 ## Force and Motion

Subject: Science

#### Overview

There are various types of force like pulling force, pushing force, etc. This note provides information about types of pulling force with activities, distance, and displacement, scalar and vector quantity and acceleration.

### Introduction

We do various types of works in our daily life like kicking a football, pressing something, twisting rods, playing cricket, pulling and pushing, lifting water from the well, etc. If we want to shift our table or anything from one place to another place then, we either push or pull the table to maintain in that place. It means that to move any object from one position to another position, that object has either to be pulled or pushed. This pushing and pulling of a body is known as force. It can also be defined as the pull or push which changes or tends to change the position (either rest or motion) of a body. It can change the state of the body. The SI unit of force is Newton (N) and the CGS unit is dyne. It has both magnitude and directions.

#### Types of force

Pulling force:
We use force to pull a table from one place to another. We pull rope towards us while playing tug of war. Similarly, while pulling Machhindranath chariot in Newari festival in Nepal, a force is used. This force is known as pulling force. It is the force that pulls or tries to pull an object.   Source: www.mstworkbooks.co.za Fig: Pulling Force

Activity 1
At first, bring a board cleaning duster and a brick. Then pull the duster by using spring balance and note down the reading shown by the spring balance. After this, pull the brick by using spring balance and also note down the readings shown by the spring balance. Find out the difference between the force required to pull duster and the brick.
The magnitude of the force shown by the spring balance is the force required to pull duster and brick.

Pushing force:
We use force to push our vehicles if it stops working. To push a cart a fruitier uses a force. To open the window we use a force. Such force is called pushing force. It is the force that pushes or tries to push an object.

Activity 2
Bring a table and a chair. Then, push the chair and table separately. Find out the difference between the force required pushing the chair and the table. What do you conclude from this activity?

Centripetal force and Centrifugal force:
When a body moves in a circular path, it experiences two types of force on it, the force that acts towards the centre is called centripetal force while the force that acts away from the centre is called centrifugal force. For an example, when an aeroplane flies in a circular motion then it slightly bends towards the centre due to the centripetal force.

Activity 3
Ride a bicycle in a circular motion. During the ride, you will bend towards the centre and the mud fly off tyres of your bicycle while riding. What is the reason behind it?

Gravitational force:
A special type of force in the universe or planets of the solar system which causes the planets to revolve around the sun in its own orbits. The moon also revolves around the earth due to the presence of force. This force is known as gravitational force. It is the force that acts between any two objects because of their masses. Similarly, if we throw something up in the sky, it returns back to the earth after few seconds due to the force of attraction exerted by the earth that pulls all object towards its centre which is known as gravity.

Activity 4
Take your eraser and throw it towards the sky. What do you observe? After some time, the eraser returns to the ground. What is the reason behind it?

Magnetic force:
It is the force of attraction exerted by the magnets. For examples when we bring the things like iron, cobalt, nickel etc near the magnets then they are pulled towards the magnet due to the magnetic force. It is used to separate iron from mixtures of dust particles and other non- magnetic substances. It is also used to remove iron dust from our eyes.

Activity 5
Take some iron nails and a bar magnet. Then put the nails near the bar magnet. What do you observe? The nails get attached with the bar magnet. What is the reason behind it ?

Electrostatic force:
It is the force exerted by the electrically charged body. It produces electrical force. For examples, when we rub the measuring scale in our dry hair and bring it near the pieces of paper then it attracts the paper towards it. It is due to the development of charges on the scale by rubbing it in dry hair.

Activity 6
Bring the small pieces of paper and a measuring scale. Then, rub your scale on your hair for some time. After this, bring the scale near the pieces of paper and observe it. The paper gets attached to the scale. What is the reason behind it?

Muscular force:
The muscles of the human beings and animals exert pulling and pushing force. This force is known as muscular force. For examples, a lion exerts muscular force for running, jumping, etc. We exert muscular force for kicking ball and lifting water.

Activity 7
Lift two stones of different sizes in your both hand. Then observe the difference in muscles force required to lift the two stones. The force required to lift the small stones is less then the force required to lift the large stone. What is the reason behind it ?

