Friction and Coefficients of Friction

Friction theory and coefficients of friction for some common materials and materials combinations

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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)

frictional force

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

N = m · g         (2)

where

m = mass of the object (kg, slugs)

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

Frictional Coefficients for some Common Materials and Materials Combinations

Materials and Material Combinations Static Frictional Coefficient - μs
Clean and Dry Surfaces Lubricated and Greasy Surfaces
Aluminum Aluminum 1.05 - 1.35 0.3
Aluminum-bronze Steel 0.45
Aluminum Mild Steel 0.61
Brake material Cast iron 0.4
Brake material 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
Cadmium Cadmium 0.5 0.05
Cadmium Chromium 0.41 0.34
Cadmium Mild Steel 0.461)
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)
Carbon (hard) Carbon 0.16 0.12 - 0.14
Carbon Steel 0.14 0.11 - 0.14
Chromium Chromium 0.41 0.34
Copper-Lead alloy Steel 0.22
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
Ice Wood 0.05  
Iron Iron 1.0 0.15 - 0.20
Lead Cast Iron 0.431)
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
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
Polystyrene Polystyrene 0.5 0.5
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
Steel Steel 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
Teflon Teflon 0.04 0.04, 0.041)
Teflon 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)
Tire, dry Road, dry 1  
Tire, wet Road, wet 0.2  
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 Concrete 0.62
Wood Brick 0.6
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 - holds only when there is a relative motion between the surfaces; otherwise they are somewhat higher

Kinetic versus Static Frictional Coefficients

Kinetic frictional coefficients are used with relative motion between objects. Static frictional coefficients are used for objects without relative motion. Static coefficients are somewhat higher than kinetic coefficients.

Example - Friction Force

The friction force of a 100 lb wooden crate pushed across a concrete floor with friction coefficient of 0.62 can be calculated as:

Ff = 0.62 · 100 (lb)

= 62 (lb)

  • 1 lb = 0.4536 kg

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