Coefficient of friction

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A coefficient of friction is a value that shows the relationship between the force of friction between two objects and the normal force between the objects. It is a value that is used in physics sometimes to find an objects normal force or frictional force, when other methods aren't available.

The coefficient of friction is shown by f = \mu F_{n}\,. In that equation, f is the frictional force, \mu is the coefficient of friction, and F_{n}\, is the normal force.

\mu can be two different things. It can be \mu_s, or it can be \mu_k. \mu_s is the coefficient of static friction. The coefficient of static friction is the friction force between two objects when neither of the objects is moving. \mu_k is the coefficient of kinetic friction. The coefficient of kinetic friction is the force between two objects when one object is moving, or if two objects are moving against each other.

The coefficient of friction is dimensionless, meaning it does not have any units. It is a vector, meaning the direction of the force does not change its magnitude.

The coefficient of friction depends on the objects that are causing friction. The value is usually between 0 and 1 but can be greater than 1. A value of 0 means there is no friction at all between the objects. This is only theoretically possible. All objects in the real world will have some friction when they touch each other. A value of 1 means the frictional force is equal to the normal force. Some people think that the coefficient of friction can never be more than 1, but this is not true. A coefficient of friction that is more than one just means that friction is stronger than the normal force. An object such as silicone rubber, for example, can have a coefficient of friction much greater than one. The coefficient of friction can also be changed by the mass and speed of the moving object.

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)


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 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 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) 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-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 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 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 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 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 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