A collision is an isolated event in which two or more moving bodies (colliding bodies) exert relatively strong forces on each other for a relatively short time.

Dynamics

Collisions involve forces (there is a change in velocity In physics, velocity is defined as the rate of change of position. It is a vector physical quantity; both speed and direction are required to define it. In the SI system, it is measured in meters per second: (m/s) or ms-1. The scalar absolute value (magnitude) of velocity is speed. For example, "5 meters per second" is a scalar and not a). Collisions can be elastic 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. Elastic collisions occur only if there is no net conversion of kinetic energy into other forms. During the collision kinetic energy is first converted to potential energy associated, meaning they conserve energy In physics, energy is a scalar physical quantity that describes the amount of work that can be performed by a force, an attribute of objects and systems that is subject to a conservation law. Different forms of energy include kinetic, potential, thermal, gravitational, sound, light, elastic, and electromagnetic energy. The forms of energy are and momentum In classical mechanics, momentum is the product of the mass and velocity of an object (p = mv). For more accurate measures of momentum, see the section "modern definitions of momentum" on this page. It is sometimes referred to as linear momentum to distinguish it from the related subject of angular momentum. Linear momentum is a vector, inelastic 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 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 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. Elastic collisions occur only if there is no net conversion of kinetic energy into other forms. During the collision kinetic energy is first converted to potential energy associated is defined as one in which there is no loss of kinetic energy The kinetic energy of an object is the extra 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 current velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. Negative work of the same magnitude in the collision. An inelastic collision 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 In thermodynamics, the internal energy of a thermodynamic system, or a body with well-defined boundaries, 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 electric energy of atoms within molecules or crystals. It includes the energy in all and other forms of energy, so no large scale impacts are perfectly elastic. Momentum In classical mechanics, momentum is the product of the mass and velocity of an object (p = mv). For more accurate measures of momentum, see the section "modern definitions of momentum" on this page. It is sometimes referred to as linear momentum to distinguish it from the related subject of angular momentum. Linear momentum is a vector 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 An ideal gas is a theoretical gas composed of a set of randomly-moving point particles that interact only through elastic collisions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics approach perfectly elastic collisions, as do scattering interactions of sub-atomic particles which are deflected by the 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. The electromagnetic force operates via the exchange of messenger particles called photons. 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 { p_i }. The state of a molecule may then be described by the range δw_i = δp₁δp₂δp₃ ... δp_r. 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 of statistical mechanics Statistical mechanics is the application of probability theory, which includes mathematical 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. It provides a framework for relating the microscopic properties of individual atoms and molecules to.

Cue Sports

In cue sports Cue sports , also known as billiard sports, are a wide variety of games of skill generally played with a cue stick which is used to strike billiard balls, moving them around a cloth-covered billiards table bounded by rubber cushions, 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 Rolling resistance, sometimes called rolling friction or rolling drag, is the resistance that occurs when a round object such as a ball or tire rolls on a flat surface. It is intimately associated with the physics concepts of inertia and friction. It is caused mainly by the deformation of the object, the deformation of the surface, or both, their behavior is often used to illustrate Newton's laws of motion Newton's laws of motion are three physical laws that form the basis for classical mechanics. They are:. 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.^[1]

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 In mathematics, the dot product, also known as the scalar product, is an operation which takes two vectors over the real numbers R and returns a real-valued scalar quantity. It is the standard inner product of the orthonormal Euclidean space. It contrasts with the cross product which produces a vector result, |v₁|² = v₁•v₁ = |V₁|²+|V₂|²+2V₁•V₂

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

Attack

Types of attack by means of a deliberate collision include:

