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Friction is the
force In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving from a Newton's first law, state of rest), i.e., to acce ...

force
resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction: *Dry friction is a force that opposes the relative lateral motion of two solid surfaces in contact. Dry friction is subdivided into ''static friction'' ("
stictionStiction is the static friction that needs to be overcome to enable relative motion of stationary objects in contact. The term is a portmanteau of the words ''static'' and ''friction'', perhaps also influenced by the verb ''adhesion, stick''. Any so ...

stiction
") between non-moving surfaces, and ''kinetic friction'' between moving surfaces. With the exception of atomic or molecular friction, dry friction generally arises from the interaction of surface features, known as asperities (see Figure 1). *Fluid friction describes the friction between layers of a
viscous The viscosity of a fluid In physics, a fluid is a substance that continually Deformation (mechanics), deforms (flows) under an applied shear stress, or external force. Fluids are a Phase (matter), phase of matter and include liquids, Gas, ...
fluid that are moving relative to each other. *Lubricated friction is a case of fluid friction where a
lubricant A lubricant is a substance that helps to reduce friction Friction is the force In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and b ...
fluid separates two solid surfaces. *Skin friction is a component of
drag Drag or The Drag may refer to: Places * Drag, Norway, a village in Tysfjord municipality, Nordland, Norway * ''Drág'', the Hungarian name for Dragu Commune in Sălaj County, Romania * Drag (Austin, Texas), the portion of Guadalupe Street adja ...
, the force resisting the motion of a fluid across the surface of a body. *Internal friction is the force resisting motion between the elements making up a solid material while it undergoes
deformation Deformation can refer to: * Deformation (engineering), changes in an object's shape or form due to the application of a force or forces. ** Deformation (mechanics), such changes considered and analyzed as displacements of continuum bodies. * Defo ...
. When surfaces in contact move relative to each other, the friction between the two surfaces converts
kinetic energy In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...
into
thermal energy Thermal radiation in visible light can be seen on this hot metalwork. Thermal energy refers to several distinct physical concepts, such as the internal energy of a system; heat or sensible heat, which are defined as types of energy transfer (as is ...
(that is, it converts
work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking * Work (physics), the product of ...

work
to
heat In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these ...

heat
). This property can have dramatic consequences, as illustrated by the use of friction created by rubbing pieces of wood together to start a fire. Kinetic energy is converted to thermal energy whenever motion with friction occurs, for example when a
viscous The viscosity of a fluid In physics, a fluid is a substance that continually Deformation (mechanics), deforms (flows) under an applied shear stress, or external force. Fluids are a Phase (matter), phase of matter and include liquids, Gas, ...
fluid is stirred. Another important consequence of many types of friction can be
wear Wear is the damaging, gradual removal or deformation of material at solid surfaces. Causes of wear can be mechanical (e.g., erosion In earth science, erosion is the action of surface processes (such as Surface runoff, water flow or wind) tha ...

wear
, which may lead to performance degradation or damage to components. Friction is a component of the science of
tribology Tribology is the science and engineering of interacting surfaces in relative motion Image:Leaving Yongsan Station.jpg, 300px, Motion involves a change in position In physics, motion is the phenomenon in which an object changes its position (ma ...
. Friction is desirable and important in supplying traction to facilitate motion on land. Most
land vehicle A vehicle (from la, vehiculum) is a machine that transports people or cargo. Vehicles include wagons, bicycles, motor vehicles (motorcycles, cars, trucks, buses), railed vehicles (trains, trams), watercraft (ships, boats), amphibious vehicles ...
s rely on friction for acceleration, deceleration and changing direction. Sudden reductions in traction can cause loss of control and accidents. Friction is not itself a
fundamental force#REDIRECT Fundamental interaction In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics ...
. Dry friction arises from a combination of inter-surface adhesion, surface roughness, surface deformation, and surface contamination. The complexity of these interactions makes the calculation of friction from
first principle A first principle is a basic proposition In logic and linguistics, a proposition is the meaning of a declarative sentence (linguistics), sentence. In philosophy, "Meaning (philosophy), meaning" is understood to be a non-linguistic entity which is ...
s impractical and necessitates the use of
empirical method Empirical research is research using empirical evidence. It is also a way of gaining knowledge by means of direct and indirect observation or experience. Empiricism values some research more than other kinds. Empirical evidence (the record of one ...
s for analysis and the development of theory. Friction is a
non-conservative force A conservative force is a force In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (phy ...
– work done against friction is path dependent. In the presence of friction, some kinetic energy is always transformed to thermal energy, so
mechanical energy In physical sciences Physical science is a branch of natural science that studies abiotic component, non-living systems, in contrast to life science. It in turn has many branches, each referred to as a "physical science", together called the "p ...
is not conserved.


History

The Greeks, including
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher A philosopher is someone who practices philosophy Philosophy (from , ) is the study of general and fundamental quest ...

Aristotle
,
Vitruvius Vitruvius (; c. 80–70 BC – after c. 15 BC) was a Roman architect and engineer during the 1st century BC, known for his multi-volume work entitled ''De architectura''. He originated the idea that all buildings should have three attribute ...

Vitruvius
, and
Pliny the Elder #REDIRECT Pliny the Elder#REDIRECT Pliny the Elder Gaius Plinius Secundus (AD 23/2479), called Pliny the Elder (), was a Roman author, a naturalist Natural history is a domain of inquiry involving organisms, including animals, fungus, fungi, ...

Pliny the Elder
, were interested in the cause and mitigation of friction. They were aware of differences between static and kinetic friction with
Themistius Themistius ( grc-gre, Θεμίστιος, ''Themistios''; 317, Paphlagonia – c. 388 AD, Constantinople la, Constantinopolis , alternate_name = Byzantion (earlier Greek name), Nova Roma ("New Rome"), Miklagard/Miklagarth (Old Norse), Tsarigr ...
stating in 350 that "it is easier to further the motion of a moving body than to move a body at rest". The classic laws of sliding friction were discovered by
Leonardo da Vinci Leonardo di ser Piero da Vinci (15 April 14522 May 1519) was an Italian of the who was active as a painter, , engineer, scientist, theorist, sculptor and architect. While his fame initially rested on his achievements as a painter, he als ...

Leonardo da Vinci
in 1493, a pioneer in
tribology Tribology is the science and engineering of interacting surfaces in relative motion Image:Leaving Yongsan Station.jpg, 300px, Motion involves a change in position In physics, motion is the phenomenon in which an object changes its position (ma ...
, but the laws documented in his notebooks were not published and remained unknown. These laws were rediscovered by
Guillaume Amontons Guillaume Amontons (31 August 1663 – 11 October 1705) was a French scientific instrument inventor and physicist A physicist is a scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge ...

