# Friction and Friction Coefficients

## Friction theory and coefficients of friction for ice, aluminum, steel, graphite and other common materials and materials combinations

The friction force is the force exerted by a surface when an object moves across it - or makes an effort to move across it.

The frictional force can be expressed as

Ff = μ N                     (1)

where

Ff = frictional force (N, lb)

μ = static (μs) or kinetic (μk) frictional coefficient

N = normal force (N, lb)

There are at least two types of friction forces

• kinetic (sliding) friction force- when an object moves
• static friction force - when an object makes an effort to move

For an object pulled or pushed horizontally the normal force - N - is simply the gravity force - or weight:

N = Fg

= m g                         (2)

where

Fg = gravity force - or weight (N, lb)

m = mass of object (kg, slugs)

g = acceleration of gravity (9.81 m/s2, 32 ft/s2)

The friction force (1) can with (2) be modified to

Ff = μ m g                      (3)

### Friction Coefficients for some Common Materials and Materials Combinations

Materials and Material CombinationsStatic Frictional Coefficient
- μs -
Clean and Dry SurfacesLubricated and Greasy Surfaces
Aluminum Aluminum 1.05 - 1.35 0.3
Aluminum-bronze Steel 0.45
Aluminum Mild Steel 0.61
Brake material2) Cast iron 0.4
Brake material2) Cast iron (wet) 0.2
Brass Steel 0.35 0.19
Brass Cast Iron 0.31)
Brick Wood 0.6
Bronze Steel 0.16
Bronze Cast Iron 0.221)
Bronze - sintered Steel 0.13
Cast Iron Cast Iron 1.1, 0.151) 0.071)
Cast Iron Oak 0.491) 0.0751
Cast iron Mild Steel 0.4, 0.231) 0.21, 0.1331)
Car tire Asphalt 0.72
Car tire Grass 0.35
Carbon (hard) Carbon 0.16 0.12 - 0.14
Carbon Steel 0.14 0.11 - 0.14
Chromium Chromium 0.41 0.34
Copper Copper 1 0.08
Copper Cast Iron 1.05, 0.291)
Copper Mild Steel 0.53, 0.361) 0.181)
Diamond Diamond 0.1 0.05 - 0.1
Diamond Metal 0.1 - 0.15 0.1
Glass Glass 0.9 - 1.0, 0.41) 0.1 - 0.6,
0.09-0.121)
Glass Metal 0.5 - 0.7 0.2 - 0.3
Glass Nickel 0.78 0.56
Graphite Steel 0.1 0.1
Graphite Graphite (in vacuum) 0.5 - 0.8
Graphite Graphite 0.1 0.1
Hemp rope Timber 0.5
Horseshoe Rubber 0.68
Horseshoe Concrete 0.58
Ice Ice 0.02 - 0.09
Ice Wood 0.05
Ice Steel 0.03
Iron Iron 1.0 0.15 - 0.20
Leather Oak 0.61, 0521
Leather Metal 0.4 0.2
Leather Wood 0.3 - 0.4
Leather Clean Metal 0.6
Leather fiber  Cast iron 0.31
Leather fiber Aluminum 0.30
Magnesium Magnesium 0.6 0.08
Masonry Brick 0.6 - 0.7
Nickel Nickel 0.7 - 1.1,
0.531)
0.28, 0.121)
Nickel Mild Steel 0.641) 0.1781)
Nylon Nylon 0.15 - 0.25
Oak Oak (parallel grain) 0.62, 0.481)
Oak Oak (cross grain) 0.54, 0.321 0.0721
Paper Cast Iron 0.20
Phosphor-bronze Steel 0.35
Platinum Platinum 1.2 0.25
Plexiglas Plexiglas 0.8 0.8
Plexiglas Steel 0.4-0.5 0.4 - 0.5
Polystyrene Polystyrene 0.5 0.5
Polystyrene Steel 0.3-0.35 0.3 - 0.35
Polythene Steel 0.2 0.2
Rubber Rubber 1.16
Rubber Cardboard 0.5 - 0.8
Rubber Dry Asphalt 0.9  (0.5 - 0.8)1)
Rubber Wet Asphalt 0.25 - 0.751)
Rubber Dry Concrete 0.6 - 0.851)
Rubber Wet Concrete 0.45 - 0.751)
Silver Silver 1.4 0.55
Sapphire Sapphire 0.2 0.2
Silver Silver 1.4 0.55
Skin Metals 0.8 - 1.0
Steel Steel 0.5 - 0.8 0.16
Straw Fiber Cast Iron 0.26
Straw Fiber  Aluminum 0.27
Tarred fiber Cast Iron 0.15
Tarred fiber Aluminum 0.18
Polytetrafluoroethylene (PTFE) Polytetrafluoroethylene (PTFE) 0.04 0.04, 0.041)
Polytetrafluoroethylene (PTFE) Steel 0.05 - 0.2
Tungsten Carbide Steel 0.4-0.6 0.1 - 0.2
Tungsten Carbide Tungsten Carbide 0.2 - 0.25 0.12
Tungsten Carbide Copper 0.35
Tungsten Carbide Iron 0.8
Tin Cast Iron 0.321)
Wood Clean Wood 0.25 - 0.5
Wood Wet Wood 0.2
Wood Clean Metal 0.2 - 0.6
Wood Wet Metals 0.2
Wood Stone 0.2 - 0.4
Wood Concrete 0.62
Wood Brick 0.6
Wood - waxed Wet snow 0.14, 0.11)
Wood - waxed Dry snow 0.041)
Zinc Cast Iron 0.85, 0.211)
Zinc Zinc 0.6 0.04

