In this article, we shall understand why does kinetic friction is smaller than the static friction and why it is easier to roll than solid. We shall also study some everyday examples in which friction is used.

To produce relative motion between two bodies in contact with each other we have to apply a larger force, but once the sliding motion begins a smaller force is sufficient to keep one body sliding over the other. This shows that kinetic friction is smaller than the static friction.

If instead of sliding one body rolls over the other, a very small force is required to maintain the rolling motion. This shows that rolling friction is smaller than the kinetic friction. Hence the order of magnitudes is as follows.  Static friction > kinetic friction > Rolling friction

It is Easy to Roll than to Slide:

The origin of the frictional force between two surfaces in contact is due to cold welded joints between the two surfaces at few points on the surface.

To create relative motion additional force is required to break these cold welded joints. This additional force explains the origin of friction and is called a force of friction.

When we are sliding the surfaces one over the other we are shearing the cold welded joints, while when we are rolling the surfaces one over other we are peeling the joints.

During sliding all cold welded joints of the surface should be broken at a time (shearing). While in rolling one line of cold-welded joints is to be broken at a time (peeling). Thus In the process of sheering more force is required than the process of peeling. which clearly indicates that it is always easy to roll than to slide.

Static friction is Greater Than Kinetic Friction:

The origin of the frictional force between two surfaces in contact is due to cold welded joints between the two surfaces at few points on the surface.

To create relative motion additional force is required to break these cold welded joints. This additional force explains the origin of friction and is called a force of friction.

During static friction the surfaces are at rest with respect to each other hence the cold welded joints are stabilised and are strong.

During kinetic friction the surfaces are in relative motion with respect to each other thus the cold welded joints are formed at one instant and broken at the other instant without giving any chance for stabilisation of the cold welded joints. Thus theses bonds are weak. Hence more force is required to overcome static friction than that required in case of kinetic friction. Hence Static friction is greater than kinetic friction

Tyres of Vehicles are Provided With Threads:

The frictional force between the two surfaces depends upon the nature of the surfaces in contact.

The threads of the tyres help to increase friction between the tyre and road.

Due to this, the tyre can get a firm grip on the road and there is no danger of the car running off the road. Hence the tyres of the motor car are provided with threads.

Moving Parts of Machine are Kept Well Oiled:

When energy is supplied to the machine some energy is utilised to overcome the frictional force between the moving parts of the machine. Thus the efficiency of the machine reduces.

The frictional force between the two surfaces depends upon the nature of the surfaces in contact. It also depends on the lubrication between the two surfaces.

The presence of the oil as a lubricant between the two surfaces prevents direct contact between them. It also prevents interlocking of hills and dales on the surfaces of contact. Due to which the friction between the parts of the machine is reduced and the efficiency of machine increases. Hence, The moving parts of the machine are kept well oiled.

Wheels of a Vehicle are Provided with Ball Bearing:

If ball bearing is not used then the force of friction between two parts of the wheel will be that of sliding. This sliding friction is considerable and it causes a significant loss of energy.

If ball bearings are used; the sliding friction is converted into rolling friction, and rolling friction is very small compared to the sliding friction and hence it causes of smaller loss of energy. Hence the wheels of a vehicle are provided with ball bearing to reduce frictional force.

Bearings Used in a Machine are Made of a Different Material:

If two bodies of the same material are in contact with each other; their surfaces in contact have smaller irregularities and therefore the get firmly interlocked. Also, the intermolecular forces of attraction between the two surfaces of the same material are strong. Therefore the friction between the bodies is large.

On the other hand; if two bodies in contact are of different materials; their surface irregularities are dissimilar and hence they cannot get firmly interlocked. Also, intermolecular forces are not very strong hence friction between the bodies is not so large. Hence the bearings used in a machine are made of a different material.

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Friction or force of friction is a force which comes into existence when two bodies in contact have relative motion or tending to have relative with respect to each other and oppose the motion.