Guillaume Amontons
in 1699 and became known as Amonton's three laws of dry friction. Amontons presented the nature of friction in terms of surface irregularities and the force required to raise the weight pressing the surfaces together. This view was further elaborated by
Bernard Forest de Bélidor Bernard Forest de Bélidor (1698, Catalonia Catalonia (; ca, Catalunya ; Aranese, Aranese Occitan: ''Catalonha'' ; es, Cataluña ) is an Autonomous communities of Spain, autonomous community in the northeastern corner of Spain, designated as ...
and
Leonhard Euler Leonhard Euler ( ; ; 15 April 170718 September 1783) was a Swiss mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ) ...

Leonhard Euler
(1750), who derived the
angle of repose The angle of repose, or critical angle of repose, of a granular material is the steepest angle of descent or dip relative to the horizontal plane to which a material can be piled without slumping. At this angle, the material on the slope face i ...

angle of repose
of a weight on an inclined plane and first distinguished between static and kinetic friction.
John Theophilus Desaguliers John Theophilus Desaguliers FRS (12 March 1683 – 29 February 1744) was a British natural philosopher, clergyman, engineer and freemason who was elected to the Royal Society The Royal Society, formally The Royal Society of London for Impr ...

John Theophilus Desaguliers
(1734) first recognized the role of
adhesion Adhesion is the tendency of dissimilar particles In the Outline of physical science, physical sciences, a particle (or corpuscule in older texts) is a small wikt:local, localized physical body, object to which can be ascribed several physic ...

adhesion
in friction. Microscopic forces cause surfaces to stick together; he proposed that friction was the force necessary to tear the adhering surfaces apart. The understanding of friction was further developed by
Charles-Augustin de Coulomb Charles-Augustin de Coulomb (; ; 14 June 1736 – 23 August 1806) was a French officer, engineer, and physicist. He is best known as the eponymous discoverer of what is now called Coulomb's law, the description of the electrostatics, electrostatic ...
(1785). Coulomb investigated the influence of four main factors on friction: the nature of the materials in contact and their surface coatings; the extent of the surface area; the normal pressure (or load); and the length of time that the surfaces remained in contact (time of repose). Coulomb further considered the influence of sliding velocity, temperature and humidity, in order to decide between the different explanations on the nature of friction that had been proposed. The distinction between static and dynamic friction is made in Coulomb's friction law (see below), although this distinction was already drawn by in 1758. The effect of the time of repose was explained by
Pieter van Musschenbroek Pieter van Musschenbroek (14 March 1692 – 19 September 1761) was a Dutch scientist. He was a professor in Duisburg Duisburg () is a city in the Ruhr metropolitan area of the western Germany, German States of Germany, state of North Rhine-We ...
(1762) by considering the surfaces of fibrous materials, with fibers meshing together, which takes a finite time in which the friction increases.
John LeslieJohn Leslie may refer to: United Kingdom * Sir John Leslie (physicist) (1766–1832), Scottish mathematician and physicist * John Leslie (TV presenter) (born 1965), Scottish former television presenter * John Leslie (bishop of Clogher) (1571–1671) ...
(1766–1832) noted a weakness in the views of Amontons and Coulomb: If friction arises from a weight being drawn up the inclined plane of successive asperities, why then isn't it balanced through descending the opposite slope? Leslie was equally skeptical about the role of adhesion proposed by Desaguliers, which should on the whole have the same tendency to accelerate as to retard the motion. In Leslie's view, friction should be seen as a time-dependent process of flattening, pressing down asperities, which creates new obstacles in what were cavities before. Arthur Jules Morin (1833) developed the concept of sliding versus rolling friction.
Osborne Reynolds Osborne Reynolds FRS (23 August 1842 – 21 February 1912) was an innovator in the understanding of fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids ...

Osborne Reynolds
(1866) derived the equation of viscous flow. This completed the classic empirical model of friction (static, kinetic, and fluid) commonly used today in engineering. In 1877,
Fleeming Jenkin Prof Henry Charles Fleeming Jenkin FRS FRSE LLD (; 25 March 1833 – 12 June 1885) was Regius Professor of Engineering at the University of Edinburgh , latin_name = Universitas Academica Edinburgensis , image_name = University of Edinburg ...

Fleeming Jenkin
and J. A. Ewing investigated the continuity between static and kinetic friction. The focus of research during the 20th century has been to understand the physical mechanisms behind friction.
Frank Philip Bowden Frank Philip Bowden CBE Royal Society, FRS (2 May 1903 – 3 September 1968) was an Australian physicist. Early life He was born in Hobart, Tasmania, the son of telegraph engineer Frank Prosser Bowden. Bowden received his Bachelor of Science ...
and
David Tabor David Tabor (né Tabrisky), FRS (23 October 1913 – 26 November 2005) was a British physicist A physicist is a scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of sci ...
(1950) showed that, at a microscopic level, the actual area of contact between surfaces is a very small fraction of the apparent area. This actual area of contact, caused by asperities increases with pressure. The development of the
atomic force microscope Atomic force microscopy (AFM) or scanning force microscopy (SFM) is a very-high-resolution type of scanning probe microscopy Scanning probe microscopy (SPM) is a branch of microscopy that forms images of surfaces using a physical probe that scans ...
(ca. 1986) enabled scientists to study friction at the
atomic scale Atomic spacing refers to the distance between the Atomic nucleus, nuclei of atoms in a material. This space is extremely large compared to the size of the atomic nucleus, and is related to the chemical bonds which bind atoms together. In solid mate ...
, showing that, on that scale, dry friction is the product of the inter-surface
shear stress Shear stress, often denoted by (Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is approx ...

shear stress
and the contact area. These two discoveries explain Amonton's first law ''(below)''; the macroscopic proportionality between normal force and static frictional force between dry surfaces.


Laws of dry friction

The elementary property of sliding (kinetic) friction were discovered by experiment in the 15th to 18th centuries and were expressed as three empirical laws: * Amontons' First Law: The force of friction is directly proportional to the applied load. *Amontons' Second Law: The force of friction is independent of the apparent area of contact. *Coulomb's Law of Friction: Kinetic friction is independent of the sliding velocity.