• with the body: unarmed striking 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. An attack with the hand closed into a fist is called a punch; an attack with the leg or foot is referred to as a kick;, punching 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, kicking In martial arts, combat sports or violence, a kick is a strike using the foot, leg, or knee . This attack is often used in hand-to-hand combat, especially in stand-up fighting. Kicks play a great part in many martial arts, such as Taekwondo, Kung fu, Wushu, Karate, Kickboxing, Muay Thai, Capoeira, Silat, Sanshou, Vovinam, Kalarippayattu, and, 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. In addition, some martial arts are linked to beliefs such as Hinduism, Buddhism, Daoism,, pugilism
• striking directly with a weapon, such as a 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 sweord, cognate to Old High German swert, Middle Dutch swaert, Old Norse sverð Old Frisian and Old Saxon swerd and Modern Dutch zwaard and German Schwert, from a Proto-, club 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 The axe, or ax, is an implement that has been used for millennia to shape, split and cut wood, harvest timber, as a weapon and a ceremonial or heraldic symbol. The axe has many forms and specialized uses but generally consists of an axe head with a handle, or helve
• 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. Thus, in warfare ramming refers to hitting a target by running oneself with an object or vehicle, e.g.:
  • a car deliberately crashing into a building to break into it
  • a battering ram A battering ram is a siege engine originating in ancient times to break open fortification walls or doors, medevil 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 A projectile is any object propelled through space by the exertion of a force which ceases after launch. A football after being kicked and a baseball after being hit could be considered projectiles. However, the word is most often used to refer to weapons designed with the appropriate size, shape and hardness, and propelled with sufficient speed,.

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 was the third manned mission by NASA intended to land on the moon, but a mid-mission technical malfunction forced the lunar landing to be aborted. The crewmembers were Commander James A. Lovell, Command Module pilot John L. "Jack" Swigert, and Lunar Module pilot Fred W. Haise, Apollo 14 Apollo 14 was the eighth manned mission in the Apollo program and the third mission to land on the Moon. The nine-day mission was launched on January 31, 1971, with lunar touch down on February 5. The Lunar Module landed in the Fra Mauro formation; this had originally been the target of the ill-fated Apollo 13 mission. During the two lunar EVA's, 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. The mission began on July 26, 1971, and concluded on August 7. NASA called, 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. The mission was launched on April 16, 1972, and concluded on April 27. It was a J-class mission, featuring a Lunar Rover and it brought back 94.7 kg of lunar samples. It included three lunar EVA: 7.2 and Apollo 17 Apollo 17 was the eleventh manned space mission in the NASA Apollo program. It was the first night launch of a U.S. human spaceflight and the sixth and final lunar landing mission of the Apollo program. The mission was launched at 12:33 a.m. EST on December 7, 1972, and concluded on December 19. It remains both the most recent manned moon landing, the 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. For lunar missions it was fired twice: first for the orbit insertion after second stage cutoff, and then for translunar injection (TLI) (the rocket's third stage) was crashed into the Moon The Moon is Earth's only natural satellite and the fifth largest satellite in the Solar System. The average centre-to-centre distance from the Earth to the Moon is 384,403 km, about thirty times the diameter of the Earth. The common centre of mass of the system is located about 1,700 km—a quarter the Earth's radius—beneath the surface of the in order to perform seismic measurement used for characterizing the lunar core.
• Deep Impact (space mission) Deep Impact is an ongoing NASA space probe launched on January 12, 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. At 5:52 UTC on July 4, 2005, the impactor of the Deep Impact probe successfully impacted the comet's nucleus, excavating debris from the
• 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 UTC from the Guiana Space Centre in Kourou, French Guiana. "SMART" stands for Small Missions for Advanced Research in Technology. On September 3, 2006 , SMART-1 was deliberately crashed into the Moon' - European Space Agency The European Space Agency , established in 1975, is an intergovernmental organisation dedicated to the exploration of space, currently with 18 member states. Headquartered in Paris, ESA has a staff of close to 2,000 with an annual budget of about €3.6 billion in 2009 satellite
• Moon impact probe - ISRO The Indian Space Research Organisation is the primary body for space research under the control of the government of India. It was established in its modern form in 1969 as a result of coordinated efforts initiated earlier. Under the guidance of a number of scientists, ISRO has conducted a variety of operations—supported by its launch vehicle probe

See also

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.
• One Dimensional Collision - One Dimensional Collision Easy Java Simulation Open Source Applet by lookang.
• Two Dimensional Collision - Two Dimensional Collision Flash Applet.

Notes

1. ^ Alciatore, David G. (January 2006). "TP 3.1 90° rule" (PDF). http://billiards.colostate.edu/technical_proofs/TP_3-1.pdf. Retrieved on 2008-03-08.

References

• Tolman, R. C. (1938). The Principles of Statistical Mechanics. Oxford: Clarendon Press. Reissued (1979) New York: Dover ISBN 0-486-63896-0.

Categories: Mechanics | Introductory physics

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• Collision
• Society: Issues: Transportation: Aviation: Accidents: Specific Crashes: Tenerife Pan Am Flight 1736 and KLM Flight 4805 Collision

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