Frictional force:
When two body surfaces are slide just opposite to each other, a special type of force acts upon it or in-between them which opposes the motion of the body. Such force is known as frictional force. Frictional force increases as the weight and the roughness of the body increases. The molecules of the two surfaces in contact attract each other because of the electrostatic force due to which they stick each other at a microscopic level opposing the motion of one another. Friction is also called the necessary evil, as it is both useful and harmful.

Activity 8
At first, bring football and roll it with equal force once on a rough floor or football ground (grass) and later on a smooth surface or basketball court. In which case does the ball stops earlier. What is the reason behind it?

Effects of friction

• It opposes the motion of a body moving on the surface of another body.
• There is heat production when both surfaces rub together.
• Friction causes wear and tear of sole of shoes and tyres

Activity 8
Rub your palms together for a while. What do you feel? What is the reason behind it?

Activity 9
Compare the sole of your old shoes with new one. What do you observe? You will see that the old ones are worn out. What do you conclude from this activity? Source: hebasoffar.blogspot.com Fig: Frictional Force

• It is easy to burn match stick and climb a tree without sliding due to friction.
• We can write and draw due to the friction between pen and paper.
• We can walk freely without sliding and falling due to the friction.
• Vehicles move on roads without skidding due to the friction.

• It reduces the efficiency of machines.
• It slows down the motion of moving part of the body.
• Due to the friction, the sole of our shoes and tyres tears away.
• Due to the friction, noise is also produced in the machine.

Methods of increasing friction

• Grooves are made in the tyres to increase friction that prevents from slipping on the road.
• Spikes are made on the soles of shoes of athletes and mountaineers to increase friction, which helps to stop and run fast without slipping.

Methods of reducing friction

• In machines where possible, sliding friction can be replaced by rolling friction by using ball bearings.
• Proper greasing between the sliding parts of machine reduces the friction.
• The parts of the machine, which are moving over one another, must be properly lubricated by using oils and lubricants of suitable viscosity.
• Friction can be reduced by changing the design of fast moving objects. Streamlined shape reduces friction.

#### Distance and displacement

Distance

It is the space or the path between any two points covered by the body. It’s SI unit is a metre. It has the only magnitude but no direction so it is a scalar quantity.
For example, You move from point A to B (3m), B to C (1m), C to D(2m) and D to E (1m). Then total distance covered by you is AB + BC + CD + DE
= 3m + 1m + 2m + 1m
Total distance covered by you from point A to B is 7m.

Displacement

It is the shortest distance between the initial position and final position. It has both magnitude and direction so it is a vector quantity and is measured in metre in SI system.
For example: let us consider the example of distance, If you move directly from point A to B to E instead of moving from A to B to C to D to E, then total distance covered by you will be the shortest distance then 1st one.
Distance covered = AB + BE
= 3m + 2m
= 5m

This shortest distance is the displacement which is in fixed direction.

#### Scalar quantity and vector quantity

Scalar quantity

These are those physical quantities that are fully described only a magnitude (or numerical value) alone. Mass, length, time, distance, area, volume, etc are some examples of a scalar quantity. Mass have magnitude but it does not have direction, so it is a scalar quantity.

Vector quantity

These physical quantities are described by both magnitude and direction. Displacement, velocity, acceleration, force, etc are some examples of the vector quantity. Force has magnitude as well as the direction of where it is applied, so it is a vector quantity.

#### Speed and velocity

Speed

It is the distance covered by the body in per unit time. It has both magnitude and direction. It’s SI unit is metre per second i.e. m/s. It is calculated by:
Speed =$\frac{Distance\; travelled (s)}{ Time\; taken (t)}$

Fast moving objects covered a large area in less time then slow moving objects. The speed of fast moving object is calculated in terms of km/sec
For example : If the motorbike travels distance of 200km in 2hour then the speed of motorbike is
Solution;
We have,
Distance covered: 200km ( 200 $\times$ 1000)m = 200000m)
Time taken: 2 hour (2$\times 60 \times 60$ seconds = 7200 seconds
Speed: ?
By using speed formula,
Speed = $\frac {Distance \;travelled (s)}{ Time \;taken (t)}$
= $\frac{200km}{2\; hour}$
= 100km/hour
Hence the speed of motorbike is 100km/hour
In meter per second,
Speed = $\frac{s}{t}$
= $\frac{200000m}{7200s}$
= 27.78m/sec

