How To Find Co-efficient Of Friction: Detailed Explanations And Problem Examples

This article answers the question: how to find coefficient of friction? We all know that the smoothest of surfaces also have some irregularities, but we cannot see them.

If we cannot see them then how will we measure the level of roughness present on the surface? The answers to this question lies in a property of the surface called as co efficient of friction. It gives us an measure of how rough the surface is. In this article we shall discuss about finding co efficient of friction in different situations.

What is friction?

We all are aware of friction and its effect on our lives. The opposing force or the resistance we feel while we push something in the forward direction is called as friction.

Friction is not necessarily bad. Without friction our lives would not be so easy if friction was absent. In this article we will study about friction, co efficient of friction, its uses and its negative effect on our lives.

What is co efficient of friction?

Co efficient of friction is that property of a surface which tells us about how rough the surface is.

We cannot observe the roughness with our naked eyes simply because the irregularities are very minute in nature. We need a property which defines these irregularities. This property is called as the co efficient of friction.

Positive effects of friction

Friction is often considered as bad and undesirable. This is true in many areas but simultaneously friction plays a very important role in our lives too.

The positive effects of friction or advantages of friction are given in the list below-

  • Brakes – Brakes make full use of friction to stop the car from moving. The brakes allow the tyres to mesh with the irregularities on the surface of roads. This way the car stops from moving. Without friction it would have been difficult to drive on roads and accidents would be prevalant more often.
how to find coefficient of friction
Image: Disc brake on two wheeler

Image Credits: anonymous, Disc brakeCC BY-SA 3.0

  • Walking – A simple task such as walking also needs the help of friction. Considering a friction less surface to walk on, a man would simply slide if he starts walking. This is because he does not have a proper grip with the floor. A proper surface for walking is that surface which is not slippery and has better grip.
  • Running – Running is a successor to walking. Running also needs friction as a friction less and slippery floor would simply lead to accidents. Accidents that can be fatal too.
  • Gear meshing – Gears have teeth protruding outside the wheels which are meshed with the teeth of other gear. The gears transmit the motion of one wheel to other, this way the gears perform their function with the help of friction.
  • Driving – Driving a car or bicycle needs friction as friction provides a better grip and forward reaction force on the wheels. We all have seen how cars are difficult to drive on slippery roads, this is because water lubricates the road making it more frictionless.
  • Holding a book – Holding a book or let say any object needs grip. This grip is provided by friction. Grip is nothing but the irregularities meshing with each other.
  • Holding a pencil – Similar to holding a book, holding a pencil is also a perfect example of use of friction.
  • Rolling a ball– Rolling a ball does not mean the ball will keep rolling till eternity. The ball comes to rest after some time. This is possible due to friction present in the system.

Negative effects of friction

We all think friction is not desirable. This is true when it comes to places where we require as maximum as possible work from the system. The places where friction acts as a slack are given below-

  • Heat generation while braking – The generation of heat in tyres will wear of the rubber present in the tyres. The tyres will become flat and will ask for maintenance. Generation of heat is not desirable during hot weather as the damage will be more.
  • Heat generation while running of machines – Heat generation in machines means some amount of fuel is used in generating heat that is of no use. Hence utmost care is taken to lubricate machine parts as heat would damage the machines as well as increase the cost of operation.
  • Slowing down of objects due to friction – Sometimes we tend to push the object to a farther distance but friction makes it stop before it reaches the destination. Hence we need to apply more force while pushing the object so that it gains enough velocity to reach the destination without any stops.
  • Pipe flow– A fluid in pipe slows down due to friction taking place between the surface of pipe and fluid. This makes a major loss in pumps as they need to push the water with more force so that it covers up losses due to friction.

How to find coefficient of friction with mass and force

Mass of an object is respinsible for weight that is mass combined with gravitational pull gives rise to weight. The frictional force acts on the object by the virtue of the its roughness.

To calculate co efficient of friction with the help of these quantities, following equation is used-

u= F/N

Where F is the force of friction

N is the normal reaction force which is equal to the weight of the object.

How to calculate co efficient of friction with acceleration

Acceleration of an object arises only when the object is moving. When the object is moving, kinetic friction comes into play.

The kinetic friction is a constant term and cannot change with any change in speed of the object. Even if the body is accelerating, the magnitude of kinetic friction acting on the body will be same. If the magnitude of kinetic friction also increases then acceleration would not be possible. The object would not be able to speed up. Mathematically, kinetic friction is given by-

u= F/N= ma/mg= a/g

Here the force is equal to the force required for the object to keep moving

How to find co efficient of friction between two materials

The co efficient of friction can be calculated using the same formula that is F/N. To find the co efficient of friction between two materials, we perform the following steps-

  • Let there be two objects rubbing against each other. These two objects are object A and object B.
  • When these two objects rub against each other, they attain a certain velocity, let us consider object B stationary and object A moving
  • To make the object A moving at that velocity, a force F is required.
  • Due to the weight of the object, there is a reaction force acting on object B written as R.
  • To find the co efficient of friction between these materials, we divide the force, F by the reaction force R.

This way the co efficient of friction is calculated between two materials.

How to calculate co efficient of friction with velocity and distance

We can find the value of co efficient of friction using velocity and distance.

The work done is given by F.s.

Force required to do work = F = force due to friction = umg

Hence force required to stop the object = umg.s

This equals kinetic energy, that is KE = O.5 mv^2

Hence, u = (v^2/2g)

How to find co efficient of friction between two surfaces

No surface is ideally smooth. It will have some amount of roughness in it. To find the amount of roughness we need to define a property called co efficient of friction.

The co efficient of friction between two surfaces can be found using the same method we discussed for finding the co efficient of friction for two materials. The fundamental formula of the co efficient of friction being the same that is, u = F/N

How to find co efficient of friction with energy

We already discussed in the above section that kinetic energy can be equated with the work required to stop the object from moving.

From the above equality, we can find the valueof co efficient of friction. Let us see again how we found co efficient of friction with the help of energy.

Kinetic energy- 1/2 mv^2

Work required to stop the object from moving- umg.s

Equating both the sides, we get u = v^2/2g

How to find co efficient of friction with centripetal force

The centripetal force is given by- Fc= mv^2/r

The frictional force acting on the object is given by – umg

Equating both the sides we will get,

u= v^2/rg

How to find co efficient of friction with only angle

When the object moves at an inclined plane. The effect of angle comes into play. For an inclined plane we resolve the forces into horizontal forces and vertical forces.

The co efficient of friction is given by u = F/N

After resolving, we get, u = mgsinA/mgcosA

A is the angle at which the plane is inclined.

After solving we get, u = tanA

This way we can find co efficient of friction using only angle.

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