Friction - Knowledge

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natural thermodynamic process, the work done by an agency in the surroundings of a thermodynamic system or working body is greater than the work received by the body, because of friction. Thermodynamic work is measured by changes in a body's state variables, sometimes called work-like variables, other than temperature and entropy. Examples of work-like variables, which are ordinary macroscopic physical variables and which occur in conjugate pairs, are pressure – volume, and electric field – electric polarization. Temperature and entropy are a specifically thermodynamic conjugate pair of state variables. They can be affected microscopically at an atomic level, by mechanisms such as friction, thermal conduction, and radiation. The part of the work done by an agency in the surroundings that does not change the volume of the working body but is dissipated in friction, is called

754: 1039:(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 1434:, 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 7690: 7543: 7589: 7502: 812: 7490: 7601: 2058: 7652: 7577: 7478: 3476:

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.

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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."

7625: 7678: 7666: 7702: 1641:(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. 7613: 2389: 7726: 7642: 7565: 7466: 1057:, 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. 3288: 7714: 7514: 7226: 3941:, 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 2104:

has a high coefficient of friction. Coefficients of friction range from near zero to greater than one. The coefficient of friction between two surfaces of similar metals is greater than that between two surfaces of different metals; for example, brass has a higher coefficient of friction when moved against brass, but less if moved against steel or aluminum.

4317:. 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 1061: 3001: 4111: 40: 4324:

When sliding takes place between two rough bodies in contact, the algebraic sum of the works done is different from zero, and the algebraic sum of the quantities of heat gained by the two bodies is equal to the quantity of work lost by friction, and the total quantity of heat gained is positive. In a

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New models are beginning to show how kinetic friction can be greater than static friction. 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

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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

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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

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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

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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

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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

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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,

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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

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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

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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

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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

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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

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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

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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

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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

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The origin of kinetic friction at nanoscale can be rationalized by an energy model. During sliding, a 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

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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.

1138:. He noted that for a driven hard surface sliding on a body driven by it, the work done by the driver exceeds the work received by the body. The difference is accounted for by heat generated by friction. Over the years, for example in his 1879 thesis, but particularly in 1926, 1494:

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

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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.

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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

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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.

3958: 2315:, 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 1068: 1066: 1064: 1062: 3637:. 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. 1011:

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

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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

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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

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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:

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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

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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.

2326:, 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 3451:. 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 1065: 7286: 7077:

Valentin L. Popov; Lars Voll; Stephan Kusche; Qiang Li; Svetlana V. Rozhkova (2018). "Generalized master curve procedure for elastomer friction taking into account dependencies on velocity, temperature and normal force".

3023:, 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 3499:, 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 2987:

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

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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

2175:. 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 3681:

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

3523:. 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 3211:

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:

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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

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In systems with significant non-uniform stress fields, because local slip occurs before the system slides, the macroscopic coefficient of static friction depends on the applied load, system size, or shape;

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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.

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Rubbing two materials against each other can lead to charge transfer, either electrons or ions. The energy required for this contributes to the friction. In addition, sliding can cause a build-up of

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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

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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.

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On the development of our views concerning the nature and constitution of radiation. Translated in: The Collected Papers of Albert Einstein, vol. 2 (Princeton University Press, Princeton, 1989)

3360: 1157:, 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 4790:

Classical Greek philosophers like Aristotle, Pliny the Elder and Vitruvius wrote about the existence of friction, the effect of lubricants and the advantages of metal bearings around 350 B.C.

4157: 4106:{\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} ,} 3262: 3284:

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.

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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.

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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

7279: 3899:, 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 2227: 2140: 2506: 1432: 849:, which may lead to performance degradation or damage to components. It is known that frictional energy losses account for about 20% of the total energy expenditure of the world. 4225: 2474: 2256: 2169: 5128: 2334:< 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, 1119:(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, 2289: 1400: 1363: 1310: 132: 2001: 1884: 1596: 6297: 3503:

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.

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Ferreira, Vanderlei; Yoshimura, Humberto Naoyuki; Sinatora, Amilton (2012-08-30). "Ultra-low friction coefficient in alumina–silicon nitride pair lubricated with water".

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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.

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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

1728: 4329:. It is received as heat, by the working body and sometimes partly by a body in the surroundings. It is not counted as thermodynamic work received by the working body. 2191:

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.

3910:: 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. 3423: 3200:, 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 1560: 7493: 6868: 3667:

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.

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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

1523: 1848: 1778: 7604: 4305:, 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 1332: 3471:

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

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Martins, J.A., Faria, L.O. & Guimarães, J. (1995). "Dynamic surface solutions in linear elasticity and viscoelasticity with frictional boundary conditions".

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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),

3644:) 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 1950: 1751: 6356: 4295:

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.

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for smooth surfaces and were later found in periodic rough surfaces. In particular, friction-related dynamical instabilities are thought to be responsible for

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advocated regarding the generation of heat by rubbing as the most specific way to define heat, and the prime example of an irreversible thermodynamic process.

872:– work done against friction is path dependent. In the presence of friction, some kinetic or mechanical energy is transformed to thermal energy as well as the 2367:

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.

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The elementary property of sliding (kinetic) friction were discovered by experiment in the 15th to 18th centuries and were expressed as three empirical laws:

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between moving surfaces. With the exception of atomic or molecular friction, dry friction generally arises from the interaction of surface features, known as

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against each other. Types of friction include dry, fluid, lubricated, skin, and internal -- an incomplete list. The study of the processes involved is called

1952:, 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 5003: 1032:

in friction. Microscopic forces cause surfaces to stick together; he proposed that friction was the force necessary to tear the adhering surfaces apart.

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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

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Higdon, C.; Cook, B.; Harringa, J.; Russell, A.; Goldsmith, J.; Qu, J.; Blau, P. (2011). "Friction and wear mechanisms in AlMgB14-TiB2 nanocoatings".

7681: 5532: 7310: 1053:(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 6885: 6691: 4441:

are used to prevent object from slipping off smooth surfaces by effectively increasing the friction coefficient between the surface and the object.

1047:(1762) by considering the surfaces of fibrous materials, with fibers meshing together, which takes a finite time in which the friction increases. 6317:

Deng, Zhao; et al. (October 14, 2012). "Adhesion-dependent negative friction coefficient on chemically modified graphite at the nanoscale".

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Otsuki, M.; Matsukawa, H. (2013-04-02). "Systematic breakdown of Amontons' law of friction for an elastic object locally obeying Amontons' law".

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attempting to slide one surface over the other is opposed by a frictional force of equal magnitude and opposite direction. Any force larger than

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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.

1233: 7568: 7358: 5682: 3883:. They are especially useful because the coefficient of friction falls with increasing imposed load. For improved wear resistance, very high 1967:

as immovable so that the corresponding tangential reaction force between them can be calculated. If this frictional reaction force satisfies

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J., Flint; J., Hultén (2002). "Lining-deformation-induced modal coupling as squeal generator in a distributed parameter disk brake model".

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M, Nosonovsky; G., Adams G. (2004). "Vibration and stability of frictional sliding of two elastic bodies with a wavy contact interface".

387: 7350: 5624: 3903:. Lubricant technology is when lubricants are mixed with the application of science, especially to industrial or commercial objectives. 3322: 2003:, then the tentative assumption was correct, and it is the actual frictional force. Otherwise, the friction force must be set equal to 1446:

that it is not the direction of movement of the vehicle they oppose, it is the direction of (potential) sliding between tire and road.

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Dry friction resists relative lateral motion of two solid surfaces in contact. The two regimes of dry friction are 'static friction' ("

506: 5136: 6521:"The bipotential method: A constructive approach to design the complete contact law with friction and improved numerical algorithms" 3035: 988:, were interested in the cause and mitigation of friction. They were aware of differences between static and kinetic friction with 479: 6248: 8424: 5827: 2322:

Most dry materials in combination have friction coefficient values between 0.3 and 0.6. Values outside this range are rarer, but

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slipping. Mountain climbers and sailing crews demonstrate a standard knowledge of belt friction when accomplishing basic tasks.

7407: 64: 7364: 4279:. Excessive erosion or wear of mating sliding surfaces occurs when work due to frictional forces rise to unacceptable levels. 7380: 7194: 7167: 7134: 6970: 6629:

Adams, G. G. (1995). "Self-excited oscillations of two elastic half-spaces sliding with a constant coefficient of friction".

6613: 6163: 6066: 6025: 5991: 5222: 5168: 4942: 4910: 4876: 4849: 4811: 4783: 4753: 4728: 4679: 4643: 2291:, and the frictional force on each surface is exerted in the direction opposite to its motion relative to the other surface. 7211: 5301: 5883: 17: 6827: 3598: 5158: 3721: 3028:

rise to the linearity between static frictional force and normal force, found for typical Amonton–Coulomb type friction.

461: 3528: 5111: 1922:. Until then, friction is whatever it needs to be to provide equilibrium, so it can be treated as simply a reaction. 1109:

frictionally generated heat in paper pulp and measured the temperature rise. In 1845, Joule published a paper entitled

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is a force that opposes the relative lateral motion of two solid surfaces in contact. Dry friction is subdivided into

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M., Kröger; M., Neubauer; K., Popp (2008). "Experimental investigation on the avoidance of self-excited vibrations".

6364: 5049:"Study reveals Leonardo da Vinci's 'irrelevant' scribbles mark the spot where he first recorded the laws of friction" 3549: 2428: 791: 4122: 3215: 1007:, but the laws documented in his notebooks were not published and remained unknown. These laws were rediscovered by 6590: 3714:

Internal friction is the force resisting motion between the elements making up a solid material while it undergoes

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operates on the principle of allowing a locked wheel to resume rotating so that the car maintains static friction.

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introduced the term and demonstrated the utility of the coefficient of friction. The coefficient of friction is an

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As briefly discussed later, there are many different contributors to the retarding force in friction, ranging from

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Friction-Induced Vibrations and Self-Organization: Mechanics and Non-Equilibrium Thermodynamics of Sliding Contact

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Lubricants to overcome friction need not always be thin, turbulent fluids or powdery solids such as graphite and

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The focus of research during the 20th century has been to understand the physical mechanisms behind friction.

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larger than that of kinetic friction; in some sets the two coefficients are equal, such as teflon-on-teflon.

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Thermodynamics: an Introductory Treatise dealing mainly with First Principles and their Direct Applications

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Friction between two objects. The blue one has more friction against the sloped surface than the green one.

7386: 5536: 5107: 1405: 1013: 8395: 7318: 5239: 5048: 4201: 3816:, which can be hazardous if flammable gases or vapours are present. When the static build-up discharges, 2450: 2232: 2145: 2039:, and then the resulting force imbalance would then determine the acceleration associated with slipping. 1227: 1201: 1173:; the macroscopic proportionality between normal force and static frictional force between dry surfaces. 1081: 1036: 1025: 451: 252: 6153: 230: 7995: 7440: 4502: 3545: 2633: 2410: 2399: 671: 560: 486: 346: 279: 3432:

is the static coefficient of friction between the objects. This formula can also be used to calculate

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is not conserved. The complexity of the interactions involved makes the calculation of friction from

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When an object is pushed along a surface along a path C, the energy converted to heat is given by a

3560:, phenomena which involve stick and slip, modelled as a drop of friction coefficient with velocity. 3141: 3114: 3087: 1601: 1230:, is an approximate model used to calculate the force of dry friction. It is governed by the model: 8374: 8364: 8236: 8226: 8056: 7794: 7592: 7423: 5679: 4492: 3171: 1044: 701: 545: 4232: 4192:

is the vector obtained by multiplying the magnitude of the normal force by a unit vector pointing

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When the surfaces are conjoined, Coulomb friction becomes a very poor approximation (for example,

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In general, process for solving any statics problem with friction is to treat contacting surfaces

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is the force resisting motion between the elements making up a solid material while it undergoes

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resistance are 0.001. One of the most common examples of rolling resistance is the movement of

3207:, and is usually less than the coefficient of static friction for the same materials. However, 2097: 2069: 1688:

tending to cause it to slide, then the normal force between the object and the surface is just

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Tian, Y.; Bastawros, A. F.; Lo, C. C. H.; Constant, A. P.; Russell, A.M.; Cook, B. A. (2003).

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is a particularly dangerous condition arising due to varying friction on either side of a car.

1525:. In this case, conditions of equilibrium tell us that the magnitude of the friction force is 1024:

of a weight on an inclined plane and first distinguished between static and kinetic friction.

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Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences

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Numerical Methods for Nonsmooth Dynamical Systems. Applications in Mechanics and Electronics

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The maximum value of static friction, when motion is impending, is sometimes referred to as

3084:. When there is no sliding occurring, the friction force can have any value from zero up to 1498: 8517: 8369: 8326: 8219: 8144: 7527: 7043: 6912: 6842: 6784: 6749: 6714: 6638: 6485: 6446: 6396: 6328: 6265: 6198: 6126: 5928: 5842: 5597: 5586:"Superhard self-lubricating AlMgB[sub 14] films for microelectromechanical devices" 5435: 5372: 5234: 4507: 4487: 3918: 3880: 3813: 3807: 1826: 1756: 1334:

is the coefficient of friction, which is an empirical property of the contacting materials,

857: 726: 686: 594: 590: 582: 572: 362: 355: 111: 6432:"A mixed formulation for frictional contact problems prone to Newton like solution method" 6111: 3447:

Determining the forces required to move atoms past each other is a challenge in designing

1780:

is the downward component of the external force. Prior to sliding, this friction force is

1317: 841:

Friction can have dramatic consequences, as illustrated by the use of friction created by

721: 8: 8293: 8283: 7839: 7824: 7784: 7757: 7532: 7522: 7256: 6244: 6086: 4314: 3732: 3631:

layers that are moving relative to each other. This internal resistance to flow is named

3527:

mechanical systems with Coulomb friction and bilateral or unilateral contact. Some quite

3512: 2342:-coated surfaces have a coefficient of friction that can be substantially larger than 1. 1146: 501: 442: 420: 165: 160: 155: 55: 7344: 7047: 6916: 6846: 6788: 6753: 6718: 6642: 6489: 6450: 6400: 6332: 6269: 6202: 6130: 5932: 5846: 5601: 5439: 5376: 3532: 1932: 1733: 996:

that "it is easier to further the motion of a moving body than to move a body at rest".