Characteristics of Friction:

• Force of friction is always opposites to the force causing the relative motion between the surface.
• Force of friction always acts at the points of contacts of the two surface.
• As the force causing motion increases the frictional force increases up to certain maximum value and that maximum value of the force of friction is called limiting friction.
• The frictional force is independent of the area of contacts.
• The frictional force is independent as nature of surface in contact.
• The frictional force depends on the nature of materials of surface in contact.
• Frictional force depends on lubrication.

Notes:

• Even there is no actual relative motion between the two bodies or surfaces the force of friction comes into play whenever the bodies are kept in contact
• Frictional force always opposes the motion.
• Friction is partially due to unevenness of the surfaces in contact and partially due to molecular attraction between the molecules of the two surfaces in contact.
• If the contact surfaces are made very smooth, it still does not minimise the frictional forces, because in this case the intermolecular forces of attraction increase due to better contact.
• Force of friction is greater in case of two surfaces made of the same material as in this case the forces of attraction between the molecules of the surfaces are cohesive forces which are greater than the adhesive forces.
• Frictional force when the body is at rest or on the verge of motion is called static friction whereas when the body is in motion the frictional force is called the kinetic friction.

Friction a Self-Adjusting Force:

Friction is a force which comes into existence when two bodies in contact have relative motion or tending to have relative with respect to each other and oppose the motion.

When the applied force is zero, the force of friction also equal to zero. If the applied force is slowly increased, the force of friction, in the same proportion up to a particular limit. This force is called the limiting force of friction. Within this limit, the force of friction is exactly equal and opposite to the applied force.

If the direction of the applied force is changed the direction of the force of friction also changes in such a way that it is opposite to the direction of the applied force.

Thus the magnitude and direction of frictional force depend upon the magnitude and direction of the applied force. Hence we can say that the force friction is called self-adjusting force. Hence the force of friction does not have an independent existence. It comes into play only when the applied force produces or tends to product relative motion between two bodies in contact.

Origin of Friction:

Earlier it was assumed that the force of friction between two surfaces in contact comes into existence due to roughness of the surfaces.

When the two surface seems to be in contact actually there is no surface to surface contact. It is due to the fact that irrespective of smoothness of the surface, it contains hills & dales (Projections and depressions). This unevenness of the surface can be observed under a microscope. These surface irregularities have the effect of interlocking the surfaces thereby opposing the relative motion of the two surfaces with respect to each other. This opposition contributes to frictional force in a small extent.

A major contribution to the frictional force can be explained on the basis of molecular theory. Due to hills and dales, there is no surface to surface contact but there is point contact. Due to point contact there exist a very high pressure at contact points. Due to high pressure, the molecules of the two surfaces at the point of contact get cold-welded and thus the bonding exists between the two surfaces in contact.

When the two surfaces in contact tend to have relative motion with respect to each other these bonds or cold-welded and joints do not allow them to so.  To create relative motion additional force is required to break these cold welded joints. This additional force explains the origin of friction and is called a force of friction.

Types of Friction:

There are three types of friction: a) Static friction  b) Kinetic friction  c) Rolling friction

Static Friction:

The frictional force which exists between the two surfaces which are at rest or which are on the verge of relative motion with respect to each other is called the static friction.

Kinetic Friction (Dynamic Friction):

The frictional force which exists between two surfaces in contact having relative motion with respect to each other is called kinetic or dynamic friction.

Rolling Friction:

The frictional force which exists between two surfaces in contact, when one body rolls over the other.

Laws of Static Friction:

• Limiting static friction between any pair of dry unlubricated surfaces is independent of the apparent area in contact.
• Limiting static friction between any pair of unlubricated surfaces depends on nature and material of the surfaces in contact.
• Limiting static friction between any pair of dry unlubricated surfaces is directly proportional to the normal reaction.

If F_S is static friction and R (N) is a normal reaction.

