WORK

Definition:

“Work is done when force acting on a body displaces it in the direction of a force”.

Mathematically:

Work is equal to the product of force F and displacement S covered in the direction of force.

Work = Force x Displacement

W = FS

Explanation:

Suppose a force ‘F’ is acting on a body. It makes the body to move from point ‘A’ to ‘B’. If the distance between these two points is ‘S’ then we say that force has done some work as shown in the figure:

If ‘W’ stands for work, ‘F’ for force and ‘S’ for distance.

Then,

Work = Force x Displacement

W = FS

Unit of Work: (LHR 2017)

In System International, its unit is Nm that is also called as joule (J).

Joule:

“The amount of Work done is one joule if a force of one newton displaces a body through one meter in the direction of the force.”

Thus,

1J=1N×1m

Bigger Units:

Joule is a smaller unit of work. Commonly bigger units of work are also in use.

1 kilo joule (kJ) = 1000 J =10³J

1 Mega Joule (MJ) =1000000J = 10⁶J

Quantity:

Work is a scalar and derived quantity.

Conditions:

For work, the following two conditions must be fulfilled:

A force should act on a body.

The body should cover some distance under the action of this force.

Work Done on a Body When a Force Makes an Angle:

Sometimes force and displacement do not have same direction. Here the force F is making an angle θ with the surface on which the body is moved. Resolving F into its perpendicular components ‘F_x’ and ‘F_y’ as shown in the figure:

F_x = F cos θ

F_y = F Sin θ

In case when force and displacement are not parallel then x-component F_x parallel to the surface causes the body to move on the surface and not y-component F_y.

Hence W = F_x S

W = (Fcos θ) S

W = FS cos θ

Dependence:

Work depends upon following factors:

Force: Greater the force greater will be the work done.

Displacement of The Body: Greater the distance covered in the direction of the force greater will be the work done on the body.

Angle: Work done also depends upon angle between force and displacement covered by the body.

CONDITIONS FOR WORK

Following are the conditions for work to be done:

A force should act on a body.

The body should cover some distance under the action of this force.

Work also depends on angle between applied force and displacement covered by the body. For work to be done both applied force and displacement covered should not be perpendicular to each other.

UNIFORM VELOCITY AND WORK DONE

When a body moves with uniform velocity means moving with zero acceleration then work done will be zero because according to Newton’s second law of motion if a = 0 then the net resultant force acting on the body is zero.

As we know that W = FS

If F = 0 then W = 0 x S = 0

ZERO WORK DONE

We know,

W = FS

W = FS cos θ

These equations show that the work done on a body will be zero if:

No net force will act on the body

As

W = FS

W = (0) S = 0

Body will not cover any distance under the action of a force

As

W = FS

W= F (0) = 0

If applied force and distance covered by the body are perpendicular to each other

W = FS cos θ

If force and displacement are perpendicular then θ = 90° so

W= FScos90⁰

cos90⁰ =0

So, W= FS(0) = 0

MAXIMUM WORK DONE

We know,

W = FS

W = FS cos θ

These equations show that the work done on a body will be maximum if:

The force acting on the body will be maximum

Body covers maximum displacement under the action of maximum applied force.

Applied force and displacement covered by the body are parallel to each other as:

W = FS cos θ

If force and displacement are parallel then θ = 0° so

W= FScos0⁰

cos0⁰ =1

So W= FS(1)

W = FS ——–( Indicates maximum work done)

NEGATIVE WORK

Yes work done on the body will be negative if applied force and displacement covered by the body are anti-parallel to each other as:

W = FS cos θ

If force and displacement are anti-parallel then θ =180° so

W= FScos0⁰

cos180⁰ =-1

So

W= FS (-1)

W = -FS ——–( Indicates negative work done)

A crate is moved by pulling the rope attached to it. It moves 10m on a straight horizontal road by a force of 100 N. How much work will be done if:

(Mini Exercise Pg. # 120)

The rope is parallel to the road:

Ans. As we know that W = FS cos.

If the rope is parallel to the road then = 0.

So

W = 100 x 10 x cos0

= 100 x 10 x 1 (as cos0 = 1)

= 1000 J

The rope is making angle of 30^o with road:

Ans. As we know that W = FS cos.

If the rope is parallel to the road then = 30^o.

So

W = 100 x 10 x cos30^o

= 100 x 10 x 0.866 (as cos0 = 0.866)

= 866 J

Result:

EXAMPLES 6.1

Given Data:

Mass of the bag = m = 10 kg

No of steps = n = 18

Height of each step = h₁= 20 cm = 0.2 m

To Find:

Work done by the girl to carry the bag = W =?

Calculations:

As we know

W = FS

First we find force F = weight = mg

F = (10)(10) = 100 N

Total distance covered by the girl = S = no of steps x height of each step

S= 18 x 0.2 = 3.6m

Now W = FS

Putting values

W = 100(3.6) = 360 J

Result:

KINETIC ENERGY

Definition:

“The energy possessed by a body due to its motion is called kinetic energy”

Formula:

It is denoted by K.E. and its formula is given below:

Examples:

Following are important examples of Kinetic energy.