8560: 8244: 7953: 7736: 7655: 7105: 7087: 7059: 6901:"Experimental evidence of flutter and divergence instabilities induced by dry friction" 6808: 6501: 6474:"A formulation of the linear discrete Coulomb friction problem via convex optimization" 6289: 6073:

Kinetic friction force is usually somewhat less than the maximum static friction force.

5962: 5916: 5866: 5425: 5393: 5360: 5274: 4569: 4551: 4512: 4472: 4467: 4462: 4287:) exacerbates wear of frictional forces. As surfaces are worn by work due to friction, 3763: 3726: 1953: 1671: 1647: 1124: 1099: 1008: 631: 372: 247: 215: 175: 6537: 6520: 6431: 5769: 5021: 4587: 2406: 2183:

between atoms in each of the bulk materials and between the material surfaces and any

8545: 8341: 8087: 7978: 7799: 7190: 7163: 7130: 7109: 7063: 7018: 6966: 6960: 6800: 6609: 6570: 6553: 6458: 6344: 6281: 6256: 6159: 6062: 6021: 6013: 5987: 5966: 5954: 5858: 5398: 5218: 5183: 5164: 4938: 4906: 4872: 4845: 4807: 4779: 4749: 4724: 4675: 4664: 4639: 4457: 4435:(friction between the head of a matchstick and the rubbing surface of the match box). 4383: 4326: 4292: 3568: 3520: 2642: 2359: 2176: 1957: 1458: 1369:

exerted by each surface on the other, directed perpendicular (normal) to the surface.

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resisting the relative motion of solid surfaces, fluid layers, and material elements

641: 598: 555: 550: 491: 267: 257: 150: 6812: 6505: 6084: 5870: 5361:"Generalized law of friction between elastomers and differently shaped rough bodies" 4573: 8391: 8278: 8169: 8134: 8109: 7968: 7789: 7101: 7097: 7051: 6930: 6860: 6792: 6757: 6722: 6673: 6646: 6565: 6532: 6493: 6454: 6412: 6404: 6336: 6319: 6273: 6206: 6134: 5944: 5936: 5850: 5741: 5653: 5605: 5566: 5443: 5388: 5380: 5251: 5198: 5088: 5029: 4995: 4565: 4561: 4482: 4452: 4298:

In the reference frame of the interface between two surfaces, static friction does

4276: 4275:. The work of friction is used to mix and join materials such as in the process of 3884: 3564: 3516: 2180: 2100: 1462: 1116: 1106: 889: 831: 736: 716: 661: 656: 602: 577: 432: 290: 235: 210: 7616: 6293: 6243:

Ternes, Markus; Lutz, Christopher P.; Hirjibehedin, Cyrus F.; Giessibl, Franz J.;

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Despite being a simplified model of friction, the Coulomb model is useful in many

3000: 842: 8507: 8331: 8249: 8184: 8179: 8077: 7943: 7814: 7669: 7280:"Effectiveness of the Application of High Friction Surfacing-Crash-Reduction.pdf" 7157: 6227: 5686: 5270: 5115: 4609: 4607:

Mitchell, Luke (November 2012). Ward, Jacob (ed.). "The Fiction of Nonfriction".

4592: 4517: 4395: 4302: 4259: 3745: 3602: 3456: 3305: 3265: 3208: 2335: 1886:

in general. Sliding commences only after this frictional force reaches the value

1223:(sometimes called sliding friction or dynamic friction) between moving surfaces. 1131: 1120: 1021: 985: 885: 731: 676: 626: 621: 540: 7076: 5940: 5917:"Dynamic stiction without static friction: The role of friction vector rotation" 4542:

Hanaor, D.; Gan, Y.; Einav, I. (2016). "Static friction at fractal interfaces".

2068: with: explanation of why kinetic friction is always lower. You can help by 1165:, showing that, on that scale, dry friction is the product of the inter-surface 8555: 8454: 8346: 8263: 8067: 7829: 7819: 7705: 6934: 6473: 6382:"Approximation of the Signorini problem with friction, obeying the Coulomb law" 6138: 6012: 5896:

Greenwood J.A. and JB Williamson (1966). "Contact of nominally flat surfaces".

5657: 5570: 5033: 4999: 4962: 4631: 4389: 3857: 3690: 3676: 3622: 3595: 2989: 2339: 1085: 1017: 954: 861: 758: 666: 567: 284: 8384: 6416: 5093: 5076: 4717: 39: 8539: 8482: 8321: 8199: 8194: 8149: 7918: 7230: 5077:"The research works of Coulomb and Amontons and generalized laws of friction" 4373: 4350: 3949: 3945:, wrongly concluded that moving objects lose energy without a driving force. 3868: 3861: 3829: 3778: 3770: 3683: 3480: 646: 473: 7689: 7542: 6277: 5745: 5188:"An inquiry concerning the source of the heat which is excited by friction," 2330:

is always < 1, but this is not true. While in most relevant applications

811: 8502: 8497: 8487: 8467: 8154: 8097: 7928: 7645: 7588: 7501: 7392: 7387:

Coefficients of friction of various material pairs in atmosphere and vacuum

6804: 6796: 6761: 6497: 6408: 6348: 6285: 5958: 5862: 5402: 5256: 5202: 4418: 3853: 3472: 3448: 3273: 2294: 1489: 1366: 1166: 1162: 711: 636: 325: 205: 7554: 7489: 6554:"An augmented lagrangian treatment of contact problems involving friction" 5949: 4828:

that kinetic friction is weaker than the maximum value of static friction.

3864:

can change sliding friction into a much smaller type of rolling friction.

8512: 8209: 8092: 8031: 7600: 5733: 5328:(1926). "Über die Begründung des zweiten Hauptsatzes der Thermodynamik", 4432: 4367: 4363: 4355: 4338: 4258:

of energy by friction in a process is a classic example of thermodynamic

4255: 3657: 3645: 3594:

instability in a simple mechanical system has been discovered, watch the

3580: 3484: 3304:

For the maximum angle of static friction between granular materials, see

2347: 2301: 2093: 1929:

such as an inclined plane, the normal force from gravity is smaller than

957:, the force resisting the motion of a fluid across the surface of a body. 877: 7651: 7576: 7477: 2057: 1169:

and the contact area. These two discoveries explain Amonton's first law

8336: 8316: 8204: 8016: 8011: 7933: 7923: 7804: 7549: 7469: 7055: 5325: 4438: 4411: 4359: 4283:

corrosion particles caught between mating surfaces in relative motion (

3641: 3557: 2848: 2355: 2312: 2184: 1197:: The force of friction is independent of the apparent area of contact. 1139: 989: 496: 170: 6864: 6726: 6677: 6650: 6606:

Nonlinear Solid Mechanics: Bifurcation Theory and Material Instability

6211: 6186: 5609: 5447: 5384: 4802:

Fishbane, Paul M.; Gasiorowicz, Stephen; Thornton, Stephen T. (1993).

8492: 8472: 8358: 8174: 8159: 7775: 7717: 7517: 6340: 4272: 3942: 3900: 3896: 3817: 3795: 3633: 3618: 2298: 1638: 1454: 1191:: The force of friction is directly proportional to the applied load. 1004: 981: 977: 942: 835: 518: 8522: 8409: 8139: 8114: 8041: 7958: 7624: 7092: 4556: 4284: 4280: 3907: 3906:

Superlubricity, a recently discovered effect, has been observed in

3553: 3497:

effectively negative coefficient of friction in the low-load regime

3460: 3010: 2351: 1216: 1029: 912: 320: 295: 7677: 7665: 6938: 5430: 3887:

grades are usually specified for heavy duty or critical bearings.

8462: 8434: 8119: 8046: 8036: 8026: 8021: 7729: 7701: 7229:

This article incorporates text from this source, which is in the

6085:

Feynman, Richard P.; Leighton, Robert B.; Sands, Matthew (1964).

4477: 3495:

As of 2012, a single study has demonstrated the potential for an

2188: 1474: 1442: 1134:

published an investigation of the foundations of thermodynamics,

1127:

investigated the continuity between static and kinetic friction.

1102:(1833) developed the concept of sliding versus rolling friction. 930: 845:. Another important consequence of many types of friction can be 816: 410: 263: 180: 7612: 5895: 5807:"The Engineering Toolbox: Friction and Coefficients of Friction" 1644:

Depending on the situation, the calculation of the normal force

1598:, with equality reached only at a critical ramp angle (given by 8444: 8439: 8429: 8419: 8351: 8124: 8072: 7882: 7725: 7641: 7564: 7343: 6226:

Nichols, Edward Leamington; Franklin, William Suddards (1898).

6057:

Meriam, James L.; Kraige, L. Glenn; Palm, William John (2002).

3926: 3572: 3490: 3452: 2363: 469: 315: 225: 7465: 6242: 5979: 3648:

which offers no resistance to shearing and so is not viscous.

3077:{\displaystyle F_{\text{max}}=\mu _{\mathrm {s} }F_{\text{n}}} 1664:

might include forces other than gravity. If an object is on a

7897: 7013:

Butt, Hans-Jürgen; Graf, Karlheinz and Kappl, Michael (2006)

6109: 4362:

that are squeezed transversely against the rotating disc. In

3872: 3790: 3628: 3576: 827: 305: 300: 242: 7713: 7513: 4376:

refers to the grip wheels of a train have on the rails, see

3794:

friction is designed to be large by choice of materials for

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in 1758. The effect of the time of repose was explained by

846: 310: 273: 6472:

Acary, V.; Cadoux, F.; Lemaréchal, C.; Malick, J. (2011).

6357:"At the nanoscale, graphite can turn friction upside down" 4723:(Eleventh ed.). Pearson, Prentice Hall. p. 393. 1273:{\displaystyle F_{\mathrm {f} }\leq \mu F_{\mathrm {n} },} 1206:: Kinetic friction is independent of the sliding velocity. 6990:. Princeton, NJ: Princeton University Press. p. 391. 5643: 5556: 5244:

Philosophical Transactions of the Royal Society of London

5191:

Philosophical Transactions of the Royal Society of London

4822: 4775:

Tribological Properties of Pseudo-elastic Nickel-titanium

4398:

affects the interaction of tires and the driving surface.

4386:

is an important design and safety factor for automobiles

1850:

is the horizontal component of the external force. Thus,

819:

rough surfaces, exhibiting static frictional interactions

103:{\displaystyle {\textbf {F}}={\frac {d\mathbf {p} }{dt}}} 5114:" ("Correct Basics of Friction Calculation"), 1737, (in 1161:(ca. 1986) enabled scientists to study friction at the 999:

The classic laws of sliding friction were discovered by

7034:

Hogan, C. Michael (1973). "Analysis of highway noise".

5583: 4421:

is a device used to measure pavement surface roughness.

2378: 1035:

The understanding of friction was further developed by

6155:

Sliding friction: physical principles and applications

6018:

Statics: Analysis and Design of Systems in Equilibrium

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Computer Methods in Applied Mechanics and Engineering

5625:"Material slicker than Teflon discovered by accident" 5345:

The Principles and Design of Foundation Brake Rigging

5341: 5160:

Transient Effects in Friction: Fractal Asperity Creep

4905:(2nd ed.). Professional Engineering Publishing. 4414:

is an instrument that measures friction on a surface.

4235: 4204: 4167: 4125: 3961: 3411: 3398:{\displaystyle \theta =\arctan {\mu _{\mathrm {s} }}} 3368: 3325: 3218: 3144: 3117: 3090: 3038: 2484: 2453: 2409:. Please help to ensure that disputed statements are 2268: 2235: 2200: 2148: 2113: 2009: 1973: 1935: 1892: 1856: 1829: 1786: 1759: 1736: 1694: 1674: 1650: 1604: 1568: 1535: 1501: 1408: 1379: 1342: 1320: 1289: 1236: 1084:, friction was recognised as a mode of conversion of 67: 7370:

Physclips: Mechanics with animations and video clips

4778:(Thesis). University of California. pp. 11–12. 3820:

can be caused by ignition of the flammable mixture.