Dry friction

Dry friction resists relative lateral motion of two solid surfaces in contact. The two regimes of dry friction are 'static friction' ("
stictionStiction is the static friction that needs to be overcome to enable relative motion of stationary objects in contact. The term is a portmanteau of the words ''static'' and ''friction'', perhaps also influenced by the verb ''adhesion, stick''. Any so ...

stiction
") between non-moving surfaces, and ''kinetic friction'' (sometimes called sliding friction or dynamic friction) between moving surfaces. Coulomb friction, named after
Charles-Augustin de Coulomb Charles-Augustin de Coulomb (; ; 14 June 1736 – 23 August 1806) was a French officer, engineer, and physicist. He is best known as the eponymous discoverer of what is now called Coulomb's law, the description of the electrostatics, electrostatic ...
, is an approximate model used to calculate the force of dry friction. It is governed by the model: :F_\mathrm \leq \mu F_\mathrm, where *F_\mathrm\, is the force of friction exerted by each surface on the other. It is parallel to the surface, in a direction opposite to the net applied force. *\mu\, is the coefficient of friction, which is an empirical property of the contacting materials, *F_\mathrm\, is the
normal force In mechanics Mechanics (Ancient Greek, Greek: ) is the area of physics concerned with the motions of physical objects, more specifically the relationships among force, matter, and motion. Forces applied to objects result in Displacement (ve ...

normal force
exerted by each surface on the other, directed perpendicular (normal) to the surface. The Coulomb friction F_\mathrm\, may take any value from zero up to \mu F_\mathrm\,, and the direction of the frictional force against a surface is opposite to the motion that surface would experience in the absence of friction. Thus, in the static case, the frictional force is exactly what it must be in order to prevent motion between the surfaces; it balances the net force tending to cause such motion. In this case, rather than providing an estimate of the actual frictional force, the Coulomb approximation provides a threshold value for this force, above which motion would commence. This maximum force is known as traction. The force of friction is always exerted in a direction that opposes movement (for kinetic friction) or potential movement (for static friction) between the two surfaces. For example, a
curling Curling is a sport Sport pertains to any form of competitive Competition is a rivalry A rivalry is the state of two people or groups engaging in a lasting competitive relationship. Rivalry is the "against each other" spirit bet ...
stone sliding along the ice experiences a kinetic force slowing it down. For an example of potential movement, the drive wheels of an accelerating car experience a frictional force pointing forward; if they did not, the wheels would spin, and the rubber would slide backwards along the pavement. Note that it is not the direction of movement of the vehicle they oppose, it is the direction of (potential) sliding between tire and road.


Normal force

The normal force is defined as the net force compressing two parallel surfaces together, and its direction is perpendicular to the surfaces. In the simple case of a mass resting on a horizontal surface, the only component of the normal force is the force due to gravity, where N=mg\,. In this case, conditions of equilibrium tell us that the magnitude of the friction force is zero, F_f=0. In fact, the friction force always satisfies F_f\le \mu N, with equality reached only at a critical ramp angle (given by \tan^\mu) that is steep enough to initiate sliding. The friction coefficient is an
empirical Empirical evidence for a proposition In logic and linguistics, a proposition is the meaning of a declarative sentence (linguistics), sentence. In philosophy, "Meaning (philosophy), meaning" is understood to be a non-linguistic entity which is s ...
(experimentally measured) structural property that depends only on various aspects of the contacting materials, such as surface roughness. The coefficient of friction is not a function of mass or volume. For instance, a large aluminum block has the same coefficient of friction as a small aluminum block. However, the magnitude of the friction force itself depends on the normal force, and hence on the mass of the block. Depending on the situation, the calculation of the normal force N might include forces other than gravity. If an object is on a level surface and subjected to an external force P tending to cause it to slide, then the normal force between the object and the surface is just N=mg+P_y, where mg is the block's weight and P_y is the downward component of the external force. Prior to sliding, this friction force is F_f=-P_x, where P_x is the horizontal component of the external force. Thus, F_f\le\mu N in general. Sliding commences only after this frictional force reaches the value F_f=\mu N. Until then, friction is whatever it needs to be to provide equilibrium, so it can be treated as simply a reaction. If the object is on a tilted surface such as an inclined plane, the normal force from gravity is smaller than mg, because less of the force of gravity is perpendicular to the face of the plane. The normal force and the frictional force are ultimately determined using
vector Vector may refer to: Biology *Vector (epidemiology) In epidemiology Epidemiology is the study and analysis of the distribution (who, when, and where), patterns and risk factor, determinants of health and disease conditions in defined pop ...
analysis, usually via a
free body diagram 200px, Block on a ramp and corresponding free body diagram of the block. A free body diagram consists of a diagrammatic representation of a single body or a subsystem of bodies isolated from its surroundings showing all the forces acting on it. In ...

free body diagram
. In general, process for solving any statics problem with friction is to treat contacting surfaces tentatively as immovable so that the corresponding tangential reaction force between them can be calculated. If this frictional reaction force satisfies F_f\le\mu N, then the tentative assumption was correct, and it is the actual frictional force. Otherwise, the friction force must be set equal to F_f=\mu N, and then the resulting force imbalance would then determine the acceleration associated with slipping.


Coefficient of friction

The coefficient of friction (COF), often symbolized by the Greek letter µ, is a
dimensionless In dimensional analysis In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantity, base quantities (such as length, mass, time, and electric curre ...
scalar Scalar may refer to: *Scalar (mathematics), an element of a field, which is used to define a vector space, usually the field of real numbers *Scalar (physics), a physical quantity that can be described by a single element of a number field such as ...
value which equals the ratio of the force of friction between two bodies and the force pressing them together, either during or at the onset of slipping. The coefficient of friction depends on the materials used; for example, ice on steel has a low coefficient of friction, while rubber on pavement has a high coefficient of friction. Coefficients of friction range from near zero to greater than one. It is an axiom of the nature of friction between metal surfaces that it is greater between two surfaces of similar metals than between two surfaces of different metals— hence, brass will have a higher coefficient of friction when moved against brass, but less if moved against steel or aluminum. For surfaces at rest relative to each other \mu = \mu_\mathrm, where \mu_\mathrm is the ''coefficient of static friction''. This is usually larger than its kinetic counterpart. The coefficient of static friction exhibited by a pair of contacting surfaces depends upon the combined effects of material deformation characteristics and
surface roughness Surface roughness, often shortened to roughness, is a component of surface finish, surface texture. It is quantified by the deviations in the direction of the normal (geometry), normal vector of a real surface from its ideal form. If these deviat ...

surface roughness
, both of which have their origins in the
chemical bonding A chemical bond is a lasting attraction between atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday o ...
between atoms in each of the bulk materials and between the material surfaces and any . The
fractal In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities a ...