Then, F_S   ∝  R

∴ F_S  = μ_S R

Where,  μ_S = coefficient of static friction.

∴ μ_S  =  F_S /R

The coefficient of static friction is defined as the ratio of the limiting static friction to the normal reaction.

Laws of Kinetic Friction:

• Kinetic friction between any pair of a dry unlubricated surface is independent of the apparent area in contact.
• Kinetic friction between any pair of dry unlubricated surfaces depends on the nature of the material in contact.
• Kinetic friction between any pair of the dry unlubricated surface is directly proportional to the normal reaction.

If F_k is kinetic friction and R (N) is a normal reaction.

Then, F_k   ∝  R

∴ F_k  = μ_k R

Where,  μ_k = coefficient of static friction.

∴ μ_S  =  F_k /R

The coefficient of Kinetic friction is defined as the ratio of the kinetic friction to the normal reaction.

Experiment to verify the law that the limiting force of friction is directly proportional to the normal reaction the two surfaces in contact.

A wooden horizontal plane with a pulley attached to one end is taken and kept on a table. A wooden block is placed on the horizontal surface. A string is tied to the weight and is passed over the pulley and a pan is attached to its free end.

Weight is added to the pan until the block began to slide. The sum of the weight of the pan and the weight put in it is equal to the limiting force of friction. The normal reaction is equal to the weight of the block.

Some weight is put on the block and the procedure is repeated as given above. In this case, the normal reaction is equal to the weight of the block plus the weight put on it. Let us call it R1, Let the corresponding frictional force be f1. The experiment is repeated with different weights on the block. If f, f1, f2, f3, ….. are the frictional forces and R, R1, R2, R3, ….. are the corresponding normal reactions then it is found that

Thus, in general  f/R = Constant

This relation proves that the limiting force of friction is directly proportional to the normal reaction. Thus the law is verified

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In this article, we shall study to solve numerical problems to calculate the magnitude of force, momentum, and change in momentum.

Example – 01:

The speed of a tortoise and hare are 1 m/s and 3 m/s respectively. The mass of the hare is 5 kg while that of tortoise is 20 kg. Which of the two has greater momentum?

Solution:

The momentum of hare = Mass of hare x Speed of hare= 5 x 3 = 15 kg m/s

The momentum of tortoise = Mass of tortoise x Speed of tortoise= 20 x 1 = 20 kg m/s

Thus the momentum of tortoise is more than that of the hare.

Example – 02:

What is the magnitude of force exerted by a horse in pulling a cart of mass 600 kg and accelerating at the rate of 1.2 m/s²?

Given: mass of cart = m = 600 kg, acceleration = a = 1.2 m/s².

To Find: F =?

Solution:

By Newton’s second law of motion, magnitude of force

F = ma = 600  x 1.2

∴ F = 720 N

Ans: The required force is 720 N.

Example – 03:

An object of mass 10 kg is moving with the initial velocity of 10 m/s. A constant force acts on it for 4 s giving it a speed of 2 m/s in opposite direction. Find the acceleration and the force.

Given: mass of object = m = 10 kg, initial velocity = u = 10 m/s, Final velocity = v = – 2m/s (negative since it is in opposite direction), time for which force is acting = t = 4 s

To Find: acceleration = a =? Force acting = F =?

Solution:

a = (v – u)/t = (-2 – 10)/4 = -12/4 = -3 m/s²

The negative sign indicated retardation.

By newton’s second law of motion we have

F = ma = 10 x (-3) = -30 N

Negative sign indicated retarding force.

Ans: The acceleration = 3 m/s² and Force = -30 N

Example – 04:

A constant force of 2 N acts on a body for 5 seconds to change its velocity. Calculate the change in the momentum.

Given: Force acting = F = 2 N, time for which the force is acting = t = 5s.

To Find:  Change in momentum =?

Solution:

Change in momentum = F x t = 2  x 5  = 10 kg m/s.