7004:, Ivison, Blakeman, Taylor & company publishers 6105: 6103: 3466: 3439:from empirical measurements of the friction angle. 6112:"Theory of rubber friction: Nonstationary sliding" 6087:"The Feynman Lectures on Physics, Vol. I, p. 12–5" 5163:. Springer Science and Business Media. p. 3. 4930: 4743: 4716: 4663: 4243: 4219: 4184: 4151: 4105: 3417: 3397: 3355:{\displaystyle \tan {\theta }=\mu _{\mathrm {s} }} 3354: 3256: 3157: 3130: 3103: 3076: 2500: 2468: 2283: 2250: 2221: 2163: 2134: 2031: 1995: 1944: 1914: 1878: 1842: 1815: 1772: 1745: 1722: 1680: 1656: 1626: 1590: 1554: 1517: 1426: 1394: 1357: 1326: 1304: 1272: 102: 7277: 5358: 5330:Sitzungsber. Preuss. Akad. Wiss., Phys. Math. Kl. 5279:On Friction between Surfaces moving at Low Speeds 5070: 5068: 4670:(fifth ed.). John Wiley & Sons. p. 3538: 8537: 7271: 6100: 5980:Bhavikatti, S. S.; K. G. Rajashekarappa (1994). 5075:Popova, Elena; Popov, Valentin L. (2015-06-01). 4767: 4765: 4744:Soutas-Little, Robert W.; Inman, Balint (2008). 3170:wheel friction changes to kinetic friction. An 1465:indicating directions and magnitudes of forces. 6379: 6249:"The Force Needed to Move an Atom on a Surface" 6225: 5415: 5335: 3689:Skin friction is caused by viscous drag in the 3442: 1562:. In fact, the friction force always satisfies 843:rubbing pieces of wood together to start a fire 7317:. Curiosity. November 11, 2015. Archived from 6905:Journal of the Mechanics and Physics of Solids 6584: 5675: 5673: 5671: 5669: 5667: 5321: 5319: 5065: 4871:. Princeton University Press. pp. 65–66. 4541: 4152:{\displaystyle \mathbf {F} _{\mathrm {fric} }} 3895:A common way to reduce friction is by using a 3257:{\displaystyle F_{k}=\mu _{\mathrm {k} }F_{n}} 3181:, although this term is not used universally. 7408: 6016:; Tongue, Benson H.; Anagnos, Thalia (2005). 5622: 5533:"Friction Factors – Coefficients of Friction" 5352: 4762: 2107:For surfaces at rest relative to each other, 1634:) that is steep enough to initiate sliding. 1076:In the long course of the development of the 1072:Heat by friction captured by a thermal camera 933:fluid that are moving relative to each other. 876:of the structural changes and other types of 838:, and has a history of more than 2000 years. 792: 7422: 7002:Principles of Physics, Or Natural Philosophy 6985: 6884:: CS1 maint: multiple names: authors list ( 6690:: CS1 maint: multiple names: authors list ( 6518: 6478:Journal of Applied Mathematics and Mechanics 6429: 6389:Mathematical Methods in the Applied Sciences 5112:Richtige Grund-Sätze der Friction-Berechnung 4926: 4924: 4922: 4737: 4661: 4638:(Sixth ed.). McGraw-Hill. p. 397. 4630: 4600: 3952:, in accordance with the definition of work 3535:, may be encountered with Coulomb friction. 2092:(COF), often symbolized by the Greek letter 892:for analysis and the development of theory. 7162:. Courier Dover Publications. p. 142. 6551: 6312: 6310: 6187:"A thermodynamic model of sliding friction" 6032:In general, for given contacting surfaces, 5914: 5764: 5762: 5664: 5527: 5525: 5523: 5521: 5519: 5517: 5515: 5513: 5511: 5509: 5507: 5505: 5503: 5501: 5499: 5497: 5495: 5493: 5491: 5489: 5487: 5485: 5483: 5481: 5479: 5477: 5316: 5074: 4694: 4185:{\displaystyle \mathbf {F} _{\mathrm {n} }} 3879:and PTFE are commonly used in low friction 3686:and rises with the square of the velocity. 929:describes the friction between layers of a 7415: 7401: 7203: 7155: 6958: 5973: 5825: 5770:"Coefficients of Friction of Human Joints" 5727: 5725: 5723: 5721: 5719: 5717: 5715: 5475: 5473: 5471: 5469: 5467: 5465: 5463: 5461: 5459: 5457: 4956: 4954: 4771: 4537: 4535: 4533: 3752: 2179:, both of which have their origins in the 2042: 799: 785: 7361:– tables of coefficients, plus many links 7091: 6924: 6854: 6828:"Stability of Steady Frictional Slipping" 6569: 6536: 6210: 5948: 5713: 5711: 5709: 5707: 5705: 5703: 5701: 5699: 5697: 5695: 5429: 5392: 5287:Series 5, volume 4, pp 308–10; link from 5255: 5092: 5022:"Leonardo da Vinci's studies of friction" 5019: 4985:"Leonardo da Vinci's studies of friction" 4982: 4919: 4896: 4894: 4892: 4890: 4888: 4864: 4555: 3507:Numerical simulation of the Coulomb model 2497: 2429:Learn how and when to remove this message 2372: 1514: 6307: 6184: 6110:Persson, B. N.; Volokitin, A. I (2002). 5826:Dienwiebel, Martin; et al. (2004). 5759: 5156: 5150: 4714: 4657: 4655: 4606: 4337:Friction is an important factor in many 3459:molecule, across surfaces of copper and 3286: 2999: 2405:Relevant discussion may be found on the 2222:{\displaystyle \mu =\mu _{\mathrm {k} }} 2135:{\displaystyle \mu =\mu _{\mathrm {s} }} 1453: 1059: 888:difficult and it is often easier to use 810: 38: 7182: 6663: 6151: 5915:Nakano, K.; Popov, V. L. (2020-12-10). 5734:"(NASA-RP-1228) Fastener Design Manual" 5731: 5454: 5213:Blundell, S.J., Blundell, K.M. (2006). 4951: 4708: 4704:. Oxford University Press. p. 713. 4530: 3801: 1176: 1096:reported on cannon boring experiments. 14: 8538: 7948: 7372:from the University of New South Wales 7246:, Harvard University Press, pp. 47–56. 6774: 6603: 6232:. Vol. 1. Macmillan. p. 101. 5986:. New Age International. p. 112. 5884:multi-scale origins of static friction 5801: 5799: 5797: 5795: 5793: 5791: 5789: 5787: 5785: 5692: 5240:"On the Mechanical Equivalent of Heat" 5217:, Oxford University Press, Oxford UK, 4900: 4885: 4626: 4624: 3651: 3590:A connection between dry friction and 7396: 7381:CRC Handbook of Chemistry and Physics 7354:. Vol. 11 (11th ed.). 1911. 7209: 7122: 7116: 7033: 6628: 5637: 5616: 5577: 5299: 5238: 4839: 4662:Meriam, J. L.; Kraige, L. G. (2002). 4652: 3932: 3777:, a process which generates heat and 3757: 3739: 2520: 2517: 2514: 2511: 2501:{\displaystyle \mu _{\mathrm {k} }\,} 900:There are several types of friction: 481:Newton's law of universal gravitation 6826:R., Rice, J.; L., Ruina, A. (1983). 6825: 6739: 6608:. Cambridge University Press, 2012. 6380:Haslinger, J.; Nedlec, J.C. (1983). 6316: 5732:Barrett, Richard T. (1 March 1990). 5550: 5046: 4960: 4868:The Physical World of Late Antiquity 4804:Physics for Scientists and Engineers 4698:Introduction to Statics and Dynamics 4688: 4431:Friction is used to heat and ignite 4358:rely on friction between a disc and 3921:actually uses sound as a lubricant. 3860:, and air cushion or other types of 3744:As a consequence of light pressure, 3697: 3563:A practically important case is the 3299: 2382: 2379:Approximate coefficients of friction 2052: 1427:{\displaystyle \mu F_{\mathrm {n} }} 1219:") between non-moving surfaces, and 1028:(1734) first recognized the role of 941:is a case of fluid friction where a 915:") between non-moving surfaces, and 7015:Physics and Chemistry of Interfaces 6704: 6525:Mathematical and Computer Modelling 5782: 5348:. Air brake association. p. 5. 4818:Themistius first stated around 350 4695:Ruina, Andy; Pratap, Rudra (2002). 4621: 4265: 4220:{\displaystyle \mu _{\mathrm {k} }} 3784: 3184: 2469:{\displaystyle \mu _{\mathrm {s} }} 2375:is not satisfied macroscopically. 2262:. The Coulomb friction is equal to 2251:{\displaystyle \mu _{\mathrm {k} }} 2164:{\displaystyle \mu _{\mathrm {s} }} 1668:and subjected to an external force 1402:may take any value from zero up to 945:fluid separates two solid surfaces. 462:Mechanics of planar particle motion 70: 24: 7376:Values for Coefficient of Friction 7214:. Leipzig, Teubner. pp. 48–49 6666:Journal of Vibration and Acoustics 6552:Simo, J.C.; Laursen, T.A. (1992). 6519:De Saxcé, G.; Feng, Z.-Q. (1998). 5740:. NASA Lewis Research Center: 16. 5135:. Nano World. 2002. Archived from 4931:Armstrong-Hélouvry, Brian (1991). 4844:(3rd ed.). Cengage Learning. 4634:; Johnston, E. Russel Jr. (1996). 4425: 4211: 4176: 4143: 4140: 4137: 4134: 4072: 4055: 4005: 4002: 3999: 3996: 3491:"Negative" coefficient of friction 3388: 3346: 3295:, when block just starts to slide. 3238: 3058: 2995: 2491: 2460: 2275: 2242: 2213: 2155: 2126: 1461:for a block on a ramp. Arrows are 1418: 1386: 1349: 1296: 1261: 1243: 25: 8572: 7433:Offshore geotechnical engineering 7336: 7311:"How Does Lighting A Match Work?" 6585:Acary, V.; Brogliato, B. (2008). 5359:Valentin L. Popov (17 Jan 2014). 4934:Control of machines with friction 4344: 3612: 3425:is the angle from horizontal and 1111:The Mechanical Equivalent of Heat 856:deformation to the generation of 7724: 7712: 7700: 7688: 7676: 7664: 7650: 7640: 7623: 7611: 7599: 7587: 7575: 7563: 7541: 7512: 7500: 7488: 7476: 7464: 7224: 7036:Water, Air, & Soil Pollution 6899:Bigoni, D.; Noselli, G. (2011). 6874:from the original on 2010-06-22. 6303:from the original on 2018-07-20. 5020:Hutchings, Ian M. (2016-08-15). 5009:from the original on 2016-08-03. 4237: 4170: 4128: 4096: 4082: 4066: 4029: 4015: 3990: 3823: 3670: 3467:Limitations of the Coulomb model 2387: 2284:{\displaystyle F_{\mathrm {f} }} 2194:For surfaces in relative motion 2056: 1395:{\displaystyle F_{\mathrm {f} }} 1358:{\displaystyle F_{\mathrm {n} }} 1305:{\displaystyle F_{\mathrm {f} }} 766: 765: 752: 85: 7303: 7292:from the original on 2017-09-03 7249: 7236: 7176: 7149: 7070: 7027: 7007: 6994: 6979: 6952: 6892: 6819: 6768: 6733: 6698: 6657: 6622: 6597: 6578: 6545: 6512: 6465: 6430:Alart, P.; Curnier, A. (1991). 6423: 6373: 6236: 6219: 6178: 6145: 6078: 6061:. Wiley and Sons. p. 330. 6050: 6020:. Wiley and Sons. p. 618. 6006: 5908: 5889: 5877: 5819: 5409: 5293: 5264: 5228: 5207: 5177: 5121: 5101: 5040: 5013: 4976: 4858: 4833: 4795: 4332: 4309:work. However, friction can do 2260:coefficient of kinetic friction 1996:{\displaystyle F_{f}\leq \mu N} 1879:{\displaystyle F_{f}\leq \mu N} 1637:The friction coefficient is an 1591:{\displaystyle F_{f}\leq \mu N} 1449: 1210: 976:Many ancient authors including 7210:Bryan, George Hartley (1907). 