# Friction

{{#invoke:Hatnote|hatnote}} Template:Pp-move-indef Template:Classical mechanics Friction is the 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 resists relative lateral motion of two solid surfaces in contact. Dry friction is subdivided into static friction ("stiction") between non-moving surfaces, and kinetic friction between moving surfaces.
• Fluid friction describes the friction between layers of a viscous fluid that are moving relative to each other.[1][2]
• Lubricated friction is a case of fluid friction where a lubricant fluid separates two solid surfaces.[3][4][5]
• Skin friction is a component of drag, 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.[2]

When surfaces in contact move relative to each other, the friction between the two surfaces converts kinetic energy into thermal energy. 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 fluid is stirred. Another important consequence of many types of friction can be wear, which may lead to performance degradation and/or damage to components. Friction is a component of the science of tribology.

Friction is not itself a fundamental force but arises from interatomic and intermolecular forces between the two contacting surfaces. The complexity of these interactions makes the calculation of friction from first principles impractical and necessitates the use of empirical methods for analysis and the development of theory.

## History

The classic rules of sliding friction were discovered by Leonardo da Vinci (1452–1519), but remained unpublished in his notebooks.[6][7][8] They were rediscovered by Guillaume Amontons (1699). 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 Belidor (representation of rough surfaces with spherical asperities, 1737)[6] and Leonhard Euler (1750), who derived the angle of repose of a weight on an inclined plane and first distinguished between static and kinetic friction.[9] A different explanation was provided by Desaguliers (1725), who demonstrated the strong cohesion forces between lead spheres of which a small cap is cut off and which were then brought into contact with each other.

The understanding of friction was further developed by Charles-Augustin de Coulomb (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).[6] 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 Johann Andreas von Segner in 1758.[6] The effect of the time of repose was explained by Musschenbroek (1762) by considering the surfaces of fibrous materials, with fibers meshing together, which takes a finite time in which the friction increases.

John Leslie (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 isn't it balanced then 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.[6] In his 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 Morrin (1833) developed the concept of sliding versus rolling friction. 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.[7]

The focus of research during the last century has been to understand the physical mechanisms behind friction. F. Phillip Bowden and David Tabor (1950) showed that at a microscopic level, the actual area of contact between surfaces is a very small fraction of the apparent area.[8] This actual area of contact, caused by "asperities" (roughness) increases with pressure, explaining the proportionality between normal force and frictional force. The development of the atomic force microscope (1986) has recently enabled scientists to study friction at the atomic scale.[7]

## 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' ("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, is an approximate model used to calculate the force of dry friction. It is governed by the model:

${\displaystyle F_{\mathrm {f} }\leq \mu F_{\mathrm {n} }}$

where

The Coulomb friction ${\displaystyle F_{\mathrm {f} }\,}$ may take any value from zero up to ${\displaystyle \mu F_{\mathrm {n} }\,}$, 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 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

Free-body diagram for a block on a ramp. Arrows are vectors indicating directions and magnitudes of forces. N is the normal force, mg is the force of gravity, and Ff is the force of friction.

{{#invoke:main|main}}

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 ${\displaystyle N=mg\,}$. In this case, the magnitude of the friction force is the product of the mass of the object, the acceleration due to gravity, and the coefficient of friction. However, the coefficient of friction is not a function of mass or volume; it depends only on the material. 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.

If an object is on a level surface and the force tending to cause it to slide is horizontal, the normal force ${\displaystyle N\,}$ between the object and the surface is just its weight, which is equal to its mass multiplied by the acceleration due to earth's gravity, g. If the object is on a tilted surface such as an inclined plane, the normal force is less, because less of the force of gravity is perpendicular to the face of the plane. Therefore, the normal force, and ultimately the frictional force, is determined using vector analysis, usually via a free body diagram. Depending on the situation, the calculation of the normal force may include forces other than gravity.

### Coefficient of friction

The coefficient of friction (COF), often symbolized by the Greek letter µ, is a dimensionless scalar value which describes the ratio of the force of friction between two bodies and the force pressing them together. 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.

For surfaces at rest relative to each other ${\displaystyle \mu =\mu _{\mathrm {s} }\,}$, where ${\displaystyle \mu _{\mathrm {s} }\,}$ is the coefficient of static friction. This is usually larger than its kinetic counterpart.

