Collision
40898
221160639
2008-06-23T08:47:10Z
Ajinx999
4952323
{{otheruses}}
A '''collision''' is an isolated event in which two or more bodies (colliding bodies) exert relatively strong forces on each other for a relatively short time.
==Dynamics==
[[Image:Deflection.png|right|thumb|250px|[[Deflection]] happens when an object hits a plane surface]]
Collisions involve forces (there is a change in [[velocity]]). Collisions can be ''[[elastic collision|elastic]]'', meaning they conserve [[energy]] and [[momentum]], ''[[inelastic collision|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 (mechanics)|dynamics]] is concerned with moving and colliding objects.
==Billiards==
In [[billiards]], collisions play an important role. 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 low-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 appears to be an important fact that many professional billiard players take into account.
Consider an elastic collision in 2 dimensions of any 2 masses m<sub>1</sub> and m<sub>2</sub>, with respective initial and final velocities v<sub>1</sub>, V<sub>1</sub> and v<sub>2</sub>, V<sub>2</sub>
'''Collision in the x Direction:''' m<sub>1</sub>v<sub>1</sub> = m<sub>1</sub>V<sub>1</sub>cosΦ+m<sub>2</sub>V<sub>2</sub>cosθ
'''Collision in the y Direction:''' 0 = m<sub>1</sub>V<sub>1</sub>sinΦ-m<sub>2</sub>V<sub>2</sub>sinθ
'''Conservation of Energy for Elastic Collision:''' 1/2m<sub>1</sub>v<sub>1</sub><sup>2</sup> = 1/2m<sub>1</sub>V<sub>1</sub><sup>2</sup>+1/2m<sub>2</sub>V<sub>2</sub><sup>2</sup>
Now consider the case m<sub>1</sub> = m<sub>2</sub>, we then obtain 3 equations:
'''1.''' v<sub>1</sub><sup>2</sup> = V<sub>1</sub><sup>2</sup>+V<sub>2</sub><sup>2</sup>.
'''2.''' v<sub>1</sub> = V<sub>1</sub>cosΦ+V<sub>2</sub>cosθ.
'''3.''' 0 = </sub>V<sub>1</sub>sinΦ-</sub>V<sub>2</sub>sinθ.
So the vector '''v<sub>1</sub>'''='''V<sub>1</sub>'''+'''V<sub>2</sub>'''.
The dot product of the vector '''v<sub>1</sub>''' yields '''v<sub>1</sub>•v<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>''' = v<sub>1</sub><sup>2</sup>
Equation 1 tells us however that v<sub>1</sub><sup>2</sup> = V<sub>1</sub><sup>2</sup>+V<sub>2</sub><sup>2</sup> and so 2'''V<sub>1</sub>V<sub>2</sub>''' = 0
Now, 2'''V<sub>1</sub>V<sub>2</sub>''' = V<sub>1</sub>V<sub>2</sub>cos(θ+Φ) = 0 so cos(θ+Φ)=0 and θ+Φ=90°.
==Traffic==
In [[traffic]] such a collision can be between two [[vehicle]]s, a vehicle and a [[person]], a vehicle and an [[object (philosophy)|object]], two persons or a person and an object (and more if an [[animal]] is involved). It is an [[accident]] or even a [[disaster]]. At [[level crossing]]s sometimes a [[train]] collides with a vehicle or person. Due to the [[velocity]] and [[mass]] of a train it needs a long distance to stop, typically longer than the train [[driving|driver]] can see ahead. When a train collides with a car this is more likely to be deadly for the people in the car than for those in the train, because the train has more [[mass]] and momentum.
==See also==
*[[Collision detection]]
*[[Car accident]]
*[[Elastic collision]]
*[[Inelastic collision]]
*[[Mid-air collision]]
*[[Friction]]
*[[Collision (physical attack)]]
*[[Projectile]]
*[[Space debris]]
*[[Impact event]]
*[[Impact crater]]
*[[Kinetic theory]] - collisions between molecules
==External links==
*[http://www.regispetit.com/bil_praa.htm Three Dimensional Collision] - Oblique inelastic collision between two homogeneous spheres.
*[http://www.publicliterature.org/tools/collisions/ Two Dimensional Collision] - Java applet that simulates elastic collisions.
*[http://www.physics-lab.net/applets.php?app=1dcollisions One Dimensional Collision] - One Dimensional Collision Flash Applet as well as theory behind it.
[[Category:Mechanics]]
[[Category:Introductory physics]]
[[ar:تصادم]]
[[da:Kollision]]
[[de:Stoß (Physik)]]
[[fr:Collision]]
[[hu:Ütközés]]
[[it:Urto]]
[[lt:Smūgis]]
[[nl:Botsing (natuurkunde)]]
[[ja:衝突]]
[[pl:Zderzenie]]
[[ro:Coliziune]]
[[ru:Удар]]
[[simple:Collision]]
[[sl:Trk]]
[[sv:Stöt (mekanik)]]
[[zh:碰撞]]