7123:Bayer, Raymond George (2004). 7102:10.1016/j.triboint.2017.12.047 6742:Journal of Sound and Vibration 6059:Engineering Mechanics: Statics 5342:Air Brake Association (1921). 5300:Bryan, George Hartley (1907). 4636:Vector Mechanics for Engineers 4593:Merriam-Webster.com Dictionary 4580: 4566:10.1016/j.triboint.2015.09.016 4404: 4251:is the position of the object. 4086: 4078: 4019: 4011: 3627:Fluid friction occurs between 3539:Dry friction and instabilities 3264:. This is responsible for the 3158:{\displaystyle F_{\text{max}}} 3131:{\displaystyle F_{\text{max}}} 3104:{\displaystyle F_{\text{max}}} 2173:coefficient of static friction 1627:{\displaystyle \tan ^{-1}\mu } 1226:Coulomb friction, named after 34:Force resisting sliding motion 13: 1: 8083:Mechanically stabilized earth 7365:Measurement of friction power 7189:. Kendall/Hunt. p. 603. 6538:10.1016/S0895-7177(98)00119-8 5855:10.1103/PhysRevLett.92.126101 5738:NASA Technical Reports Server 5289:Biodiversity Heritage Library 4963:"History of Science Friction" 4937:. USA: Springer. p. 10. 4524: 3890: 3704:Plastic deformation of solids 1078:law of conservation of energy 388:Koopman–von Neumann mechanics 7835:Hydraulic conductivity tests 7244:The Nature of Thermodynamics 7129:. CRC Press. pp. 1, 2. 6959:Nosonovsky, Michael (2013). 6835:Journal of Applied Mechanics 6707:Journal of Applied Mechanics 6631:Journal of Applied Mechanics 6571:10.1016/0045-7949(92)90540-G 6459:10.1016/0045-7825(91)90022-X 6363:. 2012-10-17. Archived from 5828:"Superlubricity of Graphite" 5623:Kleiner, Kurt (2008-11-21). 4772:Chatterjee, Sudipta (2008). 4378:Frictional contact mechanics 4244:{\displaystyle \mathbf {x} } 3842: 3550:João Arménio Correia Martins 3443:Friction at the atomic level 1816:{\displaystyle F_{f}=-P_{x}} 456:Non-inertial reference frame 7: 8396:Stress distribution in soil 7183:Leonard, William J (2000). 5941:10.1103/PhysRevE.102.063001 5215:Concepts in Thermal Physics 5047:Kirk, Tom (July 22, 2016). 4445: 2032:{\displaystyle F_{f}=\mu N} 1915:{\displaystyle F_{f}=\mu N} 1228:Charles-Augustin de Coulomb 1082:first law of thermodynamics 1037:Charles-Augustin de Coulomb 1026:John Theophilus Desaguliers 864:. Friction is not itself a 383:Appell's equation of motion 253:Inertial frame of reference 10: 8577: 7546:Pore pressure measurement 7156:Den Hartog, J. P. (1961). 7000:Silliman, Benjamin (1871) 6965:. CRC Press. p. 333. 6935:10.1016/j.jmps.2011.05.007 6591:Springer Verlag Heidelberg 6152:Persson, B. N. J. (2000). 6139:10.1103/PhysRevB.65.134106 5658:10.1016/j.wear.2010.11.044 5571:10.1016/j.wear.2012.07.030 5157:Goedecke, Andreas (2014). 5108:Forest de Bélidor, Bernard 5034:10.1016/j.wear.2016.04.019 5000:10.1016/j.wear.2016.04.019 4983:Hutchings, Ian M. (2016). 4865:Sambursky, Samuel (2014). 4503:Transient friction loading 3847: 3827: 3805: 3789:Any wheel equipped with a 3761: 3707: 3701: 3674: 3655: 3616: 3303: 3280:dominate inertial forces. 3008: 2478:Kinetic/Sliding Friction, 2046: 1753:is the block's weight and 1723:{\displaystyle N=mg+P_{y}} 1487: 971: 26: 8453: 8408: 8307: 8299:Preconsolidation pressure 8271: 8262: 8235: 8055: 8004: 7991: 7906: 7860: 7851: 7774: 7694:Standard penetration test 7452: 7439: 7430: 7278:Iskander, R; Stevens, A. 7257:"How Do Car Brakes Work?" 6604:Bigoni, D. (2012-07-30). 5094:10.1007/s40544-015-0074-6 3710:Deformation (engineering) 3111:. Any force smaller than 2477: 2446: 1484:is the force of friction. 1153:(1950) showed that, at a 1041:Johann Andreas von Segner 1014:Bernard Forest de Bélidor 29:Friction (disambiguation) 7795:California bearing ratio 7593:Rotary-pressure sounding 7424:Geotechnical engineering 7359:Coefficients of Friction 6558:Computers and Structures 4748:. Thomson. p. 329. 4715:Hibbeler, R. C. (2007). 4493:Normal contact stiffness 3937:According to the law of 3852:Devices such as wheels, 3640:All real fluids (except 3531:, such as the so-called 3172:anti-lock braking system 2634:BAM (Ceramic alloy AlMgB 2619:Silicon nitride ceramic 1956:analysis, usually via a 1045:Pieter van Musschenbroek 1020:(1750), who derived the 895: 546:Rotating reference frame 378:Hamilton–Jacobi equation 8215:Geosynthetic clay liner 8190:Expanded clay aggregate 7810:Proctor compaction test 7751:Crosshole sonic logging 7737:Nuclear densometer test 7494:Geo-electrical sounding 7351:Encyclopædia Britannica 7080:Tribology International 6278:10.1126/science.1150288 6229:The Elements of Physics 5689:. EngineersHandbook.com 5680:Coefficient of Friction 5590:Applied Physics Letters 4901:Dowson, Duncan (1997). 4544:Tribology International 3753:Other types of friction 3418:{\displaystyle \theta } 2090:coefficient of friction 2049:Coefficient of traction 2043:Coefficient of friction 1555:{\displaystyle F_{f}=0} 1159:atomic force microscope 487:Newton's laws of motion 347:Newton's laws of motion 8478:Earthquake engineering 8289:Lateral earth pressure 7914:Hydraulic conductivity 7765:Wave equation analysis 7744:Exploration geophysics 7636:Deformation monitoring 7605:Rotary weight sounding 7242:Bridgman, P.W., 1943, 6797:10.1098/rsta.2007.2127 6777:Phil. Trans. R. Soc. A 6762:10.1006/jsvi.2001.4052 6498:10.1002/zamm.201000073 6409:10.1002/mma.1670050127 5685:March 8, 2009, at the 5284:Philosophical Magazine 5257:10.1098/rstl.1850.0004 5203:10.1098/rstl.1798.0006 4840:Hecht, Eugene (2003). 4788:– via ProQuest. 4245: 4221: 4186: 4159:is the friction force, 4153: 4107: 3939:conservation of energy 3419: 3399: 3356: 3296: 3258: 3159: 3132: 3105: 3078: 3006: 2502: 2470: 2311:it has to be measured 2285: 2252: 2223: 2165: 2136: 2033: 1997: 1946: 1925:If the object is on a 1916: 1880: 1844: 1817: 1774: 1747: 1724: 1682: 1658: 1628: 1592: 1556: 1519: 1518:{\displaystyle N=mg\,} 1485: 1428: 1396: 1359: 1328: 1306: 1274: 1073: 1003:in 1493, a pioneer in 870:non-conservative force 820: 815:Simulated blocks with 514:Simple harmonic motion 427:Euler's laws of motion 221:D'Alembert's principle 104: 44: 7656:Settlement recordings 7581:Rock control drilling 7482:Cone penetration test 6986:Einstein, A. (1909). 5983:Engineering Mechanics 4842:Physics: Algebra/Trig 4746:Engineering Mechanics 4719:Engineering Mechanics 4666:Engineering Mechanics 4498:Stick-slip phenomenon 4246: 4222: 4187: 4154: 4108: 3525:numerically integrate 3515:applications such as 3420: 3400: 3357: 3290: 3259: 3160: 3133: 3106: 3079: 3003: 2813:Human synovial fluid 2503: 2471: 2286: 2253: 2224: 2166: 2137: 2034: 1998: 1947: 1917: 1881: 1845: 1843:{\displaystyle P_{x}} 1818: 1775: 1773:{\displaystyle P_{y}} 1748: 1725: 1683: 1659: 1629: 1593: 1557: 1520: 1469:is the normal force, 1457: 1429: 1397: 1373:The Coulomb friction 1360: 1329: 1307: 1275: 1071: 814: 368:Hamiltonian mechanics 186:Statistical mechanics 105: 42: 8518:Agricultural science 8220:Cellular confinement 6245:Heinrich, Andreas J. 6185:Makkonen, L (2012). 4903:History of Tribology 4617:(November 2012): 40. 4508:Triboelectric effect 4488:Non-smooth mechanics 4233: 4202: 4196:the object's motion, 4165: 4123: 3959: 3919:acoustic lubrication 3814:electrostatic charge 3808:Triboelectric effect 3802:Triboelectric effect 3556:and the 'song' of a 3513:numerical simulation 3409: 3366: 3323: 3319:. It is defined as: 3216: 3142: 3115: 3088: 3036: 2482: 2451: 2398:factual accuracy is 2266: 2233: 2198: 2146: 2111: 2007: 1971: 1933: 1890: 1854: 1827: 1784: 1757: 1734: 1692: 1672: 1648: 1602: 1566: 1533: 1499: 1406: 1377: 1340: 1327:{\displaystyle \mu } 1318: 1287: 1234: 1195:Amontons' Second Law 1177:Laws of dry friction 591:Angular acceleration 583:Rotational frequency 363:Lagrangian mechanics 356:Analytical mechanics 112:Second law of motion 65: 27:For other uses, see 18:Friction coefficient 8551:Classical mechanics 8410:Numerical analysis 8294:Overburden pressure 8284:Pore water pressure 8064:Shoring structures 7939:Reynolds' dilatancy 7840:Water content tests 7825:Triaxial shear test 7785:Soil classification 7758:Pile integrity test 7321:on November 5, 2018 7048:1973WASP....2..387H 6917:2011JMPSo..59.2208B 6847:1983JAM....50..343R 6789:2008RSPTA.366..785K 6754:2002JSV...254....1F 6719:2004JAM....71..154N 6643:1995JAM....62..867A 6490:2011ZaMM...91..155A 6451:1991CMAME..92..353A 6401:1983MMAS....5..422H 6333:2012NatMa..11.1032D 6270:2008Sci...319.1066T 6264:(5866): 1066–1069. 6203:2012AIPA....2a2179M 6131:2002PhRvB..65m4106P 5933:2020PhRvE.102f3001N 5847:2004PhRvL..92l6101D 5652:(9–10): 2111–2115. 5602:2003ApPhL..83.2781T 5440:2013NatSR...3E1586O 5377:2014NatSR...4E3750P 4965:. tribology-abc.com 4315:frames of reference 3733:Elastic deformation 3722:Plastic deformation 3652:Lubricated friction 3291:Angle of friction, 3166:friction is zero. 1147:Frank Philip Bowden 1107:Julius Robert Mayer 939:Lubricated friction 443:Harmonic oscillator 421:Equations of motion 56:Classical mechanics 50:Part of a series on 8385:Slab stabilisation 8365:Stability analysis 7056:10.1007/BF00159677 6417:10338.dmlcz/104086 5418:Scientific Reports 5304:. Leipzig, Teubner 5275:James Alfred Ewing 5197: : 80–102. 5028:. 360–361: 51–66. 4994:. 360–361: 51–66. 4632:Beer, Ferdinand P. 4596:. Merriam-Webster. 4513:Unilateral contact 4473:Frictionless plane 4468:Friction Acoustics 4463:Factor of adhesion 4241: 4217: 4182: 4149: 4103: 3933:Energy of friction 3871:materials such as 3764:Rolling resistance 3758:Rolling resistance 3740:Radiation friction 3605:for more details. 