# What is friction

1. Jul 24, 2014

### Greg Bernhardt

Definition/Summary

Friction is a force which opposes relative motion when two solid bodies are in contact.

A coefficient of friction between two materials is a number. The coefficient of static friction is higher than the coefficient of dynamic friction.

The actual force of dynamic friction is always found by multiplying the normal force by the coefficient of dynamic friction.

The actual force of static friction is always less than or equal to that found by multiplying the normal force by the coefficient of static friction.

Equations

$$F = \mu N$$

Common error:
$$F = \mu m g$$
this only applies when
$$N = m g$$

Extended explanation

Dynamic (kinetic) friction and static friction:

There are two types of friction. They have different coefficients, so it is important to know which type is which.

Dynamic (kinetic) friction is where the two surfaces are moving relative to each other: this does not include rolling motion, since the surfaces are (by definition of rolling) stationary at the area of contact.

Static friction is where the two surfaces are not moving relative to each other: this does include rolling motion.

Rolling resistance:

A vehicle is not slowed by the ordinary friction force on its tyres (if they are not slipping), since the points of contact are not moving, and so the friction is static, and static fricton does no work.

However, it is slowed by the loss of energy caused by deformation of its tyres: this loss is known as rolling resistance (or "rolling friction").

Coefficients of friction:

Coefficients of friction are dimensionless numbers. They are different for different pairs of materials.

The static coefficient is higher than the dynamic coefficient.

To remember why the static coefficient is higher, think of two sheets of corrugated plastic sliding over each other. To start moving, the bottom of the top sheet must first rise to the level of the top of the bottom sheet, which requires extra force

Tables of coefficients of friction:

Many tables can be found on a web search, eg http://engineershandbook.com/Tables/frictioncoefficients.htm, which begins
"Extreme care is needed in using friction coefficients, and additional independent references should be used. For any specific application the ideal method of determining the coefficient of friction is by trials. A short table is included above the main table to illustrate how the coefficient of friction is affected by surface films. When a metal surface is perfectly clean in a vacuum, the friction is much higher than the normal accepted value and seizure can easily occur."
For some materials, the coefficient can be greater than one, and for solids on rubber it can be as high as four.

Increasing pressure between dry surfaces may increase the coefficient, at first slightly, but eventually very quickly, leading to seizing. For this and other factors affecting coefficients of friction, see the top box in http://www.roymech.co.uk/Useful_Tables/Tribology/co_of_frict.htm

Magnitude of dynamic friction:

Between two bodies in relative motion, the strength of the force of friction is equal to the normal force (the reaction force) between the two bodies times the coefficient of dynamic friction:
$$|\mathbf{F}_k|\ =\ \mu_k\,{N}$$
The coefficient of dynamic friction is independent of speed.

Direction of dynamic friction:

The direction of the force of dynamic friction is always opposite to the direction of relative motion.

Work done:

Dynamic friction is a dissipative (non-conservative) force: it dissipates energy (mainly through heat and sound), and energy lost by moving in one direction cannot be recovered by moving in the opposite direction.

The energy dissipated (lost from mechanical energy) equals the work done by the friction:
$$W\ =\ \int \mu_k\,N\,ds$$
Magnitude of static friction:

Between two bodies not in relative motion, and not immediately about to move, the force of friction is not found from a "friction equation", but simply by applying Newton's second law. On either body, it will always be equal and opposite to the total of the other forces on that body:
$$\mathbf{F_s}\ =\ -\mathbf{F}_{\mathrm{net}}$$
It will always be less than the normal force times the coefficient of static friction:
$$|\mathbf{F_s}|\ <\ \mu_s\,N$$
Between two bodies immediately before relative motion starts, the strength of the force of friction is equal to the normal force (the reaction force) between the two bodies times the coefficient of static friction:
$$|\mathbf{F}_{\mathrm{critical}}|\ =\ \mu_s\,N$$
Direction of static friction:

The direction of the force of static friction is along the plane of contact, and is opposite to the direction in which there would be relative motion if there were no friction (for example, if one of the surfaces suddenly turned to ice).

In particular, the friction from the road on the driving or braking wheels of a car is in the same direction as the acceleration or braking, but the friction on the non-driving or non-braking wheels of a car is in the opposite direction.

Resistance from fluids:

The resistance to a solid body from contact with gas or liquid is viscosity, not friction: it is of a different nature, because part of the gas or liquid can move with the body.

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