# Friction Formula

## 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.

• ### Fluid Friction

The friction that occurs between the layers of fluid as they are moving relative to each other is known as fluid friction.

### 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 slide 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.

Ans: 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.

Ans: 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 ploughing through the softer surface.

1. What is Static Friction and Write its Formula?

Ans: 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?

Ans: 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?

Ans: The three main causes of friction are: