# Coefficient of Friction: Definition, Equation, Formula, Static & Kinetic, Units, Table

In this article, we will learn what is coefficient of friction is, its definition, equation, formula, kinetic friction, units, symbol, chart, etc.

Let’s explore!

## What is Coefficient of Friction? Definition

### Coefficient of Friction Definition

Friction is the force that repels the sliding or rolling of one solid body over another body/object.

The Coefficient of friction is the quantitative relation to quantifying the friction force between two objects concerning the normal force keeping them combined. The Coefficient of friction is a vital consideration throughout material choice and surface demand determination.

### Coefficient of Friction Explanation

It’s a degree of the quantity of resistance that a surface applies on, or materials moving over it, equivalent to the ratio between the highest frictional force that the surface applies and, therefore, the force pushing the thing towards the surface.

The power of this friction force depends on the materials that are pressing against one another. For example, a steel bar can slip rather more simply on a sheet of ice than on a block of concrete. In this example, the steel-on-ice combination includes an abundant lower constant of friction. Other examples include rubbing hands, as rubbing of hands produces heat due to friction. Hiking on a mountain/rock is an example of friction. When a hiker moves on a mountain, a force is felt in the reverse direction to oppose the motion.

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## Equation & Formula of Coefficient of Friction

### Coefficient of Friction Equation & Formula

The equation for coefficient of friction is:

μ = FF / FN

where:

• μ = Coefficient of friction
• FF = friction force
• FN = normal force

As described in the above equation, both the frictional force and the normal force play an essential part in determining the Coefficient of friction. A greater coefficient of friction means that more friction force is present compared to the normal force.

### Where from Coefficient of Friction Come?

The formula for frictional force is hereunder:

f = μ × N

Where:

• f = friction force
• μ = Coefficient of friction
• N = normal force

## Types of Coefficient of Friction

There are two categories of coefficients of friction. The Coefficient of friction isn’t always frequently equal for immovable items and things that are in movement; it should be prominent that these forces are different with a relation given below in many situations. There are as follows:

• Static Coefficient of Friction
• Kinetic coefficient of friction

Let’s try to understand both types of coefficients of friction in brief.

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## Static Coefficient of Friction

### Definition of Static Coefficient of Friction

The static Coefficient of friction is the Coefficient of friction that applies to immovable items.

The static Coefficient of friction is the degree of the quantity of friction present among surfaces at rest.  For movement to take place, that static Coefficient of friction should be overcome.

### Static Friction’s Laws

The static friction’s law states that:

• The extreme static friction force does not depend on the contact area.
• The supreme static friction force is comparable to the normal force, i.e., when the normal force increases, the maximum external force that the object can withstand without moving also increases.

### Equation or Formula of Static Coefficient of Friction

Friction could also be a force that makes it more durable for two objects to slide along each other. Static friction exists between the surfaces on which the article is resting and a stationary object. In other words, static friction may be a force that keeps an object at rest.

As an object begins moving, we will say that it’s in motion; it experiences kinetic friction. If less force is applied to an object, the static friction has an equal magnitude within the opposite direction.

Force of static friction = (Coefficient of static friction) × (normal force)
Fs = μs × N

Where:

• Fs = the force of static friction
• μs = Coefficient of static friction
• N = normal force

### Dimension of Static Coefficient of Friction

The friction coefficient is dimensionless because it’s far the ratio of forces that act, respectively, perpendicular to and parallel to the interface among the contacting bodies.

The dimensional system of coefficient of friction is given by [M0 L0 T0].

### Mathematical Derivation of Static Friction Formula

We know that the static friction (maximum) is directly proportional to the normal friction.