Moving air is called wind. Wind has kinetic energy. We can use wind energy for doing various things. It drives windmills and pushes sailing boats.

Moving water in a river has kinetic energy that can carry wooden logs through large distances and can also be used to drive turbines for generating electricity.

Mathematical Derivation:

Let a body of mass m is moving with velocity v. An opposing force F such as force of friction acting through a distance S brings it to rest. The body possesses kinetic energy and is capable to do work against opposing force F until all of its kinetic energy used up.

K.E of the body = Work done by it due to motion

K.E = FS

v_i = v

v_f = 0

As F = ma

a = – F/m

Since motion is opposed, hence, acceleration “a” is negative.

Using 3^rd equation of motion:

2 a S = v_f² – v_i²

As we know that K.E is equal to the work done,

So,

The above equation gives the K.E. possessed by a body of mass m moving with velocity v.

Conclusion:

POTENTIAL ENERGY

Definition:

“The energy possessed by a body due to its position is known as potential energy.”

Formula:

Potential energy is denoted by P.E. and its formula is given below:

P.E. = m g h

Examples:

Following are important examples of Potential energy.

Energy stored in water in dam at certain height.

Energy possessed in raised hammer.

An apple on a tree is capable to do work as it falls thus it possess energy due to its position that is Potential energy.

Types of Potential Energy:

Elastic Potential Energy:

Potential energy due to elasticity of material is called elastic potential energy. Stretched bow and stretched catapult has elastic potential energy in it.

Gravitational Potential Energy:

The potential energy of a body due to its specific height from the surface of the earth is called its gravitational potential energy.

Mathematical Derivation:

Let a body of mass m be raised up through height h from the ground. The body will acquire potential energy equal to the work done in lifting it to height h as shown in the figure:

Thus, Potential Energy = F x h

= w x h

As we know that weight of the body = w = mg

So P.E. = w h = m g h

Conclusion:

ENERGY

Definition:

“A body possesses energy if it is capable to do work”.

OR

Ability of a body to do work is known as energy.

Quantity:

It is a scalar quantity

Unit:

Joule (Nm) is the unit of energy same as that of work.

Types of Energy:

Energy exists in various forms such as mechanical energy, heat energy, light energy, sound energy, electrical energy, chemical energy and nuclear energy etc.

Example:

Water running down the stream has Kinetic energy in it.

ELASTIC POTENTIAL ENERGY

Definition:

“Potential energy of a body due to elasticity of material is called elastic potential energy”.

Examples:

Energy in stretched bow and stretched catapult is elastic potential energy.

GRAVITATIONAL POTENTIAL ENERGY

Definition:

“The potential energy of a body due to its specific height from the surface of the earth is called its gravitational potential energy”.

Examples:

Energy in a ball placed at height “h” from the surface of the earth.

Given Data:

Kinetic energy of the body =K.E. = 25J

Mass of the body = m = 2kg

To Find:

Speed of the body= v =?

Calculations:

We know

and

2 K.E.= mv²

Taking square root on both sides we get

v = 5ms^-1

Result:

EXAMPLE 6.2

Given Data:

Mass of the stone = m = 500g = 0.5kg

Velocity with which the stone strikes with ground = v = 20ms^-1

To Find:

Kinetic energy of the stone = K.E. = ?

Calculations:

We know,

Putting values,

K.E =½ (0.5) (20)²

K.E = 100J

Result:

EXAMPLE 6.3

Given Data:

Mass of the body = m = 50 kg

Height of the body = h = 3m

Gravitational acceleration = g = 10ms^-2

To Find:

Potential energy of the body=P.E. = ?

Calculations:

We know

P.E. =mgh

Putting values

P.E.= (50)(10)(3)

P.E. = 1500 J

Result:

EXAMPLE 6.4

Given Data:

Force acting on the body = F= 200N

Mass of the body = m = 20kg

Velocity of the body = v = 50ms^-1

To Find:

Distance through which the force acts = S=?

Calculations:

In this case the work done on the body will be equal to its K.E. as

Work done on the body = K.E. gained by the body

F.S = ½ m v²

Putting values

(200) S = ½ (20)(50)²

(200)S = 25000

Result:

FORMS OF ENERGY

Energy exists in various forms. Some of the main forms of energy are explained below:

1) Mechanical Energy:

“The energy possessed by a body both due to its motion or position is called mechanical energy”.

Examples:

Following possess mechanical energy:

Water running down a stream

Wind

A moving car

A lifted hammer

A stretched bow

A catapult or a compressed spring

Types of Mechanical Energy:

Mechanical energy possessed by a body is of two types:

Kinetic Energy

Potential Energy

2) Heat Energy:

Heat is a form of energy given out by hot bodies. Large amount of heat is obtained by burning fuel. Heat is also produced when motion is opposed by frictional forces. The foods we take provide us heat energy. The Sun is the main source of heat energy.