1) Kinetic or sliding frictional coefficient - only when there is a relative motion between the surfaces. Without motion the values are somewhat higher.

2) Note! It is commonly thought that the static coefficients of friction are higher than the dynamic or kinetic values. This is a very simplistic statement and quite misleading for brake materials. With many brake materials the dynamic coefficient of friction quoted is an "average" value when the material is subject to a range of sliding speeds, surface pressures and most importantly operating temperatures. If the static situation is considered at the same pressure, but at ambient temperature, then the static coefficient of friction is often significantly LOWER than the average quoted dynamic value. It can be as low as 40 - 50% of the quoted dynamic value.

### Kinetic (Sliding) versus Static Frictional Coefficients

Kinetic or sliding frictional coefficients are used with relative motion between objects. Static frictional coefficients are used for objects without relative motion. Note that static coefficients are somewhat higher than the kinetic or sliding coefficients.

### Example - Friction Force

A 100 lb wooden crate is pushed across a concrete floor. The friction coefficient between the object and the surface is 0.62. The friction force can be calculated as

Ff = 0.62 (100 lb)

= 62 (lb)

• 1 lb = 0.4536 kg

### Example - Car, Braking, Friction Force and Required Distance to Stop

A car with mass 2000 kg drives with speed 100 km/h on a wet road with friction coefficient 0.2.

Note! - The friction work required to stop the car is equal to the kinetic energy of the car.

The kinetic energy of the car is

Ekinetic = 1/2 m v2                           (4)

where

Ekinetic = kinetic energy of the moving car (J)

m = mass (kg)

v = velocity (m/s)

Ekinetic = 1/2 (2000 kg) ((100 km/h) (1000 m/km) / (3600 s/h))2

=  771605 J

The friction work (energy) to stop the car can be expressed as

Wfriction = Ff d                                (5)

where

Wfriction = friction work to stop the car (J)

Ff = friction force (N)

d = braking (stopping) distance (m)

Since the kinetic energy of the car is converted to friction energy (work) - we have the expression

Ekinetic = Wfriction                              (6)

The friction force Ff can be calculated from (3)

Ff = μ m g

= 0.2 (2000 kg) (9.81 m/s2)

= 3924 N

The stop distance for the car can be calculated by modifying (5) to

d = Wfriction / Ff

= (771605 J) / (3924 N)

= 197 m

## Related Topics

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