fractal
ity of surfaces, a parameter describing the scaling behavior of surface asperities, is known to play an important role in determining the magnitude of the static friction. For surfaces in relative motion \mu = \mu_\mathrm, where \mu_\mathrm\, is the ''coefficient of kinetic friction''. The Coulomb friction is equal to F_\mathrm, and the frictional force on each surface is exerted in the direction opposite to its motion relative to the other surface. Arthur Morin introduced the term and demonstrated the utility of the coefficient of friction. The coefficient of friction is an
empirical Empirical evidence for a proposition In logic and linguistics, a proposition is the meaning of a declarative sentence (linguistics), sentence. In philosophy, "Meaning (philosophy), meaning" is understood to be a non-linguistic entity which is s ...
measurement Measurement is the quantification (science), quantification of variable and attribute (research), attributes of an object or event, which can be used to compare with other objects or events. The scope and application of measurement are dependen ...

measurement
– it has to be measured
experiment An experiment is a procedure carried out to support or refute a , or determine the or of something previously untried. Experiments provide insight into by demonstrating what outcome occurs when a particular factor is manipulated. Experime ...

experiment
ally, and cannot be found through calculations. Rougher surfaces tend to have higher effective values. Both static and kinetic coefficients of friction depend on the pair of surfaces in contact; for a given pair of surfaces, the coefficient of static friction is ''usually'' larger than that of kinetic friction; in some sets the two coefficients are equal, such as teflon-on-teflon. Most dry materials in combination have friction coefficient values between 0.3 and 0.6. Values outside this range are rarer, but
teflon Polytetrafluoroethylene (PTFE) is a synthetic of that has numerous applications. The commonly known brand name of PTFE-based compositions is Teflon by , a from , which originally discovered the compound in 1938. Polytetrafluoroethylene is a ...

teflon
, for example, can have a coefficient as low as 0.04. A value of zero would mean no friction at all, an elusive property. Rubber in contact with other surfaces can yield friction coefficients from 1 to 2. Occasionally it is maintained that ''μ'' is always < 1, but this is not true. While in most relevant applications ''μ'' < 1, a value above 1 merely implies that the force required to slide an object along the surface is greater than the normal force of the surface on the object. For example,
silicone rubber Silicone rubber is an elastomer An elastomer is a polymer A polymer (; Greek ''wikt:poly-, poly-'', "many" + ''wikt:-mer, -mer'', "part") is a Chemical substance, substance or material consisting of very large molecules, or macromolecules, c ...
or
acrylic rubberAcrylic rubber, known by the chemical name alkyl acrylate copolymer (ACM) or the tradename HyTemp, is a type of rubber that has outstanding resistance to hot oil and oxidation. It belongs to specialty rubbers. It has a continuous working temperature ...
-coated surfaces have a coefficient of friction that can be substantially larger than 1. While it is often stated that the COF is a "material property," it is better categorized as a "system property." Unlike true material properties (such as conductivity, dielectric constant, yield strength), the COF for any two materials depends on system variables like
temperature Temperature ( ) is a physical quantity that expresses hot and cold. It is the manifestation of thermal energy Thermal radiation in visible light can be seen on this hot metalwork. Thermal energy refers to several distinct physical concept ...

temperature
,
velocity The velocity of an object is the Time derivative, rate of change of its Position (vector), position with respect to a frame of reference, and is a function of time. Velocity is equivalent to a specification of an object's speed and direction ...

velocity
,
atmosphere An atmosphere (from the greek words ἀτμός ''(atmos)'', meaning 'vapour', and σφαῖρα ''(sphaira)'', meaning 'ball' or 'sphere') is a layer or a set of layers of gases surrounding a planet or other material body, that is held in ...

atmosphere
and also what are now popularly described as aging and deaging times; as well as on geometric properties of the interface between the materials, namely . For example, a
copper Copper is a chemical element In chemistry, an element is a pure Chemical substance, substance consisting only of atoms that all have the same numbers of protons in their atomic nucleus, nuclei. Unlike chemical compounds, chemical elem ...

copper
pin sliding against a thick copper plate can have a COF that varies from 0.6 at low speeds (metal sliding against metal) to below 0.2 at high speeds when the copper surface begins to melt due to frictional heating. The latter speed, of course, does not determine the COF uniquely; if the pin diameter is increased so that the frictional heating is removed rapidly, the temperature drops, the pin remains solid and the COF rises to that of a 'low speed' test.


Approximate coefficients of friction

Under certain conditions some materials have very low friction coefficients. An example is (highly ordered pyrolytic) graphite which can have a friction coefficient below 0.01. This ultralow-friction regime is called
superlubricity Superlubricity is a regime of motion in which friction vanishes or very nearly vanishes. What is a "vanishing" friction level is not clear, which makes the term superlubricity quite vague. As an ''ad hoc'' definition, a kinetic Friction, coefficien ...
.


Static friction

Static friction is friction between two or more solid objects that are not moving relative to each other. For example, static friction can prevent an object from sliding down a sloped surface. The coefficient of static friction, typically denoted as ''μ''s, is usually higher than the coefficient of kinetic friction. Static friction is considered to arise as the result of surface roughness features across multiple length scales at solid surfaces. These features, known as asperities are present down to nano-scale dimensions and result in true solid to solid contact existing only at a limited number of points accounting for only a fraction of the apparent or nominal contact area. The linearity between applied load and true contact area, arising from asperity deformation, gives rise to the linearity between static frictional force and normal force, found for typical Amonton–Coulomb type friction. The static friction force must be overcome by an applied force before an object can move. The maximum possible friction force between two surfaces before sliding begins is the product of the coefficient of static friction and the normal force: F_\text = \mu_\mathrm F_\text. When there is no sliding occurring, the friction force can have any value from zero up to F_\text. Any force smaller than F_\text attempting to slide one surface over the other is opposed by a frictional force of equal magnitude and opposite direction. Any force larger than F_\text overcomes the force of static friction and causes sliding to occur. The instant sliding occurs, static friction is no longer applicable—the friction between the two surfaces is then called kinetic friction. However, an apparent static friction can be observed even in the case when the true static friction is zero. An example of static friction is the force that prevents a car wheel from slipping as it rolls on the ground. Even though the wheel is in motion, the patch of the tire in contact with the ground is stationary relative to the ground, so it is static rather than kinetic friction. Upon slipping, the wheel friction changes to kinetic friction. An
anti-lock braking system An anti-lock braking system (ABS) is a safety Safety is the state of being "safe", the condition of being protected from harm Harm is a moral A moral (from Latin Latin (, or , ) is a classical language belonging to the Italic lan ...
operates on the principle of allowing a locked wheel to resume rotating so that the car maintains static friction. The maximum value of static friction, when motion is impending, is sometimes referred to as limiting friction, although this term is not used universally.