Velocity

It is the displacement per unit time. It has both magnitude and direction. It has both magnitude as well as direction. It’s SI unit is metre per seconds. It is calculated by the given formula:
Velocity = $\frac{Displacement (s)}{ Time taken (t)}$

For examples: If the motorbike travels from point A to B in a fixed direction and covers a distance of 50 km in 55 minutes. Then the velocity of car is given by,
Solution:
We have,
Distance covered: 50km = 50$\times$ 1000 m = 50,000m
Time taken: 55 minutes = 55$\times$ 60 seconds = 3300 seconds
Velocity = ?
By using formula,
Velocity = $\frac{Displacement (s)}{ Time taken (t)}$
= $\frac{s}{t}$
=$\frac{50,000m}{3300sec}$
= 15.15m/sec
$\therefore$ the velocity of motorbike is 15.15m/sec.

Uniform velocity and Variable velocity

Uniform velocity

A body is said to be in uniform velocity if it covers the equal distance in equal interval of time in a fixed direction. It is a vector quantity and is measured in metre in SI system.
Suppose, a cycle is moving from point A to B. It covers 5m in every second. So, it is moving with uniform velocity.

Variable Velocity

A body is said to be moving in variable velocity if it covers the unequal distance in equal interval of time in a fixed direction. It is also a vector quantity and measured in metre in SI system.
Suppose, a cycle is moving from point A to B. It covers the unequal distance in equal interval of time or vice versa. So, it is moving with variable velocity.

Variable velocity

The mean or average value of initial velocity and final velocity of a moving body is called average velocity. It is calculated by:
Average velocity= $\frac{Initial\;velocity (u) + final\; velocity (v)}{ 2 }$
= $\frac{u +v}{2}$
Suppose if the initial velocity of the moving car is 30km/hour and final velocity is 40km/hour. Then its average velocity is given by:
Solution:
We have,
Average velocity= $\frac{Initial\; velocity (u) + final\; velocity (v)}{ 2 }$
= $\frac{u +v}{2}$
= $\frac{30 + 40}{2}$
=$\frac{70}{2}$
= 35km/hour
$\therefore$ The average velocity of the car is 30km/hour.

#### Acceleration

Acceleration is the rate of change of velocity with time. It’s SI unit is metre per second square. It has both magnitude and direction. The change in velocity is described in terms of acceleration. It is the rate at which object changes its velocity. Acceleration is zero when a body moves with uniform velocity as there is no change in velocity. It is calculated by given formula,
Acceleration = $\frac{Change \; in \; velocity }{ Time \; taken}$
= $\frac{ Final \; velocity (v) – Initial \; velocity (u)}{ Time \; taken (t)}$
= $\frac{ v – u}{t}$
Where,
u = initial velocity
v = final velocity
t = time taken

For an example, when a car starts from rest and gains a velocity of 30 m\s in a fixed direction after 10 seconds then its acceleration is given by
Solution:
We have,
Initial velocity (u) = 0
Final velocity (v) = 30m/s
Time taken (t) = 10s
Acceleration = ?
By using formula,
a = $\frac{v\; –\; u}{t}$
= $\frac{30 \;– \;0}{10}$
= 3m/s2

##### Things to remember
• The SI unit of force is Newton (N) and the CGS unit is dyne.
• When a body moves in a circular path, it experiences two types of force on it, the force that acts towards the centre is called centripetal force while the force that acts away from the centre is called centrifugal force.
• The muscles of the human beings and animals exert pulling and pushing force. This force is known as muscular force.
• When two body surfaces are slide just opposite to each other, a special type of force acts upon it or in-between them which opposes the motion of the body. Such force is known as frictional force.
• A body is said to be in uniform velocity if it covers the equal distance in equal interval of time in a fixed direction. It is a vector quantity and is measured in metre in SI system.
• A body is said to be moving in variable velocity if it covers the unequal distance in equal interval of time in a fixed direction. It is also a vector quantity and measured in metre in SI system.
• It includes every relationship which established among the people.
• There can be more than one community in a society. Community smaller than society.
• It is a network of social relationships which cannot see or touched.
• common interests and common objectives are not necessary for society.
 Pushing force Pulling force Pulling force can be defined as the force that pulls or tries to pull an object. Pushing force can be defined as the force that pushes or tries to push an object. Example: horse pulling cart and lifting water from well. Example: throwing stone and kicking football.

