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Sliding (motion)
Sliding (motion)
Sliding (motion)
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Sliding is a type of motion between two surfaces in contact. This can be contrasted to rolling motion. Both types of motion may occur in bearings.

The relative motion or tendency toward such motion between two surfaces is resisted by friction. This means that the force of friction always acts on an object in the direction opposite to its velocity (relative to the surface it's sliding on). Friction may damage or "wear" the surfaces in contact. However, wear can be reduced by lubrication. The science and technology of friction, lubrication, and wear is known as tribology.

Sliding may occur between two objects of arbitrary shape, whereas rolling friction is the frictional force associated with the rotational movement of a somewhat disclike or other circular object along a surface. Generally, the frictional force of rolling friction is less than that associated with sliding kinetic friction.[1] Typical values for the coefficient of rolling friction are less than that of sliding friction.[2] Correspondingly sliding friction typically produces greater sound and thermal bi-products. One of the most common examples of sliding friction is the movement of braking motor vehicle tires on a roadway, a process which generates considerable heat and sound, and is typically taken into account in assessing the magnitude of roadway noise pollution.[3]

Sliding friction

[edit]

Sliding friction (also called kinetic friction) is a contact force that resists the sliding motion of two objects or an object and a surface. Sliding friction is almost always less than that of static friction; this is why it is easier to move an object once it starts moving rather than to get the object to begin moving from a rest position.

Where Fk, is the force of kinetic friction. μk is the coefficient of kinetic friction, and N is the normal force.

Examples of sliding friction

[edit]
Slippery when wet signs alert drivers that they need to slow down because the kinetic friction between the tires and a wet surface is much less than that of a dry surface.
  • Sledding
  • Pushing an object across a surface
  • Rubbing one's hands together (The friction force generates heat.)
  • A car sliding on ice
  • A car skidding as it turns a corner
  • Opening a window
  • Almost any motion where there is contact between an object and a surface
Animation of an idealized prism sliding across a flat plane
  • Falling down a bowling lane

Motion of sliding friction

[edit]

The motion of sliding friction can be modelled (in simple systems of motion) by Newton's second law

Where is the external force.

  • Acceleration occurs when the external force is greater than the force of kinetic friction.
  • Slowing Down (or Stopping) occurs when the force of kinetic friction is greater than that of the external force.
    • This also follows Newton's first law of motion as there exists a net force on the object.
  • Constant Velocity occurs when there is no net force on the object, that is the external force is equal to force of kinetic friction.

Motion on an inclined plane

[edit]
Free body diagram for a block subject to friction as it slides on an inclined plane

A common problem presented in introductory physics classes is a block subject to friction as it slides up or down an inclined plane. This is shown in the free body diagram to the right.

The component of the force of gravity in the direction of the incline is given by:[4]

The normal force (perpendicular to the surface) is given by:

Therefore, since the force of friction opposes the motion of the block,

To find the coefficient of kinetic friction on an inclined plane, one must find the moment where the force parallel to the plane is equal to the force perpendicular; this occurs when the block is moving at a constant velocity at some angle

or

Here it is found that:

where is the angle at which the block begins moving at a constant velocity[5]

References

[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Sliding (motion)

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from Grokipedia
Sliding motion, also referred to as sliding or translational motion under , describes the relative displacement between two solid surfaces in contact where kinetic acts to oppose the direction of movement. This type of motion begins once the applied force surpasses the maximum static , allowing the surfaces to slide past each other rather than remain at rest or roll. In physics, sliding is fundamental to understanding everyday phenomena like braking vehicles or dragging objects across floors, where the frictional force remains relatively constant across a range of low speeds. Unlike static friction, which prevents initial motion and can vary up to a maximum value, kinetic friction during sliding is typically lower in magnitude and acts consistently to slow or resist the ongoing between the surfaces. The of kinetic friction, fkf_k, is given by fk=μkNf_k = \mu_k N, where μk\mu_k is the of kinetic friction (a dimensionless value dependent on the materials in contact) and NN is the normal pressing the surfaces together. This μk\mu_k is generally less than the static friction μs\mu_s, requiring less to maintain sliding than to initiate it. Notably, kinetic friction is approximately independent of sliding speed for most dry surfaces at low velocities, though it can vary with factors like , temperature, and lubrication. In and , sliding motion is critical for analyzing , dissipation, and stability in systems such as machine parts, conveyor belts, and inclined planes. The Amontons-Coulomb law, which underpins the basic model of sliding , posits that the is proportional to the normal load and independent of the apparent contact area for many materials. Experimental studies confirm that real-world sliding often deviates from ideal models due to microscopic interactions like asperity deformation and at the contact points.

