# Kinetic friction

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## Definition

QUICK PHRASES: force that slows down slipping of surfaces in contact, retarding force for contact surfaces slipping, component along contact plane of contact force for slipping surfaces

### Intensional definition

Kinetic friction, or dynamic friction, is defined as the form of friction between two bodies via their surface of contact (i.e., the force acting parallel to the plane of contact) when the two surfaces of contact are slipping against each other.

### Tendency-based definition

Kinetic friction is the form of friction that opposes the slipping against each other of two surfaces in contact. Its direction is opposite the direction of relative motion of the surfaces in contact. Note that it need not oppose the net external force between the surfaces in contact.

## Model

The typical model used for kinetic friction, which is applicable for small relative speeds, is the Coulomb model of friction, which states that the magnitude of kinetic friction is $\mu_kN$, where $\mu_k$ is the coefficient of kinetic friction (dependent on the nature of the surfaces in contact) and $N$ is the normal force between the bodies (measuring how hard they are pressed against each other).

## Caveats

Quick phrase for caveat Explanation Partial rescue
Relative motion versus absolute motion Kinetic friction depends on whether the surfaces are slipping relative to each other. Thus, even if both surfaces are moving, as long as they are moving together, there is no kinetic friction. An example might be one box placed on top of another box that is being dragged along. If the two boxes move together, there is no kinetic friction between them. When one of the surfaces is fixed (for instance, a fixed floor), then the relative motion of the surfaces corresponds to the absolute motion of the other surfaces.
Body versus surface Kinetic friction operates when the surfaces are slipping against each other, and opposes the direction of slippage of the surfaces, rather than the direction of relative motion of the bodies. Thus, in the case of rolling, there is no kinetic friction between the bodies. In other cases of mixed translation-cum-rotation, the direction in which the surfaces are slipping against each other depends on the contributions of both the translation and rotation components of the relative motion. For instance, if a wheel in contact with the ground is undergoing pure rotation, it will encounter kinetic friction from the ground opposing the direction of rotation. In cases where the bodies are not changing in orientation, the direction of relative motion of surfaces is the same as the direction of relative motion of bodies.
Independent of speed For small speeds, the magnitude of kinetic friction is independent of the magnitude of the speed.
Independent of other forces Kinetic friction may support, oppose, or be orthogonal to other external forces that act parallel to the plane of contact. For instance, a body sliding downhill along an inclined plane experiences kinetic friction in the uphill direction and a component of gravitational force in the downhill direction. A body sliding uphill, on the other hand, experiences both kinetic friction and a component of gravitational force in the downhill direction.

## Energy

Kinetic friction causes a loss of mechanical energy (specifically, kinetic energy, or in some cases potential energy that could have been converted to kinetic energy but is instead diverted into omvercoming kinetic friction), which may be dissipated as heat, light, or sound. The mechanical energy lost is $\int |F| ds$ where $F$ is the magnitude of the kinetic friction force and $ds$ is the differential along the direction of motion.

### Heat

Part of the kinetic energy lost may be converted to heat, which may cause the surfaces slipping against each other to become warmer. Generally, this excess heat is dissipated quickly into the atmosphere if the surfaces are exposed to the atmosphere. Some examples include:

• In cold climates, people rub their hands together to warm the hands. The faster the rubbing, the more quickly the hands warm up. The hands cool back to body temperature pretty quickly.
• If a box is dragged for a long time along a fixed face, that face tends to get warm.

The generation of heat can also be used as a conceptual way of differentiating kinetic friction from static friction.

### Sound

Part of the kinetic energy lost may be converted to sound. Some examples include:

• When objects are dragged, they tend to create a sound, which is often unpleasant.
• When a chalk or pen is used for writing, a (usually mild) sound is created.

The generation of sound can also be used as a conceptual way of differentiating kinetic friction from static friction.