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The friction theory and friction coefficients at different conditions for various of materials like ice, aluminum, steel, graphite and other common materials and materials combinations

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

  1. A 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.
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The frictional force can be expressed as https://truegload251.weebly.com/leo-gambling-horoscope.html.

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:

Snagit all in one capture. Bingo slot machine. N = Fg

= m ag (2)

where

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

m= mass of object (kg, slugs)

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

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

Ff = μ m ag (3)

Friction Force Calculator

m - mass (kg, slugs)

ag - acceleration og gravity (9.81 m/s2, 32 ft/s2)

μ - friction coefficient Nzbvortex 3 4 3 – lightweight usenet nzb download client.

Friction Coefficients for some Common Materials and Materials Combinations

Materials and Material CombinationsSurface ConditionsFrictional Coefficient
Static
- μstatic -
Kinetic (sliding)
- μsliding -
AluminumAluminumClean and Dry1.05 - 1.351.4
AluminumAluminumLubricated and Greasy0.3
Aluminum-bronzeSteelClean and Dry0.45
AluminumMild SteelClean and Dry0.610.47
AluminumSnowWet 0oC0.4
AluminumSnowDry 0oC0.35
Brake material2)Cast ironClean and Dry0.4
Brake material2)Cast iron (wet)Clean and Dry0.2
BrassSteelClean and Dry0.510.44
BrassSteelLubricated and Greasy0.19
BrassSteelCastor oil0.11
BrassCast IronClean and Dry0.3
BrassIceClean 0oC0.02
BrassIceClean -80oC0.15
BrickWoodClean and Dry0.6
BronzeSteelLubricated and Greasy0.16
BronzeCast IronClean and Dry0.22
Bronze - sinteredSteelLubricated and Greasy0.13
CadmiumCadmiumClean and Dry0.5
CadmiumCadmiumLubricated and Greasy0.05
CadmiumChromiumClean and Dry0.41
CadmiumChromiumLubricated and Greasy0.34
CadmiumMild SteelClean and Dry0.46
Cast IronCast IronClean and Dry1.10.15
Cast IronCast IronClean and Dry0.15
Cast IronCast IronLubricated and Greasy0.07
Cast IronOakClean and Dry0.49
Cast IronOakLubricated and Greasy0.075
Cast ironMild SteelClean and Dry0.4
Cast ironMild SteelClean and Dry0.23
Cast ironMild SteelLubricated and Greasy0.210.133
Car tireAsphaltClean and Dry0.72
Car tireGrassClean and Dry0.35
Carbon (hard)CarbonClean and Dry0.16
Carbon (hard)CarbonLubricated and Greasy0.12 - 0.14
CarbonSteelClean and Dry0.14
CarbonSteelLubricated and Greasy0.11 - 0.14
ChromiumChromiumClean and Dry0.41
ChromiumChromiumLubricated and Greasy0.34
Copper-Lead alloySteelClean and Dry0.22
CopperCopperClean and Dry1.6
CopperCopperLubricated and Greasy0.08
CopperCast IronClean and Dry1.050.29
CopperMild SteelClean and Dry0.530.36
CopperMild SteelLubricated and Greasy0.18
CopperMild SteelOleic acid0.18
CopperGlassClean and Dry0.680.53
CottonCottonThreads0.3
DiamondDiamondClean and Dry0.1
DiamondDiamondLubricated and Greasy0.05 - 0.1
DiamondMetalsClean and Dry0.1 - 0.15
DiamondMetalLubricated and Greasy0.1
GarnetSteelClean and Dry0.39
GlassGlassClean and Dry0.9 - 1.00.4
GlassGlassLubricated and Greasy0.1 - 0.60.09 - 0.12
GlassMetalClean and Dry0.5 - 0.7
GlassMetalLubricated and Greasy0.2 - 0.3
GlassNickelClean and Dry0.78
GlassNickelLubricated and Greasy0.56
GraphiteSteelClean and Dry0.1
GraphiteSteelLubricated and Greasy0.1
GraphiteGraphite (in vacuum)Clean and Dry0.5 - 0.8
GraphiteGraphiteClean and Dry0.1
GraphiteGraphiteLubricated and Greasy0.1
Hemp ropeTimberClean and Dry0.5
HorseshoeRubberClean and Dry0.68
HorseshoeConcreteClean and Dry0.58
IceIceClean 0oC0.10.02
IceIceClean -12oC0.30.035
IceIceClean -80oC0.50.09
IceWoodClean and Dry0.05
IceSteelClean and Dry0.03
IronIronClean and Dry1.0
IronIronLubricated and Greasy0.15 - 0.20
LeadCast IronClean and Dry0.43
LeatherOakParallel to grain0.610.52
LeatherMetalClean and Dry0.4
LeatherMetalLubricated and Greasy0.2
LeatherWoodClean and Dry0.3 - 0.4
LeatherClean MetalClean and Dry0.6
LeatherCast IronClean and Dry0.60.56
Leather fiber Cast ironClean and Dry0.31
Leather fiberAluminumClean and Dry0.30
MagnesiumMagnesiumClean and Dry0.6
MagnesiumMagnesiumLubricated and Greasy0.08
MagnesiumSteelClean and Dry0.42
MagnesiumCast IronClean and Dry0.25
MasonryBrickClean and Dry0.6 - 0.7
MicaMicaFreshly cleaved1.0
NickelNickelClean and Dry0.7 - 1.10.53
NickelNickelLubricated and Greasy0.280.12
NickelMild SteelClean and Dry0.64
NickelMild SteelLubricated and Greasy0.178
NylonNylonClean and Dry0.15 - 0.25
NylonSteelClean and Dry0.4
NylonSnowWet 0oC0.4
NylonSnowDry -10oC0.3
OakOak (parallel grain)Clean and Dry0.620.48
OakOak (cross grain)Clean and Dry0.540.32
OakOak (cross grain)Lubricated and Greasy0.072
PaperCast IronClean and Dry0.20
Phosphor-bronzeSteelClean and Dry0.35
PlatinumPlatinumClean and Dry1.2
PlatinumPlatinumLubricated and Greasy0.25
PlexiglasPlexiglasClean and Dry0.8
PlexiglasPlexiglasLubricated and Greasy0.8
PlexiglasSteelClean and Dry0.4 - 0.5
PlexiglasSteelLubricated and Greasy0.4 - 0.5
PolystyrenePolystyreneClean and Dry0.5
PolystyrenePolystyreneLubricated and Greasy0.5
PolystyreneSteelClean and Dry0.3 - 0.35
PolystyreneSteelLubricated and Greasy0.3 - 0.35
PolyethylenePolytehyleneClean and Dry0.2
PolyethyleneSteelClean and Dry0.2
PolyethyleneSteelLubricated and Greasy0.2
RubberRubberClean and Dry1.16
RubberCardboardClean and Dry0.5 - 0.8
RubberDry AsphaltClean and Dry0.90.5 - 0.8
RubberWet AsphaltClean and Dry0.25 - 0.75
RubberDry ConcreteClean and Dry0.6 - 0.85
RubberWet ConcreteClean and Dry0.45 - 0.75
SilkSilkClean0.25
SilverSilverClean and Dry1.4
SilverSilverLubricated and Greasy0.55
SapphireSapphireClean and Dry0.2
SapphireSapphireLubricated and Greasy0.2
SilverSilverClean and Dry1.4
SilverSilverLubricated and Greasy0.55
SkinMetalsClean and Dry0.8 - 1.0
SteelSteelClean and Dry0.5 - 0.80.42
SteelSteelLubricated and Greasy0.16
SteelSteelCastor oil0.150.081
SteelSteelStearic Acid0.15
SteelSteelLight mineral oil0.23
SteelSteelLard0.110.084
SteelSteelGraphite0.058
SteelGraphiteClean and Dry0.21
Straw FiberCast IronClean and Dry0.26
Straw Fiber AluminumClean and Dry0.27
Tarred fiberCast IronClean and Dry0.15
Tarred fiberAluminumClean and Dry0.18
Polytetrafluoroethylene (PTFE) (Teflon)Polytetrafluoroethylene (PTFE)Clean and Dry0.040.04
Polytetrafluoroethylene (PTFE)Polytetrafluoroethylene (PTFE)Lubricated and Greasy0.04
Polytetrafluoroethylene (PTFE)SteelClean and Dry0.05 - 0.2
Polytetrafluoroethylene (PTFE)SnowWet 0oC0.05
Polytetrafluoroethylene (PTFE)SnowDry 0oC0.02
Tungsten CarbideSteelClean and Dry0.4 - 0.6
Tungsten CarbideSteelLubricated and Greasy0.1 - 0.2
Tungsten CarbideTungsten CarbideClean and Dry0.2 - 0.25
Tungsten CarbideTungsten CarbideLubricated and Greasy0.12
Tungsten CarbideCopperClean and Dry0.35
Tungsten CarbideIronClean and Dry0.8
TinCast IronClean and Dry0.32
Tire, dryRoad, dryClean and Dry1
Tire, wetRoad, wetClean and Dry0.2
Wax, skiSnowWet 0oC0.1
Wax, skiSnowDry 0oC0.04
Wax, skiSnowDry -10oC0.2
WoodClean WoodClean and Dry0.25 - 0.5
WoodWet WoodClean and Dry0.2
WoodClean MetalClean and Dry0.2 - 0.6
WoodWet MetalsClean and Dry0.2
WoodStoneClean and Dry0.2 - 0.4
WoodConcreteClean and Dry0.62
WoodBrickClean and Dry0.6
Wood - waxedWet snowClean and Dry0.140.1
Wood - waxedDry snowClean and Dry0.04
ZincCast IronClean and Dry0.850.21
ZincZincClean and Dry0.6
ZincZincLubricated and Greasy0.04