Kinetic friction

Kinetic friction, also known as dynamic friction or sliding friction, occurs when two objects are moving relative to each other and rub together (like a sled on the ground). The coefficient of kinetic friction is typically denoted as ''μ''k, and is usually less than the coefficient of static friction for the same materials. However,
Richard Feynman Richard Phillips Feynman (; May 11, 1918 – February 15, 1988) was an American theoretical physicist, known for his work in the path integral formulation The path integral formulation is a description in quantum mechanics Quantum mech ...

Richard Feynman
comments that "with dry metals it is very hard to show any difference." The friction force between two surfaces after sliding begins is the product of the coefficient of kinetic friction and the normal force: F_ = \mu_\mathrm F_\,. This is responsible for the Coulomb damping of an
oscillating Oscillation is the repetitive variation, typically in time, of some measure about a central value (often a point of Mechanical equilibrium, equilibrium) or between two or more different states. The term ''vibration'' is precisely used to describ ...
or
vibrating Oscillation is the repetitive variation, typically in time Time is the continued of and that occurs in an apparently succession from the , through the , into the . It is a component quantity of various s used to events, to compare the ...
system. New models are beginning to show how kinetic friction can be greater than static friction. Kinetic friction is now understood, in many cases, to be primarily caused by chemical bonding between the surfaces, rather than interlocking asperities; however, in many other cases roughness effects are dominant, for example in rubber to road friction. Surface roughness and contact area affect kinetic friction for micro- and nano-scale objects where surface area forces dominate inertial forces. The origin of kinetic friction at nanoscale can be explained by thermodynamics. Upon sliding, new surface forms at the back of a sliding true contact, and existing surface disappears at the front of it. Since all surfaces involve the thermodynamic surface energy, work must be spent in creating the new surface, and energy is released as heat in removing the surface. Thus, a force is required to move the back of the contact, and frictional heat is released at the front.


Angle of friction

For certain applications, it is more useful to define static friction in terms of the maximum angle before which one of the items will begin sliding. This is called the ''angle of friction'' or ''friction angle''. It is defined as: :\tan = \mu_\mathrm\, where \theta is the angle from horizontal and ''μs'' is the static coefficient of friction between the objects. This formula can also be used to calculate ''μs'' from empirical measurements of the friction angle.


Friction at the atomic level

Determining the forces required to move atoms past each other is a challenge in designing
nanomachines A molecular machine, nanite, or nanomachine is a molecular component that produces quasi-mechanical movements (output) in response to specific stimuli (input). In cellular biology, macromolecular machines frequently perform tasks essential for l ...
. In 2008 scientists for the first time were able to move a single atom across a surface, and measure the forces required. Using ultrahigh vacuum and nearly zero temperature (5 K), a modified atomic force microscope was used to drag a
cobalt Cobalt is a chemical element In chemistry, an element is a pure Chemical substance, substance consisting only of atoms that all have the same numbers of protons in their atomic nucleus, nuclei. Unlike chemical compounds, chemical element ...

cobalt
atom, and a
carbon monoxide Carbon monoxide (chemical formula CO) is a colorless, odorless, tasteless, flammable gas that is slightly less dense than air. Carbon monoxide consists of one carbon atom and one oxygen atom. It is the simplest molecule of the oxocarbon family. In ...

carbon monoxide
molecule, across surfaces of copper and
platinum Platinum is a chemical element In chemistry, an element is a pure Chemical substance, substance consisting only of atoms that all have the same numbers of protons in their atomic nucleus, nuclei. Unlike chemical compounds, chemical el ...

platinum
.


Limitations of the Coulomb model

The Coulomb approximation follows from the assumptions that: surfaces are in atomically close contact only over a small fraction of their overall area; that this contact area is proportional to the normal force (until saturation, which takes place when all area is in atomic contact); and that the frictional force is proportional to the applied normal force, independently of the contact area. The Coulomb approximation is fundamentally an empirical construct. It is a rule-of-thumb describing the approximate outcome of an extremely complicated physical interaction. The strength of the approximation is its simplicity and versatility. Though the relationship between normal force and frictional force is not exactly linear (and so the frictional force is not entirely independent of the contact area of the surfaces), the Coulomb approximation is an adequate representation of friction for the analysis of many physical systems. When the surfaces are conjoined, Coulomb friction becomes a very poor approximation (for example,
adhesive tape Adhesive tape refers to any one of a variety of combinations of backing materials coated with an adhesive adhesive dispensed from a tube Adhesive, also known as glue, cement, mucilage, or paste, is any non-metallic substance applied to one or ...
resists sliding even when there is no normal force, or a negative normal force). In this case, the frictional force may depend strongly on the area of contact. Some
drag racing Drag racing is a type of motor racing Motorsport, motorsports or motor sport is a global term used to encompass the group of competitive sporting Sporting may refer to: *Sport, recreational games and play *Sporting (neighborhood), in Alexa ...
tires are adhesive for this reason. However, despite the complexity of the fundamental physics behind friction, the relationships are accurate enough to be useful in many applications.


"Negative" coefficient of friction

, a single study has demonstrated the potential for an ''effectively negative coefficient of friction in the low-load regime'', meaning that a decrease in normal force leads to an increase in friction. This contradicts everyday experience in which an increase in normal force leads to an increase in friction. This was reported in the journal ''Nature'' in October 2012 and involved the friction encountered by an atomic force microscope stylus when dragged across a graphene sheet in the presence of graphene-adsorbed oxygen.


Numerical simulation of the Coulomb model

Despite being a simplified model of friction, the Coulomb model is useful in many
numerical simulation Computer simulation is the process of mathematical modelling, performed on a computer A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations automatically. Modern computers can perform ...
applications such as
multibody system Multibody system is the study of the dynamic behavior of interconnected rigid or flexible bodies, each of which may undergo large Translation (physics), translational and rotational displacements. Introduction The systematic treatment of the dyn ...
s and
granular material A granular material is a conglomeration of discrete solid, macroscopic scale, macroscopic particles characterized by a loss of energy whenever the particles interact (the most common example would be friction when granulation, grains collide). Th ...
. Even its most simple expression encapsulates the fundamental effects of sticking and sliding which are required in many applied cases, although specific algorithms have to be designed in order to efficiently numerically integrate mechanical systems with Coulomb friction and bilateral or unilateral contact. Some quite nonlinear effects, such as the so-called Painlevé paradoxes, may be encountered with Coulomb friction.


