 ## Work, Energy and Power

Subject: Science

#### Overview

Work is said to be done when the body moves through a distance when a force is applied to it. The capacity or ability to do work is called energy. The rate of doing work is called power. This note provides information about work, energy and power with activities.

### Introduction

We perform various types of work in our daily life. To perform work, we need energy. We cannot do work without energy. Work is said to be done when the force acts upon an object to cause a displacement. Energy is the capacity of doing work. Energy and work are measured in terms of a joule (J). Power is defined as the rate at which work is done upon an object. Power is related to how fast a work is done. The unit of power is watt (W) which is joule/second.

### Energy

We need the energy to perform daily activities in our life. Food and respiration provide us energy. Energy is the capacity or ability to do work. The SI unit of energy is joule and in CGS system, it is erg. It has the only magnitude so it is a scalar quantity. Kinetic energy, potential energy, heat energy etc are some of the examples of energy. To calculate the amount of energy, we use the formula of work as the magnitude of energy is equal to the magnitude of work done.

There are various types of energy, which are as follows,  #### Mechanical Energy

The energy possessed by a body when the body is at rest or in motion is called mechanical energy. There are two forms of mechanical energy. They are given below,

Kinetic Energy

Kinetic energy can be defined as the energy possessed by a body due to its motion. It is a scalar quantity. All the objects in motion have kinetic energy whether it is in vertical or horizontal motion. There are various forms of kinetic energy like vibrational energy, rotational energy etc. Flying an aeroplane, travelling car, flowing river, falling asteroid etc. possesses kinetic energy.
If ‘m’ is the mass of the moving body and ‘v’ is the velocity at which the body is moving then kinetic energy of the moving body is given by,
Kinetic energy (KE) = $\frac{1}{2}$ mass $\times$ (velocity)2
Or, KE = $\frac{1}{2}$ m $\times$ v2
This equation reveals that kinetic energy of a moving body is directly proportional to the product of mass and square of the velocity of a body.

Potential energy

Potential energy is the energy stored in a body at rest. Chemical energy from a battery is a potential form of energy, elastic energy in a stretched rubber band is a form of potential energy, but the most commonly referred to the form of potential energy in physics is that of gravitational potential energy. This energy is stored due to the object’s position.
Potential energy of a body can be calculated by the following formula,
Potential energy (PE) = m $\times$ g $\times$ h
Where,
m = mass of the body
g = acceleration due to gravity whose value is 9.8m/s2
h = height of the object
$\therefore$ PE = mgh

#### Heat energy

Heat is the form of energy which gives the sensation of warmth to us. It is obtained from hot bodies. Sun is the main source of heat energy. Heat energy can also be obtained from the burning of fuels like petrol, diesel, etc.

#### Sound energy

A sound is a form of energy which gives the sensation of hearing. It is produced due to the vibration of a body. It cannot travel through the vacuum. Some examples of sources of sound energy are a loudspeaker, radio, drum, noise etc.

Activity
Bring a guitar. Play the string of the guitar. What do you observe while playing while playing the guitar? What do you conclude from this activity?

#### Light Energy

Light is a form of energy which gives the sensation of vision. Sunlight is the main source of light energy which is used by all the living organisms of the earth. The burning of fuel like coal, petrol, etc also produce light energy.

Activity
Bring a plant in a pot. Then put the plant in a place where there is sunlight for 2- 3 days. Now, put the plant inside the house where there is no sunlight for next 2- 3 days. What do you observe? What do you conclude from this experiment?

#### Chemical Energy

Chemical energy is the energy stored in chemicals. It is produced due to the chemical change of a substance. Since chemical energy is a stored energy, it is also the form of potential energy. Battery, food, petroleum, biomass, etc. are some of the examples of stored chemical energy.

#### Nuclear Energy

The energy which is obtained through the nuclear reaction whether through nuclear fission or nuclear fusion is called nuclear energy. The energy obtained through the sun is a type of nuclear energy. Nuclear energy produces a large amount of heat, light and sound energy. When a nuclear bomb is exploded then it produces a large amount of heat, light and sound energy.

#### Electrical energy

Electrical energy is a form of energy produced by the moving electric charges. It can be easily converted to the other form of energy like heat energy, light energy, sound energy etc. Electrical energy is used in various types of work. In a car battery, the chemical reaction creates an electron which has the energy to move in an electric current. These moving charges provide electrical energy to the circuits in the car.

