- Inelastic collision
An

**inelastic collision**is acollision in which kinetic energy is not conserved (see**elastic collision**).In collisions of macroscopic bodies, some kinetic energy is turned into

vibrational energy of theatom s, causing aheat ing effect.The

molecule s of agas orliquid rarely experience perfectlyelastic collision s because kinetic energy is exchanged between the molecules' translational motion and their internal degrees of freedom with each collision. At any one instant, half the collisions are – to a varying extent – inelastic (the pair possesses less kinetic energy after the collision than before), and half could be described as “super-elastic” (possessing "more" kinetic energy after the collision than before). Averaged across an entire sample, molecular collisions are elastic.Inelastic collisions may not conserve kinetic energy, but they do obey

conservation of momentum . Simpleballistic pendulum problems obey the conservation of kinetic energy "only" when the block swings to its largest angle.In

nuclear physics , an inelastic collision is one in which the incoming particle causes the nucleus it strikes to become excited or to break up.Deep inelastic scattering is a method of probing the structure of subatomic particles in much the same way as Rutherford probed the inside of the atom (seeRutherford scattering ). Such experiments were performed onproton s in the late 1960s using high-energyelectron s at theStanford Linear Accelerator (SLAC). As in Rutherford scattering, deep inelastic scattering of electrons by proton targets revealed that most of the incident electrons interact very little and pass straight through, with only a small number bouncing back. This indicates that the charge in the proton is concentrated in small lumps, reminiscent of Rutherford's discovery that the positive charge in an atom is concentrated at the nucleus. However, in the case of the proton, the evidence suggested three distinct concentrations of charge (quark s) and not one.**Formulas**The formulas for the velocities after a one-dimensional collision are:

:$V\_\{1f\}=frac\{(C\_R\; +\; 1)M\_\{2\}V\_2+V\_\{1\}(M\_1-C\_R\; M\_2)\}\{M\_1+M\_2\}$:$V\_\{2f\}=frac\{(C\_R\; +\; 1)M\_\{1\}V\_1+V\_\{2\}(M\_2-C\_R\; M\_1)\}\{M\_1+\; M\_2\}$

where

:$V\_\{1f\}$ is the final velocity of the first object after impact:$V\_\{2f\}$ is the final velocity of the second object after impact:$V\_\{1\}$ is the initial velocity of the first object before impact:$V\_\{2\}$ is the initial velocity of the second object before impact:$M\_\{1\}$ is the mass of the first object:$M\_\{2\}$ is the mass of the second object:$C\_\{R\}$ is the

coefficient of restitution ; if it is 1 we have anelastic collision ; if it is 0 we have a perfectly inelastic collision, see below.In a

center of momentum frame the formulas reduce to::$V\_\{1f\}=-C\_R\; V\_\{1\}$:$V\_\{2f\}=-C\_R\; V\_\{2\}$

For two- and three-dimensional collisions the velocities in these formulas are the components perpendicular to the tangent line/plane at the point of contact.

**Perfectly inelastic collision**In a perfectly inelastic collision [] , i.e., a zero

coefficientcient of restitution , the colliding particles stick together. We have due to conservation of momentum:::$m\_1\; mathbf\; v\_\{1,i\}\; +\; m\_2\; mathbf\; v\_\{2,i\}\; =\; left(\; m\_1\; +\; m\_2\; ight)\; mathbf\; v\_f\; ,$hence the final velocity is::$mathbf\; v\_f=frac\{m\_1\; mathbf\; v\_\{1,i\}\; +\; m\_2\; mathbf\; v\_\{2,i\{m\_1\; +\; m\_2\}$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 arocket applyingthrust (compare the derivation of the Tsiolkovsky rocket equation).**ee also***

Elastic collision

*Coefficient of restitution

* Oblique inelastic collision between two homogeneous spheres : see article "The Art of Billiards Play" on http://www.regispetit.com/bil_praa.htm which gives the general vector equations of a collision between two bodies of any speed.**Animation**

*Wikimedia Foundation.
2010.*