Dry friction and instabilities

Dry friction can induce several types of instabilities in mechanical systems which display a stable behaviour in the absence of friction. These instabilities may be caused by the decrease of the friction force with an increasing velocity of sliding, by material expansion due to heat generation during friction (the thermo-elastic instabilities), or by pure dynamic effects of sliding of two elastic materials (the Adams–Martins instabilities). The latter were originally discovered in 1995 by George G. Adams and João Arménio Correia Martins for smooth surfaces and were later found in periodic rough surfaces. In particular, friction-related dynamical instabilities are thought to be responsible for and the 'song' of a
glass harp :''For the band, see Glass Harp (band) or for the similar instrument, see Glass harmonica''. A glass harp (also called musical glasses, singing glasses, angelic organ, verrillon or ghost fiddle) is a musical instrument A musical instrument is a ...
, phenomena which involve stick and slip, modelled as a drop of friction coefficient with velocity. A practically important case is the
self-oscillation Self-oscillation is the generation and maintenance of a periodic motion by a source of power that lacks any corresponding periodicity. The oscillator itself controls the phase with which the external power acts on it. Self-oscillators are therefor ...
of the strings of
bowed instruments Bowed string instruments are a subcategory of string instruments that are played by a bow (music), bow rubbing the string (music), strings. The bow rubbing the string causes vibration which the instrument emits as sound. The Arabic rabāb is the ...
such as the
violin The violin, sometimes known as a ''fiddle'', is a wooden chordophone (string instrument) in the violin family. Most violins have a hollow wooden body. It is the smallest and thus highest-pitched instrument (soprano) in the family in regular ...

violin
,
cello The cello ( ; plural celli or cellos) or violoncello ( ; ) is a Bow (music), bowed (sometimes pizzicato, plucked and occasionally col legno, hit) string instrument of the violin family. Its four strings are usually intonation (music), tuned in ...

cello
,
hurdy-gurdy The hurdy-gurdy is a string instrument that produces sound by a hand-crank-turned, rosined wheel rubbing against the strings. The wheel functions much like a violin bow, and single notes played on the instrument sound similar to those of a viol ...
,
erhu The ''erhu'' (; ), is a two-stringed Bowed string instrument, bowed musical instrument, more specifically a spike fiddle, which may also be called a ''Southern Fiddle'', and is sometimes known in the Western world as the ''Chinese violin'' or ...

erhu
, etc. A connection between dry friction and instability in a simple mechanical system has been discovered, watch th
movie
for more details. Frictional instabilities can lead to the formation of new self-organized patterns (or "secondary structures") at the sliding interface, such as in-situ formed tribofilms which are utilized for the reduction of friction and wear in so-called self-lubricating materials.


Fluid friction

Fluid friction occurs between
fluid In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular s ...
layers that are moving relative to each other. This internal resistance to flow is named ''
viscosity The viscosity of a fluid In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, ...

viscosity
''. In everyday terms, the viscosity of a fluid is described as its "thickness". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity. The less viscous the fluid, the greater its ease of deformation or movement. All real fluids (except
superfluid Superfluidity is the characteristic property of a fluid with zero viscosity which therefore flows without any loss of kinetic energy. When stirred, a superfluid forms vortex, vortices that continue to rotate indefinitely. Superfluidity occurs ...
s) offer some resistance to shearing and therefore are viscous. For teaching and explanatory purposes it is helpful to use the concept of an inviscid fluid or an
ideal fluid In physics, a perfect fluid is a fluid that can be completely characterized by its rest frame mass density \rho_m and ''isotropic'' pressure ''p''. Real fluids are "sticky" and contain (and conduct) heat. Perfect fluids are idealized models in whi ...
which offers no resistance to shearing and so is not viscous.


Lubricated friction

Lubricated friction is a case of fluid friction where a fluid separates two solid surfaces. Lubrication is a technique employed to reduce wear of one or both surfaces in close proximity moving relative to each another by interposing a substance called a lubricant between the surfaces. In most cases the applied load is carried by pressure generated within the fluid due to the frictional viscous resistance to motion of the lubricating fluid between the surfaces. Adequate lubrication allows smooth continuous operation of equipment, with only mild wear, and without excessive stresses or seizures at bearings. When lubrication breaks down, metal or other components can rub destructively over each other, causing heat and possibly damage or failure.


Skin friction

Skin friction arises from the interaction between the fluid and the skin of the body, and is directly related to the area of the surface of the body that is in contact with the fluid. Skin friction follows the
drag equation In fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including aerodynamics (the study of air and other gases in ...
and rises with the square of the velocity. Skin friction is caused by viscous drag in the
boundary layer In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular su ...
around the object. There are two ways to decrease skin friction: the first is to shape the moving body so that smooth flow is possible, like an airfoil. The second method is to decrease the length and cross-section of the moving object as much as is practicable.


Internal friction

Internal friction is the force resisting motion between the elements making up a solid material while it undergoes
deformation Deformation can refer to: * Deformation (engineering), changes in an object's shape or form due to the application of a force or forces. ** Deformation (mechanics), such changes considered and analyzed as displacements of continuum bodies. * Defo ...
.
Plastic deformation In engineering, deformation refers to the change in size or shape of an object. ''Displacements'' are the ''absolute'' change in position of a point on the object. Deflection (engineering) , Deflection is the relative change in external displace ...
in solids is an irreversible change in the internal molecular structure of an object. This change may be due to either (or both) an applied force or a change in temperature. The change of an object's shape is called strain. The force causing it is called stress.
Elastic deformation In engineering Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad ran ...
in solids is reversible change in the internal molecular structure of an object. Stress does not necessarily cause permanent change. As deformation occurs, internal forces oppose the applied force. If the applied stress is not too large these opposing forces may completely resist the applied force, allowing the object to assume a new equilibrium state and to return to its original shape when the force is removed. This is known as elastic deformation or elasticity.


Radiation friction

As a consequence of light pressure,
Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest physicists of all time. Einstein is known for developing the theory of relativity The theory ...

Einstein
in 1909 predicted the existence of "radiation friction" which would oppose the movement of matter. He wrote, “radiation will exert pressure on both sides of the plate. The forces of pressure exerted on the two sides are equal if the plate is at rest. However, if it is in motion, more radiation will be reflected on the surface that is ahead during the motion (front surface) than on the back surface. The backward-acting force of pressure exerted on the front surface is thus larger than the force of pressure acting on the back. Hence, as the resultant of the two forces, there remains a force that counteracts the motion of the plate and that increases with the velocity of the plate. We will call this resultant 'radiation friction' in brief.”


