Collision
Encyclopedia
A collision is an isolated event which two or more moving bodies (colliding bodies) exert forces on each other for a relatively short time.
Although the most common colloquial use of the word "collision" refers to accident
s in which two or more objects collide, the scientific use of the word "collision" implies nothing about the magnitude of the forces.
Some examples of physical interactions that scientists would consider collisions:
Some colloquial uses of the word collision are:
). The magnitude of the velocity difference at impact is called the closing speed. All collisions conserve momentum
. What distinguishes different types of collisions is whether they also conserve kinetic energy
.
Specifically, collisions can either be elastic
, meaning they conserve both momentum and kinetic energy, or inelastic
, meaning they conserve momentum but not kinetic energy. An inelastic collision is sometimes also called a plastic collision.
A “perfectly-inelastic” collision (also called a "perfectly-plastic" collision) is a limiting case of inelastic collision in which the two bodies stick together after impact.
The degree to which a collision is elastic or inelastic is quantified by the coefficient of restitution
, a value that generally ranges between zero and one. A perfectly elastic collision has a coefficient of restitution of one; a perfectly-inelastic collision has a coefficient of restitution of zero.
is defined as one in which there is no loss of kinetic energy
in the collision. In reality, any macroscopic collision between objects will convert some kinetic energy to internal energy
and other forms of energy, so no large scale impacts are perfectly elastic. However, some problems are sufficiently close to perfectly elastic that they can be approximated as such.
An inelastic collision
is one in which part of the kinetic energy is changed to some other form of energy in the collision. Momentum
is conserved in inelastic collisions (as it is for elastic 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. 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.
.
.
. 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 is an important fact that professional billiard players take into account.
Consider an elastic collision in 2 dimensions of any 2 masses m1 and m2, with respective initial velocities u1 in the x-direction, and u2 = 0, and final velocities V1 and V2.
Conservation of momentum: m1u1 = m1V1+ m2V2.
Conservation of energy for elastic collision: (1/2)m1|u1|2 = (1/2)m1|V1|2 + (1/2)m2|V2|2
Now consider the case m1 = m2, we then obtain u1=V1+V2 and |u1|2 = |V1|2+|V2|2
Using the dot product
, |u1|2 = u1•u1 = |V1|2+|V2|2+2V1•V2
So V1•V2 = 0, so they are perpendicular.
, the colliding particles stick together. It is necessary to consider conservation of momentum:
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
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 a rocket
applying thrust
(compare the derivation of the Tsiolkovsky rocket equation).
(sometimes called a "force plate") as well as detailed kinematic and dynamic (sometimes termed kinetic) analysis.
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
of statistical mechanics
.
An attacking collision with a distant object can be achieved by throwing or launching a projectile
.
Although the most common colloquial use of the word "collision" refers to accident
Accident
An accident or mishap is an unforeseen and unplanned event or circumstance, often with lack of intention or necessity. It implies a generally negative outcome which may have been avoided or prevented had circumstances leading up to the accident been recognized, and acted upon, prior to its...
s in which two or more objects collide, the scientific use of the word "collision" implies nothing about the magnitude of the forces.
Some examples of physical interactions that scientists would consider collisions:
- An insect touches its antenna to the leaf of a plant. The antenna is said to collide with leaf.
- A cat walks delicately through the grass. Each contact that its paws make with the ground is a collision. Each brush of its fur against a blade of grass is a collision.
Some colloquial uses of the word collision are:
- automobile collision, two cars colliding
- mid-air collisionMid-air collisionA mid-air collision is an aviation accident in which two or more aircraft come into contact during flight. Owing 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...
, two planes colliding - ship collisionShip collisionShip collision is the structural impact between two ships or one ship and a floating or still object such as an iceberg. Ship collisions are of particular importance in marine accidents...
, two ships colliding
Overview
Collisions involve forces (there is a change in velocityVelocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...
). The magnitude of the velocity difference at impact is called the closing speed. All collisions conserve momentum
Momentum
In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...
. What distinguishes different types of collisions is whether they also conserve kinetic energy
Kinetic energy
The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...
.
Specifically, collisions can either be elastic
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...
, meaning they conserve both momentum and kinetic energy, or inelastic
Inelastic collision
An inelastic collision, in contrast to an elastic 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.The molecules of a gas...
, meaning they conserve momentum but not kinetic energy. An inelastic collision is sometimes also called a plastic collision.
A “perfectly-inelastic” collision (also called a "perfectly-plastic" collision) is a limiting case of inelastic collision in which the two bodies stick together after impact.
The degree to which a collision is elastic or inelastic is quantified by 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...
, a value that generally ranges between zero and one. A perfectly elastic collision has a coefficient of restitution of one; a perfectly-inelastic collision has a coefficient of restitution of zero.
