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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.

isions involve forces (there is a change in velocity
Velocity

In physics, velocity is defined as the Derivative of Position vector. It is a vector physical quantity; both speed and direction are required to define it....
). Collisions can be elastic
Elastic collision

An elastic collision is a collision in which the total kinetic energy of the colliding bodies after collision is equal to their total kinetic energy before collision....
, meaning they conserve energy
Energy

In physics, energy is a scalar physical quantity that describes the amount of Work_ that can be performed by a force. Energy is an attribute of objects and systems that is subject to a conservation law....
 and momentum
Momentum

In classical mechanics, momentum is the product of the mass and velocity of an object . For more accurate measures of momentum, see the section Momentum#Modern definitions of momentum on this page....
, inelastic
Inelastic collision

An inelastic collision is a collision in which kinetic energy is not conserved .In collisions of macroscopic bodies, some kinetic energy is turned into vibrational energy of the atoms, causing a heating effect, and the bodies are deformed....
, 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
Dynamics (mechanics)

In physics the term dynamics customarily refers to the time evolution of physical processes. These processes may be microscopic as in particle physics, kinetic theory, and chemical reactions, or macroscopic as in the predictions of statistical mechanics and nonequilibrium thermodynamics....
 is concerned with moving and colliding objects.

Elastic and Inelastic Collisions
A perfectly elastic collision
Elastic collision

An elastic collision is a collision in which the total kinetic energy of the colliding bodies after collision is equal to their total kinetic energy before collision....
 is defined as one in which there is no loss of kinetic energy
Kinetic energy

The kinetic energy of an object is the extra energy which it possesses due to its motion. It is defined as the mechanical work needed to accelerate a body of a given mass from rest to its current velocity....
 in the collision.






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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

Deflection
Collisions involve forces (there is a change in velocity
Velocity

In physics, velocity is defined as the Derivative of Position vector. It is a vector physical quantity; both speed and direction are required to define it....
). Collisions can be elastic
Elastic collision

An elastic collision is a collision in which the total kinetic energy of the colliding bodies after collision is equal to their total kinetic energy before collision....
, meaning they conserve energy
Energy

In physics, energy is a scalar physical quantity that describes the amount of Work_ that can be performed by a force. Energy is an attribute of objects and systems that is subject to a conservation law....
 and momentum
Momentum

In classical mechanics, momentum is the product of the mass and velocity of an object . For more accurate measures of momentum, see the section Momentum#Modern definitions of momentum on this page....
, inelastic
Inelastic collision

An inelastic collision is a collision in which kinetic energy is not conserved .In collisions of macroscopic bodies, some kinetic energy is turned into vibrational energy of the atoms, causing a heating effect, and the bodies are deformed....
, 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
Dynamics (mechanics)

In physics the term dynamics customarily refers to the time evolution of physical processes. These processes may be microscopic as in particle physics, kinetic theory, and chemical reactions, or macroscopic as in the predictions of statistical mechanics and nonequilibrium thermodynamics....
 is concerned with moving and colliding objects.

Elastic and Inelastic Collisions


A perfectly elastic collision
Elastic collision

An elastic collision is a collision in which the total kinetic energy of the colliding bodies after collision is equal to their total kinetic energy before collision....
 is defined as one in which there is no loss of kinetic energy
Kinetic energy

The kinetic energy of an object is the extra energy which it possesses due to its motion. It is defined as the mechanical work needed to accelerate a body of a given mass from rest to its current velocity....
 in the collision. An inelastic collision
Inelastic collision

An inelastic collision is a collision in which kinetic energy is not conserved .In collisions of macroscopic bodies, some kinetic energy is turned into vibrational energy of the atoms, causing a heating effect, and the bodies are deformed....
 is one in which part of the kinetic energy is changed to some other form of energy in the collision. Any macroscopic collision between objects will convert some of the kinetic energy into internal energy
Internal energy

In thermodynamics, the internal energy of a thermodynamic system, or a physical body with well-defined dimension, denoted by U, or sometimes E, is the total of the kinetic energy due to the motion of molecules and the potential energy associated with the vibrational and electricity energy of atoms within molecules or crysta...
 and other forms of energy, so no large scale impacts are perfectly elastic. Momentum
Momentum

