Friction - Friction Coefficients and Calculator

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

F_f = μ N                     (1)

where

F_f = frictional force (N, lb)

μ = static (μ_s) or kinetic (μ_k) 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 = F_g

    = m a_g                         (2)

where

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

m = mass of object (kg, slugs)

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

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

F_f = μ m a_g                      (3)

Friction Force Calculator

m - mass (kg, slugs)

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

μ - friction coefficient

• Load Calculator!

• Friction forces on inclined planes
• Weight vs mass - the difference

Friction Coefficients for some Common Materials and Materials Combinations

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

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

F_f = 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

E_kinetic = 1/2 m v²                           (4)

where

E_kinetic = kinetic energy of the moving car (J)

m = mass (kg)

v = velocity (m/s)

E_kinetic = 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

W_friction = F_f d                                (5)

where

W_friction = friction work to stop the car (J)

F_f = 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

E_kinetic = W_friction                              (6)

The friction force F_f can be calculated from (3)  

F_f = 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 = W_friction / F_f

  = (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.

"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.