Activity
Bring a battery and the radio. Then placed the battery inside the radio and listen to the radio. What do you observe from this activity? What do you conclude from this activity?

#### Magnetic energy

Magnetic energy is the energy possessed by a magnet. It is the energy within a magnetic field. Magnetic energy is used to produce electrical energy. It is used in various electrical devices like a loudspeaker, telephone, radio etc. It is used in various factories to lift the loads made of magnetic substances.

Activity
Bring the bar magnet and the pieces of iron nails. Then, placed the iron nails near the bar magnet. What do you observe? What do you conclude from this activity?

### Work

We perform various types of activities in our daily life. These all activities are called work. Some of the examples of work are writing, reading, driving, etc. Work is said to be done if the force applied on a body changes the position of the body in the direction of force applied. The SI unit of work is Joule. Since work has the only magnitude without direction, so it is a scalar quantity. Work done is the product of force and displacement that is,
Work done (W) = Force $\times$ Displacement (s)
$\therefore$ W = F $\times$ s
When 1N force displaces a body through 1m in the direction of the force then the work done is said to be one-joule work.

#### Work done

Work done by a force is zero when force is applied perpendicular to the displacement. Sometimes in some cases, work done by a gravity becomes zero. Like, when you move on the ground carrying a load of 5 kg then work done by gravity is zero. But the work done by you is not zero. There are two types of work which are as follow,

Work done against gravity

Gravity is defined as the force of attraction exerted by the earth which pulls all objects towards its centre. When work is done against the earth’s gravity then it is called work done against gravity. Throwing ball upward, lifting water from well, etc. are some examples of work done against gravity.

Work done against friction

The force, which opposes the motion of one body over the other when they are in close contact, is called frictional force. When work is done against friction then it is called work done against friction. Some of the examples of work done against friction are pushing a box of certain mass across the rough surface, pushing vehicles in roads, etc.

Example 1

If a boy applied a force of 100N to displace a box at a distance of 20m then what is the work done by the boy?
Solutions:
We have,
Force applied (F) = 100N
Displacement (s) = 20m
Work done (w) = ?
According to the formula,
w = F $\times$ s
= 100 $\times$ 20
= 20000J
$\therefore$ The work done = 20000J

### Power

Power is defined as the rate of doing work. The SI unit of power is watt (W) which is joule per second. It is a scalar quantity. If ‘w’ be the work done by the body at ‘t’ time then the rate of doing work or power is given by,
Power = $\frac{Work done (w)}{Time\; taken}$
$\therefore$P = $\frac{w}{t}$

If a body takes less time to do some work then the rate of doing work is said to be more and if the body takes more time to do work then the rate of doing work is said to be less.

When 1-joule work is done in 1 second then the rate of doing work is said to be one-watt power.

Horsepower

A horsepower is a unit of measurement of power. The electrical equivalent of one horsepower is 746 watts in the international Systems of Unit (SI). It is mainly used in engineering and is denoted by H.P.

Relationship between watt (W), kilowatt (KW) and megawatt (MW)
1000 W = 1 kW
1000 kW = 1 MW
1 MW = 1000000 W

Example 2

A man does 40J of work in a certain time. If the power of the man is 10 watt then what time does it take to complete work?
Solution:
Given,
Work done (w) = 40J
Power (P) = 10watt
Time taken = ?
By using formula,
P = $\frac{w}{t}$
Or, 10 = $\frac{40}{t}$
Or, 10t = 40
Or, t = $\frac{40}{10}$
Or, t = 4s
$\therefore$ The time of work done is 4 seconds.