3601:2015-01-10 at the 3567:of the strings of 3533:Painlevé paradoxes 3415: 3395: 3352: 3297: 3254: 3155: 3128: 3101: 3074: 3007: 2498: 2466: 2281: 2248: 2219: 2161: 2132: 2029: 1993: 1945:{\displaystyle mg} 1942: 1912: 1876: 1840: 1813: 1770: 1746:{\displaystyle mg} 1743: 1720: 1678: 1654: 1624: 1588: 1552: 1515: 1486: 1424: 1392: 1355: 1324: 1302: 1270: 1204:'s Law of Friction 1100:Arthur Jules Morin 1074: 1009:Guillaume Amontons 953:is a component of 821: 759:Physics portal 373:Routhian mechanics 248:Frame of reference 100: 45: 8533: 8532: 8404: 8403: 8380:Sliding criterion 8342:Response spectrum 8258: 8257: 8088:Pressure grouting 7987: 7986: 7847: 7846: 7800:Direct shear test 7506:Permeability test 7196:978-0-7872-3932-9 7169:978-0-486-60754-2 7136:978-0-8247-4620-9 6972:978-1-4665-0401-1 6911:(10): 2208–2226. 6865:10.1115/1.3167042 6783:(1866): 785–810. 6727:10.1115/1.1653684 6678:10.1115/1.2874477 6651:10.1115/1.2896013 6615:978-1-107-02541-7 6212:10.1063/1.3699027 6165:978-3-540-67192-3 6119:Physical Review B 6068:978-0-471-40646-4 6027:978-0-471-37299-8 5993:978-81-224-0617-7 5921:Physical Review E 5610:10.1063/1.1615677 5448:10.1038/srep01586 5385:10.1038/srep03750 5223:978-0-19-856769-1 5184:Benjamin Thompson 5170:978-3-7091-1506-0 4961:van Beek, Anton. 4944:978-0-7923-9133-3 4912:978-1-86058-070-3 4878:978-1-4008-5898-9 4851:978-0-534-37729-8 4813:978-0-13-663246-7 4785:978-0-549-84437-2 4755:978-0-495-29610-2 4730:978-0-13-127146-3 4681:978-0-471-60293-4 4645:978-0-07-297688-5 4458:Contact mechanics 4384:Road slipperiness 4351:Automobile brakes 4063: 4035: 3698:Internal friction 3569:bowed instruments 3529:nonlinear effects 3521:granular material 3517:multibody systems 3313:angle of friction 3300:Angle of friction 3179:limiting friction 3152: 3125: 3098: 3071: 3046: 2985: 2984: 2447:Static Friction, 2439: 2438: 2431: 2362:. For example, a 2360:surface structure 2185:adsorbed material 2177:surface roughness 2086: 2085: 1958:free body diagram 1681:{\displaystyle P} 1657:{\displaystyle N} 1459:Free-body diagram 1155:microscopic level 1094:Benjamin Thompson 1069: 1001:Leonardo da Vinci 961:Internal friction 890:empirical methods 882:mechanical energy 866:fundamental force 809: 808: 556:Centrifugal force 551:Centripetal force 507:Euler's equations 492:Relative velocity 268:Moment of inertia 98: 72: 16:(Redirected from 8568: 8392:Bearing capacity 8279:Effective stress 8269: 8268: 8170:Land reclamation 8110:Land development 8005:Natural features 8002: 8001: 7969:Specific storage 7858: 7857: 7790:Atterberg limits 7728: 7716: 7704: 7692: 7680: 7668: 7654: 7644: 7629:Screw plate test 7627: 7615: 7603: 7591: 7579: 7567: 7545: 7516: 7504: 7492: 7480: 7468: 7450: 7449: 7417: 7410: 7403: 7394: 7393: 7355: 7347: 7345:"Friction" 7331: 7330: 7328: 7326: 7307: 7301: 7300: 7298: 7297: 7291: 7284: 7275: 7269: 7268: 7266: 7264: 7253: 7247: 7240: 7234: 7228: 7227: 7223: 7221: 7219: 7207: 7201: 7200: 7186:Minds-on Physics 7180: 7174: 7173: 7153: 7147: 7146: 7144: 7143: 7120: 7114: 7113: 7095: 7074: 7068: 7067: 7031: 7025: 7011: 7005: 6998: 6992: 6991: 6983: 6977: 6976: 6956: 6950: 6949: 6947: 6946: 6937:. Archived from 6928: 6896: 6890: 6889: 6883: 6875: 6873: 6858: 6832: 6823: 6817: 6816: 6772: 6766: 6765: 6737: 6731: 6730: 6702: 6696: 6695: 6689: 6681: 6661: 6655: 6654: 6626: 6620: 6619: 6601: 6595: 6594: 6589:. Vol. 35. 6582: 6576: 6575: 6573: 6549: 6543: 6542: 6540: 6516: 6510: 6509: 6469: 6463: 6462: 6436: 6427: 6421: 6420: 6386: 6377: 6371: 6368: 6361:R&D Magazine 6352: 6341:10.1038/nmat3452 6314: 6305: 6304: 6302: 6253: 6240: 6234: 6233: 6223: 6217: 6216: 6214: 6182: 6176: 6175: 6173: 6172: 6149: 6143: 6142: 6116: 6107: 6098: 6097: 6095: 6094: 6089:. Addison-Wesley 6082: 6076: 6075: 6054: 6048: 6047: 6010: 6004: 6003: 6001: 6000: 5977: 5971: 5970: 5952: 5912: 5906: 5905: 5893: 5887: 5881: 5875: 5874: 5832: 5823: 5817: 5816: 5814: 5813: 5803: 5780: 5779: 5777: 5776: 5766: 5757: 5756: 5754: 5752: 5746:2060/19900009424 5729: 5690: 5677: 5662: 5661: 5641: 5635: 5634: 5632: 5631: 5620: 5614: 5613: 5581: 5575: 5574: 5565:(1–2): 656–659. 5554: 5548: 5547: 5545: 5544: 5535:. Archived from 5529: 5452: 5451: 5433: 5413: 5407: 5406: 5396: 5356: 5350: 5349: 5339: 5333: 5323: 5314: 5313: 5311: 5309: 5297: 5291: 5268: 5262: 5261: 5259: 5232: 5226: 5211: 5205: 5181: 5175: 5174: 5154: 5148: 5147: 5145: 5144: 5129:"Leonhard Euler" 5125: 5119: 5105: 5099: 5098: 5096: 5072: 5063: 5062: 5060: 5059: 5044: 5038: 5037: 5017: 5011: 5010: 5008: 4989: 4980: 4974: 4973: 4971: 4970: 4958: 4949: 4948: 4928: 4917: 4916: 4898: 4883: 4882: 4862: 4856: 4855: 4837: 4831: 4830: 4827: 4799: 4793: 4792: 4769: 4760: 4759: 4741: 4735: 4734: 4722: 4712: 4706: 4705: 4703: 4692: 4686: 4685: 4669: 4659: 4650: 4649: 4628: 4619: 4618: 4604: 4598: 4597: 4584: 4578: 4577: 4559: 4539: 4483:Lateral adhesion 4453:Contact dynamics 4313:work in certain 4277:friction welding 4266:Work of friction 4250: 4248: 4247: 4242: 4240: 4226: 4224: 4223: 4218: 4216: 4215: 4214: 4191: 4189: 4188: 4183: 4181: 4180: 4179: 4173: 4158: 4156: 4155: 4150: 4148: 4147: 4146: 4131: 4112: 4110: 4109: 4104: 4099: 4085: 4077: 4076: 4075: 4069: 4061: 4060: 4059: 4058: 4048: 4047: 4033: 4032: 4018: 4010: 4009: 4008: 3993: 3987: 3986: 3974: 3973: 3885:molecular weight 3785:Braking friction 3781:as by-products. 3565:self-oscillation 3424: 3422: 3421: 3416: 3404: 3402: 3401: 3396: 3394: 3393: 3392: 3391: 3361: 3359: 3358: 3353: 3351: 3350: 3349: 3336: 3263: 3261: 3260: 3255: 3253: 3252: 3243: 3242: 3241: 3228: 3227: 3198:sliding friction 3194:dynamic friction 3192:, also known as 3190:Kinetic friction 3185:Kinetic friction 3164: 3162: 3161: 3156: 3154: 3153: 3150: 3137: 3135: 3134: 3129: 3127: 3126: 3123: 3110: 3108: 3107: 3102: 3100: 3099: 3096: 3083: 3081: 3080: 3075: 3073: 3072: 3069: 3063: 3062: 3061: 3048: 3047: 3044: 2816:Human cartilage 2734:0.45–0.75 (wet) 2616:Alumina ceramic 2507: 2505: 2504: 2499: 2496: 2495: 2494: 2475: 2473: 2472: 2467: 2465: 2464: 2463: 2441: 2440: 2434: 2427: 2423: 2420: 2414: 2411:reliably sourced 2391: 2390: 2383: 2310: 2306: 2290: 2288: 2287: 2282: 2280: 2279: 2278: 2257: 2255: 2254: 2249: 2247: 2246: 2245: 2228: 2226: 2225: 2220: 2218: 2217: 2216: 2181:chemical bonding 2170: 2168: 2167: 2162: 2160: 2159: 2158: 2141: 2139: 2138: 2133: 2131: 2130: 2129: 2081: 2078: 2060: 2053: 2038: 2036: 2035: 2030: 2019: 2018: 2002: 2000: 1999: 1994: 1983: 1982: 1951: 1949: 1948: 1943: 1921: 1919: 1918: 1913: 1902: 1901: 1885: 1883: 1882: 1877: 1866: 1865: 1849: 1847: 1846: 1841: 1839: 1838: 1822: 1820: 1819: 1814: 1812: 1811: 1796: 1795: 1779: 1777: 1776: 1771: 1769: 1768: 1752: 1750: 1749: 1744: 1729: 1727: 1726: 1721: 1719: 1718: 1687: 1685: 1684: 1679: 1663: 1661: 1660: 1655: 1633: 1631: 1630: 1625: 1617: 1616: 1597: 1595: 1594: 1589: 1578: 1577: 1561: 1559: 1558: 1553: 1545: 1544: 1524: 1522: 1521: 1516: 1473:is the force of 1433: 1431: 1430: 1425: 1423: 1422: 1421: 1401: 1399: 1398: 1393: 1391: 1390: 1389: 1364: 1362: 1361: 1356: 1354: 1353: 1352: 1333: 1331: 1330: 1325: 1311: 1309: 1308: 1303: 1301: 1300: 1299: 1279: 1277: 1276: 1271: 1266: 1265: 1264: 1248: 1247: 1246: 1221:kinetic friction 1117:Osborne Reynolds 1070: 995: 917:kinetic friction 886:first principles 801: 794: 787: 774: 769: 768: 761: 757: 756: 662:Johann Bernoulli 657:Daniel Bernoulli 578:Tangential speed 482: 458: 433:Fictitious force 428: 280:Mechanical power 270: 211:Angular momentum 109: 107: 106: 101: 99: 97: 89: 88: 79: 74: 73: 47: 46: 21: 8576: 8575: 8571: 8570: 8569: 8567: 8566: 8565: 8536: 8535: 8534: 8529: 8508:Earth materials 8449: 8411: 8400: 8309: 8303: 8254: 8231: 8185:Earth structure 8180:Erosion control 8078:Ground freezing 8068:Retaining walls 8051: 7993: 7983: 7944:Angle of repose 7902: 7843: 7777: 7770: 7769: 7730:Visible bedrock 7682:Simple sounding 7670:Shear vane test 7446:instrumentation 7445: 7443: 7435: 7426: 7421: 7342: 7339: 7334: 7324: 7322: 7309: 7308: 7304: 7295: 7293: 7289: 7282: 7276: 7272: 7262: 7260: 7255: 7254: 7250: 7241: 7237: 7225: 7217: 7215: 7208: 7204: 7197: 7181: 7177: 7170: 7154: 7150: 7141: 7139: 7137: 7126:Mechanical wear 7121: 7117: 7075: 7071: 7032: 7028: 7012: 7008: 6999: 6995: 6984: 6980: 6973: 6957: 6953: 6944: 6942: 6926:10.1.1.700.5291 6897: 6893: 6877: 6876: 6871: 6856:10.1.1.161.5207 6830: 6824: 6820: 6773: 6769: 6738: 6734: 6703: 6699: 6683: 6682: 6662: 6658: 6627: 6623: 6616: 6602: 6598: 6583: 6579: 6550: 6546: 6517: 6513: 6470: 6466: 6434: 6428: 6424: 6384: 6378: 6374: 6355: 6315: 6308: 6300: 6251: 6241: 6237: 6224: 6220: 6183: 6179: 6170: 6168: 6166: 6150: 6146: 6114: 6108: 6101: 6092: 6090: 6083: 6079: 6069: 6055: 6051: 6045: 6038: 6028: 6014:Sheppard, Sheri 6011: 6007: 5998: 5996: 5994: 5978: 5974: 5913: 5909: 5894: 5890: 5882: 5878: 5835:Phys. Rev. Lett 5830: 5824: 5820: 5811: 5809: 5805: 5804: 5783: 5774: 5772: 5768: 5767: 5760: 5750: 5748: 5730: 5693: 5687:Wayback Machine 5678: 5665: 5642: 5638: 5629: 5627: 5621: 5617: 5582: 5578: 5555: 5551: 5542: 5540: 5531: 5530: 5455: 5414: 5410: 5357: 5353: 5340: 5336: 5324: 5317: 5307: 5305: 5298: 5294: 5271:Fleeming Jenkin 5269: 5265: 5250:: 61–82. 1850. 