In classical mechanics, momentum is the product of the mass and velocity of an object . For more accurate measures of momentum, see the section Momentum#Modern definitions of momentum on this page....
 is conserved in inelastic collisions, but one cannot track the kinetic energy through the collision since some of it is converted to other forms of energy. Collisions in ideal gases approach perfectly elastic collisions, as do scattering interactions of sub-atomic particles which are deflected by the electromagnetic force
Electromagnetic force

In physics, the electromagnetic force is the force that the electromagnetic field exerts on electrically charged particles. It is the electromagnetic force that holds electrons and protons together in atoms, and which hold atoms together to make molecules....
. Some large-scale interactions like the slingshot type gravitational interactions between satellites and planets are perfectly elastic. 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.

Mathematical description

Let the linear, angular and internal momenta of a molecule be given by the set of r variables . The state of a molecule may then be described by the range dwi = dp1dp2dp3 ... dpr. 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.)

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 , which refers to the constellation (i, j) before the collision, and the (in general different) constellation (k, l) after the collision.

This notation is convenient in proving Boltzmann's H-theorem
H-theorem

In thermodynamics, the H-theorem, introduced by Ludwig Boltzmann in 1872, describes the increase in the entropy of an ideal gas in an irreversible process, by considering the Boltzmann equation....
 of statistical mechanics
Statistical mechanics

Statistical mechanics is the application of probability theory, which includes Mathematics tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force....
.

Cue Sports

In cue sports, 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
Newton's laws of motion

Newton's laws of motion are three physical laws that form the basis for classical mechanics, Direct relationship the forces acting on a Physical body to the motion of the body....
. 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 m1 and m2, with respective initial velocities v1 in the x-direction, and v2 = 0, and final velocities V1 and V2.

Conservation of momentum: m1v1 = m1V1+ m2V2.

Conservation of energy for elastic collision: (1/2)m1|v1|2 = (1/2)m1|V1|2 + (1/2)m2|V2|2

Now consider the case m1 = m2, we then obtain v1=V1+V2 and |v1|2 = |V1|2+|V2|2

Using the dot product
Dot product

In mathematics, the dot product, also known as the scalar product, is an operation which takes two vector over the real numbers R and returns a real-valued scalar quantity....
, |v1|2 = v1•v1 = |V1|2+|V2|2+2V1•V2

So V1•V2 = 0, so they are perpendicular.

Traffic

In traffic
Traffic

Traffic on roads may consist of pedestrians, ridden or herded animals, vehicles, streetcars and other conveyances, either singly or together, while using the public way for purposes of travel....
 such a collision can be between two vehicle
Vehicle

Vehicles, derived from the Latin word, vehiculum, are non-living means of transport. Most often they are manufactured , although some other means of transport which are not made by humans also may be called vehicles; examples include icebergs and floating tree trunks....
s, a vehicle and a person
Person

The term person in common usage means an individual human being. In the fields of law, philosophy, medicine, and others, the term also has specialised context-specific meanings....
, a vehicle and an object
Object (philosophy)

In philosophy, an object is a thing, an entity, or a being. This may be taken in several senses.In its weakest sense, the word object is the most all-purpose of nouns, and can replace a noun in any sentence at all....
, two persons or a person and an object (and more if an animal
Animal

Animals are a major group of multicellular, eukaryotic organisms of the Kingdom Animalia or Metazoa. Their body plan eventually becomes fixed as they develop, although some undergo a process of metamorphosis later on in their life....
 is involved). It is an accident
Accident

An accident is a specific, identifiable, unexpected, unusual and unintended external action which occurs in a particular time and place, without apparent or deliberate cause but with marked effects....
 or even a disaster
Disaster

File:Post-and-Grant-Avenue.-Look.jpgA disaster is the tragedy of a natural hazard or man-made hazard that negatively affects society or environment ....
. At level crossing
Level crossing

The term level crossing is a crossing on one level ? without recourse to a bridge or tunnel — of a railway line by a road, path, or another railroad....
s sometimes a train
Train

A train is a connected series of vehicles that move along a track to rail transport from one place to another. The track usually consists of two rail tracks, but might also be a monorail or magnetic levitation train guideway....
 collides with a vehicle or person. Due to the velocity
Velocity

In physics, velocity is defined as the Derivative of Position vector. It is a vector physical quantity; both speed and direction are required to define it....
 and mass
Mass

In physical science, mass refers to the degree of acceleration a body acquires when subject to a force: bodies with greater mass are accelerated less by the same force....
 of a train it needs a long distance to stop, typically longer than the train operator can see. 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
Mass

In physical science, mass refers to the degree of acceleration a body acquires when subject to a force: bodies with greater mass are accelerated less by the same force....
 and momentum
Momentum

In classical mechanics, momentum is the product of the mass and velocity of an object . For more accurate measures of momentum, see the section Momentum#Modern definitions of momentum on this page....
.