Ans: the change in momentum is 10 kg m/s.

Example – 05:

An empty truck of mass 1000 kg is moving at a speed of 36 km/hr. It is loaded with 500 kg of material on its way and again moves at the same speed. Will the momentum of the truck remain the same after loading? if not, find the momentum of the truck after loading.

Given: Mass of a truck = 1000 kg, Mass of Load = 500 kg, Speed of the vehicle = v = 36 km/hr = 36 x 5/18 = 10 m/s.

To Find: Momentum of truck = p =?

Solution:

The momentum of a body depends on its mass. In this case, the truck is loaded on the way, hence its momentum should change.

Total Mass = m = 1000 + 500 = 1500 kg

New momentum = Total Mass x Velocity = 1500 X 10 = 15000 kg m/s

Ans: The momentum of the truck after loading is 15000 kg m/s.

Example – 06:

A railway wagon of mass 1000 kg is pulled with a force of 10000 N. What is the acceleration?

Given : Force applied = F = 10000 N, mass of wagon = m = 1000 kg.

To Find:  acceleration = a =?,

Solution:

By Newton’s second law of motion, magnitude of force

F = ma

∴ 10000 = 1000 x a

∴ a = 10000/1000 = 10 m/s².

Ans: The acceleration is 10 m/s².

Example – 07:

A car of mass 1000 kg is moving at a certain speed when a constant braking force 1000 N acts on it for 5 s and speed of the car reduced to half the original speed. Find the further time required to stop the car, if the same constant force acts on it.

Given: mass of car = m = 1000 kg, Force acting = F = 1000 N,time taken =  t = 5 s, Final speed (v) = 1/2 Initial speed (u) = u/2

To find: t =? when v = 0

Solution:

By Newton’s second law of motion, magnitude of force

F = ma

∴1000 = 1000 x a

∴ a = 1000/1000 = 1 m/s².

By the first equation of motion

∴ a = (v – u)/t  = (u/2 – u)/5 = (-u/2)/5 = (-u/10)

∴ a = -u/10 = – 1

∴ u = 10 m/s

We have v = u + at

∴ 0 = 10 + (-1)t

∴ -10 = – t

∴ t = 10 s

Ans: The further time required to stop the car is 10 s

Example – 08:

Find the magnitude of the force applied to a block of mass 5 kg at rest, if it moves 36 m, in first 3 seconds. Neglect the force of friction.

Given: mass of block = m = 5 kg, Initial velocity = u = 0, Distance traveled = s = 36 m, time taken = t = 3 s,

To find: F =?

Solution:

s = ut + 1/2 at²

∴   36 = (0)(3) + 1/2 a(3)²

∴   36 = 1/2 a(9)

∴   72 = a (9)

∴ a = 72/9 = 8 m/s².

By Newton’s second law of motion, the magnitude of force

F = ma = 5 x 8 = 40 N

Ans: The force applied = 40 N

Example – 09:

Two spheres of mass 10 g and 100 g each fall on the two pans of a table balance from a height of 40 cm and 10 cm respectively. If both are brought to rest in 0.1 seconds. Determine the force exerted by each sphere on the pans.

Solution:

For the first sphere: 

Given : m₁ = 10 g = 0.01 kg, h = – 40 cm  = – 0.4 m,  t = 0.1 s, g = – 9.8 m/s²

v² = u² + 2gh

∴  v² = (0)² + 2(-9.8)(-0.4)

∴  v² =  7.84

∴  v = 2.8 m/s

F₁ = m₁a

F₁ = m₁ (v – u)/t  = 0.01 x (2.8 – 0)/0.1 = 0.28 N

For the second sphere: 

Given : m₁ = 100 g = 0.1 kg, h = – 10 cm  = – 0.1 m,  t = 0.1 s, g = – 9.8 m/s²

v² = u² + 2gh

∴ v² = (0)² + 2(-9.8)(-0.1)

∴ v² =  1.96

∴ v = 1.4 m/s

F₂ = m₂a

F₂ = m₂ (v – u)/t  = 0.1 x (1.4 – 0)/0.1 = 1.4 N

Ans: The force exerted by the first sphere is 0.28 N and that by second sphere is 1.4 N

Example – 10:

Calculate the density of a cubical ice block of side 50 cm. If a force of 1125 N applied to it produces an acceleration of 10 m/s² in it. Neglect the force of friction. Assume the ice block remains in solid state without melting.