Example 3

A man lifts a stone of 100N to a height of 5 metres in 2 seconds. Calculate the work done and power of the man to lift a stone.
Solution:
Given,
Force of stone (F) = 100N
Displacement (s) = 5 metre
Time taken (t) = 2 seconds
Work done (w) = ?
Power (P) = ?
According to the formula,
w = F $\times$ s
= 10 $\times$ 5
= 50 joule
$\therefore$ Work done by a man to lift a stone is 50 joule.
Now,
P = $\frac{w}{t}$
= $\frac{50}{2}$
= 25 watt
$\therefore$ The power of man is 25 joule per second

##### Things to remember
• Work is said to be done when the body moves through a distance when a force is applied to it.
•  The capacity or ability to do work is called energy.
• The rate of doing work is called power.
• The energy possessed by a body when the body is at rest or in motion is called mechanical energy.
• Heat is the form of energy which gives the sensation of warmth to us.
• The energy which is obtained through the nuclear reaction whether through nuclear fission or nuclear fusion is called nuclear energy.
• Work done by a force is zero when force is applied perpendicular to the displacement.
• A horsepower is a unit of measurement of power. The electrical equivalent of one horsepower is 746 watts in the international Systems of Unit (SI).
• When 1 joule work is done in 1 second then the rate of doing work is said to be one watt power.
• 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.
##### Videos for Work, Energy and Power

The energy contained by a body at rest or in motion is called mechanical energy. It is the sum of kinetic energy and potential energy. There are two kinds of mechanical energy which are as follows,

• Kinetic energy: water falling from the dam possess kinetic energy.
• Potential energy: water stored in a dam contain potential energy.

The energy of a body in motion is called kinetic energy. For example, energy possessed by moving water is a kinetic energy.
If a body of mass ‘m’ is moving with a velocity ‘v’ then kinetic energy of a body is given by,
Kinetic energy (KE) = $\frac{1}{2}$mass $\times$ (velocity)2
i.e. K.E. = $\frac{1}{2}$ m $\times$ v2
Where,
m = mass of the moving body
v = velocity of the moving body
The kinetic energy of a moving body is directly proportional to the product of the mass and square of the velocity of a body.

The energy stored in or contained by a body at rest is calledpotential energy. Energy stored in a stretched rubber and energy of water stored in a dam are the examples of potential energy.
If a body of mass’m’ is raised to a height ‘h’, the energy contained by the body (PE) is given by,

Potential Energy (PE) = m $\times$ g $\times$ h
$\therefore$ PE = mgh.
Where,
g = acceleration due to gravity whose value is 9.8m/s2.

The form of energy, which gives sensation of warmth, is called heat energy. The two sources of heat energy are sun and heater. Sound is a form of energy that is produced due to the vibration of a body. Any two sources of sound energy are loudspeaker and radio.

The work dine is said to be 1 joule when 1N force can displace a body through 1m distance in the direction of the force applied. The formula relating the work, force and displacement is,
Work (W) = Force (F) $\times$ Displacement (d).

When a porter stands with load on his back, he does not do any work or he is not working. Because in science, to do work, the force applied always should cover a certain distance. But the porter is not covering any distance.

Any six examples of potential energy are given below:

1. The stretched rubber of catapult.
2. Water in a dam.
3. A hammer raised to strike.
4. A compressed spring.
5. A leg lifted to kick a ball.
6. A stone raised at a certain height.

Any six examples of kinetic energy are as follows,

1. Water falling from the dam.
2. A flying bird.
3. A flying airplane.
4. Water moving in a river.
5. Moving vehicles.
6. A fired bullet.

Work is said to be done if a force applied on a body displace the body in the direction of the force. There are two types of work done which are as follows,

1. Work done against gravity
If a work is done against gravity, it is called the work done against gravity.
Examples: lifting water from the well and throwing ball upward.
2. Work done against friction
The wok done against friction is called work done against friction.
Examples: pulling table in the ground and pushing vehicles on the road.

Solutions:
We have,
Force applied (F) = 50N
Displacement (d) = 10m
According to the formula,
Work done (w) = F $\times$ d
= 50 $\times$ 10
= 500 joule
$\therefore$ The work done is 500J.

Solutions:
We have,
Force applied (F) = ?
Displacement (d) = 25m
Work done = 5000J
According to the formula,
Work done (w) = F $\times$ d
Or, 5000 = F $\times$ 25
Or, F = $\frac{5000}{25}$
Or, F = 200N
$\therefore$ The effort applied is 200N.

Solutions:
We have,
Force applied (F) = 100N
Displacement (d) = ?
Work done (w) = 2000J
According to the formula,
Work done (w) = F $\times$ d
Or, 2000 = 100 $\times$ d
Or, d = $\frac{2000}{100}$
Or, d = 2
$\therefore$ The displacement of the body is 2m.