5233: 5229: 5212: 5208: 5182: 5178: 5171: 5155: 5151: 5142: 5140: 5133:Friction Module 5127: 5126: 5122: 5106: 5102: 5073: 5066: 5057: 5055: 5045: 5041: 5018: 5014: 5006: 4987: 4981: 4977: 4968: 4966: 4959: 4952: 4945: 4929: 4920: 4913: 4899: 4886: 4879: 4863: 4859: 4852: 4838: 4834: 4819: 4814: 4800: 4796: 4786: 4770: 4763: 4756: 4742: 4738: 4731: 4713: 4709: 4701: 4693: 4689: 4682: 4660: 4653: 4646: 4629: 4622: 4610:Popular Science 4605: 4601: 4586: 4585: 4581: 4540: 4531: 4527: 4522: 4518:Friction torque 4448: 4428: 4426:Household usage 4407: 4347: 4335: 4268: 4260:irreversibility 4236: 4234: 4231: 4230: 4210: 4209: 4205: 4203: 4200: 4199: 4175: 4174: 4169: 4168: 4166: 4163: 4162: 4133: 4132: 4127: 4126: 4124: 4121: 4120: 4095: 4081: 4071: 4070: 4065: 4064: 4054: 4053: 4049: 4043: 4039: 4028: 4014: 3995: 3994: 3989: 3988: 3982: 3978: 3966: 3962: 3960: 3957: 3956: 3935: 3893: 3858:roller bearings 3850: 3845: 3832: 3826: 3810: 3804: 3787: 3766: 3760: 3755: 3742: 3712: 3706: 3700: 3679: 3673: 3660: 3654: 3625: 3617:Main articles: 3615: 3603:Wayback Machine 3546:George G. Adams 3541: 3509: 3493: 3469: 3457:carbon monoxide 3445: 3437: 3430: 3410: 3407: 3406: 3387: 3386: 3382: 3381: 3367: 3364: 3363: 3345: 3344: 3340: 3332: 3324: 3321: 3320: 3309: 3306:Angle of repose 3302: 3266:Coulomb damping 3248: 3244: 3237: 3236: 3232: 3223: 3219: 3217: 3214: 3213: 3209:Richard Feynman 3206: 3187: 3149: 3145: 3143: 3140: 3139: 3122: 3118: 3116: 3113: 3112: 3095: 3091: 3089: 3086: 3085: 3068: 3064: 3057: 3056: 3052: 3043: 3039: 3037: 3034: 3033: 3022: 3013: 2998: 2996:Static friction 2648: 2643:Titanium boride 2637: 2490: 2489: 2485: 2483: 2480: 2479: 2459: 2458: 2454: 2452: 2449: 2448: 2435: 2424: 2418: 2415: 2404: 2396:This section's 2392: 2388: 2381: 2336:silicone rubber 2308: 2304: 2274: 2273: 2269: 2267: 2264: 2263: 2241: 2240: 2236: 2234: 2231: 2230: 2212: 2211: 2207: 2199: 2196: 2195: 2154: 2153: 2149: 2147: 2144: 2143: 2125: 2124: 2120: 2112: 2109: 2108: 2082: 2076: 2073: 2066:needs expansion 2051: 2045: 2014: 2010: 2008: 2005: 2004: 1978: 1974: 1972: 1969: 1968: 1934: 1931: 1930: 1897: 1893: 1891: 1888: 1887: 1861: 1857: 1855: 1852: 1851: 1834: 1830: 1828: 1825: 1824: 1807: 1803: 1791: 1787: 1785: 1782: 1781: 1764: 1760: 1758: 1755: 1754: 1735: 1732: 1731: 1714: 1710: 1693: 1690: 1689: 1673: 1670: 1669: 1649: 1646: 1645: 1609: 1605: 1603: 1600: 1599: 1573: 1569: 1567: 1564: 1563: 1540: 1536: 1534: 1531: 1530: 1500: 1497: 1496: 1492: 1482: 1452: 1417: 1416: 1412: 1407: 1404: 1403: 1385: 1384: 1380: 1378: 1375: 1374: 1348: 1347: 1343: 1341: 1338: 1337: 1319: 1316: 1315: 1295: 1294: 1290: 1288: 1285: 1284: 1260: 1259: 1255: 1242: 1241: 1237: 1235: 1232: 1231: 1213: 1179: 1121:Fleeming Jenkin 1086:mechanical work 1060: 1022:angle of repose 993: 992:stating in 350 986:Pliny the Elder 974: 909:static friction 898: 862:local structure 860:and changes in 805: 764: 751: 750: 743: 742: 741: 616: 608: 607: 587: 541:Circular motion 535: 525: 524: 523: 480: 450: 447: 426: 405: 397: 396: 393: 392: 350: 340: 332: 331: 330: 289: 285:Mechanical work 278: 262: 200: 192: 191: 190: 145: 137: 114: 90: 84: 80: 78: 69: 68: 66: 63: 62: 35: 32: 23: 22: 15: 12: 11: 5: 8574: 8564: 8563: 8558: 8553: 8548: 8531: 8530: 8528: 8527: 8526: 8525: 8515: 8510: 8505: 8500: 8495: 8490: 8485: 8480: 8475: 8470: 8465: 8459: 8457: 8455:Related fields 8451: 8450: 8448: 8447: 8442: 8437: 8432: 8427: 8422: 8416: 8414: 8406: 8405: 8402: 8401: 8399: 8398: 8389: 8388: 8387: 8382: 8377: 8375:Classification 8372: 8367: 8356: 8355: 8354: 8349: 8347:Seismic hazard 8344: 8334: 8329: 8324: 8319: 8313: 8311: 8305: 8304: 8302: 8301: 8296: 8291: 8286: 8281: 8275: 8273: 8266: 8260: 8259: 8256: 8255: 8253: 8252: 8247: 8241: 8239: 8233: 8232: 8230: 8229: 8224: 8223: 8222: 8217: 8212: 8207: 8197: 8192: 8187: 8182: 8177: 8172: 8167: 8162: 8157: 8152: 8147: 8142: 8137: 8132: 8127: 8122: 8117: 8112: 8107: 8106: 8105: 8100: 8095: 8090: 8085: 8080: 8075: 8070: 8061: 8059: 8053: 8052: 8050: 8049: 8044: 8039: 8034: 8029: 8024: 8019: 8014: 8008: 8006: 7999: 7989: 7988: 7985: 7984: 7982: 7981: 7976: 7974:Shear strength 7971: 7966: 7961: 7956: 7951: 7949:Friction angle 7946: 7941: 7936: 7931: 7926: 7921: 7916: 7910: 7908: 7904: 7903: 7901: 7900: 7895: 7890: 7885: 7880: 7875: 7870: 7864: 7862: 7855: 7849: 7848: 7845: 7844: 7842: 7837: 7832: 7830:Oedometer test 7827: 7822: 7820:Sieve analysis 7817: 7812: 7807: 7802: 7797: 7792: 7787: 7782: 7780: 7772: 7771: 7768: 7767: 7761: 7760: 7754: 7753: 7747: 7746: 7740: 7739: 7733: 7732: 7721: 7720: 7709: 7708: 7706:Total sounding 7697: 7696: 7685: 7684: 7673: 7672: 7661: 7660: 7659: 7658: 7648: 7632: 7631: 7620: 7619: 7608: 7607: 7596: 7595: 7584: 7583: 7572: 7571: 7560: 7559: 7558: 7557: 7552: 7538: 7537: 7536: 7535: 7530: 7525: 7509: 7508: 7497: 7496: 7485: 7484: 7473: 7472: 7461: 7460: 7458: 7447: 7437: 7436: 7431: 7428: 7427: 7420: 7419: 7412: 7405: 7397: 7391: 7390: 7384: 7373: 7367: 7362: 7356: 7338: 7337:External links 7335: 7333: 7332: 7302: 7270: 7259:. Wonderopolis 7248: 7235: 7202: 7195: 7175: 7168: 7148: 7135: 7115: 7069: 7042:(3): 387–392. 7026: 7006: 6993: 6978: 6971: 6951: 6891: 6841:(2): 343–349. 6818: 6767: 6732: 6713:(2): 154–161. 6697: 6672:(4): 445–451. 6656: 6637:(4): 867–872. 6621: 6614: 6596: 6577: 6544: 6531:(4): 225–245. 6511: 6484:(2): 155–175. 6464: 6445:(3): 353–375. 6422: 6395:(1): 422–437. 6372: 6370: 6369: 6367:on 2013-07-31. 6327:(12): 1032–7. 6306: 6247:(2008-02-22). 6235: 6218: 6177: 6164: 6144: 6125:(13): 134106. 6099: 6077: 6067: 6049: 6043: 6036: 6026: 6005: 5992: 5972: 5950:10131/00013921 5907: 5888: 5876: 5841:(12): 126101. 5818: 5781: 5758: 5691: 5663: 5636: 5615: 5576: 5549: 5453: 5408: 5351: 5334: 5315: 5292: 5263: 5227: 5206: 5176: 5169: 5149: 5120: 5100: 5087:(2): 183–190. 5064: 5039: 5012: 4975: 4950: 4943: 4918: 4911: 4884: 4877: 4857: 4850: 4832: 4820:B.C. [ 4812: 4794: 4784: 4761: 4754: 4736: 4729: 4707: 4687: 4680: 4651: 4644: 4620: 4599: 4579: 4528: 4526: 4523: 4521: 4520: 4515: 4510: 4505: 4500: 4495: 4490: 4485: 4480: 4475: 4470: 4465: 4460: 4455: 4449: 4447: 4444: 4443: 4442: 4436: 4427: 4424: 4423: 4422: 4415: 4406: 4403: 4402: 4401: 4400: 4399: 4393: 4390:Split friction 4381: 4371: 4346: 4345:Transportation 4343: 4334: 4331: 4327:isochoric work 4293:surface finish 4267: 4264: 4253: 4252: 4239: 4228: 4213: 4208: 4197: 4178: 4172: 4160: 4145: 4142: 4139: 4136: 4130: 4114: 4113: 4102: 4098: 4094: 4091: 4088: 4084: 4080: 4074: 4068: 4057: 4052: 4046: 4042: 4038: 4031: 4027: 4024: 4021: 4017: 4013: 4007: 4004: 4001: 3998: 3992: 3985: 3981: 3977: 3972: 3969: 3965: 3934: 3931: 3892: 3889: 3862:fluid bearings 3849: 3846: 3844: 3841: 3828:Main article: 3825: 3822: 3806:Main article: 3803: 3800: 3786: 3783: 3762:Main article: 3759: 3756: 3754: 3751: 3741: 3738: 3702:Main article: 3699: 3696: 3691:boundary layer 3677:Parasitic drag 3675:Main article: 3672: 3669: 3656:Main article: 3653: 3650: 3623:Drag (physics) 3614: 3613:Fluid friction 3611: 3540: 3537: 3508: 3505: 3492: 3489: 3468: 3465: 3444: 3441: 3435: 3428: 3414: 3390: 3385: 3380: 3377: 3374: 3371: 3348: 3343: 3339: 3335: 3331: 3328: 3317:friction angle 3301: 3298: 3251: 3247: 3240: 3235: 3231: 3226: 3222: 3204: 3186: 3183: 3148: 3121: 3094: 3067: 3060: 3055: 3051: 3042: 3020: 3009:Main article: 2997: 2994: 2990:superlubricity 2983: 2982: 2979: 2976: 2973: 2970: 2967: 2963: 2962: 2959: 2956: 2953: 2950: 2947: 2943: 2942: 2939: 2936: 2933: 2930: 2927: 2923: 2922: 2919: 2917: 2914: 2911: 2910:PTFE (Teflon) 2908: 2904: 2903: 2901: 2899: 2897: 2894: 2891: 2887: 2886: 2883: 2881: 2878: 2875: 2874:PTFE (Teflon) 2872: 2865: 2864: 2862: 2860: 2857: 2854: 2851: 2845: 2844: 2842: 2840: 2838: 2835: 2832: 2828: 2827: 2824: 2822: 2819: 2817: 2814: 2810: 2809: 2806: 2803: 2800: 2797: 2794: 2790: 2789: 2786: 2783: 2781: 2778: 2775: 2771: 2770: 2768: 2765: 2763: 2760: 2757: 2753: 2752: 2750: 2748: 2746: 2743: 2740: 2736: 2735: 2732: 2729: 2726: 2723: 2720: 2716: 2715: 2713: 2710: 2708: 2705: 2702: 2698: 2697: 2695: 2692: 2690: 2687: 2684: 2680: 2679: 2677: 2674: 2671: 2668: 2665: 2661: 2660: 2658: 2656: 2653: 2650: 2646: 2640: 2635: 2630: 2629: 2626: 2624: 2622: 2620: 2617: 2613: 2612: 2610: 2607: 2604: 2601: 2598: 2594: 2593: 2591: 2588: 2585: 2582: 2579: 2575: 2574: 2572: 2569: 2567: 2565: 2562: 2558: 2557: 2554: 2551: 2548: 2545: 2541: 2540: 2538: 2535: 2533: 2530: 2527: 2523: 2522: 2519: 2516: 2513: 2509: 2508: 2493: 2488: 2476: 2462: 2457: 2445: 2437: 2436: 2395: 2393: 2386: 2380: 2377: 2340:acrylic rubber 2313:experimentally 2277: 2272: 2244: 2239: 2215: 2210: 2206: 2203: 2157: 2152: 2128: 2123: 2119: 2116: 2084: 2083: 2063: 2061: 2044: 2041: 2028: 2025: 2022: 2017: 2013: 1992: 1989: 1986: 1981: 1977: 1941: 1938: 1928: 1927:tilted surface 1911: 1908: 1905: 1900: 1896: 1875: 1872: 1869: 1864: 1860: 1837: 1833: 1810: 1806: 1802: 1799: 1794: 1790: 1767: 1763: 1742: 1739: 1717: 1713: 1709: 1706: 1703: 1700: 1697: 1677: 1667: 1653: 1623: 1620: 1615: 1612: 1608: 1587: 1584: 1581: 1576: 1572: 1551: 1548: 1543: 1539: 1513: 1510: 1507: 1504: 1488:Main article: 1480: 1451: 1448: 1420: 1415: 1411: 1388: 1383: 1371: 1370: 1351: 1346: 1335: 1323: 1313: 1298: 1293: 1269: 1263: 1258: 1254: 1251: 1245: 1240: 1212: 1209: 1208: 1207: 1198: 1192: 1178: 1175: 1018:Leonhard Euler 973: 970: 969: 968: 958: 947: 946: 935: 934: 927:Fluid friction 924: 897: 894: 807: 806: 804: 803: 796: 789: 781: 778: 777: 776: 775: 762: 745: 744: 740: 739: 734: 729: 724: 719: 714: 709: 704: 699: 694: 689: 684: 679: 674: 669: 664: 659: 654: 649: 644: 639: 634: 629: 624: 618: 617: 614: 613: 610: 609: 606: 605: 586: 585: 580: 575: 570: 568:Coriolis force 565: 564: 563: 553: 548: 543: 537: 536: 531: 530: 527: 526: 522: 521: 516: 511: 510: 509: 504: 494: 489: 484: 477: 466: 465: 464: 459: 446: 445: 440: 435: 430: 423: 418: 413: 407: 406: 403: 402: 399: 398: 395: 394: 