Listing of the coefficient of sliding friction values for a variety of hard clean materials - Succeed in Understanding Physics. Key words: Physical Science, sliding, static, kinetic, surface roughness, clean, oxidation, lubricated, greased, engineering, measurements, scientific, School for Champions. Copyright © Restrictions

# Coefficient of Friction

by Ron Kurtus (2 November 2005)

The coefficient of friction is the ratio between the force resisting motion between the objects and the normal or perpendicular force pushing them together. It is a number that determines the amount of friction between two objects or materials, as seen in the standard friction equation.

The coefficient is very dependent on the types of materials and their surfaces. It is independent of the normal force, as well as the speed of motion.

proportionality consa number related to the two specific surfaces that are in contact with each other. It is very dependent on the roughness of each surface and how the materials slide against each other.

Engineering laboratories have measured the coefficient of friction for a number of materials and have tabulated the results. These coefficient of friction values apply only to hard, clean surfaces sliding against each other. Since various experimental parameters such as surface conditions are not listed, considerations should be made in using these tabulated values because they may not directly relate to your application.

Questions you may have include:

• What considerations must be made in using such tables?
• Why are surface conditions important?
• What are the coefficient values?

This lesson will answer those questions. Useful tool: Units Conversion

## Standard friction equation

When a force is applied to an object, the resistive force of friction acts in the opposite direction, parallel to the surfaces.

The standard friction equation:

Fr = μN

can be rewritten as:

μ = Fr/N

where:

• μ is the coefficient of friction for the two surfaces (Greek letter "mu")
• Fr is the resistive force of friction
• N is the normal or perpendicular force pushing the two objects together

Frand N are measured in units of force, which are pounds or newtons. μ is a number between 0 (zero) and ∞ (infinity).

## Coefficient of friction

The coefficient of friction, μ (mu), is a number related to the two specific surfaces that are in contact with each other. It is very dependent on the roughness of each surface and how the materials slide against each other.

### Established by experiment

Although there are charts listing average values of the coefficient of friction for various materials, the only true way to establish the number is by experiment and testing or empirical measurements. Also, there are no good formulae or equations to predict μ.

By dividing both sides of the standard friction equation Fr = μN by N, you will get the equation μ = Fr/N, where Fr/N is Frdivided by N.

This relationship indicates that if you can measure the friction force Fr and know the normal force N pushing the two objects together, you can determine the coefficient of friction μ.

### Wide range of numbers

The coefficient of friction can range between 0 (zero) and ∞ (infinity).

#### Close to zero

When μ = 0, there is no friction. If μ is close to 0, there is little friction. For example, leather-soled shoes on slippery ice has a very small coefficient of friction, close to zero. That is why you can easily slide on ice or even take a fall. Even rubber-soled shoes on ice has a very small coefficient of friction.

#### Close to infinity

Many students and teachers mistakenly think that μ must be less than 1. That is incorrect, since Fr could be many times the normal force.

One extreme example is if you glued an object to another. The resistance to moving the objects would be very large and the coefficient of friction would also be very large. If the glue was so strong that they could never be slid against each other, then μ would equal infinity.

The reason people think that μ must be less than 1 is probably since most listing of coefficients of friction have values less than 1. That is because most materials of interest usually slide relatively easy on each other.

### Examples of coefficient

The following table shows the coefficient of sliding friction for a number of materials. Note that the static coefficient is larger than the kinetic coefficient.

(See Coefficient of Friction Values for an extensive list of coefficients.)

Coefficient of Friction
Surfaces Static Friction Kinetic Friction
Steel on steel (dry)

0.6

0.4

Steel on steel (greasy) 0.1 0.05
Teflon on steel 0.041 0.04
Brake lining on cast iron 0.4 0.3
Rubber tires on dry pavement 0.9 0.8
Metal on ice 0.022 0.02
Rubber tip of crutch on rough wood 0.7 --

### Coefficient when surfaces not hard and sliding

In the case where a surface is soft, there is molecular adhesion, and in rolling and fluid friction, the coefficient of friction is not a simple number. The coefficient may be dependent on the area of the surfaces, the amount of deformation, the amount of adhesion, the shape of the surfaces, the radius of the wheel or the viscosity of the fluid.

What this means is that although the standard friction equation holds in these cases, the coefficient of friction will only hold for a specific configuration. In other words, you can't accurately give something like the coefficient of rolling friction for a rubber tire on pavement without stating the type of rubber, area on the pavement, inflation of the tire, and its tread pattern.

## Considerations

The information available on the various coefficients of friction provide a starting point on the subject, but unfortunately the values lack a good scientific basis. The values should be used just as a guide.

### Surface roughness

Effective scientific measurements typically state the exact condition of materials and that of the surrounding environment. In the determination of the coefficient of friction of various materials, it is important to at least given an indication of the surface roughness of the tested materials, as well as their physical condition.

### Test setup

Describing the test setup is important in order to allow others to duplicate and verify the measurements. With friction, the normal force can be a factor in the case of hard materials that may deform slightly under high pressure. That value should be part of the test description.

### Testing environment

It is also important to state the testing environment. Although it is unlikely measurements were made under extreme temperature and humidity conditions that affect the coefficient, at the very least those items should be noted.

## Surface conditions

Other effects like oxidation of a metal surface, dirt, water or grease can dramatically change the coefficient of friction for the given materials.

### Effect of oxidation

For example, clean dry steel sliding on steel has a coefficient of friction of μ = 0.78, but if the surface has oxidized, the coefficient changes to μ = 0.27.

Likewise, clean dry copper sliding on copper has a coefficient of μ = 1.21, while oxidized copper has a value of μ = 0.76.

### Need to know surface conditions

The biggest problem in using values established by others in such tables is that you do not know the actual surface condition of the materials used or how the values were determined.

## Table

The following chart lists the static and kinetic coefficient of frictions for a variety of common material combinations. In most cases, the materials are assumed to be clean and dry. A few are listed as being wetted by water.

These values are the average of those from a number of sources. In some cases there are no values listed for the static friction coefficient or for the kinetic. Also, a few list a range of values.

## Summary

Coefficient of friction for a number of materials have been tabulated. These values apply only to hard, clean surfaces sliding against each other. Since various experimental parameters are not listed, considerations should be made in using these tabulated values because they may not directly relate to your application.

Be proud of what you do

## Resources and references

Ron Kurtus' Credentials

### Websites

Engineer's Handbook - Coefficient of Friction

RoyMech (UK) - Friction Factors

Friction Resources - Extensive list

### Books

The following books are available from Amazon.com.

#### Basic

Complete Idiot's Guide To Physics by Johnnie T. Dennis; Alpha (2003) \$18.95

What Is Friction? (Ages 4-8) by Lisa Trumbauer; Children's Press (CT) (2004) \$4.95

Friction Science and Technology (Mechanical Engineering Series) by Peter J. Blau; Marcel Dekker Pub. (1995) \$89.95

Physics of Sliding Friction (NATO Science Series E:) by B.N. Persson, E. Tosatti; Springer Pub. (1996) \$358.00

Do you have any questions, comments, or opinions on this subject? If so, send an email with your feedback. I will try to get back to you as soon as possible.

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