Attack

Types of attack by means of a deliberate collision include:
  • with the body: unarmed striking
    Strike (attack)

    A strike is an attack with an inanimate object, such as a weapon, or with a part of the human body intended to cause an effect upon an opponent or to simply cause harm to an opponent....
    , punching
    Punch (strike)

    A punch is "a thrusting blow, esp. with the fist." In some sports and disciplines, such as boxing or martial arts, where punches are regularly practiced, hand wraps or other padding such as gloves may be employed to protect athletes and practitioners from injuring themselves....
    , kick
    Kick

    In martial arts, combat sports or violence, a kick is a strike using the foot, Human leg, or knee . This attack is often used in hand-to-hand combat, especially in stand-up fighting....
    ing, martial arts
    Martial arts

    Martial arts are systems of codified practices and traditions of training for combat. While they may be studied for various reasons, martial arts share a single objective: to physically defeat other persons and to defend oneself or others from physical threat....
    , pugilism
  • striking directly with a weapon, such as a sword
    Sword

    A sword is a long, edged piece of metal, used as a cutting, thrusting, and clubbing weapon in many civilizations throughout the world. The word sword comes from the Old English language wikt:sweord, cognate to Old High German swert, Middle Dutch swaert, Old Norse sver? Old Frisian and Old Saxon swerd and Dutch langua...
    , club
    Club (weapon)

    A club is among the simplest of all weapons. A club is essentially a short staff , or stick, usually made of wood, and wielded as a weapon....
     or axe
    Axe

    The axe, or ax, is an implement that has been used for Millennium to shape, split and cut wood, harvest Lumber, as a weapon and a ceremony or Heraldry symbol....
  • ramming
    Ramming

    In warfare, ramming is a technique that was used in the air, sea and land combat. The term originated from battering ram, which is a siege weapon used to bring down fortifications by hitting it with force, of which the momentum of the ram being sufficient to damage the target....
     with an object or vehicle, e.g.:
    • a car deliberately crashing into a building to break into it
    • a plane deliberately crashing into a building to cause destruction


An attacking collision with a distant object can be achieved by throwing or launching a projectile
Projectile

A projectile is any object propelled through space by the exertion of a force, which ceases after launch. In a general sense, even a Football or baseball may be considered a projectile....
.

Space exploration

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:
  • During Apollo 13
    Apollo 13

    Apollo 13 was the third manned lunar-landing mission, part of Project Apollo under NASA in the United States. The crew members were Commander Jim Lovell, Command Module pilot Jack Swigert, and Lunar Module pilot Fred W....
    , Apollo 14
    Apollo 14

    Apollo 14 was the eighth manned mission in the Apollo program and the third mission to land on the Moon. The 9 day mission was launched on January 31 1971, with lunar touch down on February 5....
    , Apollo 15
    Apollo 15

    Apollo 15 was the ninth manned mission in the Apollo program and the fourth mission to land on the Moon. It was the first of what were termed "J missions", long duration stays on the Moon with a greater focus on science than had been possible on previous missions....
    , Apollo 16
    Apollo 16

    Apollo 16 was the tenth manned mission in the Apollo program, the fifth mission to land on the Moon and the first to land in the highlands area....
     and Apollo 17
    Apollo 17

    Apollo 17 was the eleventh Human spaceflight in the NASA Apollo program. It was the first night launch of a United States human spaceflight and the sixth and final lunar landing mission of the Apollo program....
    , the S-IVB
    S-IVB

    The S-IVB was built by the Douglas Aircraft Company and served as the third stage on the Saturn V and second stage on the Saturn IB. It had one J-2 engine....
     (the rocket's third stage) was crashed into the Moon
    Moon