The differences between centripetal force and centrifugal force are given below,

 Centripetal force Centrifugal force It is the force that acts towards the centre during circular motion. It is the force that acts away from the centre during circular motion. When there is more centripetal force then centrifugal force, a moving body bends towards the centre. When there is more centrifugal force then centripetal force, a moving body bends away from the centre. Example: a cyclist bends towards the centre during circular motion. Example: mud flying from spinning wheel.

The differences between gravitational force and magnetic force are given below,

 Gravitational force Magnetic force The force that acts between any two objects because of their masses is called gravitational force. The force exerted by a magnet is called magnetic force. This force exists between two heavenly bodies. These force exists between the magnet and magnetic substances. Example: Earth revolves around the sun due to the gravitational force. Example: Iron nails get attached with bar magnet due to the magnetic force.

The differences between distance and displacement are as follows,

 Distance Displacement It is the length of the path covered by the body. It is the moving body in a fixed direction the shortest distance covers it. It is a scalar quantity. It is a vector quantity. It does not have fixed direction. It has fixed direction.

The differences between scalar quantity and vector quantity are as follows,

 Scalar quantity Vector quantity The physical quantity having only magnitude but no direction is called scalar quantity. The physical quantity having both magnitude and direction is called vector quantity. It is described completely by its magnitude. It is described completely by its magnitude as well as direction. Example; volume and area. Example; velocity and acceleration.

The differences between speed and velocity are as follows,

 Speed Velocity The speed of a body is the distance covered by the body per unit time. The velocity of a body is the distance covered by the body per unit time in a fixed direction. It is a scalar quantity. It is a vector quantity. It is calculated by, Speed = $\frac{Distance travelled}{ Time taken}$ It is calculated by, Velocity = $\frac{Displacement}{ Time taken}$

Solution:
We have,
Distance travelled = 500m
Time taken = 30 seconds
Speed = ?
By using formula,
Speed = $\frac{ distance travelled}{ Time taken}$
= $\frac{500}{30}$
= 16.67m/s
$\therefore$ The speed of the car is 16.67m/s

Solution:
We have,
Velocity = 30m/s
Now, the distance covered by bus in 15 seconds is
By formula,
Velocity = $\frac{Displacement}{ Time taken}$
Or, V = $\frac{d}{15}$
Or, 30 = $\frac{d}{15}$
Or, 30 $\times$ 15 = d
Or, d = 450m

$\therefore$ The distance travelled by a bus in 15 seconds is 450metres.

Solutions:
We have,
Initial velocity (u) = 15m\s
Final velocity (v) = 25m\s
Time taken (t) = 5 seconds
Average velocity = ?
Acceleration = ?
By using formula,
Average velocity = $\frac{Initial\; velocity + Final\; velocity}{2}$
= $\frac{u + v}{2}$
= $\frac{15 + 25}{2}$
= 20m/s
Now,
Acceleration = $\frac{Final\; velocity – Initial\; velocity}{Time \;taken}$
= $\frac{v – u}{t}$
= $\frac{25 – 15}{5}$
= 2m/s
$\therefore$ The average velocity is 20m/s and acceleration is 2 m/s2

Solution:
We have,
Acceleration = 10m/s2
Time taken = 5 seconds
Final velocity = ?
By formula, we have
Acceleration (a) = $\frac{Final\; velocity – Initial\; velocity}{time\; taken}$
Or, 10 = $\frac{v – u }{t}$
Or, 10 = $\frac{v – o}{5}$
Or, 10 = $\frac{v}{5}$
Or, 10 $\times$ 5 = v
Or, v = 50m/s

$\therefore$ The final velocity of the bus is 10m/s.

The earth revolves around the sun due to the gravitational force. Gravitational force acts between sun and earth because of their masses. It holds the earth in its orbit around the sun. To balance the gravitational force earth revolves around the sun.