Fundamentals of Sliding Motion

Definition and Characteristics

Sliding motion is defined as the relative tangential displacement of one body over another while the surfaces remain in continuous contact, encompassing both linear and curvilinear paths under kinetic conditions where motion has been initiated. This type of motion occurs in tribological systems, where the interacting surfaces experience relative movement without separation, distinguishing it from other forms of contact dynamics. Key characteristics of sliding motion include the maintenance of persistent contact at the interface, accompanied by shear deformation of the material at the points of interaction. Microscopically, this deformation arises from the of surface asperities—protrusions on rough surfaces—that initially interlock under load before yielding to enable the relative displacement. During sliding, is dissipated primarily as through processes at the interface, contributing to the thermodynamic aspects of the motion. In contrast to intermittent motions like bouncing, which involve repeated separation and impact, sliding features unbroken contact throughout the displacement. Early observations of sliding motion trace back to the late , when systematically studied it in the context of mechanical devices such as axles and screw threads, recognizing its role in rotational resistance and establishing foundational insights into tribological phenomena. These investigations highlighted sliding as a core interaction in engineering systems, influencing later developments in the science of interacting surfaces. This motion is inherently opposed by , a tangential force that resists the relative movement, though detailed analysis of such forces lies beyond the qualitative description here.

Comparison with Other Motions

Sliding motion fundamentally differs from static , where no relative motion occurs between contacting surfaces, as sliding involves continuous relative displacement opposed by kinetic . In static , the frictional adjusts up to a maximum value to prevent motion, whereas in sliding, the kinetic frictional remains constant and opposes the direction of motion once sliding begins. This distinction highlights sliding's role in dissipative processes, where energy is lost as due to surface interactions. Compared to rolling motion, sliding lacks rotational components, leading to higher dissipation through surface shearing without the friction-minimizing effect of . Rolling relies on static at the point of contact to enable pure without , resulting in lower overall resistance, while sliding converts primarily into thermal losses via kinetic . Sliding also contrasts with motion, such as in viscous flows, where resistance arises from shear within the rather than solid-solid contact, avoiding the associated with sliding's asperity interactions. The transition from static to sliding occurs at the yield point, or impending motion, where the applied force exceeds the maximum static , initiating kinetic and relative sliding. This boundary is characterized by a drop in frictional force, often abrupt in dry contacts, marking the onset of through sliding.
AspectSliding MotionRolling Motion
Friction TypeKinetic (opposes sliding)Static (prevents at contact)
Energy EfficiencyLow; high as High; minimal losses due to
Wear CharacteristicsHigh; direct surface abrasionLow; reduced contact deformation
Setup ComplexitySimple (flat surfaces)Complex (requires rounded objects)
These pros and cons underscore sliding's simplicity for basic applications but favor rolling for efficiency in transport. The conceptual evolution of sliding's distinctions traces to 17th- and 18th-century work by Guillaume Amontons and Charles-Augustin de Coulomb, who formulated friction laws emphasizing sliding's proportionality to normal load and independence from contact area or velocity, underscoring its inherently dissipative nature separate from static or rolling regimes. Amontons' experiments on sliding wooden blocks established these empirical laws, later refined by Coulomb to differentiate kinetic sliding from static resistance.