Types of collisions
A perfectly elastic collisionElastic 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 defined as one in which there is no loss of kinetic energy
Kinetic energy
The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...
in the collision. In reality, any macroscopic collision between objects will convert some kinetic energy to internal energy
Internal energy
In thermodynamics, the internal energy is the total energy contained by a thermodynamic system. It is the energy needed to create the system, but excludes the energy to displace the system's surroundings, any energy associated with a move as a whole, or due to external force fields. Internal...
and other forms of energy, so no large scale impacts are perfectly elastic. However, some problems are sufficiently close to perfectly elastic that they can be approximated as such.
An inelastic collision
Inelastic collision
An inelastic collision, in contrast to an elastic 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.The molecules of a gas...
is one in which part of the kinetic energy is changed to some other form of energy in the collision. Momentum
Momentum
In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...
is conserved in inelastic collisions (as it is for elastic 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. 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.
Analytical vs. numerical approaches towards resolving collisions
Relatively few problems involving collisions can be solved analytically; the remainder require numerical methods. An important problem in simulating collisions is determining whether two objects have in fact collided. This problem is called collision detectionCollision detection
Collision detection typically refers to the computational problem of detecting the intersection of two or more objects. While the topic is most often associated with its use in video games and other physical simulations, it also has applications in robotics...
.
.
Billiards
Collisions play an important role in cue sports. 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 motionNewton's laws of motion
Newton's laws of motion are three physical laws that form the basis for classical mechanics. They describe the relationship between the forces acting on a body and its motion due to those forces...
. 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 is an important fact that professional billiard players take into account.
Consider an elastic collision in 2 dimensions of any 2 masses m1 and m2, with respective initial velocities u1 in the x-direction, and u2 = 0, and final velocities V1 and V2.
Conservation of momentum: m1u1 = m1V1+ m2V2.
Conservation of energy for elastic collision: (1/2)m1|u1|2 = (1/2)m1|V1|2 + (1/2)m2|V2|2
Now consider the case m1 = m2, we then obtain u1=V1+V2 and |u1|2 = |V1|2+|V2|2
Using the dot product
Dot product
In mathematics, the dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers and returns a single number obtained by multiplying corresponding entries and then summing those products...
, |u1|2 = u1•u1 = |V1|2+|V2|2+2V1•V2
So V1•V2 = 0, so they are perpendicular.
Perfectly inelastic collision
In a perfectly inelastic collision, i.e., a zero coefficient of restitutionCoefficient 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:
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).
Animal locomotion
Collisions of an animal's foot or paw with the underlying substrate are generally termed ground reaction forces. These collisions are inelastic, as kinetic energy is not conserved. An important research topic in prosthetics is quantifying the forces generated during the foot-ground collisions associated with both disabled and non-disabled gait. This quantification typically requires subjects to walk across a force platformForce platform
Force platforms or force plates are measuring instruments that measure the ground reaction forces generated by a body standing on or moving across them, to quantify balance, gait and other parameters of biomechanics. Most common areas of application are medicine and sports.The simplest force...
(sometimes called a "force plate") as well as detailed kinematic and dynamic (sometimes termed kinetic) analysis.
Collisions used as a experimental tool
Collisions can be used as an experimental technique to study material properties of objects and other physical phenomena.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 13Apollo 13Apollo 13 was the seventh manned mission in the American Apollo space program and the third intended to land on the Moon. The craft was launched on April 11, 1970, at 13:13 CST. The landing was aborted after an oxygen tank exploded two days later, crippling the service module upon which the Command...
, Apollo 14Apollo 14Apollo 14 was the eighth manned mission in the American Apollo program, and the third to land on the Moon. It was the last of the "H missions", targeted landings with two-day stays on the Moon with two lunar EVAs, or moonwalks....
, Apollo 15Apollo 15Apollo 15 was the ninth manned mission in the American Apollo space program, the fourth to land on the Moon and the eighth successful manned mission. 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...
, Apollo 16Apollo 16Young and Duke served as the backup crew for Apollo 13; Mattingly was slated to be the Apollo 13 command module pilot until being pulled from the mission due to his exposure to rubella through Duke.-Backup crew:...
and Apollo 17Apollo 17Apollo 17 was the eleventh and final manned mission in the American Apollo space program. Launched at 12:33 a.m. EST on December 7, 1972, with a three-member crew consisting of Commander Eugene Cernan, Command Module Pilot Ronald Evans, and Lunar Module Pilot Harrison Schmitt, Apollo 17 remains the...
, the S-IVBS-IVBThe 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 MoonMoonThe Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...
in order to perform seismic measurement used for characterizing the lunar core. - Deep Impact
- SMART-1SMART-1SMART-1 was a Swedish-designed European Space Agency satellite that orbited around the Moon. It was launched on September 27, 2003 at 23:14 UTC from the Guiana Space Centre in Kourou, French Guiana. "SMART" stands for Small Missions for Advanced Research in Technology...
- European Space AgencyEuropean Space AgencyThe European Space Agency , established in 1975, is an intergovernmental organisation dedicated to the exploration of space, currently with 18 member states...
satellite - Moon impact probeMoon Impact ProbeThe Moon Impact Probe developed by the Indian Space Research Organisation , India's national space agency, was a lunar probe that was released by ISRO's Chandrayaan-1 lunar remote sensing orbiter which in turn was launched, on 22 October 2008, aboard a modified version of ISRO's Polar Satellite...