For surfaces in relative motion ${\displaystyle \mu =\mu _{\mathrm {k} }\,}$, where ${\displaystyle \mu _{\mathrm {k} }\,}$ is the coefficient of kinetic friction. The Coulomb friction is equal to ${\displaystyle F_{\mathrm {f} }\,}$, 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.[6] The coefficient of friction is an empirical measurement – it has to be measured experimentally, and cannot be found through calculations.{{ safesubst:#invoke:Unsubst||date=__DATE__ |$B= {{#invoke:Category handler|main}}{{#invoke:Category handler|main}}[citation needed] }} 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, for example, can have a coefficient as low as 0.04. A value of zero would mean no friction at all, an elusive property – even magnetic levitation vehicles have drag. 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 or acrylic rubber-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, velocity, 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. For example, a 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.{{ safesubst:#invoke:Unsubst||date=__DATE__ |$B= {{#invoke:Category handler|main}}{{#invoke:Category handler|main}}[citation needed] }}

#### Approximate coefficients of friction

Materials Static friction, ${\displaystyle \mu _{s}\,}$
Dry and clean Lubricated
Aluminium Steel 0.61
Copper Steel 0.53
Brass Steel 0.51
Cast iron Copper 1.05
Cast iron Zinc 0.85
Concrete Rubber 1.0 0.30 (wet)
Concrete Wood 0.62[10]
Copper Glass 0.68
Glass Glass 0.94
Metal Wood 0.2–0.6[10] 0.2 (wet)[10]
Polyethene Steel 0.2[11] 0.2[11]
Steel Steel 0.80[11] 0.16[11]
Steel PTFE (Teflon) 0.05-0.2[11]
PTFE (Teflon) PTFE (Teflon) 0.04[11] 0.04[11]
Wood Wood 0.25–0.5[10] 0.2 (wet)[10]

An AlMgB14-TiB2 composite has an approximate coefficient of friction of 0.02 in water-glycol-based lubricants,[12][13] and 0.04–0.05 when dry.[14] Under certain conditions, some materials have even lower friction coefficients. An example is (highly ordered pyrolytic) graphite, which can have a friction coefficient below 0.01.[15] This ultralow-friction regime is called superlubricity.

#### "Negative" coefficient of friction

Template:As of, 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.[16] 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.[16]

### Static friction

File:Static kinetic friction vs time.png
When the mass is not moving, the object experiences static friction. The friction increases as the applied force increases until the block moves. After the block moves, it experiences kinetic friction, which is less than the maximum 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 μs, is usually higher than the coefficient of kinetic 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: ${\displaystyle F_{max}=\mu _{s}F_{n}\,}$. When there is no sliding occurring, the friction force can have any value from zero up to ${\displaystyle F_{max}\,}$. Any force smaller than ${\displaystyle F_{max}\,}$ attempting to slide one surface over the other is opposed by a frictional force of equal magnitude and opposite direction. Any force larger than ${\displaystyle F_{max}\,}$ 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.

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.

### Lubricants

A common way to reduce friction is by using a lubricant, 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. 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: 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; 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.

## Energy of friction

According to the law of conservation of energy, 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, 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 accordance with the definition of work.

${\displaystyle E_{th}=\int _{C}\mathbf {F} _{\mathrm {fric} }(\mathbf {x} )\cdot d\mathbf {x} \ =\int _{C}\mu _{\mathrm {k} }\ \mathbf {F} _{\mathrm {n} }(\mathbf {x} )\cdot d\mathbf {x} \,}$

where

${\displaystyle \mathbf {F} _{fric}\,}$ is the friction force,
${\displaystyle \mathbf {F} _{n}\,}$ is the vector obtained by multiplying the magnitude of the normal force by a unit vector pointing against the object's motion,
${\displaystyle \mu _{\mathrm {k} }\,}$ 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)
${\displaystyle \mathbf {x} \,}$ is the position of the object

Energy lost to a system as a result of friction is a classic example of thermodynamic irreversibility.

### Work of friction

In the reference frame of the interface between two surfaces, static friction does no work, 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.[44] However, friction can do positive work in certain frames of reference. 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.[45]

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. The work of friction is used to mix and join materials such as in the process of friction welding. Excessive erosion or wear of mating sliding surfaces occurs when work due frictional forces rise to unacceptable levels. Harder corrosion particles caught between mating surfaces in relative motion (fretting) exacerbates wear of frictional forces. Bearing seizure or failure may result from excessive wear due to work of friction. As surfaces are worn by work due to friction, fit and surface finish of an object may degrade until it no longer functions properly.[46]

## Applications

Friction is an important factor in many 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.
• Rail adhesion refers to the grip wheels of a train have on the rails, see Frictional contact mechanics.
• Road slipperiness 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.
• 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).

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