An inelastic collision, in contrast to an elastic collision

Elastic collision

An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies after the encounter is equal to their total kinetic energy before the encounter...

, is a collision

Collision

A collision is an isolated event which two or more moving bodies exert forces on each other for a relatively short time.Although the most common colloquial use of the word "collision" refers to accidents in which two or more objects collide, the scientific use of the word "collision" implies...

 in which kinetic energy is not conserved.

In collisions of macroscopic bodies, some kinetic energy is turned into vibrational energy of the atom

Atom

The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...

s, causing a heat

Heat

In physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between...

ing effect, and the bodies are deformed.

The molecule

Molecule

A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...

s of a gas

Gas

Gas is one of the three classical states of matter . Near absolute zero, a substance exists as a solid. As heat is added to this substance it melts into a liquid at its melting point , boils into a gas at its boiling point, and if heated high enough would enter a plasma state in which the electrons...

 or liquid

Liquid

Liquid is one of the three classical states of matter . Like a gas, a liquid is able to flow and take the shape of a container. Some liquids resist compression, while others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly...

 rarely experience perfectly elastic collision

Elastic collision

An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies after the encounter is equal to their total kinetic energy before the encounter...

s because kinetic energy is exchanged between the molecules' translational motion and their internal degrees of freedom

Degrees of freedom (physics and chemistry)

A degree of freedom is an independent physical parameter, often called a dimension, in the formal description of the state of a physical system...

 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. Simple ballistic pendulum

Ballistic pendulum

A ballistic pendulum is a device for measuring a bullet's momentum, from which it is possible to calculate the velocity and kinetic energy. Ballistic pendulums have been largely rendered obsolete by modern chronographs, which allow direct measurement of the projectile velocity.Although the...

 problems obey the conservation of kinetic energy only when the block swings to its largest angle.

In nuclear physics

Nuclear physics

Nuclear physics is the field of physics that studies the building blocks and interactions of atomic nuclei. The most commonly known applications of nuclear physics are nuclear power generation and nuclear weapons technology, but the research has provided application in many fields, including those...

, an inelastic collision is one in which the incoming particle

Subatomic particle

In physics or chemistry, subatomic particles are the smaller particles composing nucleons and atoms. There are two types of subatomic particles: elementary particles, which are not made of other particles, and composite particles...

 causes the nucleus

Atomic nucleus

The nucleus is the very dense region consisting of protons and neutrons at the center of an atom. It was discovered in 1911, as a result of Ernest Rutherford's interpretation of the famous 1909 Rutherford experiment performed by Hans Geiger and Ernest Marsden, under the direction of Rutherford. The...

 it strikes to become excited

Excited state

Excitation is an elevation in energy level above an arbitrary baseline energy state. In physics there is a specific technical definition for energy level which is often associated with an atom being excited to an excited state....

 or to break up. Deep inelastic scattering

Deep Inelastic Scattering

Deep inelastic scattering is the name given to a process used to probe the insides of hadrons , using electrons, muons and neutrinos. It provided the first convincing evidence of the reality of quarks, which up until that point had been considered by many to be a purely mathematical phenomenon...

 is a method of probing the structure of subatomic particles in much the same way as Rutherford probed the inside of the atom (see Rutherford scattering

Rutherford scattering

In physics, Rutherford scattering is a phenomenon that was explained by Ernest Rutherford in 1911, and led to the development of the Rutherford model of the atom, and eventually to the Bohr model. It is now exploited by the materials analytical technique Rutherford backscattering...

). Such experiments were performed on proton

Proton

The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....

s in the late 1960s using high-energy electron

Electron

The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

s at the Stanford 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

Electric charge

Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...

 in an atom is concentrated at the nucleus. However, in the case of the proton, the evidence suggested three distinct concentrations of charge (quark

Quark

A quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly...

s) and not one.

Formula

The formula for the velocities after a one-dimensional collision are:

where

v_a is the final velocity of the first object after impact

v_b is the final velocity of the second object after impact

u_a is the initial velocity of the first object before impact

u_b is the initial velocity of the second object before impact

m_a is the mass of the first object

m_b is the mass of the second object

C_R is the coefficient of restitution

Coefficient of restitution

The coefficient of restitution of two colliding objects is a fractional value representing the ratio of speeds after and before an impact, taken along the line of the impact...

; if it is 1 we have an elastic collision

Elastic collision

An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies after the encounter is equal to their total kinetic energy before the encounter...

; if it is 0 we have a perfectly inelastic collision, see below.

In a center of momentum frame

Center of momentum frame

A center-of-momentum frame of a system is any inertial frame in which the center of mass is at rest . Note that the center of momentum of a system is not a location, but rather defines a particular inertial frame...

 the formulas reduce to:


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 coefficient of restitution

Coefficient of restitution

The coefficient of restitution of two colliding objects is a fractional value representing the ratio of speeds after and before an impact, taken along the line of the impact...

, the colliding particles stick together. It is necessary to consider conservation of momentum: (Note: In the sliding block example above, momentum is only conserved if the surface has zero friction.)

where v is the final velocity, which is hence given by

The reduction of total kinetic energy is equal to the total kinetic energy before the collision in a center of momentum frame

Center of momentum frame

A center-of-momentum frame of a system is any inertial frame in which the center of mass is at rest . Note that the center of momentum of a system is not a location, but rather defines a particular inertial 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

Projectile

A projectile is any object projected into space by the exertion of a force. Although a thrown baseball is technically a projectile too, the term more commonly refers to a weapon....

, or a rocket

Rocket

A rocket is a missile, spacecraft, aircraft or other vehicle which obtains thrust from a rocket engine. In all rockets, the exhaust is formed entirely from propellants carried within the rocket before use. Rocket engines work by action and reaction...

 applying thrust

Thrust

Thrust is a reaction force described quantitatively by Newton's second and third laws. When a system expels or accelerates mass in one direction the accelerated mass will cause a force of equal magnitude but opposite direction on that system....

 (compare the derivation of the Tsiolkovsky rocket equation).

External link

• 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.