Given: Force applied = F = 1125 N, acceleration = a = 10 ms-1, Side of a block = 50 cm = 0.5 m

To Find:  Density = ρ = ?,

Solution:

By Newton’s second law of motion

F = m.a

∴ 1125 = m x 10

∴ m = 1125/10 = 112.5 kg

Ans: The density of ice block is 900 kg/m³.

Example – 11:

A ball of mass 50 g at rest is hit by a bat and the ball covers a distance of 400 m, in 2 seconds. If the ball was in contact with it for 0.1 s, find the magnitude of the force acting on it. Assuming no other force acts on a ball after it is hit by the bat.

Given: mass of ball = m = 50 g = 0.05 kg,  time of contact = 0.1 s, distance covered  s= 400 m, time taken to cover the distance = t = 2 s.

To find: Force acting =F =?

Solution:

No other force acts on a ball after it is hit by the bat. Thus it is in uniform motion after hit.

v = s/t = 400/2 = 200 m/s

Now Force, F = ma

F = m (v – u)/t  = 0.05 x (200 – 0)/0.1 = 100 N

Ans: The force acting = 100 N

Example – 12:

A force of 500 N acts on a body of mass 1000 kg and the body is brought to rest within a distance of 64 m. Find the initial velocity and time taken by the body to come to rest.

Given: mass of body = m = 1000 kg, Force acting = F = 500 N, Final velocity = v = 0 ms-1, distance traveled = s = 64m.

To find: initial velocity =u =? time taken = t = ?

Solution:

We have     F = ma

∴   500 = 1000 x a

∴ a = 500/1000 = 0.5 m/s²

As the body is brought to rest a = – 0.5 m/s²

v² = u² + 2as

∴ (0)² = u² + 2(-0.5)(64)

∴ (0)² = u² – (64)

∴ u² = 64

∴ u = 8 m/s

By first equation of motion

v = u + at

∴ 0 = 8 + (- 0.5) x t

∴ 8 = – 0.5 x t

∴ t = 8/0.5 = 16 s

Ans: Initial velocity = 8 m/s, time taken to come to rest = 16 s

Example – 13:

A car of mass 1000 kg is moving uniformly with 10 m/s. If the engine of the car develops an extra linear momentum of 1000 kg m/s. Calculate the new velocity with which the car runs.

Solution:

Given : mass of car = m = 100 kg, initial velocity = u = 10 m/s, Extra momentum = 1000 kg m/s,

To find: Final velocity = v = ?

Initial momentum = p₁ = mu = 1000 x 10 = 10000 kg m/s

Final momentum = p₂ = 10000 + 1000 = 11000 kg ms-1.

Now, Final momentum = p₂ = mv

∴ 11000 = 1000 x v

∴ v = 11000/1000 = 11m/s

Ans: New Velocity = 11 m/s

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Depending upon the interaction between the bodies and level of contact forces are classified a) Contact forces b) Non-contact forces. Muscular force is a contact force. Electrostatic force is non contact force.

Contact Forces:

A force which can be applied only when it is in contact with an object is called a contact force. All mechanical forces are contact forces. The following are the examples of contact force.