Kinetic or sliding frictional coefficient only when there is a relative motion between the surfaces.

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

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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

Note! - since the mass of the car is present on both sides of eq. 6 it cancels out. The stop distance is not dependent on the mass of the car.

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'Laws of Friction'

Unlubricated Dry Surfaces

  1. for low pressure the friction is proportional to the normal force between the surfaces. With rising pressure the friction will not rise proportionally. With extreme pressure friction will rise and surfaces seize.
  2. at moderate pressure the friction force - and coefficient - is not dependent of the surface areas in contact as long as the normal force is the same. With extreme pressure friction will rice and surfaces seize.
  3. at very low velocity between the surfaces the friction is independent of the velocity of rubbing. With increased velocity the the friction decrease.

Lubricated Surfaces

  1. friction force is almost independent of pressure - normal force - if the surfaces are flooded with lubricant
  2. friction varies with speed at low pressure. At higher pressure the minimum friction is at velocity 2 ft/s (0.7 m/s) and friction increases with approximately square root of velocity afterwards.
  3. friction varies with temperature
  4. for well lubricated surfaces the friction is almost independent of surface material

Typically steel on steel dry static friction coefficient 0.8 drops to 0.4 when sliding is initiated - and steel on steel lubricated static friction coefficient 0.16 drops to 0.04 when sliding is initiated.

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