- ISRO probe
Mathematical description of molecular collisions
Let the linear, angular and internal momenta of a molecule be given by the set of r variables { pi }. The state of a molecule may then be described by the range δwi = δp1δp2δp3 ... δpr. 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 Classical Statistical Mechanics, the H-theorem, introduced by Ludwig Boltzmann in 1872, describes the increase in the entropy of an ideal gas in an irreversible process. H-theorem follows from considerations of Boltzmann's equation...
of statistical mechanics
Statistical mechanics
Statistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...
.
Attack by means of a deliberate collision
Types of attack by means of a deliberate collision include:- with the body: unarmed strikingStrike (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. There are many different varieties of strikes...
, punchingPunch (strike)A punch is a striking blow with the fist. It is the most commonly used attack in hand to hand combat. It is used in some martial arts and combat sports, most notably boxing where it is the only type of technique allowed...
, kickKickIn combat sports and hand-to-hand combat, a kick is a physical strike using the foot, leg, or knee . This type of attack is used frequently, especially in stand-up fighting...
ing, martial artsMartial artsMartial arts are extensive systems of codified practices and traditions of combat, practiced for a variety of reasons, including self-defense, competition, physical health and fitness, as well as mental and spiritual development....
, pugilism - striking directly with a weapon, such as a swordSwordA sword is a bladed weapon used primarily for cutting or thrusting. The precise definition of the term varies with the historical epoch or the geographical region under consideration...
, clubClub (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 since prehistoric times....
or axeAxeThe axe, or ax, is an implement that has been used for millennia to shape, split and cut wood; to harvest timber; as a weapon; and as a ceremonial or heraldic symbol... - rammingRammingIn warfare, ramming is a technique that was used in air, sea and land combat. The term originated from battering ram, a siege weapon used to bring down fortifications by hitting it with the force of the ram's momentum...
with an object or vehicle, e.g.:- a car deliberately crashing into a building to break into it
- a battering ramBattering ramA battering ram is a siege engine originating in ancient times and designed to break open the masonry walls of fortifications or splinter their wooden gates...
, medieval weapon used for breaking down large doors, also a modern version is used by police forces during raids
An attacking collision with a distant object can be achieved by throwing or launching 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....
.
See also
- Coefficient of restitutionCoefficient of restitutionThe 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...
- Collision detectionCollision detectionCollision detection typically refers to the computational problem of detecting the intersection of two or more objects. While the topic is most often associated with its use in video games and other physical simulations, it also has applications in robotics...
- Collision (telecommunications)
- Car accidentCar accidentA traffic collision, also known as a traffic accident, motor vehicle collision, motor vehicle accident, car accident, automobile accident, Road Traffic Collision or car crash, occurs when a vehicle collides with another vehicle, pedestrian, animal, road debris, or other stationary obstruction,...
- Elastic collisionElastic collisionAn 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...
- FrictionFrictionFriction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of friction:...
- Head-on collisionHead-on collisionA head-on collision is one where the front ends of two ships, trains, planes or vehicles hit each other, as opposed to a side collision or rear-end collision.-Rail transport:...
- Impact craterImpact craterIn 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 a larger body...
- Impact eventImpact eventAn impact event is the collision of a large meteorite, asteroid, comet, or other celestial object with the Earth or another planet. Throughout recorded history, hundreds of minor impact events have been reported, with some occurrences causing deaths, injuries, property damage or other significant...
- Inelastic collisionInelastic collisionAn inelastic collision, in contrast to an elastic 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.The molecules of a gas...
- Kinetic theoryKinetic theoryThe kinetic theory of gases describes a gas as a large number of small particles , all of which are in constant, random motion. The rapidly moving particles constantly collide with each other and with the walls of the container...
- collisions between moleculeMoleculeA 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 - Mid-air collisionMid-air collisionA mid-air collision is an aviation accident in which two or more aircraft come into contact during flight. Owing 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...
- ProjectileProjectileA 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....
- Space debrisSpace debrisSpace debris, also known as orbital debris, space junk, and space waste, is the collection of objects in orbit around Earth that were created by humans but no longer serve any useful purpose. These objects consist of everything from spent rocket stages and defunct satellites to erosion, explosion...
- Train wreckTrain wreckA train wreck or train crash is a type of disaster involving one or more trains. Train wrecks often occur as a result of miscommunication, as when a moving train meets another train on the same track; or an accident, such as when a train wheel jumps off a track in a derailment; or when a boiler...
External links
- Three Dimensional Collision - Oblique inelastic collision between two homogeneous spheres.
- Two Dimensional Collision - Java applet that simulates elastic collisions.
- One Dimensional Collision - One Dimensional Collision Flash Applet.
- Two Dimensional Collision - Two Dimensional Collision Flash Applet.