The physical quantity having the only magnitude but no direction is called a scalar quantity and the physical quantity having both magnitude and direction is called vector quantity. Since time has the only magnitude so it is a scalar quantity.

The physical quantity having only magnitude but no direction is called a scalar quantity and the physical quantity having both magnitude and direction is called vector quantity. Since, velocity has both magnitude and direction so it is a vector quantity.

The force which opposes the motion of one body over the other when they are in close contact is called frictional force. The effects of frictional force are as follows,

• Friction always opposes the motion of a body moving on the surface of another body.
• Friction produces heat as both the surface are rub together.
• It causes wear and tear of sole of shoes, tyres and damagemachines.

The advantages of friction are as follows,

• Nails and the screw hold things together due to friction.
• It is easy to write and draw on a paper due to friction.
• Friction helps us to walk in road and ground without falling and slipping.

The disadvantages of friction are as follows,

• The main disadvantage of friction is that it produces heat in various parts of machine. In this way, some useful energy is lost as heat.
• Due to friction we have to exert more power in machines.
• It opposes the motion.
• Due to friction, noise is also produced in machine.
• Due to friction, engines of automobiles consume more fuel which is money less.

The methods of reducing friction are as follows,

• In the machine where possible, sliding friction can be replaced by rolling friction by using ball bearings.
• Proper greasing between the sliding part of the machine reduces the friction.
• Lubricants of suitable viscosity can be used to reduce friction.
• Friction can be reduced by changing the design of the fast moving objects. The front of vehicles and aeroplanes made oblong to minimize friction.

In some cases, friction is useful and in other cases it is harmful and needs to be reduced. Therefore, friction is a necessary evil.

The five types of forces are as follows,

• Gravitational force
• Magnetic force
• Electrostatic force
• Frictional force
• Muscular force

Pulling force can be defined as the force that pulls or tries to pull an object. For example: horse pulling a cart, pulling door to close it.
Pushing force can be defined as the force that pushes or tries to push an object. For examples: kicking football and throwing stone.

The physical quantity having only magnitude but no direction is called scalar quantity. For examples: mass, length, and time.
The physical quantity having both magnitude and direction is called vector quantity. For examples: displacement, velocity, and acceleration.

If a body covers equal displacement in equal interval of time then velocity is known as uniform velocity and a body is said to be invariable velocity if a body does not cover equal displacement in equal interval of time.

The force, which acts between any two objects because of their masses, is called gravitational force. For example, the earth revolves around the sun due to the gravitational force between them.
Gravity is defined as the force of attraction exerted by the earth which pulls all objects towards its centre. For example, fruits fall on the ground due to earth’s gravity.

When an objects moves in a circular path, the force that acts towards the centre is called centripetal force and the force that acts away from the centre is called centrifugal force. To maintain the circular rotation of a body, both centripetal and centrifugal force should be equal.

Force can be defined as the pull or push which changes or tends to change the position (either rest or motion) of a body.
Pulling force can be defined as the force that pulls or tries to pull an object.
Pushing force can be defined as the force that pushes or tries to pull an object.
The force that acts towards the centre when object is in circular motion is called centripetal force.
The force that acts away from the centre during circular motion is called centrifugal force.
The force exerted by muscles of a body is called muscular force.
The force which acts between any two objects because of their masses is called gravitational force.

Gravity is defined as the force of attraction exerted by the earth which pulls all objects towards its centre.

The force exerted by a magnet is called magnetic force.
The force exerted by an electrically charged object is called electrostatic force.
The force which opposes the motion of one body over the other when they are in close ontact is called frictional force.
The shortest distance covered by a moving body in a fixed direction is called displacement.
The speed of a body is defined as the distance covered by the body per unit time.
The mean of initial velocity and final velocity of a moving body is called average velocity.
The rate of change in velocity of a body with time is called acceleration.
The physical quantity having only magnitude but no direction is called a scalar quantity.

The physical quantity having both magnitude and direction is called a vector quantity.

If a body covers equal displacement in equal interval of time then the velocity is called uniform velocity.
It is defined as the velocity of a body when the body cover equal displacement in equal interval of time.

Friction reduces the efficiency of machines.