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# Friction Formula Last updated date: 08th Dec 2023
Total views: 281.1k
Views today: 7.81k     Friction can be defined as that force which offers resistance to two surfaces that are moving against each other. It is mainly due to the intermolecular or IM attractions that occur between the particles of the two adjoining surfaces. There are different types of this force namely static, sliding, rolling and fluid. Let us understand this in detail.

Static friction occurs when an object starts to move which means that for such friction to occur the object has to overcome the static force friction and start moving. Sliding friction occurs when an object moves on the surface of the other object present. This is called ‘slide’. This results in opposing the movement or slide of the two objects. Additionally, rolling friction occurs when an object rolls on another surface or object. Lastly, fluid friction occurs when a fluid exerts a friction force on the object. It can either be air friction where the medium of travel is air or it can be viscous friction where the medium is water.

There are some variables on which the friction depends on. The first one is the normal force or. It is the force between the adjacent surfaces that slide against each other. Second, it depends on the coefficient of Friction which is denoted by µ. It gives us the nature of the surfaces that slide against each other.

### What is the Friction Formula?

Friction is the resisting force that prevents rigid surfaces, fluid layers, and material elements from slipping against each other from moving in the same direction. Friction between two surfaces transforms kinetic energy into thermal energy, or work to heat, as they shift relative to each other. Friction is beneficial and essential for providing traction and facilitating movement on the ground. For acceleration, deceleration, and changing direction, most land vehicles depend on friction. Sudden traction failure can result in a loss of control and an accident.

### Types of Friction

There are four types of friction:

### Static Friction

Between a stationary object and the surface on which it is resting, static friction occurs.

### Sliding Friction

When two things slide against each other, sliding friction occurs.

### Rolling Friction

The resistive force that slows the motion of a moving ball or wheel is known as rolling friction. It's often referred to as rolling resistance.

### Friction Force Formula

Consider a solid block resting on a horizontal surface. When a force of ‘P’ is applied to the block, the block does not move along the force applied. This is because the frictional

force is more than the applied force which balances the solid block. Here the frictional force also increases accordingly when the applied force is increased. Once the applied force reaches more than the frictional force then. The solid block slides over the horizontal surface. This force when the body begins to move is called limiting friction.

This friction is called static friction because one body is sliding over the other which is stationary.

To derive the static friction force formula we have to consider all the forces acting on the body.

The static friction equation or the coefficient of friction formula or force of friction equation is given as follows

Here the static frictional force is directly proportional to the normal force acting on the body.

F α N

F = μN

Where F is the maximum force of static friction.

N is the normal force which is equal to the mass of the body multiplied by the acceleration due to gravity.

N = mg

μ is the coefficient of friction.

### Rolling Friction Formula

Consider a ball placed on the flat horizontal surface. When a ball is given a motion to move forward the frictional force from the ground makes the ball stop. This friction is known as rolling friction.

The rolling friction formula or the coefficient of friction formula for rolling is given as follows

F = Crr N

Where F is the rolling resistance force.

Crr is the dimensionless rolling resistance coefficient or the coefficient of rolling

friction (CRF).

N is the normal force that is the force perpendicular to the surface on which the ball is rolling.

### Friction Force Formula for an Inclined Plane

Consider a mass m that is lying on an inclined plane. If the mass is moving down the plane, the frictional force F will act up the plane.

The friction formula or the coefficient of friction equation or angle of friction formula is given as follows:

F = μN

Where F = Frictional force.

N = normal force exerted on the body by the plane due to the force of gravity = mg Cos θ

μ = coefficient of

friction = tan θ

θ = Angle of inclination of the plane over the body slides.

The optimum value of θ for static friction can be obtained by steadily rising θ until the mass begins to move. This is known as the limiting angle of repose.

### Problems on Friction Formula

1) A boy pulls a body of mass 50Kg resting on a flat horizontal surface. Calculate the frictional force if the coefficient of friction is 0.3.