Fs(max) ∝ Fn

whereas, Fs(max) = μs × Fn

Where μs is the constant for proportionality, and it is known as the coefficient of static friction.

it depends on the nature of the surfaces in contact before sliding, but if we have to find the coefficient of static friction, then by rearranging the above formula:

μs = Fs (max)/ Fn

### Experiment for Measurement of Coefficient of Static Friction of Long Human Bones

The measurement for the coefficient of static friction for bone-to-bone joining surfaces has been done. Unembalmed human cadaver tibia and femoral bones had been reduced with 3 forms of surgical saw, energy pushed, and one hand detained. The static friction turned into the decided use of an in vitro shear method. It determined that each form of saw and the form of bone affected the coefficient of friction. Larger coefficients of static friction had been determined with a rough decreasing noticed in addition to tibia bone that is more problematic than femoral bone. The results instruct that a difficult surface end to decrease bone needs re-establishment in a well-decreased fracture by stabilizing the fracture interface.

## Solved Problem of Static Coefficient of Friction & Calculation

### Coefficient of Static Friction Solved Problem#1

The normal force and the static frictional force of an object are 80N and 90N, respectively. Find the Coefficient of static friction?

Solution:
Given data:
N = 80N,
F = 90N and
μs =?

The formula for the Coefficient of static friction is,
μs = F/N
(now, putting value from the problem into the given equation)
= 90/80
= 1.125
So, the Coefficient of static friction is 1.125.

### Coefficient of Static Friction Solved Problem#2

A teenager attempts to push a 15-kg rubber box horizontally along a rubber floor. The static friction coefficient is 1.16. What is the maximum force the teenager can use ​without​ the box moving at all?

Solution:
Given data:
μs = 1.16
m =15-kg
Fs =?

Fg = mg​ where ​Fg​ is the force of gravity, ​m​ is the object’s mass, and ​g​ is the acceleration due to gravity on Earth.
FN
= Fg = mg​
(as we already know, the value of g which is 9.8)
FN ​= Fg ​= 15 × 9.8 = 147 N

Now, solve for Fs with the equation above:

Fs​ = μs ​× FN ​= 1.16 × 147 = 170.52 N

So, the Coefficient of static friction is 170.52.

## Kinetic or Sliding Coefficient of Friction

### Definition of Kinetic Coefficient of Friction

The kinetic or sliding Coefficient of friction is the Coefficient of friction that applies to items in movement. This Coefficient of friction is the measure of the quantity of friction present for substances in motion.

### Kinetic Friction’s Laws

There are four laws of kinetic friction:

• First law: The strength of kinetic friction (Fk) is directly proportional to the normal reaction (N) between two surfaces in connection. (Where μk​ = constant called the Coefficient of kinetic friction).
• Second law: Force of kinetic friction is free from the figure and exposed area of the surfaces in contact.
• Third law: It depends upon in contact nature and material of surface(s).
• Fourth law: It is independent of the velocity of the touching object as long as the relative speed between the object and the surface is not too great.

### Equation or Formula of Kinetic Coefficient of Friction

The friction force is well-defined using the equation given below. The frictional force depends on the friction coefficient for the specific type of friction under deliberation. It also depends on the magnitude of the normal force.

The Retarding force between the two moving objects when they are in contact with each other is known as Kinetic Friction. Kinetic Friction Formula is given as:

Fk = μkFn

Also, if the problem involves a horizontal surface and no other vertical forces are acting, i.e., Fn = mg,

Whereas,

• Fk = Force of kinetic friction
• μk = Coefficient of sliding friction or kinetic friction
• Fn = Normal force, equal to the object’s weight
• m = Object’s mass
• g = acceleration due to gravity

Since the unit of the frictional force is the newton (N). Likewise, the Coefficient of kinetic friction will be a unitless quantity.

The equation for static friction is the same. But the exception is that coefficients will be replaced by the static friction coefficient μs and Coefficient of sliding friction or kinetic friction μk. It is thought of as a maximum value since it rises to a definite point, and then if you put more force on the object, it will start moving.

### Mathematical Derivation of Kinetic Friction Formula

We know that the kinetic friction (maximum) is directly proportional to the normal friction, but it is independent of the speed.

Fk (max) ∝ Fn

or Fk (max) = μkFn.

