Friction
Friction is a contact force that opposes the relative motion or tendency toward motion between two surfaces or systems in physical contact, acting parallel to their interface and always in the direction opposite to the impending or actual motion.[1] This force arises from microscopic interactions, such as interlocking asperities and adhesion between surface atoms, and is crucial for enabling locomotion—such as walking, where static friction between shoes and ground propels the body forward—while also dissipating energy and causing wear in mechanical systems.[1] Friction is categorized into two primary types: static friction, which acts on stationary objects to prevent the initiation of motion and can vary in magnitude up to a maximum value, and kinetic friction, which acts on moving objects to oppose sliding and remains roughly constant during uniform motion.[2] The magnitude of frictional forces follows empirical laws primarily attributed to Guillaume Amontons and Charles-Augustin de Coulomb, though refined through modern observations.[3] For both static and kinetic friction, the force is directly proportional to the normal force pressing the surfaces together, expressed as f_s \leq \mu_s N for static friction and f_k = \mu_k N for kinetic friction, where \mu_s and \mu_k are dimensionless coefficients of friction specific to the material pair, and N is the normal force.[1] Typically, \mu_s > \mu_k, meaning it is easier to maintain motion than to start it, and kinetic friction is largely independent of sliding speed over typical ranges, though it does depend weakly on factors like surface roughness and lubrication.[2] These coefficients vary widely; for example, rubber on dry concrete has \mu_s \approx 1.0 and \mu_k \approx 0.7, while polished steel on steel yields \mu_s \approx 0.6 and \mu_k \approx 0.3.[1] Beyond these basics, friction plays a pivotal role in diverse fields, from engineering—where it influences tire grip, brake performance, and conveyor belt efficiency—to geophysics, such as in earthquake dynamics via stick-slip motion modeled by rate-and-state friction laws that account for velocity dependence and contact history.[4] In biological systems, friction enables tactile sensation and muscle control, while in nanotechnology, it affects the operation of microelectromechanical systems (MEMS) at scales where atomic forces dominate.[5] Reducing unwanted friction through lubricants or surface treatments is a key focus in tribology, the science of interacting surfaces in relative motion, which aims to minimize energy loss—estimated to contribute to approximately 23% of the world's total energy consumption.[6]Fundamentals
Definition and Scope
Friction is the tangential force that acts to oppose the relative motion or tendency of relative motion between two surfaces in contact or between a surface and a surrounding medium. This force arises at the interface where the bodies interact, acting parallel to that interface and in a direction that resists sliding or separation. In physics, friction—particularly kinetic friction—is a dissipative force that converts mechanical energy into thermal energy, whereas static friction often enables motion without dissipation; it plays a central role in both natural phenomena and human-engineered devices.[1][2][7] At a high level, friction can be distinguished by the nature of interaction: contact friction, often termed dry or solid friction, occurs between solid surfaces through direct atomic and molecular interactions, while non-contact friction encompasses fluid types, involving viscous resistance in liquids or gases, and electromagnetic types, which arise from magnetic or electric fields without physical touching. Fluid friction, for instance, manifests as drag on an object moving through air or water, whereas electromagnetic friction appears in applications like magnetic braking systems where eddy currents induce opposing forces. These distinctions highlight friction's broad scope beyond mere solid-solid contacts.[8][9][10] Friction is crucial for enabling motion control in everyday activities and technologies, such as providing the grip necessary for walking on the ground or holding tools without slippage, which relies on static friction to prevent unintended movement. In engineered systems, it allows vehicles to accelerate, brake, and turn by transferring forces between tires and roads. Conversely, friction causes energy dissipation through heat generation and material wear, accounting for significant energy losses in machinery—estimated at about one-third of global energy resources—and necessitating designs that balance utility with efficiency.[11][12][13] The occurrence of friction presupposes a normal force perpendicular to the contact surface, which presses the bodies together, and either actual relative motion or an impending motion between them. As a vector quantity, the friction force has a magnitude measured in newtons (N) and a direction opposite to the relative velocity or attempted motion, ensuring it always acts to impede rather than assist the interaction.[5][14]Historical Overview
