In order to understand the concept of coefficient of friction, we must be well versed with friction, friction force, and type of friction. A surface can be classified as frictional if it resists relative motion between two surfaces in contact, for example, two surfaces might be in contact while sliding or rolling, or resting. Rough surfaces are usually responsible for friction. It means that if the surfaces are not designed for motion, the relative motion between them will lead to friction. Surface roughness is always directly correlated with friction. Surfaces with more roughness experience more friction. Smoother surfaces will have less friction than rough ones.
Friction Force or Force of Friction
In a vector quantity, the friction force has both a magnitude and a direction. In simpler terms, friction is a reaction force. In other words, the friction force doesn’t exist directly, it’s the reaction of another force on the body. Additionally, friction is a resistive force.
The formula for the coefficient of friction
In terms of friction between two surfaces, the coefficient of friction indicates the amount of interaction between the two surfaces. Surface roughness can be determined by the coefficient of friction value. Any object under observation experiences friction when it is subjected to the normal force acting on it. This can be expressed mathematically as follows:
⇒Fᵣ ⍺ N …… (1)
An object of mass m is placed horizontally on a rough surface (and even inclined). As the object’s weight acts downward, the block’s normal force is in the opposite direction as the weight of the object. Assuming that the block is moving to the left, the friction force will be directed to the left as well.
There exists a direct relationship between the friction force and the normal force acting on it, but this relationship breaks down when a coefficient of friction is introduced.
Mathematically, we write:
⇒Fᵣ=μN……..(2)
Where,
μ – The coefficient of friction
⇒μ=Fᵣ / N ………(3)
A coefficient of friction equation can also be known as the coefficient of friction formula. It is clear from equation (3) that friction causes force to be directly proportional to the friction coefficient. It stands to reason that if the coefficient of friction is greater, then the force of friction will also be greater.
The formula for static friction
When an object is at rest, static friction is defined as the tendency to move relative to it. The force of static friction acts even before we slide the object as long as the normal force exists between the two surfaces.
The static friction formula is given by:
⇒ Fₛ=μₛN
Where,
μₛ- Coefficient of static friction.
⇒μₛ=Fₛ / N……..(1)
Equation (1) is known as the coefficient of static friction formula.
The formula for Kinetic Friction:
In its simplest form, kinetic friction is the resistance to relative motion between surfaces when the motion starts. The formula for kinetic friction can be translated as follows:
⇒ Fₖ=μₖN
Where,
μₖ- Coefficient of kinetic friction
⇒ μₖ=Fₖ / N
The above expression is known as the Coefficient of kinetic friction formula.
Did You Know?
Every material will have a different coefficient of friction depending on the roughness of its surface. For example, if you slide the glass over the glass, you can slide easily without any jerk in the motion. At the same time, if you slide a piece of glass over a road or any unfinished surface, the motion will not be smooth and observe variation in the force.
Let us have a look at the coefficient of friction of a few materials as listed below:
|
Materials |
Kinetic friction coefficient 𝞵k |
Static friction coefficient 𝞵s |
|
Glass on Glass |
0.4 |
0.94 |
|
Ice on Ice |
0.03 |
0.1 |
|
Aluminium on Steel |
0.47 |
0.61 |
|
Synovial joints of the human |
0.003 |
0.01 |
There are also coefficients of friction calculators available which will ease our calculation while doing numerical.