391: 390: 385: 380: 375: 370: 365: 359: 353: 351: 344: 341: 338: 337: 334: 333: 329: 328: 323: 318: 313: 308: 303: 298: 293: 287: 282: 276: 271: 260: 255: 250: 245: 240: 239: 238: 233: 223: 218: 213: 208: 202: 201: 198: 197: 194: 193: 189: 188: 183: 178: 173: 168: 163: 158: 153: 147: 146: 143: 142: 139: 138: 136: 135: 130: 125: 119: 116: 115: 110: 96: 93: 87: 83: 77: 59: 58: 52: 51: 33: 9: 6: 4: 3: 2: 8573: 8562: 8559: 8557: 8554: 8552: 8549: 8547: 8544: 8543: 8541: 8524: 8521: 8520: 8519: 8516: 8514: 8511: 8509: 8506: 8504: 8501: 8499: 8496: 8494: 8491: 8489: 8486: 8484: 8483:Geomorphology 8481: 8479: 8476: 8474: 8471: 8469: 8466: 8464: 8461: 8460: 8458: 8456: 8452: 8446: 8443: 8441: 8438: 8436: 8433: 8431: 8428: 8426: 8423: 8421: 8418: 8417: 8415: 8413: 8407: 8397: 8393: 8390: 8386: 8383: 8381: 8378: 8376: 8373: 8371: 8368: 8366: 8363: 8362: 8360: 8357: 8353: 8350: 8348: 8345: 8343: 8340: 8339: 8338: 8335: 8333: 8330: 8328: 8327:Consolidation 8325: 8323: 8322:Frost heaving 8320: 8318: 8315: 8314: 8312: 8306: 8300: 8297: 8295: 8292: 8290: 8287: 8285: 8282: 8280: 8277: 8276: 8274: 8270: 8267: 8265: 8261: 8251: 8248: 8246: 8243: 8242: 8240: 8238: 8234: 8228: 8225: 8221: 8218: 8216: 8213: 8211: 8208: 8206: 8203: 8202: 8201: 8200:Geosynthetics 8198: 8196: 8195:Crushed stone 8193: 8191: 8188: 8186: 8183: 8181: 8178: 8176: 8173: 8171: 8168: 8166: 8163: 8161: 8158: 8156: 8153: 8151: 8150:Cut-and-cover 8148: 8146: 8143: 8141: 8138: 8136: 8133: 8131: 8128: 8126: 8123: 8121: 8118: 8116: 8113: 8111: 8108: 8104: 8101: 8099: 8096: 8094: 8091: 8089: 8086: 8084: 8081: 8079: 8076: 8074: 8071: 8069: 8066: 8065: 8063: 8062: 8060: 8058: 8054: 8048: 8045: 8043: 8040: 8038: 8035: 8033: 8030: 8028: 8025: 8023: 8020: 8018: 8015: 8013: 8010: 8009: 8007: 8003: 8000: 7997: 7990: 7980: 7977: 7975: 7972: 7970: 7967: 7965: 7962: 7960: 7957: 7955: 7952: 7950: 7947: 7945: 7942: 7940: 7937: 7935: 7932: 7930: 7927: 7925: 7922: 7920: 7919:Water content 7917: 7915: 7912: 7911: 7909: 7905: 7899: 7896: 7894: 7891: 7889: 7886: 7884: 7881: 7879: 7876: 7874: 7871: 7869: 7866: 7865: 7863: 7859: 7856: 7854: 7850: 7841: 7838: 7836: 7833: 7831: 7828: 7826: 7823: 7821: 7818: 7816: 7813: 7811: 7808: 7806: 7803: 7801: 7798: 7796: 7793: 7791: 7788: 7786: 7783: 7781: 7779: 7773: 7766: 7763: 7762: 7759: 7756: 7755: 7752: 7749: 7748: 7745: 7742: 7741: 7738: 7735: 7734: 7731: 7727: 7723: 7722: 7719: 7715: 7711: 7710: 7707: 7703: 7699: 7698: 7695: 7691: 7687: 7686: 7683: 7679: 7675: 7674: 7671: 7667: 7663: 7662: 7657: 7653: 7649: 7647: 7643: 7639: 7638: 7637: 7634: 7633: 7630: 7626: 7622: 7621: 7618: 7617:Sample series 7614: 7610: 7609: 7606: 7602: 7598: 7597: 7594: 7590: 7586: 7585: 7582: 7578: 7574: 7573: 7570: 7566: 7562: 7561: 7556: 7553: 7551: 7548: 7547: 7544: 7540: 7539: 7534: 7531: 7529: 7526: 7524: 7521: 7520: 7519: 7515: 7511: 7510: 7507: 7503: 7499: 7498: 7495: 7491: 7487: 7486: 7483: 7479: 7475: 7474: 7471: 7467: 7463: 7462: 7459: 7456: 7451: 7448: 7442: 7441:Investigation 7438: 7434: 7429: 7425: 7418: 7413: 7411: 7406: 7404: 7399: 7398: 7395: 7388: 7385: 7383: 7382: 7377: 7374: 7371: 7368: 7366: 7363: 7360: 7357: 7353: 7352: 7346: 7341: 7340: 7320: 7316: 7315:curiosity.com 7312: 7306: 7288: 7281: 7274: 7258: 7252: 7245: 7239: 7232: 7231:public domain 7213: 7206: 7198: 7192: 7188: 7187: 7179: 7171: 7165: 7161: 7160: 7152: 7138: 7132: 7128: 7127: 7119: 7111: 7107: 7103: 7099: 7094: 7089: 7085: 7081: 7073: 7065: 7061: 7057: 7053: 7049: 7045: 7041: 7037: 7030: 7024: 7023:3-527-40413-9 7020: 7016: 7010: 7003: 6997: 6989: 6982: 6974: 6968: 6964: 6963: 6955: 6941:on 2020-08-18 6940: 6936: 6932: 6927: 6922: 6918: 6914: 6910: 6906: 6902: 6895: 6887: 6881: 6870: 6866: 6862: 6857: 6852: 6848: 6844: 6840: 6836: 6829: 6822: 6814: 6810: 6806: 6802: 6798: 6794: 6790: 6786: 6782: 6778: 6771: 6763: 6759: 6755: 6751: 6747: 6743: 6736: 6728: 6724: 6720: 6716: 6712: 6708: 6701: 6693: 6687: 6679: 6675: 6671: 6667: 6660: 6652: 6648: 6644: 6640: 6636: 6632: 6625: 6617: 6611: 6607: 6600: 6592: 6588: 6581: 6572: 6567: 6564:(2): 97–116. 6563: 6559: 6555: 6548: 6539: 6534: 6530: 6526: 6522: 6515: 6507: 6503: 6499: 6495: 6491: 6487: 6483: 6479: 6475: 6468: 6460: 6456: 6452: 6448: 6444: 6440: 6433: 6426: 6418: 6414: 6410: 6406: 6402: 6398: 6394: 6390: 6383: 6376: 6366: 6362: 6358: 6354: 6353: 6350: 6346: 6342: 6338: 6334: 6330: 6326: 6322: 6321: 6313: 6311: 6299: 6295: 6291: 6287: 6283: 6279: 6275: 6271: 6267: 6263: 6259: 6258: 6250: 6246: 6239: 6231: 6230: 6222: 6213: 6208: 6204: 6200: 6197:(1): 012179. 6196: 6192: 6188: 6181: 6167: 6161: 6157: 6156: 6148: 6140: 6136: 6132: 6128: 6124: 6120: 6113: 6106: 6104: 6088: 6081: 6074: 6070: 6064: 6060: 6053: 6046: 6042: 6035: 6029: 6023: 6019: 6015: 6009: 5995: 5989: 5985: 5984: 5976: 5968: 5964: 5960: 5956: 5951: 5946: 5942: 5938: 5934: 5930: 5927:(6): 063001. 5926: 5922: 5918: 5911: 5903: 5899: 5892: 5885: 5880: 5872: 5868: 5864: 5860: 5856: 5852: 5848: 5844: 5840: 5836: 5829: 5822: 5808: 5802: 5800: 5798: 5796: 5794: 5792: 5790: 5788: 5786: 5771: 5765: 5763: 5747: 5743: 5739: 5735: 5728: 5726: 5724: 5722: 5720: 5718: 5716: 5714: 5712: 5710: 5708: 5706: 5704: 5702: 5700: 5698: 5696: 5688: 5684: 5681: 5676: 5674: 5672: 5670: 5668: 5659: 5655: 5651: 5647: 5640: 5626: 5619: 5611: 5607: 5603: 5599: 5595: 5591: 5587: 5580: 5572: 5568: 5564: 5560: 5553: 5539:on 2019-02-01 5538: 5534: 5528: 5526: 5524: 5522: 5520: 5518: 5516: 5514: 5512: 5510: 5508: 5506: 5504: 5502: 5500: 5498: 5496: 5494: 5492: 5490: 5488: 5486: 5484: 5482: 5480: 5478: 5476: 5474: 5472: 5470: 5468: 5466: 5464: 5462: 5460: 5458: 5449: 5445: 5441: 5437: 5432: 5427: 5423: 5419: 5412: 5404: 5400: 5395: 5390: 5386: 5382: 5378: 5374: 5370: 5366: 5362: 5355: 5347: 5346: 5338: 5331: 5327: 5322: 5320: 5303: 5296: 5290: 5286: 5285: 5280: 5276: 5272: 5267: 5258: 5253: 5249: 5245: 5241: 5236: 5231: 5224: 5220: 5216: 5210: 5204: 5200: 5196: 5192: 5189: 5185: 5180: 5172: 5166: 5162: 5161: 5153: 5139:on 2011-05-07 5138: 5134: 5130: 5124: 5117: 5113: 5109: 5104: 5095: 5090: 5086: 5082: 5078: 5071: 5069: 5054: 5050: 5043: 5035: 5031: 5027: 5023: 5016: 5005: 5001: 4997: 4993: 4986: 4979: 4964: 4957: 4955: 4946: 4940: 4936: 4935: 4927: 4925: 4923: 4914: 4908: 4904: 4897: 4895: 4893: 4891: 4889: 4880: 4874: 4870: 4869: 4861: 4853: 4847: 4843: 4836: 4829: 4825: 4824: 4815: 4809: 4805: 4798: 4791: 4787: 4781: 4777: 4776: 4768: 4766: 4757: 4751: 4747: 4740: 4732: 4726: 4721: 4720: 4711: 4700: 4699: 4691: 4683: 4677: 4673: 4668: 4667: 4658: 4656: 4647: 4641: 4637: 4633: 4627: 4625: 4616: 4612: 4611: 4603: 4595: 4594: 4589: 4583: 4575: 4571: 4567: 4563: 4558: 4553: 4549: 4545: 4538: 4536: 4534: 4529: 4519: 4516: 4514: 4511: 4509: 4506: 4504: 4501: 4499: 4496: 4494: 4491: 4489: 4486: 4484: 4481: 4479: 4476: 4474: 4471: 4469: 4466: 4464: 4461: 4459: 4456: 4454: 4451: 4450: 4440: 4437: 4434: 4430: 4429: 4420: 4416: 4413: 4409: 4408: 4397: 4394: 4391: 4388: 4387: 4385: 4382: 4379: 4375: 4374:Rail adhesion 4372: 4369: 4365: 4361: 4357: 4352: 4349: 4348: 4342: 4341:disciplines. 4340: 4330: 4328: 4322: 4320: 4316: 4312: 4308: 4304: 4301: 4296: 4294: 4290: 4286: 4282: 4278: 4274: 4263: 4261: 4257: 4229: 4206: 4198: 4195: 4161: 4119: 4118: 4117: 4100: 4092: 4089: 4050: 4044: 4040: 4036: 4025: 4022: 3983: 3979: 3975: 3970: 3967: 3963: 3955: 3954: 3953: 3951: 3950:line integral 3946: 3944: 3940: 3930: 3928: 3922: 3920: 3916: 3911: 3909: 3904: 3902: 3898: 3888: 3886: 3882: 3878: 3874: 3870: 3869:thermoplastic 3865: 3863: 3859: 3855: 3854:ball bearings 3840: 3836: 3831: 3830:Belt friction 3824:Belt friction 3821: 3819: 3815: 3809: 3799: 3797: 3792: 3782: 3780: 3776: 3772: 3771:motor vehicle 3765: 3750: 3747: 3737: 3734: 3730: 3728: 3723: 3719: 3717: 3711: 3705: 3695: 3692: 3687: 3685: 3684:drag equation 3678: 3671:Skin friction 3668: 3664: 3659: 3649: 3647: 3643: 3638: 3636: 3635: 3630: 3624: 3620: 3610: 3606: 3604: 3600: 3597: 3593: 3588: 3586: 3582: 3578: 3574: 3570: 3566: 3561: 3559: 3555: 3551: 3547: 3536: 3534: 3530: 3526: 3522: 3518: 3514: 3504: 3502: 3498: 3488: 3486: 3482: 3481:adhesive tape 3477: 3474: 3464: 3462: 3458: 3454: 3450: 3440: 3438: 3431: 3412: 3383: 3378: 3375: 3372: 3369: 3341: 3337: 3333: 3329: 3326: 3318: 3314: 3307: 3294: 3289: 3285: 3281: 3277: 3275: 3271: 3267: 3249: 3245: 3233: 3229: 3224: 3220: 3210: 3203: 3199: 3195: 3191: 3182: 3180: 3175: 3173: 3167: 3146: 3119: 3092: 3065: 3053: 3049: 3040: 3029: 3026: 3019: 3012: 3002: 2993: 2991: 2980: 2977: 2974: 2971: 2968: 2965: 2964: 2960: 2957: 2954: 2951: 2948: 2945: 2944: 2940: 2937: 2934: 2931: 2928: 2925: 2924: 2920: 2918: 2915: 2912: 2909: 2906: 2905: 2902: 2900: 2898: 2895: 2892: 2889: 2888: 2884: 2882: 2879: 2876: 2873: 2870: 2867: 2866: 2863: 2861: 2858: 2855: 2852: 2850: 2847: 2846: 2843: 2841: 2839: 2836: 2833: 2830: 2829: 2825: 2823: 2820: 2818: 2815: 2812: 2811: 2807: 2804: 2801: 2798: 2795: 2792: 2791: 2787: 2784: 2782: 2779: 2776: 2773: 2772: 2769: 2766: 2764: 2761: 2758: 2755: 2754: 2751: 2749: 2747: 2744: 2741: 2738: 2737: 2733: 2730: 2727: 2724: 2721: 2718: 2717: 2714: 2711: 2709: 2706: 2703: 2700: 2699: 2696: 2693: 2691: 2688: 2685: 2682: 2681: 2678: 2675: 2672: 2669: 2666: 2663: 2662: 2659: 2657: 2654: 2651: 2644: 2641: 2639: 2632: 2631: 2627: 2625: 2623: 2621: 2618: 2615: 2614: 2611: 2608: 2605: 2602: 2599: 2596: 2595: 2592: 2589: 2586: 2583: 2580: 2577: 2576: 2573: 2570: 2568: 2566: 2563: 2560: 2559: 2555: 2552: 2549: 2546: 2543: 2542: 2539: 2536: 2534: 2531: 2528: 2525: 2524: 2518:Dry and clean 2512:Dry and clean 2510: 2486: 2455: 2442: 2433: 