Principles of Sliding Friction

Kinetic Friction Force

Kinetic friction is the tangential force that opposes the relative motion between two surfaces in contact while sliding occurs. This force, denoted as FkF_k, is empirically described by Amontons' first law of friction, which states that Fk=μkNF_k = \mu_k N, where μk\mu_k is the coefficient of kinetic friction (a dimensionless material-dependent constant) and NN is the normal force pressing the surfaces together. Amontons formulated this relationship in 1699 based on experiments with sliding wooden blocks, establishing that the frictional resistance is independent of the apparent contact area but proportional to the load. The coefficient μk\mu_k typically ranges from 0.1 to 1.0 for dry engineering surfaces, reflecting the efficiency of energy dissipation during motion. At the microscopic level, kinetic friction arises from interactions at the asperities— the microscopic peaks and valleys on contacting surfaces— leading to energy loss through several mechanisms. Adhesion occurs when clean surface atoms form junctions that must be sheared during sliding, contributing significantly to the frictional force as described in the adhesion theory developed by Bowden and Tabor in the 1930s and 1940s. Plowing involves the harder asperities indenting and displacing the softer material, creating grooves that require work to overcome, while asperity deformation encompasses elastic and plastic straining at contact points, all resulting in irreversible energy dissipation as heat or vibrations. These processes collectively explain why kinetic friction converts mechanical work into thermal energy, with the real contact area (much smaller than the apparent area) determining the scale of interactions. The direction of the kinetic friction force is always opposite to the direction of the between the sliding surfaces, ensuring it acts to impede motion. For dry sliding at low speeds (typically below 1 m/s), the magnitude of FkF_k remains approximately constant, independent of velocity, as per Amontons' second law, which aligns with the steady-state nature of asperity interactions. However, in lubricated conditions, slight velocity dependence can emerge due to changes in lubricant film thickness and shear behavior, where higher speeds may reduce μk\mu_k through hydrodynamic effects. This empirical law and its microscopic basis have been verified experimentally using , which measure lateral s during controlled sliding under varying loads. Pin-on-disk or ball-on-flat , for instance, confirm the linear load dependence and near-constant for dry contacts, with precision sensors detecting FkF_k to within 0.01 . In lubricated systems, such as those with oils, tests reveal modest increases or decreases in μk\mu_k with , attributed to viscous shearing in the layer.

Factors Influencing Friction

The magnitude of sliding friction is primarily determined by , the properties of the interacting s, and the applied normal load. affects friction through interactions between asperities, the microscopic peaks and valleys on contacting surfaces; the effect on the kinetic friction coefficient (μ_k) varies depending on the dominant mechanism—in dry contacts where plowing or mechanical interlocking prevails, rougher surfaces can increase μ_k, while in adhesion-dominated regimes, they may decrease it by reducing the real contact area. For instance, in dry metal contacts, the influence of roughness depends on the specific pair and conditions. The specific combination of materials also plays a key role, as different pairs exhibit characteristic μ_k values due to variations in , , and surface chemistry. Typical μ_k for dry on ranges from 0.3 to 0.6, reflecting strong and deformation under load. Similarly, on yields a low μ_k of approximately 0.03, attributed to minimal and easy shear at the interface. The following table summarizes representative μ_k values for common dry material pairs, measured under standard conditions:
Material 1Material 2Approximate μ_k (dry)
0.3
0.03
0.3
RubberConcrete0.7
Teflon0.04
These values are obtained from controlled tribological tests and illustrate the wide range (0.01 to 1.0) possible across material pairs. The normal load exerts a linear influence on friction, as described by Amontons' first law, where the friction force F_f = μ_k N, with N being the normal force; higher loads increase the real contact area through elastic and deformation, proportionally elevating friction without altering μ_k itself in most macroscopic cases. This proportionality holds for a broad range of loads in dry sliding but can deviate at extremes due to surface alterations. Secondary factors include environmental conditions such as , , and sliding speed. In polymers, increasing often decreases friction by softening the material, reducing shear strength at the interface; for example, in films, frictional drops with rising as molecular mobility enhances slip. significantly lowers μ_k by introducing boundary layers—thin films of that separate asperities and minimize direct solid-solid contact. Sliding speed has minimal impact in dry conditions, consistent with the Amontons-Coulomb law's assumption of velocity independence for typical macroscopic speeds, though subtle variations may arise from thermal effects at very high velocities. μ_k values are commonly measured using pin-on-disk tests, where a stationary pin slides against a rotating disk under controlled load and speed, allowing precise quantification of frictional and ; this method is standardized for evaluating pairs in dry or lubricated states. In modern contexts, such as microelectromechanical systems () devices developed post-2000, nanoscale effects dominate , where forces from van der Waals interactions often exceed traditional asperity contributions, leading to higher-than-expected μ_k and issues despite smooth surfaces. Research in this area emphasizes surface treatments to mitigate , highlighting deviations from classical models at scales below 100 nm.

