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 between the surfaces (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 due to gravity (1) can with (2) be modified to
Ff = μ m g (3)
Friction 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 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 | |
| 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) | |
| 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 |
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. More force are required to start a motion
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
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