Editing Momentum (section)

====Inelastic collisions====
{{Main|Inelastic collision}}

[[File:Inelastischer stoß.gif|thumb|right|a perfectly inelastic collision between equal masses]]
In an inelastic collision, some of the kinetic energy of the colliding bodies is converted into other forms of energy (such as [[heat]] or [[sound]]). Examples include [[traffic collisions]],<ref>{{cite web |url=http://hyperphysics.phy-astr.gsu.edu/hbase/carcr.html#cc1 |title=Forces in car crashes |work=Hyperphysics |first=Carl |last=Nave |date=2010 |access-date=2 August 2012 |url-status=live |archive-url=https://web.archive.org/web/20120822034313/http://hyperphysics.phy-astr.gsu.edu/hbase/carcr.html#cc1 |archive-date=22 August 2012 }}</ref> in which the effect of loss of kinetic energy can be seen in the damage to the vehicles; electrons losing some of their energy to atoms (as in the [[Franck–Hertz experiment]]);<ref>{{cite web |url=http://hyperphysics.phy-astr.gsu.edu/hbase/FrHz.html |title=The Franck-Hertz Experiment |work=Hyperphysics |first=Carl |last=Nave |date=2010 |access-date=2 August 2012 |url-status=live |archive-url=https://web.archive.org/web/20120716180316/http://hyperphysics.phy-astr.gsu.edu/hbase/FrHz.html |archive-date=16 July 2012 }}</ref> and [[particle accelerator]]s in which the kinetic energy is converted into mass in the form of new particles.

In a perfectly inelastic collision (such as a bug hitting a windshield), both bodies have the same motion afterwards. A head-on inelastic collision between two bodies can be represented by velocities in one dimension, along a line passing through the bodies. If the velocities are {{math|{{var|v}}{{sub|A1}}}} and {{math|{{var|v}}{{sub|B1}}}} before the collision then in a perfectly inelastic collision both bodies will be travelling with velocity {{mvar|v}}{{sub|2}} after the collision. The equation expressing conservation of momentum is:

<math display="block">\begin{align} m_A v_{A1} + m_B v_{B1} &= \left( m_A + m_B \right) v_2\,.\end{align}</math>

If one body is motionless to begin with (e.g. <math> u_2 = 0 </math>), the equation for conservation of momentum is

<math display="block">m_A v_{A1} = \left( m_A + m_B \right) v_2\,,</math>

so

<math display="block"> v_2 = \frac{m_{A}}{m_{A}+m_{B}} v_{A1}\,.</math>

In a different situation, if the frame of reference is moving at the final velocity such that <math> v_2 = 0 </math>, the objects would be brought to rest by a perfectly inelastic collision and 100% of the kinetic energy is converted to other forms of energy. In this instance the initial velocities of the bodies would be non-zero, or the bodies would have to be massless.

One measure of the inelasticity of the collision is the [[coefficient of restitution]] {{math|{{var|C}}{{sub|R}}}}, defined as the ratio of relative velocity of separation to relative velocity of approach. In applying this measure to a ball bouncing from a solid surface, this can be easily measured using the following formula:<ref>{{cite book|last=McGinnis|first=Peter M.|title=Biomechanics of sport and exercise|date=2005|publisher=Human Kinetics|location=Champaign, Illinois |isbn=978-0-7360-5101-9|page=85|edition=2nd|url=https://books.google.com/books?id=PrOKEcZXJ58C&q=coefficient+of+restitution+bounciness&pg=PA85|url-status=live|archive-url=https://web.archive.org/web/20160819020542/https://books.google.com/books?id=PrOKEcZXJ58C&pg=PA85&lpg=PA85&dq=coefficient+of+restitution+bounciness|archive-date=2016-08-19}}</ref>

<math display="block">C_\text{R} = \sqrt{\frac{\text{bounce height}}{\text{drop height}}}\,.</math>

The momentum and energy equations also apply to the motions of objects that begin together and then move apart. For example, an [[explosion]] is the result of a chain reaction that transforms potential energy stored in chemical, mechanical, or nuclear form into kinetic energy, acoustic energy, and electromagnetic radiation. [[Rocket]]s also make use of conservation of momentum: propellant is thrust outward, gaining momentum, and an equal and opposite momentum is imparted to the rocket.<ref>{{cite book | last = Sutton | first = George | title = Rocket Propulsion Elements |edition=7th |chapter-url=https://books.google.com/books?id=LQbDOxg3XZcC | publisher = John Wiley & Sons | location = Chichester | date = 2001 | isbn = 978-0-471-32642-7 |chapter=Chapter 1: Classification}}</ref>