    The Moon is Earth's only natural satellite and the List of natural satellites by diameter satellite in the Solar System. The average centre-to-centre distance from the Earth to the Moon is km, about thirty times the diameter of the Earth....
     in order to perform seismic measurement used for characterizing the lunar core.
  • Deep Impact (space mission)
    Deep Impact (space mission)

    Deep Impact is an ongoing NASA space probe launched on 12 January 2005 that was designed to study the composition of the interior of the comet 9P/Tempel by colliding a section of the spacecraft into the comet....
  • SMART-1
    SMART-1

    SMART-1 was a Swedish-designed European Space Agency satellite that orbited around the Moon. It was launched on September 27, 2003 at 23:14 Coordinated Universal Time from the Guiana Space Centre in Kourou, French Guiana....
     - European Space Agency
    European Space Agency

    The European Space Agency , established in 1975, is an intergovernmentalism organisation dedicated to the Space exploration, currently with 18 member states....
     satellite
  • Moon impact probe
    Moon Impact Probe

    The Moon Impact Probe developed by the Indian Space Research Organisation, India's national space agency, was a moon probe that was released by ISRO's Chandrayaan-1 Exploration of the Moon orbiter which in turn was launched, on 22nd October, 2008, aboard a modified version of ISRO's Polar Satellite Launch Vehicle....
     - ISRO probe


See also

  • Coefficient of restitution
    Coefficient of restitution

    The coefficient of restitution or COR of an object is a Fraction al value representing the ratio of velocities before and after an impact....
  • Collision detection
    Collision detection

    In physical simulations, video games and computational geometry, collision detection involves algorithms for checking for collision, i.e. intersection, of two given solids....
  • Collision (telecommunications)
    Collision (telecommunications)

    In telecommunication, the term collision has the following meanings:# In a data transmission system, the situation that occurs when two or more demands are made simultaneously on equipment that can handle only one at any given instant....
  • Car accident
    Car accident

    A car accident is a road traffic incident that usually involves one road vehicle collision with another vehicle or other road user, animal, or a stationary roadside object, and may result in injury, property damage, and possibly death....
  • Elastic collision
    Elastic collision

    An elastic collision is a collision in which the total kinetic energy of the colliding bodies after collision is equal to their total kinetic energy before collision....
  • Friction
    Friction

    File:Friction alt.svgFriction is the force resisting the relative lateral motion of solid surfaces, fluid layers, or material elements in contact....
  • Impact crater
    Impact crater

    In the broadest sense, the term impact crater can be applied to any depression, natural or manmade, resulting from the high velocity impact of a projectile with larger body....
  • Impact event
    Impact event

    An impact event is the collision of a large meteoroid, asteroid or comet with the Earth. Impact events have been a plot and background element in science fiction since knowledge of real impacts became established in the scientific mainstream....
  • Inelastic collision
    Inelastic collision

    An inelastic collision is a collision in which kinetic energy is not conserved .In collisions of macroscopic bodies, some kinetic energy is turned into vibrational energy of the atoms, causing a heating effect, and the bodies are deformed....
  • Kinetic theory
    Kinetic theory

    Kinetic theory attempts to explain macroscopic properties of gases, such as pressure, temperature, or volume, by considering their molecule composition and motion ....

    - collisions between molecule
    Molecule

    In chemistry, a molecule is defined as a sufficiently stable, electric charge neutral group of at least two atoms in a definite arrangement held together by very strong chemical bonds....
    s
  • Mid-air collision
    Mid-air collision

    A mid-air collision is an aviation accident in which two or more aircraft come into unplanned contact during flight. Due to the relatively high velocities involved and any subsequent impact on the ground or sea, very severe damage or the total destruction of at least one of the aircraft involved usually results....
  • Projectile
    Projectile

    A projectile is any object propelled through space by the exertion of a force, which ceases after launch. In a general sense, even a Football or baseball may be considered a projectile....
  • Space debris
    Space debris

    Space debris or orbital debris, also called space junk and space waste, are the objects in orbit around Earth created by humans, and that no longer serve any useful purpose....


External links

  • - Oblique inelastic collision between two homogeneous spheres.
  • - Java applet that simulates elastic collisions.
  • - One Dimensional Collision Flash Applet.
  • - One Dimensional Collision Easy Java Simulation Open Source Applet by lookang.
  • - Two Dimensional Collision Flash Applet.