Other types of friction


Rolling resistance

Rolling resistance is the force that resists the rolling of a wheel or other circular object along a surface caused by deformations in the object or surface. Generally the force of rolling resistance is less than that associated with kinetic friction. Typical values for the coefficient of rolling resistance are 0.001. One of the most common examples of rolling resistance is the movement of
motor vehicle A motor vehicle, also known as motorized vehicle or automotive vehicle, is a self-propelled vehicle A vehicle (from la, vehiculum) is a machine that transports people or cargo. Vehicles include wagons, bicycles, motor vehicles (motorcycles ...
tires on a
road A road is a wide way leading from one place to another, typically one with a specially prepared surface which vehicles and bikes can use. Roads consist of one or two roadway A carriageway (British English British English (BrE) is the ...

road
, a process which generates heat and
sound In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...
as by-products.


Braking friction

Any wheel equipped with a
brake A brake is a mechanical device A machine is a man-made Artificiality (the state of being artificial or man-made) is the state of being the product of intentional human manufacture, rather than occurring naturally through processes not involv ...

brake
is capable of generating a large retarding force, usually for the purpose of slowing and stopping a vehicle or piece of rotating machinery. Braking friction differs from rolling friction because the coefficient of friction for rolling friction is small whereas the coefficient of friction for braking friction is designed to be large by choice of materials for
brake pad Brake pads are a component of disc brake A disc brake is a type of brake A brake is a mechanical device A machine is a man-made Artificiality (the state of being artificial or man-made) is the state of being the product of intentional human ...

brake pad
s.


Triboelectric effect

Rubbing dissimilar materials against one another can cause a build-up of
electrostatic charge Electric charge is the physical property A physical property is any property Property (''latin: Res Privata'') in the Abstract and concrete, abstract is what belongs to or with something, whether as an attribute or as a component of said thi ...
, which can be hazardous if flammable gases or vapours are present. When the static build-up discharges,
explosion An explosion is a rapid expansion in volume Volume is a expressing the of enclosed by a . For example, the space that a substance (, , , or ) or occupies or contains. Volume is often quantified numerically using the , the . The volum ...

explosion
s can be caused by ignition of the flammable mixture.


Belt friction

Belt friction is a physical property observed from the forces acting on a belt wrapped around a pulley, when one end is being pulled. The resulting tension, which acts on both ends of the belt, can be modeled by the belt friction equation. In practice, the theoretical tension acting on the belt or rope calculated by the belt friction equation can be compared to the maximum tension the belt can support. This helps a designer of such a rig to know how many times the belt or rope must be wrapped around the pulley to prevent it from slipping. Mountain climbers and sailing crews demonstrate a standard knowledge of belt friction when accomplishing basic tasks.


Reducing friction


Devices

Devices such as wheels,
ball bearing A ball bearing is a type of rolling-element bearing A rolling-element bearing, also known as a rolling bearing, is a bearing Bearing may refer to: * Bearing (angle), a term for direction * Bearing (mechanical), a component that separates mov ...

ball bearing
s,
roller bearing A rolling-element bearing, also known as a rolling bearing, is a bearing which carries a load by placing rolling elements (such as balls or rollers) between two bearing rings called races. The relative motion of the races causes the rolling eleme ...
s, and air cushion or other types of
fluid bearing Fluid bearings are bearing (mechanical), bearings in which the load is supported by a thin layer of rapidly moving pressurized liquid or gas between the bearing surfaces. Since there is no contact between the moving parts, there is no sliding fri ...
s can change sliding friction into a much smaller type of rolling friction. Many
thermoplastic A thermoplastic, or thermosoft plastic, is a plastic polymer material that becomes pliable or moldable at a certain elevated temperature and solidifies upon cooling. Most thermoplastics have a high molecular mass, molecular weight. The polymer ch ...
materials such as
nylon Nylon is a generic designation for a family of s composed of s ( linked by links).The polyamides may be or . Nylon is a -like , generally made from , that can be melt-processed into fibers, , or shapes. Nylon polymers can be mixed with a w ...

nylon
,
HDPE High-density polyethylene Polyethylene or (incorrectly) polythene (abbreviated PE; IUPAC The International Union of Pure and Applied Chemistry (IUPAC ) is an international federation of National Adhering Organizations that represents c ...
and PTFE are commonly used in low friction bearings. They are especially useful because the coefficient of friction falls with increasing imposed load. For improved wear resistance, very high
molecular weight A scanning tunneling microscopy image of pentacene molecules, which consist of linear chains of five carbon rings. A molecule is an electrically Electricity is the set of physical phenomena associated with the presence and motion I ...
grades are usually specified for heavy duty or critical bearings.


Lubricants

A common way to reduce friction is by using a
lubricant A lubricant is a substance that helps to reduce friction Friction is the force In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and b ...
, such as oil, water, or grease, which is placed between the two surfaces, often dramatically lessening the coefficient of friction. The science of friction and lubrication is called
tribology Tribology is the science and engineering of interacting surfaces in relative motion Image:Leaving Yongsan Station.jpg, 300px, Motion involves a change in position In physics, motion is the phenomenon in which an object changes its position (ma ...
. Lubricant technology is when lubricants are mixed with the application of science, especially to industrial or commercial objectives. Superlubricity, a recently discovered effect, has been observed in
graphite Graphite (), archaically referred to as plumbago, is a Crystallinity, crystalline form of the element carbon with its atoms arranged in a Hexagonal crystal system, hexagonal structure. It occurs naturally in this form and is the most stable for ...

graphite
: it is the substantial decrease of friction between two sliding objects, approaching zero levels. A very small amount of frictional energy would still be dissipated. Lubricants to overcome friction need not always be thin, turbulent fluids or powdery solids such as graphite and
talc Talc, or talcum, is a clay mineral Clay minerals are , sometimes with variable amounts of , , s, s, and other s found on or near some s. Clay minerals form in the presence of water and have been important to life, and many theories of ...

talc
; acoustic lubrication actually uses sound as a lubricant. Another way to reduce friction between two parts is to superimpose micro-scale vibration to one of the parts. This can be sinusoidal vibration as used in ultrasound-assisted cutting or vibration noise, known as
dither Dither is an intentionally applied form of noise Noise is unwanted sound In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid. In human physiology and psyc ...

dither
.