Observations of friction date back to ancient civilizations, where practical experiences with sliding and rolling objects informed engineering feats like the construction of pyramids and the use of sledges lubricated with water. However, systematic scientific investigation began in the 15th century with Leonardo da Vinci (1452–1519), who conducted pioneering experiments on friction in mechanical systems such as axles and screw threads. Through detailed sketches in his notebooks, da Vinci established that frictional resistance is proportional to the applied load and independent of the apparent contact area, insights derived from observing blocks sliding on inclined planes and rotating components.[15] In the late 17th century, Guillaume Amontons (1663–1705) independently rediscovered and experimentally validated these principles in his 1699 memoir presented to the Académie Royale des Sciences. Amontons' experiments with wooden blocks on inclined planes and pulleys demonstrated that the force required to initiate and maintain motion is roughly one-third of the normal load, confirming proportionality to load and independence from contact area or speed for dry surfaces. Building on this, Charles-Augustin de Coulomb (1736–1806) in his 1785 treatise "Mémoire sur un nouveau genre d'expérience pour déterminer les lois du frottement" refined the laws through precise measurements using torsion balances and inclined planes, notably introducing the critical distinction between static friction—which must be overcome to start motion—and kinetic friction, which opposes ongoing sliding. Coulomb's work also quantified that static friction exceeds kinetic friction, providing a foundational framework for engineering applications.[16][17][18] The 19th and early 20th centuries saw incremental refinements, including more precise distinctions between static and kinetic regimes and explorations of influencing factors like surface roughness and material pairs. Advances in rolling resistance, a related phenomenon distinct from sliding friction, gained prominence in the 1920s amid growing automotive and tire industries, with experimental methods like coastdown tests emerging to quantify energy losses in wheels. These studies emphasized hysteresis in tire deformation as a primary cause, informing designs for reduced fuel consumption.[19][20] The modern era of friction research accelerated in the 1960s with the Jost Report of 1966, commissioned by the British government, which coined the term "tribology" to encompass friction, wear, and lubrication, estimating annual economic losses from poor tribological practices at hundreds of millions of pounds and advocating for interdisciplinary study. In the 1980s and 1990s, the advent of scanning probe microscopy, including the atomic force microscope (AFM) invented in 1986, birthed nanotribology by enabling atomic-scale measurements of friction forces and revealing mechanisms like atomic stick-slip behavior. These tools uncovered deviations from classical laws at the nanoscale, such as velocity dependence and single-asperity contacts, profoundly influencing fields from microelectronics to biomaterials.[21][22][23]Dry Friction
Basic Laws
The basic laws of dry friction, known as the Amontons-Coulomb laws, describe the frictional force between two dry surfaces in macroscopic contact as being proportional to the normal force pressing the surfaces together and independent of the apparent contact area. These empirical relations form the foundation of classical friction theory and were established through systematic experiments in the late 17th and 18th centuries.[24][25] Guillaume Amontons derived the core principles in 1699 through pressure-based experiments involving sliding blocks of materials such as iron, copper, lead, and wood, often under light grease lubrication to simulate dry conditions. By varying the applied pressure while keeping the contact area constant, Amontons observed that the frictional resistance increased linearly with the normal pressure, leading to the first law: the magnitude of the frictional force f is directly proportional to the normal force N, expressed as f = \mu N, where \mu is a constant coefficient of friction specific to the material pair. In further tests, he altered the apparent contact area—such as by changing block dimensions or using inclined surfaces—without observing a corresponding change in friction for a given normal force, establishing the second law: frictional force is independent of the apparent contact area. These findings built on earlier qualitative observations but provided the first quantitative empirical basis, assuming rough surfaces where adhesion was negligible.[26][24][25] Charles-Augustin de Coulomb refined and validated these laws in the 1770s and 1780s using a torsion balance apparatus to measure sliding and static friction under controlled conditions. His experiments systematically varied parameters including normal force, contact area, surface materials (e.g., wood, metal, brick), velocity, and lubrication, confirming Amontons' proportionality and area independence across diverse setups. Coulomb's torsion balance involved suspending a weight via a twisted wire to quantify the torque required to initiate or maintain motion, revealing that friction arises primarily from the interlocking of surface asperities rather than cohesive forces, with the frictional force modeled as f = \mu N for sliding contacts. He also noted a small adhesive component in some cases but emphasized its minor role (<5% of total force) under typical dry conditions, solidifying the two-law framework.