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Coefficient of Friction

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Friction is the force that acts parallel to the interface of two surfaces that are in contact with each other. The coefficient of friction is a dimensionless scalar value that gives the ratio of the force of friction between two bodies and the force pressing them together. It depends on the materials used like ice on steel has low coefficient of friction while rubber on pavement has a high coefficient of friction. Lets see more about this.

Coefficient of Friction Definition

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The Coefficient of friction is defined as that ratio which keeps the contact with body and surface. In short it is the ratio of frictional force that resists the motion of body. It is the dimensionless quantity that decides how much amount of friction lies between the two surfaces.It is denoted by symbol $\mu$.

Coefficient of Friction Formula

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The coefficient of friction is the ratio of the frictional force to the force acting perpendicular to the two surfaces in contact.It is denoted by symbol $\mu$ given as
$\mu$ = $\frac{F}{N}$
Here F is the friction force and
N is the normal force between two surfaces in contact

It is obtained by dividing the value of force necessary to move one body over another at a constant speed by the weight of the body. It varies with temperature, pressure and density. It has no unit as the two force units cancel out.

Dynamic Coefficient of Friction

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The dynamic coefficient of friction, also called the kinetic or sliding coefficient of friction or friction coefficient (symbol $\mu$ or f, dimensionless), is a measure of how large the friction forces are which act between two solids in motion. It is given as
$\mu_D$ = $\frac{F}{N}$
Here F is the kinetic friction force and
N is the normal kinetic force between two surfaces in contact
$\mu_D$ is coefficient of dynamic friction.

Can Coefficient of Friction be Greater Than 1?

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A coefficient of friction that is greater than one tells that the frictional force resisting the movement is greater than the force pushing the object into the surface. It occurs when two surfaces touch other quickly.

How to Find Coefficient of Friction?

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To find the coefficient of friction read the given quantities and see whether some of the quantities are given .Use the formula
$\mu$ = $\frac{F}{N}$
Here F is the friction force and
N is the normal force between two surfaces in contact
$\mu$ is coefficient of friction
Substitute the values in above formula and get the answer.

Coefficient of Friction Table

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Here is the table of coefficient of friction for various materials:

Materials
Static coefficient
$\mu_s$
Kinetic Coefficient
$\mu_k$
Steel on Steel
0.74 0.57
Aluminium on steel
0.61
0.47
Copper on steel
0.53
0.36
Rubber on concrete (dry)
1.0
0.8
Rubber on concrete (wet)
0.3
0.25
Wood on wood
0.25 - 0.5
0.2
Glass on glass 0.94
0.4
Teflon on Teflon
0.04
0.04
Teflon on steel
0.04
0.04
Waxed wood on wet snow
0.14
0.1
Waxed wood on dry snow
0.10
0.04
Metal on metal
0.15
0.06
Ice on ice
0.1
0.03
Synovial joints in humans
0.01
0.003
Very rough surfaces

1.5

Coefficient of Friction of Materials

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The coefficient of friction for steel is different for static friction ($\mu_s$) and kinetic friction ($\mu_k$). It varies from material to material.

Materials
Static friction $\mu_s$ Kinetic friction $\mu_k$
Coefficient of friction steel 0.7 0.6
Coefficient of friction rubber 0.5 - 0.8 0.25 - 0.8
Coefficient of friction wood 0.2 - 0.6 0.25 - 0.6
Coefficient of friction aluminum 0.67 0.41

Coefficient of Friction Problems

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Lets go through some coefficient of friction problems you can go through it :

Solved Examples

Question 1: A force of 100 N acts on 50 kg mass on a wooden floor. Calculate the coefficient of friction between mass and floor.
Solution:
 
Given: Force F = 100 N, Mass m = 50 kg, so Normal force N = 50 kg $\times$ 9.8 = 490 N
$\therefore$ Coefficient of friction $\mu$ = $\frac{100 N}{490 N}$ = 0.204.
 

Question 2: A box is lying on floor with coefficient of friction as 0.6. Calculate kinetic force coefficient if it is given a push with a force of 80 N.
Solution:
 
Given: Coefficient of friction $\mu_k$ = 0.6, Normal Force N = 80 N,
$\therefore$ Kinetic force Fk = $\mu_k$ $\times$ N
                                                   = 0.6 $\times$ 80 N = 48 N.