Here it is given that mass of the body m = 50Kg and coefficient of friction =0.3

The friction formula is given as

F = μN

Here N is the normal force given by the formula

N = mg

g is the acceleration due to gravity = 9.81 m/s2

So N = 50 × 9.81 = 5395.5

Kgm/s2 = 5395.5

N , Now substituting the values in the friction formula we get the required frictional force

F = 0.3 × 5395.5 = 1618.65 N

2) A boy is rolling a ball over the flat horizontal surface. The mass of the ball is 10 Kg and the coefficient of rolling friction 0.2. Calculate the rolling resistance force.

Here the

mass of the ball is m = 10 Kg

Coefficient of rolling friction, Crr = 0.2

The rolling resistance force is given by the formula

F = Crr N

Here N is the normal force of the body which is given as N = mg

Here g is the acceleration

due to gravity = 9.81 m/s2

N = 10 × 9.81 = 98.1 Kgm/s2 = 98.1 N.

Substituting the values we will get the required rolling resistance force

F = 0.2 × 98.1 = 19.62 N

### Conclusion

The friction force prevents one rigid object from slipping or rolling over another. Frictional forces, such as the traction required to walk without falling, may be helpful, but they also create significant resistance to motion. Around 20% of an automobile's engine power is used to overcome frictional forces in the moving parts. The forces of attraction, known as adhesion, between the contact regions of the surfaces, which are often microscopically irregular, tend to be the primary cause of friction between metals. Shearing these welded junctions cause friction, as do the irregularities of the rough surface plowing through the softer surface.

## FAQs on Friction Formula

1. What is Static Friction and Write its Formula?

Static friction is the friction that occurs as we attempt to move a stationary object on a surface without necessarily causing any relative motion between the body and the surface it is on.

Static friction equation is given by the formula

F = μN

Where F is the maximum force of static friction.

N is the normal force which is equal to the mass of the body multiplied by the acceleration due to gravity.

N = mg

μ is the coefficient of friction.

2. What is Rolling Friction and Write Its Formula?

When a body rolls on a surface, rolling friction or rolling drag is the force that resists the motion.

The rolling friction formula is given as follows

F = Crr N

Where F is the rolling resistance force.

Crr is the Dimensionless rolling resistance coefficient or the coefficient of rolling friction (CRF).

N is the Normal Force that is the force perpendicular to the surface on which the ball is rolling.

3. What are the Causes of Friction?

The three main causes of friction are:

• Surface roughness

• Plowing effect

4. Give some of the advantages of the frictional force.

• It helps us to walk.

• It is required when we write something on a surface or paper.

• It helps us fix a nail inside the wall.

• If there would have been no friction then an object that is moving will never stop ever.

• It helps us in driving automobiles on the road.

•  It is crucial in the construction of buildings.

5. State some of the disadvantages of friction.

Some of the disadvantages are as follows:

• It results in the wear and tear of the surfaces like the parts of a moving vehicle or the sole of the shoes.

• It leads to heat production which results in a waste of energy.

• Sometimes this force causes the moving object to stop or decrease its speed.

• It sometimes causes noise pollution like it has been observed in the aircrafts when they provide resistance to the air.

6. What are the factors that affect friction?

Some of the affecting factors are as follows:

•  Friction is dependent on the nature of the surfaces that are sliding against each other.

• When there are different surfaces present then the friction is dependent on the smoothness or roughness of the surfaces that are showing the friction force. It occurs less in the smooth surfaces.

•  It is independent of the contact area.

• It also depends on the hardness of the two surfaces that are pressed against each other.

7. When can we observe friction?

We can observe friction in our day-to-day lives. It can be observed when we rub our hands vigorously against each other then there is a production of heat. It can be seen to be the wear and tear of machines’ parts. The friction force decreases the machine’s efficiency as its energy is lost in the friction created. Friction is also observed when we walk or write something. Furthermore, it is necessary for starting or stopping a mechanical action and also for gripping or holding an item with our hands. Thus, friction is present almost everywhere in our daily lives.

8. How can friction be reduced?

It can be reduced by various means. The first way to reduce friction between moving objects is by using grease, powder, oil, ball bearing or some cushion of dry air. Secondly, we can use anti-friction alloys. The friction can be also increased by making the surfaces rough.