Friction and Coefficients of FrictionFriction theory and coefficients of friction for some common materials and materials combinationsFrictional force can be expressed asFf = N(1)whereFf = frictional force (N, lb) = static (s) or kinetic (k) frictional coefficientN = normal force (N, lb)

For an object pulled or pushed horizontally, the normal force - N - is simply the weight:N = m g(2)wherem = 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 CombinationsMaterials and Material CombinationsStatic Frictional Coefficient - s

Clean and Dry SurfacesLubricated and Greasy Surfaces

AluminumAluminum1.05 - 1.350.3

Aluminum-bronzeSteel0.45

AluminumMild Steel0.61

Brake material2)Cast iron0.4

Brake material2)Cast iron (wet)0.2

BrassSteel0.350.19

BrassCast Iron0.31)

BrickWood0.6

BronzeSteel0.16

BronzeCast Iron0.221)

Bronze - sinteredSteel0.13

CadmiumCadmium0.50.05

CadmiumChromium0.410.34

CadmiumMild Steel0.461)

Cast IronCast Iron1.1, 0.151)0.071)

Cast IronOak0.491)0.0751

Cast ironMild Steel0.4, 0.231)0.21, 0.1331)

Car tireAsphalt0.72

Car tireGrass0.35

Carbon (hard)Carbon0.160.12 - 0.14

CarbonSteel0.140.11 - 0.14

ChromiumChromium0.410.34

Copper-Lead alloySteel0.22

CopperCopper10.08

CopperCast Iron1.05, 0.291)

CopperMild Steel0.53, 0.361)0.181)

DiamondDiamond0.10.05 - 0.1

DiamondMetal0.1 - 0.150.1

GlassGlass0.9 - 1.0, 0.41)0.1 - 0.6,0.09-0.121)

GlassMetal0.5 - 0.70.2 - 0.3

GlassNickel0.780.56

GraphiteSteel0.10.1

GraphiteGraphite (in vacuum)0.5 - 0.8

GraphiteGraphite0.10.1

Hemp ropeTimber0.5

HorseshoeRubber0.68

HorseshoeConcrete0.58

IceIce0.02 - 0.09

IceWood0.05

IceSteel0.03

IronIron1.00.15 - 0.20

LeadCast Iron0.431)

LeatherOak0.61, 0521

LeatherMetal0.40.2

LeatherWood0.3 - 0.4

LeatherClean Metal0.6

Leather fiberCast iron0.31

Leather fiberAluminum0.30

MagnesiumMagnesium0.60.08

MasonryBrick0.6 - 0.7

NickelNickel0.7 - 1.1,0.531)0.28, 0.121)

NickelMild Steel0.641)0.1781)

NylonNylon0.15 - 0.25

OakOak (parallel grain)0.62, 0.481)

OakOak (cross grain)0.54, 0.3210.0721

PaperCast Iron0.20

Phosphor-bronzeSteel0.35

PlatinumPlatinum1.20.25

PlexiglasPlexiglas0.80.8

PlexiglasSteel0.4-0.50.4 - 0.5

PolystyrenePolystyrene0.50.5

PolystyreneSteel0.3-0.350.3 - 0.35

PolytheneSteel0.20.2

PolystyrenePolystyrene0.50.5

RubberRubber1.16

RubberCardboard0.5 - 0.8

RubberDry Asphalt0.9 (0.5 - 0.8)1)

RubberWet Asphalt0.25 - 0.751)

RubberDry Concrete0.6 - 0.851)

RubberWet Concrete0.45 - 0.751)

SilverSilver1.40.55

SapphireSapphire0.20.2

SilverSilver1.40.55

SkinMetals0.8 - 1.0

SteelSteel0.5 - 0.80.16

Straw FiberCast Iron0.26

Straw FiberAluminum0.27

Tarred fiberCast Iron0.15

Tarred fiberAluminum0.18

TeflonTeflon0.040.04, 0.041)

TeflonSteel0.05 - 0.2

Tungsten CarbideSteel0.4-0.60.1 - 0.2

Tungsten CarbideTungsten Carbide0.2 - 0.250.12

Tungsten CarbideCopper0.35

Tungsten CarbideIron0.8

TinCast Iron0.321)

Tire, dryRoad, dry1

Tire, wetRoad, wet0.2

WoodClean Wood0.25 - 0.5

WoodWet Wood0.2

WoodClean Metal0.2 - 0.6

WoodWet Metals0.2

WoodStone0.2 - 0.4

WoodConcrete0.62

WoodBrick0.6

Wood - waxedWet snow0.14, 0.11)

Wood - waxedDry snow0.041)

ZincCast Iron0.85, 0.211)

ZincZinc0.60.04

1) Kinetic or sliding frictional coefficient - holds only when there is a relative motion between the surfaces; otherwise they are somewhat higher2) 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 versus Static Frictional CoefficientsKinetic 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 ForceThe 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 kgExample - Car Stopping DistanceA car with mass 2000 kg drives with speed 100 km/h on a wet road with friction coefficient 0.2.The friction work required to stop the car is equal to the kinetic energy of the car and can be calculated asEkinetic = 1/2 m v2(3) = 1/2 (2000 kg) ((100 km/h) (1000 m/km) / (3600 s/h))2 = 771605 JThe friction work can be expressed asWfriction = Ff d(4)where d = stopping distance (m)(4) can be modified tod = Wfriction / m g = (771605 J) / (0.2 (2000 kg) (9.81 m/s2)) = 197 m