Dynamics of Sliding Motion

Basic Equations of Motion

In the context of sliding motion on a horizontal surface, Newton's second law of motion provides the foundation for deriving the acceleration of an object, where the net horizontal force equals the mass times the acceleration: ∑Fx=max\sum F_x = m a_x. The primary forces acting horizontally are any applied force FappliedF_\text{applied} and the kinetic friction force FkF_k, which opposes the direction of motion and is given by Fk=μkNF_k = \mu_k N, with μk\mu_k as the coefficient of kinetic friction and NN as the normal force. For a horizontal surface, the normal force equals the object's weight, N=mgN = m g, where gg is the acceleration due to gravity, so Fk=μkmgF_k = \mu_k m g. Thus, the acceleration is ax=Fapplied−μkmgm=Fappliedm−μkga_x = \frac{F_\text{applied} - \mu_k m g}{m} = \frac{F_\text{applied}}{m} - \mu_k g. If no applied force acts (Fapplied=0F_\text{applied} = 0), the motion experiences constant deceleration ax=−μkga_x = -\mu_k g. Since the acceleration is constant under these conditions, the standard kinematic equations for one-dimensional motion with constant acceleration describe the velocity and displacement. The final velocity vv after time tt is v=u+axtv = u + a_x t, where uu is the initial velocity. The displacement ss is given by s=ut+12axt2s = u t + \frac{1}{2} a_x t^2. These equations allow prediction of how the object's speed diminishes over time or distance due to friction. From an energy perspective, the work done by the kinetic friction force over a displacement dd is W=−Fkd=−μkmgdW = -F_k d = -\mu_k m g d, which is negative as it opposes the motion. According to the work-energy theorem, this work equals the change in kinetic energy: ΔKE=12mv2−12mu2=−μkmgd\Delta KE = \frac{1}{2} m v^2 - \frac{1}{2} m u^2 = -\mu_k m g d. Rearranging yields v2=u2−2μkgdv^2 = u^2 - 2 \mu_k g d, providing an alternative relation between initial and final speeds without explicit time dependence. These equations assume a constant of kinetic friction μk\mu_k, independent of speed, and neglect other forces such as air resistance. The model applies to rigid surfaces in contact at low speeds, where behaves empirically as proportional to the normal .

Sliding on Inclined Planes

When an object slides on an , the gravitational must be resolved into components parallel and perpendicular to the surface to analyze the motion. The component parallel to the plane, mgsin⁡θmg \sin \theta, where mm is the , gg is the acceleration due to gravity, and θ\theta is the incline , acts down the plane and drives the sliding. The perpendicular component, mgcos⁡θmg \cos \theta, is balanced by the normal N=mgcos⁡θN = mg \cos \theta, assuming no acceleration perpendicular to the plane. The kinetic friction force opposes the motion and acts up the plane, with magnitude fk=μkN=μkmgcos⁡θf_k = \mu_k N = \mu_k mg \cos \theta, where μk\mu_k is the coefficient of kinetic friction. Applying Newton's second law along the plane (taking down the plane as positive), the net force is mgsin⁡θ−μkmgcos⁡θ=mamg \sin \theta - \mu_k mg \cos \theta = ma, yielding the acceleration a=g(sin⁡θ−μkcos⁡θ)a = g (\sin \theta - \mu_k \cos \theta). This derivation assumes constant kinetic friction and no other forces. Sliding begins when the parallel gravitational component exceeds the maximum static friction force fsmax⁡=μsN=μsmgcos⁡θf_s^{\max} = \mu_s N = \mu_s mg \cos \theta, where μs\mu_s is the coefficient of static friction. The minimum angle for sliding, known as the critical angle θc=arctan⁡μs\theta_c = \arctan \mu_s, marks the transition from rest to motion, as at this angle mgsin⁡θc=μsmgcos⁡θcmg \sin \theta_c = \mu_s mg \cos \theta_c. Once sliding occurs, kinetic friction governs, and if θ=arctan⁡μk\theta = \arctan \mu_k, the acceleration is zero, resulting in constant . In cases with initial velocity or external forces, the equations adapt using or modified . For an object projected up the plane with initial speed vv, and both act down the plane, producing deceleration a=−g(sin⁡θ+μkcos⁡θ)a = -g (\sin \theta + \mu_k \cos \theta). The stopping distance dd along the plane is then d=v22g(sin⁡θ+μkcos⁡θ)d = \frac{v^2}{2 g (\sin \theta + \mu_k \cos \theta)}, derived from vf2=vi2+2adv_f^2 = v_i^2 + 2 a d with final zero. An external push adds a force component parallel to the plane, altering the in Newton's law accordingly.