Where μs is the constant for proportionality, and it is known as the coefficient of kinetic friction.

it depends on the nature of the surfaces in contact before sliding, but if we have to find the coefficient of kinetic friction, then by rearranging the above formula:

μs = Fs (max)/ Fn

### Experiment for Determining of Coefficient of Friction for Aluminium

The translational and rotational motions of a cylinder journeying down an immediate incline, which affords a steady linear acceleration, rely on the attitude of inclination. For small angles above the horizontal, unfastened rolling takes place; however, above a vital attitude, rolling and slipping occur. This significant attitude is used to assess the coefficient of friction for metal cylinders progressing over aluminium surfaces. The second inertia is various via strong and annular cylinders, and the aluminium floor is smooth, difficult, or corrugated. The coefficient of friction is proven independent of the instant of inertia; however, it relies on the sort of surface and angle of inclination.

## Units of Coefficient of Friction

As μ is the ratio of force, therefore it has no units.

mathematically,

μ = force / force

= n / n.

= no units.

coefficient of friction is constant for a given pair of surfaces; for each different pair, it has a different value

## How do some objects possess higher coefficients of friction than while others don’t?

Let us understand it by trying to touch different surfaces like sandpaper, glass, steel, wood, etc., and we will feel that a few of the surfaces are even and smoother compared to the others. It is because the rougher surfaces have a tinier projection than the smoother surfaces. Therefore, it affects the coefficient of friction.

## Solved Problem of Kinetic Friction

### Coefficient of Kinetic Friction Solved Problem#1

A boy is playing football. Calculate the kinetic friction now if the friction coefficient is 1.5 and the football is kicked with the force of 280 N?

Solution

Given information,Coefficient of friction μk =1.5,Normal force Fn = 280 N,

By putting the information in the given equation, the Kinetic friction is,

Fk = μkFnFk =1.5×280Fk = 420 N.

So, kinetic energy calculated is 420 N.

### Coefficient of Kinetic Friction Solved Problem#2

A car is traveling at a constant speed with the normal force of 1500 N.  the kinetic friction on this car applied is 700 N. Then figure out the Coefficient of the kinetic friction involved here?

Solution

Given information:
Normal force Fn = 1500N,
Kinetic friction Fk = 700N,

The equation for the Coefficient of kinetic energy is as below:

Fk = μkFn

Now, by rearranging it:
μk = Fk/Fn
(as we are supposed to calculate μk)

Now put values in the rearranged equation:
μk = 700/1500
μk = 0.467.

So, the Coefficient of the kinetic friction = 0.5

## Table or Chart for Coefficient of Friction

Let’s see a table of chart of Coefficient of static & kinetic Friction as follows:

## Working With Inclined Planes (for Both Static & Kinetic Friction)

When an object rests on a horizontal surface, there’s a standard force supporting it equal in magnitude to its load. Until now, we dealt solely with normal force in one dimension, with gravity and normal force acting perpendicular to the surface in opposing directions (gravity downward and normal force upward). Currently, that you can figure out the forces in two dimensions, we can explore what happens to weight, and therefore the normal force on a canted surface can be seen as a simple machine. For inclined plane problems, it’s easier to break down the forces into their parts if we rotate the coordinate system. The primary step when setting up the problem is to break the force of weight into components.

Figure: The diagram shows perpendicular and horizontal components of weight on an inclined plane.

When an object rests on an incline that produces an angle θ with the horizontal, the force of gravity working on the thing is split into 2 components: A force acting perpendicular to the plane, w⊥ and a force acting parallel to the plane, w||. The perpendicular force of weight, w⊥, is often equal in magnitude and opposite in direction to the conventional force, N. The force acting parallel to the plane, w||, causes the object to accelerate down the incline. The force of friction, f, opposes the object’s motion. Thus, it acts upward on the plane.