Energy of friction

According to the law of
conservation of energy In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular s ...
, no energy is destroyed due to friction, though it may be lost to the system of concern. Energy is transformed from other forms into thermal energy. A sliding hockey puck comes to rest because friction converts its kinetic energy into heat which raises the thermal energy of the puck and the ice surface. Since heat quickly dissipates, many early philosophers, including
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher A philosopher is someone who practices philosophy Philosophy (from , ) is the study of general and fundamental quest ...

Aristotle
, wrongly concluded that moving objects lose energy without a driving force. When an object is pushed along a surface along a path C, the energy converted to heat is given by a
line integral In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It ...
, in accordance with the definition of work :E_ = \int_C \mathbf_\mathrm(\mathbf) \cdot d\mathbf\ = \int_C \mu_\mathrm\ \mathbf_\mathrm(\mathbf) \cdot d\mathbf, where : \mathbf_\mathrm\, is the friction force, : \mathbf_\mathrm\, is the vector obtained by multiplying the magnitude of the normal force by a unit vector pointing ''against'' the object's motion, : \mu_\mathrm\, is the coefficient of kinetic friction, which is inside the integral because it may vary from location to location (e.g. if the material changes along the path), : \mathbf\, is the position of the object. Energy lost to a system as a result of friction is a classic example of thermodynamic
irreversibility In science, a process A process is a series or set of Action (philosophy), activities that interact to produce a result; it may occur once-only or be recurrent or periodic. Things called a process include: Business and management *Business proc ...
.


Work of friction

In the reference frame of the interface between two surfaces, static friction does ''no''
work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking * Work (physics), the product of ...
, because there is never displacement between the surfaces. In the same reference frame, kinetic friction is always in the direction opposite the motion, and does ''negative'' work. However, friction can do ''positive'' work in certain
frames of reference In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), motion and behavior through ...
. One can see this by placing a heavy box on a rug, then pulling on the rug quickly. In this case, the box slides backwards relative to the rug, but moves forward relative to the frame of reference in which the floor is stationary. Thus, the kinetic friction between the box and rug accelerates the box in the same direction that the box moves, doing ''positive'' work. The work done by friction can translate into deformation, wear, and heat that can affect the contact surface properties (even the coefficient of friction between the surfaces). This can be beneficial as in
polishing Polishing is the process of creating a smooth and shiny surface by rubbing it or by applying a chemical treatment, leaving a clean surface with a significant specular reflection Reflections on still water are an example of specular reflectio ...
. The work of friction is used to mix and join materials such as in the process of
friction welding Friction welding (FRW) is a solid-state process that generates heat through mechanical between workpieces in relative motion to one another, with the addition of a lateral force called "upset" to plastically displace and fuse the materials. Becau ...
. Excessive erosion or wear of mating sliding surfaces occurs when work due to frictional forces rise to unacceptable levels. Harder corrosion particles caught between mating surfaces in relative motion (
fretting Fretting refers to wear Wear is the damaging, gradual removal or deformation of material at solid surfaces. Causes of wear can be mechanical (e.g., erosion In earth science, erosion is the action of surface processes (such as Surface run ...
) exacerbates wear of frictional forces. As surfaces are worn by work due to friction, fit and
surface finish A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight Visual percep ...

surface finish
of an object may degrade until it no longer functions properly. For example, bearing seizure or failure may result from excessive wear due to work of friction.


Applications

Friction is an important factor in many
engineering Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more speciali ...

engineering
disciplines.


Transportation

* Automobile brakes inherently rely on friction, slowing a vehicle by converting its kinetic energy into heat. Incidentally, dispersing this large amount of heat safely is one technical challenge in designing brake systems. Disk brakes rely on friction between a disc and
brake padsBrake pads are a component of disc brake A disc brake is a type of brake that uses the #Calipers, calipers to squeeze pairs of #Brake pads, pads against a disc or a "rotor" to create friction. This action slows the rotation of a shaft, such as a veh ...
that are squeezed transversely against the rotating disc. In
drum brakes , at the Battle of Gettysburg The Battle of Gettysburg () was fought July 1–3, 1863, in and around the town of Gettysburg, Pennsylvania Pennsylvania ( ) ( pdc, Pennsilfaani), officially the Commonwealth of Pennsylvania, is a U. ...
,
brake shoes A brake shoe is the part of a braking system which carries the brake lining in the drum brakes used on automobiles, or the brake block in Brake (railway), train brakes and bicycle brakes. A device that is put on a track to slow down railroad cars i ...

brake shoes
or pads are pressed outwards against a rotating cylinder (brake drum) to create friction. Since braking discs can be more efficiently cooled than drums, disc brakes have better stopping performance. *
Rail adhesion An adhesion railway relies on adhesion traction to move the train. Adhesion traction is the friction between the drive wheels and the steel rail. The term "adhesion railway" is used only when it is necessary to distinguish adhesion railways from r ...
refers to the grip wheels of a train have on the rails, see
Frictional contact mechanics Contact mechanics is the study of the Deformation (mechanics), deformation of solids that touch each other at one or more points. This can be divided into compressive and adhesive forces in the direction perpendicular to the interface, and friction ...
. *
Road slipperiness A surface friction tester, used to measure road slipperiness Road slipperiness is a condition of low skid resistance due to insufficient road friction. It is a result of snow Snow comprises individual ice crystals that grow while suspende ...
is an important design and safety factor for automobiles ** Split friction is a particularly dangerous condition arising due to varying friction on either side of a car. **Texture (roads), Road texture affects the interaction of tires and the driving surface.


Measurement

*A tribometer is an instrument that measures friction on a surface. *A profilograph is a device used to measure pavement surface roughness.


Household usage

*Friction is used to heat and ignite matchsticks (friction between the head of a matchstick and the rubbing surface of the match box). *Sticky pads are used to prevent object from slipping off smooth surfaces by effectively increasing the friction coefficient between the surface and the object.


See also

*Contact dynamics *Contact mechanics *Factor of adhesion *Frictionless plane *Galling *Non-smooth mechanics *Normal contact stiffness *Stick-slip phenomenon *Transient friction loading *Triboelectric effect *Unilateral contact *Friction torque


References


External links

*
Coefficients of Friction
– tables of coefficients, plus many links
Physclips: Mechanics with animations and video clips
from the University of New South Wales
Values for Coefficient of Friction
– ''CRC Handbook of Chemistry and Physics''
Characteristic Phenomena in Conveyor ChainAtomic-scale Friction Research and Education Synergy Hub (AFRESH)
an Engineering Virtual Organization for the atomic-scale friction community to share, archive, link, and discuss data, knowledge and tools related to atomic-scale friction.
Coefficients of friction of various material pairs in atmosphere and vacuum
{{Authority control Friction, Classical mechanics Force Tribology