Solutions:
We have,
Force applied (F) = ?
Displacement (d) = 25m
Work done (w) = 2500J
According to the formula,
Work done (w) = F $\times$ d
Or, 2500 = F $\times$ 25
Or, F = $\frac{2500}{25}$
Or, F = 100N
$\therefore$ The force applied is 100N.

Solutions:
We have,
Work done (w) = 5000J
Time taken (t) = 50 seconds
Power (P) = ?
By using formula,
Power (P) = $\frac{ Work done (w)}{ Time taken (t)} Or, P = \(\frac{w}{t}$
Or, P = $\fract{5000}{50}$
Or, P = 100 watt
$\therefore$ The power of the man is 100 watt.

Solutions:
We have,
Work done (w) = 2000J
Time taken (t) = 50 seconds
Power (P) = ?
By using formula,
Power (P) = $\frac{ Work done (w)}{ Time taken (t)} Or, P = \(\frac{w}{t}$
Or, P = $\fract{2000}{50}$
Or, p = 40 watt
$\therefore$ The power of the men is 40 watt.

Solutions:
We have,
Work done (w) = 2500J
Time taken (t) = ?
Power (P) = 50 watt
By using formula,
Power (P) = $\frac{ Work done (w)}{ Time taken (t)} Or, P = \(\frac{w}{t}$
Or, P = $\fract{2500}{t}$
Or, 50 = $\fract{2500}{t}$
Or, t = $\fract{2500}{50}$
Or, t = 50 seconds
$\therefore$ The time taken is 50 seconds.

Solutions:
We have,
Work done (w) = ?
Time taken (t) = 12 seconds
Power (P) = 60 watt
By using formula,
Power (P) = $\frac{ Work done (w)}{ Time taken (t)} Or, P = \(\frac{w}{t}$
Or, 60 = $\fract{work done }{12}$
Or, Work done (w) = 60 $\times$ 12
Or, Work done (w) = 720 joule

$\therefore$ The work done is 720 Joule.

The differences between power and energy are given below,

 Energy Power The capacity of doing work is called energy. The rate of doing work is called power. The SI unit of energy is joule (J). The SI unit of power is watt (W). Energy of the body is measured by the total work done by the body. Time is not considered. Power is measured by work done in unit time.

The differences between potential energy and kinetic energy are given below,

 Potential energy Kinetic energy The energy possessed by a body in rest is called potential energy. The energy possessed by a body in its motion is called kinetic energy. The potential energy of the body depends on its mass, height and change in condition. The kinetic energy of a body depends on its mass and speed. Example: stretched rubber Example: a hammer striking a nail.

The differences between work done and energy are given below,

 Work done Energy Work is said to be done when a body moves in the direction of the applied force. The capacity of doing work is called energy. It is mathematically written as Work done (w) = Force (F) $\times$ Displacement (d). It is either given as K.E = \(\frac{1}{2}mv2 or P.E = mgh. For example,when aboy is displaced (d) from one position to another by applying force (F). For example, sound energy, mechanical energy, kinetic energy, etc.

The ability or capacity to do work is called energy.
The energy possessed by a body at rest is called potential energy.
Heat energy is a form of energy which gives sensation of warmth to us.
Sound energy is a form of energy which gives sensation of hearing.
Light energy is a form of energy which gives sensation of vision.
The energy possessed by a magnet is called magnetic energy.
The energy produced from the chemical reaction of a substance is called chemical energy.
Power is defined as the rate of doing work.
When 1N force displaces a body through 1m in the direction of force is called 1 joule work.
The energy which is obtained through nuclear fission or nuclear fusion is called nuclear energy.
The SI unit of power is watt (W).
Electrical energy can be defined as the energy produced due to the continuous flow of electrons through a conductor.
Work is said to be done if a force applied on a body displaces the body in the direction of the force.
Any two sources of heat energy are sun and petroleum.
The rate of doing one joule work in one second time is called one watt power.
Any two sources of sound energy are loudspeaker and radio.
The energy possessed by a body in motion is called is called kinectic energy.
If the work is done against the frictional force then it is called work done against friction.
Any two examples of work done against gravity are lifting bag from the ground and lifting water from the well.