is the zero vector (which occurs if and only if the collision is head-on).
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| ===Perfectly inelastic collision===
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| [[Image:Inelastischer stoß.gif|a completely inelastic collision between equal masses]]
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| 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:
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| ::<math>m_a \mathbf u_a + m_b \mathbf u_b = \left( m_a + m_b \right) \mathbf v \,</math>
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| where '''v''' is the final velocity, which is hence given by
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| ::<math>\mathbf v=\frac{m_a \mathbf u_a + m_b \mathbf u_b}{m_a + m_b}</math>
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| 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.
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| 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]]).
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| == Examples of collisions analyzed numerically==
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| ===Animal locomotion===
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| 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.
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| == Collisions used as a experimental tool == | |
| Collisions can be used as an experimental technique to study material properties of objects and other physical phenomena.
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| === Space exploration===
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| 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.:
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| *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.
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| * [[Deep Impact (spacecraft)|''Deep Impact'']]
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| * [[SMART-1]] - [[European Space Agency]] satellite
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| * [[Moon impact probe]] - [[ISRO]] probe
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| === Mathematical description of molecular collisions ===
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| Let the linear, angular and internal momenta of a molecule be given by the set of ''r'' variables { ''p''<sub>i</sub> }. The state of a molecule may then be described by the range ''δw''<sub>i</sub> = δ''p''<sub>1</sub>δ''p''<sub>2</sub>δ''p''<sub>3</sub> ... δ''p''<sub>r</sub>. 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''.)
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| 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 <math>\begin{pmatrix}i&j\\k&l\end{pmatrix} </math>, which refers to the constellation (''i'', ''j'') before the collision, and the (in general different) constellation (''k'', ''l'') after the collision.
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| This notation is convenient in proving Boltzmann's [[H-theorem]] of [[statistical mechanics]].
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| ==Attack by means of a deliberate collision== | |
| Types of attack by means of a deliberate collision include:
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| * with the body: unarmed [[Strike (attack)|striking]], [[Punch (strike)|punching]], [[kick]]ing, [[martial arts]], [[pugilism]]
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| * striking directly with a weapon, such as a [[sword]], [[club (weapon)|club]] or [[axe]]
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| * [[ramming]] with an object or vehicle, e.g.:
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| ** a car deliberately crashing into a building to break into it
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| ** a [[battering ram]], medieval weapon used for breaking down large doors, also a modern version is used by police forces during raids
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| An attacking collision with a distant object can be achieved by throwing or launching a [[projectile]].
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| ==See also==
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| {{multicol}}
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| *[[Ballistic pendulum]]
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| *[[Coefficient of restitution]]
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| *[[Collision detection]]
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| *[[Collision (telecommunications)]]
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| *[[Car accident]]
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| *[[Elastic collision]]
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| *[[Friction]]
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| * [[Head-on collision]]
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| *[[Impact crater]]
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| {{multicol-break}}
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| *[[Impact event]]
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| *[[Inelastic collision]]
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| *[[Kinetic theory]]<br /> - collisions between [[molecule]]s
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| *[[Mid-air collision]]
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| *[[Projectile]]
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| *[[Space debris]]
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| * [[Train wreck]]
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| {{multicol-end}}
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| ==Notes==
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| {{reflist|1}}
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| ==References==
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| * {{cite book | author=Tolman, R. C. | title=The Principles of Statistical Mechanics | publisher=Clarendon Press | year=1938 | location=Oxford}} Reissued (1979) New York: Dover ISBN 0-486-63896-0.
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| ==External links==
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| *[http://www.regispetit.com/bil_praa.htm Three Dimensional Collision] - Oblique inelastic collision between two homogeneous spheres.
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| *[http://www.publicliterature.org/tools/collisions/ Two Dimensional Collision] - Java applet that simulates elastic collisions.
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| *[http://www.physics-lab.net/applets/one-dimensional-collisions One Dimensional Collision] - One Dimensional Collision Flash Applet.
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| *[http://www.physics-lab.net/applets/two-dimensional-collisions Two Dimensional Collision] - Two Dimensional Collision Flash Applet.
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| [[Category:Mechanics]]
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| [[Category:Introductory physics]]
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| [[ar:تصادم]]
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| [[da:Kollision]]
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| [[de:Stoß (Physik)]]
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| [[fa:برخورد]]
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| [[fr:Collision]]
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| [[ko:충돌]]
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| [[it:Urto]]
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| [[lt:Smūgis]]
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| [[hu:Ütközés]]
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| [[nl:Botsing (natuurkunde)]]
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| [[ja:衝突]]
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| [[pl:Zderzenie]]
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| [[ro:Coliziune]]
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| [[ru:Удар]]
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| [[simple:Collision]]
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| [[sl:Trk]]
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| [[sv:Stöt (mekanik)]]
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| [[zh:碰撞]]
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