What is the coefficient of friction?
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:
There are also coefficients of friction calculators available which will ease our calculation while doing numerical.
FAQs on Coefficient of Friction
1. What is the fundamental definition of the coefficient of friction in Physics?
The coefficient of friction, symbolised by the Greek letter μ (mu), is a dimensionless scalar value that represents the ratio of the force of friction (Fᵣ) between two bodies and the normal force (N) pressing them together. It quantifies the roughness or adhesive quality between the surfaces in contact. The higher the value of μ, the greater the friction.
2. What are the two primary types of coefficients of friction?
The two main types of coefficients of friction are:
- Coefficient of Static Friction (μₛ): This applies when the objects are at rest relative to each other. It relates to the maximum force of static friction that must be overcome to initiate motion.
- Coefficient of Kinetic Friction (μₖ): This applies when the objects are in relative motion (sliding). It is the ratio of the kinetic friction force to the normal force.
3. What is the formula used to calculate the coefficient of friction?
The general formula for the coefficient of friction (μ) is derived from the relationship between the frictional force (Fᵣ) and the normal force (N). The formula is:
μ = Fᵣ / N
This means the coefficient of friction is the frictional force per unit of normal force.
4. On what key factors does the coefficient of friction depend?
The coefficient of friction primarily depends on the nature and properties of the two surfaces in contact. This includes their material composition, texture (smoothness or roughness), and any contaminants or lubricants present. It is important to note that for a given pair of surfaces, it is largely independent of the contact area and the relative speed of sliding (at low speeds).
5. Why is the coefficient of static friction (μₛ) typically greater than the coefficient of kinetic friction (μₖ)?
The coefficient of static friction is generally higher because more force is needed to overcome the initial inertia and the microscopic interlocking (adhesion) between surfaces at rest. Once motion begins, these bonds are continuously breaking and reforming, and the surfaces may 'ride' over each other's peaks, which requires less force to maintain motion. Therefore, μₛ > μₖ for most material pairs.
6. Does the coefficient of friction have units or a dimensional formula?
No, the coefficient of friction is a dimensionless quantity. Since it is a ratio of two forces (Frictional Force / Normal Force), the units of force (Newtons) in the numerator and denominator cancel each other out. Consequently, its dimensional formula is [M⁰L⁰T⁰].
7. How does doubling the weight of an object affect its coefficient of friction with a surface?
Doubling the weight of an object does not change the coefficient of friction. The coefficient (μ) is an intrinsic property of the surfaces in contact. While doubling the weight will double the normal force (N) and consequently double the maximum force of friction (Fᵣ = μN), the ratio μ itself remains constant.
8. Can the coefficient of friction have a value greater than 1, and what would that signify?
Yes, it is possible for the coefficient of friction, especially the static coefficient (μₛ), to be greater than 1. A value greater than 1 signifies that the force required to slide an object is greater than the normal force pressing it against the surface. This is common with highly adhesive or interlocking surfaces, such as silicone rubber on glass or two very rough, jagged materials.
9. How does the concept of 'angle of repose' relate to the coefficient of static friction?
The angle of repose is the maximum angle of an inclined plane at which an object can rest without sliding down. This angle is directly related to the coefficient of static friction (μₛ). Mathematically, the tangent of the angle of repose (θ) is equal to the coefficient of static friction. The formula is:
μₛ = tan(θ)
This provides a practical method to experimentally determine the value of μₛ.