[26][25][24] These laws apply specifically to dry, macroscopic contacts at low sliding speeds, where velocity dependence is negligible and surfaces are non-adhering with multi-asperity interactions; they neglect microscopic adhesion or high-speed effects. The frictional force always acts tangential to the surfaces and opposes the direction of impending relative motion, ensuring it either prevents sliding (static case) or resists ongoing motion (kinetic case). Experimental validation commonly employs inclined plane setups, where the angle at which an object begins to slide yields \mu = \tan \theta, directly testing proportionality to normal force (via weight component N = mg \cos \theta) and confirming area independence by comparing blocks of varying sizes. While the laws distinguish between maximum static friction and kinetic friction during sliding, their core formulation remains unified under f = \mu N.[24][26][25]Static and Kinetic Components
In dry friction, the static component refers to the frictional force that acts between two surfaces in contact when there is no relative motion between them. This force opposes the initiation of sliding and can vary in magnitude up to a maximum value given by f_s \leq \mu_s N, where \mu_s is the coefficient of static friction and N is the normal force pressing the surfaces together.[27] The static friction adjusts dynamically to match the applied tangential force, preventing motion as long as this force remains below the maximum threshold, thereby maintaining equilibrium in systems like a parked vehicle on an incline.[28] Once relative motion begins, the frictional resistance transitions to the kinetic component, which provides a nearly constant opposing force during sliding, expressed as f_k = \mu_k N, where \mu_k is the coefficient of kinetic friction.[2] Typically, \mu_k < \mu_s, meaning the force required to sustain motion is less than that needed to start it, a relationship observed across various material pairs and attributed to differences in contact mechanics at the interface.[29] This distinction is evident in practical scenarios, such as brake pads that rely on static friction to hold a vehicle stationary but experience kinetic friction during sliding to decelerate it.[30] The transition from static to kinetic friction occurs when the applied force exceeds the breakaway value of \mu_s N, initiating sliding.[27] Factors like surface roughness can influence this onset by altering the real area of contact and the interlocking of asperities, often increasing the static friction threshold on rougher surfaces. In some systems, this transition leads to the stick-slip phenomenon, where motion alternates between static "stick" phases (building up shear stress) and rapid kinetic "slip" phases (releasing that stress), resulting in vibrations or oscillations.[31] For instance, a wooden block sliding on a rough table may exhibit stick-slip if pulled slowly, causing jerky motion, while smoother surfaces like lubricated metal sliders minimize this effect.[32]Coefficient and Normal Force
The normal force, denoted as N, is the component of the contact force between two objects that acts perpendicular to their interface at the point of contact.[2] In vector terms, it is the force exerted by a surface to prevent interpenetration, directed orthogonally outward from the surface and balancing any perpendicular components of other forces, such as gravity.[1] For an object on an inclined plane, the normal force often equals mg \cos \theta, where m is the mass, g is gravitational acceleration, and \theta is the incline angle, assuming no acceleration perpendicular to the surface.[1] The coefficient of friction, \mu, is a dimensionless empirical parameter defined as the ratio of the frictional force f to the normal force N, such that f = \mu N.[33] It quantifies the frictional resistance between two surfaces and is inherently material-dependent, varying based on the specific pair of contacting materials.[1] Separate coefficients exist for static friction (\mu_s), which opposes impending motion, and kinetic friction (\mu_k), which acts during sliding, with \mu_s typically greater than \mu_k.[34] According to Amontons' laws, the frictional force (and thus \mu) is independent of the apparent contact area, depending only on N and the materials involved.[35] Several factors influence the value of \mu, including temperature, which can alter surface properties and lubrication effects, and surface finish, such as roughness or cleanliness, which affects asperity interactions.[14] Despite these variations, the basic model assumes \mu remains constant for given conditions, as an empirical approximation.[36] Typical coefficients for common material pairs are summarized in the following table, illustrating approximate ranges under dry conditions:| Material Pair | \mu_s (Static) | \mu_k (Kinetic) |
|---|---|---|
| Rubber on concrete | 0.6–0.85 | 0.45–0.75 |
| Steel on steel (dry) | 0.5–0.8 | 0.42 |
| Ice on ice | 0.1 | 0.02 |