It is vital to use caution once resolving the load of the thing into elements. If the angle of the incline is at an angle θ to the horizontal, then the magnitudes of the weight components are

w||=wsin(θ)=mgsin(θ)
and
w
=wcos(θ)=mgcos(θ)

Instead of learning these equations, it is helpful to be able to determine them from reason. To do this, draw the right triangle shaped by the three weight vectors. Note that the angle of incline is similar to the angle shaped between w and w⊥. Knowing this property, you can use trigonometry to determine the magnitude of the weight components

cos(θ)=w/w
w
=wcos(θ)=mgcos(θ)

sin(θ)=w||/w
w||=wsin(θ)=mgsin(θ)

## Application of Coefficient of Friction or Friction in Daily Life

Following are the few applications of friction in our daily life:

• Driving an automobile on a surface.
• Applying brakes to stop a moving automobile.
• Skating.
• Walking on the road.
• Writing on the notebook/chalkboard.
• Flying a plane.
• Hit a nail in the wall.
• Slide on a garden slide.
• Light a match.
• Remove dust from a carpet by tapping it with a stick.

## Advantages of Coefficient of Friction or Friction

Friction plays a vital role in our daily life. Without friction, we are handicapped.

• It becomes problematic to walk on a slippery road/surface if friction is not as much. When we move on the ice, it becomes difficult to walk on it because of less friction.
• We wouldn’t have been able to hit a nail on the wood or wall if there wasn’t any friction. It is friction that grips the nail.
• A horse couldn’t pull a cart until friction provided the horse a protected position.
• We can write on paper or a board due to the presence of friction.
• Friction assists in applying the brakes.
• It aids in walking on the floor.
• The coffee cup stays on the board.
• Crawl on a carpet to meet someone.
• Dragging the atmosphere with the Earth is possible.
• Help prevent life on Earth by burning asteroids.

## Disadvantages of Coefficient of Friction or Friction

Even though friction is significant in our daily life, it also has some drawbacks, which are described below:

• The foremost disadvantage of friction is that it generates heat in many machines, valuable as thermal energy.
• Due to friction, we have to use more force in the machines.
• Friction also creates noise in machines.
• Due to friction, engines of automobiles consume more fuel which is a money loss.
• Machine efficiency is decreased: energy input is lost to heat.
• Getting shocked by door knobs.
• Rugburn.
• It counteracts movement and therefore requires more energy to move, can cause unwanted heat (e.g., on machine parts), and wears out things like shoes.
• Forest fires are caused by friction between branches.

## Conclusion

Friction’s coefficient, the proportion of frictional force, resists the movement of two surfaces in contact with the normal force that cooperates the two surfaces. It is symbolized by the Greek letter ‘μ’ (mu). Mathematically, μ = F/N, where ‘F’ is the frictional force and ‘N’ is the normal force. The Coefficient of friction depends only on the nature of the surfaces; it does not depend on any other factor, including the relative speed of the surfaces and the area of ​​the contact area. The equation being used for the Coefficient of friction is as follows:
μ = FF / FN

There are two classes of coefficients of friction; one is static Coefficient of friction, and the other is kinetic or sliding Coefficient of friction. The static Coefficient of friction is the Coefficient of friction that applies to immovable items. Static friction exists between the surfaces on which the article is resting and a stationary object.

The kinetic or sliding Coefficient of friction is the Coefficient of friction that applies to items in movement. This Coefficient of friction is the measure of the quantity of friction present for substances in motion. The Kinetic Friction Formula is given as Fk = μk × Fn.

As described earlier, friction plays a crucial role in our daily lives. Few friction applications are skating, walking on the road, sliding on a garden slide, lighting a match stick, etc. The advantages we get from friction are that walking on wet roads or ice is much easier because of low friction; friction assists in applying the brakes. On a larger scale, friction helps prevent life on Earth by burning asteroids. Due to friction, we have to use more force in the machines, and it also creates noise in machines; due to friction, engines of automobiles consume more fuel which is a money loss; the friction causes forest fires also. Therefore, friction has many advantages as well as disadvantages. They are discussed thoroughly in the above sections.

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