2430: 2422: 2419:November 2021 2412: 2408: 2402: 2401: 2394: 2385: 2384: 2376: 2374: 2373:Amontons' law 2368: 2365: 2361: 2357: 2353: 2349: 2343: 2341: 2337: 2333: 2329: 2325: 2320: 2318: 2314: 2303: 2300: 2296: 2292: 2270: 2261: 2237: 2208: 2204: 2201: 2192: 2190: 2186: 2182: 2178: 2174: 2150: 2121: 2117: 2114: 2105: 2102: 2099: 2098:dimensionless 2095: 2091: 2080: 2071: 2067: 2064:This section 2062: 2059: 2055: 2054: 2050: 2040: 2026: 2023: 2020: 2015: 2011: 1990: 1987: 1984: 1979: 1975: 1966: 1961: 1959: 1955: 1939: 1936: 1926: 1923: 1909: 1906: 1903: 1898: 1894: 1873: 1870: 1867: 1862: 1858: 1835: 1831: 1808: 1804: 1800: 1797: 1792: 1788: 1765: 1761: 1740: 1737: 1715: 1711: 1707: 1704: 1701: 1698: 1695: 1675: 1666:level surface 1665: 1651: 1642: 1640: 1635: 1621: 1618: 1613: 1610: 1606: 1585: 1582: 1579: 1574: 1570: 1549: 1546: 1541: 1537: 1528: 1511: 1508: 1505: 1502: 1491: 1483: 1476: 1472: 1468: 1464: 1460: 1456: 1447: 1444: 1439: 1437: 1413: 1409: 1381: 1368: 1344: 1336: 1321: 1314: 1291: 1283: 1282: 1281: 1267: 1256: 1252: 1249: 1238: 1229: 1224: 1222: 1218: 1205: 1203: 1199: 1196: 1193: 1190: 1188: 1184: 1183: 1182: 1174: 1172: 1168: 1164: 1160: 1156: 1152: 1148: 1143: 1141: 1137: 1133: 1128: 1126: 1122: 1118: 1114: 1112: 1108: 1103: 1101: 1097: 1095: 1091: 1087: 1083: 1079: 1058: 1056: 1052: 1048: 1046: 1042: 1038: 1033: 1031: 1027: 1023: 1019: 1015: 1010: 1006: 1002: 997: 991: 987: 983: 979: 966: 962: 959: 956: 952: 951:Skin friction 949: 948: 944: 940: 937: 936: 932: 928: 925: 923:(see Figure). 922: 918: 914: 910: 906: 903: 902: 901: 893: 891: 887: 883: 879: 875: 871: 867: 863: 859: 855: 850: 848: 844: 839: 837: 833: 829: 825: 818: 813: 802: 797: 795: 790: 788: 783: 782: 780: 779: 773: 763: 760: 755: 749: 748: 747: 746: 738: 735: 733: 730: 728: 725: 723: 720: 718: 715: 713: 710: 708: 705: 703: 700: 698: 695: 693: 690: 688: 685: 683: 680: 678: 675: 673: 670: 668: 665: 663: 660: 658: 655: 653: 650: 648: 645: 643: 640: 638: 635: 633: 630: 628: 625: 623: 620: 619: 612: 611: 604: 600: 596: 592: 589: 588: 584: 581: 579: 576: 574: 571: 569: 566: 562: 559: 558: 557: 554: 552: 549: 547: 544: 542: 539: 538: 534: 529: 528: 520: 517: 515: 512: 508: 505: 503: 500: 499: 498: 495: 493: 490: 488: 485: 483: 478: 475: 471: 468: 467: 463: 460: 457: 453: 449: 448: 444: 441: 439: 436: 434: 431: 429: 424: 422: 419: 417: 414: 412: 409: 408: 401: 400: 389: 386: 384: 381: 379: 376: 374: 371: 369: 366: 364: 361: 360: 358: 357: 352: 349: 348: 343: 342: 336: 335: 327: 324: 322: 319: 317: 314: 312: 309: 307: 304: 302: 299: 297: 294: 292: 288: 286: 283: 281: 277: 275: 272: 269: 265: 261: 259: 256: 254: 251: 249: 246: 244: 241: 237: 234: 232: 229: 228: 227: 224: 222: 219: 217: 214: 212: 209: 207: 204: 203: 196: 195: 187: 184: 182: 179: 177: 174: 172: 169: 167: 164: 162: 159: 157: 154: 152: 149: 148: 141: 140: 134: 131: 129: 126: 124: 121: 120: 118: 117: 113: 94: 91: 81: 75: 61: 60: 57: 54: 53: 49: 48: 41: 37: 30: 19: 8503:Biogeography 8498:Hydrogeology 8488:Soil science 8468:Geochemistry 8227:Infiltration 8155:Cut and fill 8098:Soil nailing 7964:Permeability 7929:Bulk density 7646:Inclinometer 7569:Ram sounding 7454: 7379: 7349: 7323:. Retrieved 7319:the original 7314: 7305: 7294:. Retrieved 7273: 7261:. Retrieved 7251: 7243: 7238: 7216:. Retrieved 7205: 7185: 7178: 7158: 7151: 7140:. Retrieved 7125: 7118: 7083: 7079: 7072: 7039: 7035: 7029: 7014: 7009: 7001: 6996: 6987: 6981: 6961: 6954: 6943:. Retrieved 6939:the original 6908: 6904: 6894: 6880:cite journal 6838: 6834: 6821: 6780: 6776: 6770: 6745: 6741: 6735: 6710: 6706: 6700: 6686:cite journal 6669: 6665: 6659: 6634: 6630: 6624: 6605: 6599: 6586: 6580: 6561: 6557: 6547: 6528: 6524: 6514: 6481: 6477: 6467: 6442: 6438: 6425: 6392: 6388: 6375: 6365:the original 6360: 6324: 6318: 6261: 6255: 6238: 6228: 6221: 6194: 6191:AIP Advances 6190: 6180: 6169:. Retrieved 6158:. Springer. 6154: 6147: 6122: 6118: 6091:. Retrieved 6080: 6072: 6058: 6052: 6040: 6033: 6031: 6017: 6008: 5997:. Retrieved 5982: 5975: 5924: 5920: 5910: 5901: 5897: 5891: 5879: 5838: 5834: 5821: 5810:. Retrieved 5773:. Retrieved 5749:. Retrieved 5737: 5649: 5645: 5639: 5628:. Retrieved 5618: 5596:(14): 2781. 5593: 5589: 5579: 5562: 5558: 5552: 5541:. Retrieved 5537:the original 5421: 5417: 5411: 5368: 5364: 5354: 5344: 5337: 5329: 5306:. Retrieved 5295: 5282: 5266: 5247: 5243: 5230: 5214: 5209: 5194: 5190: 5179: 5159: 5152: 5141:. Retrieved 5137:the original 5132: 5123: 5103: 5084: 5080: 5056:. Retrieved 5052: 5042: 5025: 5015: 4991: 4978: 4967:. Retrieved 4933: 4902: 4867: 4860: 4841: 4835: 4821: 4817: 4803: 4797: 4789: 4774: 4745: 4739: 4718: 4710: 4697: 4690: 4665: 4635: 4614: 4608: 4602: 4591: 4582: 4547: 4543: 4419:profilograph 4396:Road texture 4336: 4333:Applications 4323: 4318: 4310: 4306: 4299: 4297: 4269: 4254: 4193: 4115: 3947: 3936: 3923: 3912: 3905: 3894: 3866: 3851: 3837: 3833: 3811: 3788: 3767: 3743: 3731: 3720: 3713: 3688: 3680: 3665: 3661: 3639: 3632: 3626: 3607: 3589: 3571:such as the 3562: 3554:brake squeal 3542: 3510: 3500: 3496: 3494: 3478: 3473:contact area 3470: 3455:atom, and a 3449:nanomachines 3446: 3433: 3426: 3316: 3312: 3310: 3292: 3282: 3278: 3201: 3197: 3193: 3189: 3188: 3178: 3176: 3168: 3030: 3017: 3014: 2986: 2981:0.067–0.167 2628:0.004 (wet) 2425: 2416: 2397: 2369: 2344: 2331: 2327: 2321: 2316: 2295:Arthur Morin 2293: 2259: 2193: 2172: 2106: 2089: 2087: 2074: 2070:adding to it 2065: 1964: 1962: 1924: 1643: 1636: 1526: 1493: 1490:Normal force 1478: 1470: 1466: 1450:Normal force 1440: 1372: 1367:normal force 1225: 1220: 1214: 1211:Dry friction 1200: 1194: 1185: 1180: 1170: 1167:shear stress 1163:atomic scale 1144: 1135: 1129: 1115: 1110: 1104: 1098: 1075: 1049: 1034: 998: 975: 960: 950: 938: 926: 916: 908: 905:Dry friction 904: 899: 851: 840: 823: 822: 601: / 597: / 595:displacement 593: / 454: / 437: 416:Displacement 354: 345: 339:Formulations 326:Virtual work 266: / 206:Acceleration 199:Fundamentals 36: 8513:Archaeology 8237:Foundations 8210:Geomembrane 8093:Slurry wall 8032:Water table 7996:Interaction 7992:Structures 7979:Sensitivity 7776:Laboratory 7325:November 4, 7263:November 4, 7086:: 376–380. 6748:(1): 1–21. 5235:Joule, J.P. 4550:: 229–238. 4439:Sticky pads 4433:matchsticks 4405:Measurement 4368:brake shoes 4364:drum brakes 4356:Disk brakes 4339:engineering 4256:Dissipation 3773:tires on a 3716:deformation 3658:Lubrication 3646:ideal fluid 3642:superfluids 3581:hurdy-gurdy 3485:drag racing 3270:oscillating 2941:0.029–0.19 2935:0.005–0.23 2808:0.09–0.116 2802:0.005–0.01 2728:0.30 (wet) 2521:Lubricated 2515:Lubricated 2348:temperature 2302:measurement 2077:August 2020 1965:tentatively 1151:David Tabor 1125:J. A. Ewing 1092:. In 1798, 1080:and of the 1051:John Leslie 965:deformation 878:dissipation 874:free energy 737:von Neumann 404:Core topics 8540:Categories 8370:Mitigation 8352:Shear wave 8337:Earthquake 8332:Compaction 8317:Permafrost 8308:Phenomena/ 8205:Geotextile 8130:Embankment 8120:Excavation 8057:Earthworks 8017:Vegetation 8012:Topography 7934:Thixotropy 7924:Void ratio 7907:Properties 7805:Hydrometer 7550:Piezometer 7470:Core drill 7296:2017-09-03 7142:2008-07-07 7093:1604.03407 6945:2011-11-30 6171:2016-01-23 6093:2009-10-16 5999:2007-10-21 5812:2008-11-23 5775:2015-04-27 5630:2008-12-25 5543:2015-04-27 5332:, 453—463. 5326:Planck, M. 5143:2011-03-25 5058:2016-07-26 4969:2011-03-24 4588:"friction" 4557:2106.01473 4525:References 4412:tribometer 4360:brake pads 3891:Lubricants 3818:explosions 3796:brake pads 3708:See also: 3558:glass harp 3362:and thus: 3025:asperities 2978:0.32–0.48 2975:0.2 (wet) 2972:0.25–0.62 2955:0.2 (wet) 2938:0.42–0.62 2932:0.74−0.80 2849:Polyethene 2837:0.02–0.09 2701:Cast iron 2683:Cast iron 2670:0.35–0.51 2652:0.04–0.05 2550:1.05–1.35 2547:Aluminium 2544:Aluminium 2526:Aluminium 2356:atmosphere 2189:fractality 2047:See also: 1132:G.H. Bryan 1055:asperities 990:Themistius 921:asperities 868:, it is a 672:d'Alembert 652:Maupertuis 615:Scientists 497:Rigid body 171:Kinematics 8561:Tribology 8493:Hydrology 8473:Petrology 8361:analysis 8359:Landslide 8264:Mechanics 8175:Track bed 8160:Fill dirt 8145:Terracing 7718:Trial pit 7533:Statnamic 7518:Load test 7159:Mechanics 7110:119288819 7064:109914430 7017:, Wiley, 6921:CiteSeerX 6851:CiteSeerX 5967:230599544 5431:1202.1716 5225:, p. 106. 4613:. No. 5. 4273:polishing 4207:μ 4090:⋅ 4051:μ 4041:∫ 4023:⋅ 3980:∫ 3943:Aristotle 3901:tribology 3897:lubricant 3843:Reduction 3634:viscosity 3619:Viscosity 3413:θ 3384:μ 3379:⁡ 3370:θ 3342:μ 3334:θ 3330:⁡ 3274:vibrating 3234:μ 3054:μ 3005:friction. 2913:0.04−0.2 2871:(Teflon) 2739:Concrete 2731:0.6–0.85 2719:Concrete 2581:Platinum 2578:Platinum 2487:μ 2456:μ 2444:Materials 2407:talk page 2299:empirical 2238:μ 2209:μ 2202:μ 2151:μ 2122:μ 2115:μ 2024:μ 1988:μ 1985:≤ 1907:μ 1871:μ 1868:≤ 1801:− 1639:empirical 1622:μ 1619:⁡ 1611:− 1583:μ 1580:≤ 1410:μ 1322:μ 1253:μ 1250:≤ 1189:First Law 1187:Amontons' 1130:In 1907, 1105:In 1842, 1005:tribology 982:Vitruvius 978:Aristotle 943:lubricant 836:tribology 717:Liouville 599:frequency 519:Vibration 236:potential 161:Continuum 156:Celestial 133:Textbooks 8546:Friction 8523:Agrology 8412:software 8310:problems 8140:Causeway 8115:Landfill 8042:Subgrade 7959:Porosity 7954:Cohesion 7287:Archived 6869:Archived 6813:16395796 6805:17947204 6506:17280625 6349:23064494 6298:Archived 6286:18292336 5959:33466084 5871:26811802 5863:15089689 5751:3 August 5683:Archived 5424:: 1586. 5403:24435002 5371:: 3750. 5365:Sci. 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