Muscular Force: The force resulting due to the action of muscles is known as muscular force. Muscular force can be applied only when it is in contact with the object. For ease, a rope or handle may be used. We use muscular force to different activities using hands like lifting, throwing, catching, etc. We use the muscular force of animals to simplify our work. We use instruments with the help of muscular force. Examples of the use of muscular force are cutting of vegetables or fruits using a knife, hammering of a nail, kneading of the dough, bullocks ploughing in the field, horse pulling a cart, etc.

Friction: The force of friction always acts on all the moving objects and its direction is always opposite to the direction of motion. It always acts a point of contact between the two bodies. i.e. It arises due to contact between the two surfaces. Examples: When a vehicle is moving on a road, there is a force of friction between the surface of the road and tyres at the point of contact. Other examples are a ball rolling on ground stops after some time due to friction between the ball and the ground. If we stop pedaling a bicycle. It stops after some distance. It is due to friction between the road surface and the tyres. It is difficult to slide heavier objects on the ground. After some time the tyres of vehicle wear and tear.

Types Of Contact Forces

There are 6 kinds of forces which act on objects when they come into contact with one another. Remember, a force is either a push or a pull.

• Normal Force: A book resting on a table has the force of gravity pulling it toward the Earth. But the book is not moving or accelerating, so there must be opposing forces acting on the book. This force is caused by the table and is known as the normal force.
• Applied Force: Applied force refers to a force that is applied to an object such as when a person moves a piece of furniture across the room or pushes a button on the remote control. A force is applied.
• Frictional Force: Frictional force is the force caused by the relative motion of two surfaces that come into contact with each other.
• Tension Force: Tension force is the force applied to a cable or wire that is anchored on opposite ends to opposing walls or other objects. This causes a force that pulls equally in both directions.
• Spring Force: The spring force is the force created by a compressed or stretched spring. Depending upon how the spring is attached, it can pull or push in order to create a force.
• Resisting Forces: The air resistance is a special type of frictional force that acts upon objects as they travel through the air. The force of air resistance is often observed to oppose the motion of an object. This force will frequently be neglected due to its negligible magnitude (and due to the fact that it is mathematically difficult to predict its value). It is most noticeable for objects that travel at high speeds (e.g., a skydiver or a downhill skier) or for objects with large surface areas.

Non-Contact Forces:

A force which can be applied without any contact with two bodies is called a non-contact force. The following are examples of non-contact force.

• Magnetic Force: The force exerted by a magnet is called a magnetic force e.g. Like poles of a magnet repel each other, while unlike poles attract each other. These forces exist without contact between the two magnets. e.g. i) Magnet attracts Cobalt, Nickel, Iron and steel towards itself. ii) When two magnets are brought near then South-South, North – North poles repel each other. While North and South pole attracts each other.
• Electrostatic force: The force exerted by a charged body is called an electrostatic force e.g. Like charges repel each other, while unlike charges attract each other. These forces exist without contact between the two bodies. e.g. i) When a comb is run through dry hair, then the comb can attract small pieces of paper. ii) If we bring a charged comb near our hair, they rise towards the comb. iii) A charge is developed on synthetic fibre due to rubbing. iv) We can hear the cracking sound of sparks when taking off or putting on woolen or synthetic clothes.
• Gravitational force: The force exerted by the earth on a body is called gravitational force. Actually this force exists between any two bodies in the universe. This force is always of attraction. e.g. When a body is dropped from a height it moves in a downward direction towards the Earth with increasing speed (with constant acceleration). This constant acceleration by which all bodies fall down is called acceleration due to gravity. Its value is 9.8 m/s² (approx 10  m/s² )on the surface of the earth. e.g. i) A fruit from tree falls down; ii) Water falls down on the ground from a tap. iii) We feel the weight of a bucket full of water holding in our hand.

Force field:

Region or space in which non-contact force such as magnetic force, gravitational force, electrostatic force acts is called force field. The region surrounding a magnet, where magnetic substance experiences force is called the magnetic field. The region surrounding an electric charge, where electric charge experiences force is called the electric field. Thus a field is a sphere of influence of non-contact force.

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