Applications and Examples

Everyday Examples

In households, sliding motion is commonly observed when pushing wooden furniture across carpeted floors, where the kinetic is approximately 0.3, requiring moderate to initiate and sustain movement. provide another routine example, as the frame and edges rub against tracks, generating resistance that eases opening but can produce intermittent sticking if not lubricated. During braking, tires interact with the road surface through sliding , particularly when wheels lock, with a of about 0.7 on dry pavement that drops to 0.4 on wet surfaces, influencing stopping distances. Natural settings highlight sliding under low-friction conditions, such as on , where frictional heat melts a thin layer for self-lubrication, resulting in a very low kinetic that allows smooth . Children experience similar effects on playground slides, where clothing slides against the surface, moderated by that controls descent speed and prevents excessive velocity. Observable sensory effects accompany many sliding instances, including heat generation from , as when rubbing hands together converts into through atomic collisions and electron excitations, warming the skin. Audible squeaks often arise from stick-slip behavior, where surfaces alternately stick and suddenly slip, such as in door hinges or shoe soles on floors, producing jerky vibrations and . In sports like , players exploit controlled sliding friction on pebbled ice, using brooms to sweep ahead of stones and temporarily reduce the friction coefficient via localized heating, enabling precise curving paths.

Engineering and Scientific Uses

In industrial settings, sliding motion is harnessed in systems for efficient , where greased or lubricated slides minimize kinetic to reduce and prevent equipment . For instance, researchers at the are developing graphite-based solid lubricant coatings that bond tightly to conveyor surfaces, addressing over 50% of energy losses due to sliding in flat systems and offering environmental advantages over traditional oils. In processes like metal forming, lubricants are applied to control sliding between tools and workpieces, reducing and enabling complex shapes without ; multi-phase lubricants, including solid additives, are particularly effective for high-pressure operations such as and . Scientific investigations of sliding often occur in tribology laboratories, where atomic force microscopy (AFM) enables precise measurement of nanoscale friction during controlled sliding experiments. AFM techniques, including friction force microscopy, reveal how surface topography and material properties influence kinetic friction coefficients at velocities up to several micrometers per second, aiding the design of low-wear interfaces in microelectromechanical systems (MEMS). In geophysics, earthquake modeling employs tribological simulations of fault sliding to replicate stick-slip dynamics, where discrete element methods model granular gouge layers that accommodate shear and evolve with cumulative slip, producing stress drops akin to seismic events. Engineering designs frequently aim to minimize unwanted sliding for , as seen in applications where non-slip surfaces incorporate aggregates and textured finishes to enhance traction under wet conditions, reducing skid risk by maintaining higher coefficients at speeds up to 40 mph. Conversely, controlled sliding is optimized in , such as waxes that tune the kinetic friction coefficient (μ_k) by impregnating porous bases with hydrocarbons matched to conditions, where and brushing reset base structures for minimal glide resistance. Recent advancements in the include self-lubricating coatings for space applications, exemplified by the Mars Perseverance rover's use of NyeBar® barrier films, which exhibit low and oil migration control to ensure reliable sliding in camera mechanisms under and thermal extremes from -125°C to 20°C. Solid lubricants like (MoS₂) further address abrasive Martian dust in rover wheel systems, providing durable friction reduction without liquid volatility, as tested in ongoing missions.

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