3) Electrical Energy: (GRW 2015)

Electricity is one of the widely used forms of energy. Electrical energy can be supplied easily to any desired place through wires.

Sources:

We get electrical energy from batteries and electrical generators. These electric generators are run by hydro power, thermal or nuclear power.

4) Sound Energy: (GRW 2015)

Sound is a form of energy. It is produced when a body vibrates.

Examples:

Sound is produced by:

By knocking at the door

By vibrating diaphragm of a drum

By vibrating strings of a sitar

By vibrating air column of wind instruments as flute pipe

5) Light Energy:

Light is an important form of energy. Plants produce food in the presence of light. We also need light to see things.

Sources:

We get light from candles, electric bulbs, and fluorescent tubes and also by burning fuel. However, most of the light comes from the Sun.

6) Chemical Energy:

Chemical energy is present in food, fuels and in other substances. We get other forms energy these substances during chemical reactions.

Examples:

The burning of food, coal or natural gas in air is a chemical reaction which releases energy as heat and light.

Electric energy is obtained from electric cells and batteries as a result of chemical substances present in them.

Animals get heat and muscular energy from the food they eat.

7) Nuclear Energy:

Nuclear energy is the energy released in the form of nuclear radiations in addition to heat and light during nuclear reactions such as fission and fusion reactions. Heat energy released in nuclear reactors is converted into electrical energy. A nuclear power plant uses the energy released in nuclear reactor such as Fission to generate electric power.

Usually we carried fission and fusion reactions in nuclear reactors.

In fission reaction a heavy nuclei splits into smaller nuclei with the emission of large amount of nuclear energy

In fusion reaction small nuclei combine to form a heavy nucleus with the emission of tremendous amount of nuclear energy. This reaction is taking place in the Sun.

Biggest Source of Energy:

The energy coming from the Sun for the last billions of years is the result of nuclear reactions taking place on the Sun. Sun is the biggest source of energy.

INTER CONSERSION OF ENERGY

Introduction:

In order to explain conversion of energy from one form to another form a law has been presented that is called law of conservation of energy.

According to law of conservation of energy:

“During the inter conversion of energy from one form to other forms, the total energy at any time remains constant.”

Energy cannot be destroyed however it can be converted into some other forms.

Example:

Rub your hands together quickly. You will feel them warm. You have used your muscular energy in rubbing hands as a result heat is produced. In the process of rubbing hands, mechanical energy is converted into heat energy.

Explanation:

Processes in nature are the results of energy changes. For example, some of the heat energy form the Sun is taken up by water in the oceans. This increases the thermal energy. Thermal energy causes water to evaporate from the surface to form water vapors. These vapors rise and form clouds. As they cool down, they form water drops and fall down as rain. Potential energy changes to kinetic energy as the rain falls. This rain water may reach a lake or a dam. As the rain water flows down, its kinetic energy changes into thermal energy while parts of the kinetic energy flowing water is used to wash away soil particles of rocks known as soil erosion.

Conclusion:

MECHANICAL ENERGY

Definition:

“The energy possessed by a body due to its motion or position is called mechanical energy”.

Examples:

Water running down a stream

A moving car

A lifted hammer

A stretched bow

A catapult or a compressed spring

Types of Mechanical Energy:

Mechanical energy possessed by a body is of two types:

Kinetic Energy:

“The energy possessed by a body due to its motion is called kinetic energy”.

Formula:

It is denoted by K.E. and its formula is given below:

K.E. = ½ m v²

Potential Energy:

“The energy possessed by a body due to its position is known as potential energy”.

Formula:

Potential energy is denoted by P.E. and its formula is given below:

P.E. = m g h

ENERGIES USED IN DAILY LIFE

There are many kinds of energies are used in our body. Some of them are given below:

Mechanical Energy:

For the moving of our body.

Chemical Energy:

For making body molecules.

Electrical Energy:

For the propagation of electrical signals in the body.

Heat Energy:

For maintaining the body temperature

LAW OF CONSERVATION OF ENERGY

Statement:

According to law of conservation of energy:

“During the inter conversion of energy from one form to other forms, the total energy at any time remains constant.”

Example:

Rub your hands together quickly. You will feel them warm. You have used your muscular energy in rubbing hands as a result heat is produced. In the process of rubbing hands, mechanical energy is converted into heat energy.

CHEMICAL ENERGY

Chemical energy is present in food, fuels and in other substances. We get other forms energy these substances during chemical reactions.

Sources:

The sources of chemical energy are as follows:

The burning of food, coal or natural gas in air is a chemical reaction which releases energy as heat and light.

Electric energy is obtained from electric cells and batteries as a result of chemical substances present in them.

Animals get heat and muscular energy from the food they eat.

INTERCONVERSION OF ENERGY

Inter-conversion of Kinetic energy and Potential energy is shown below:

NONRENEWABLE SOURCES OF ENERGY

Definition:

“The sources of energy that take billions of years to reproduce and have chances to run-out in future are called non-renewable energy sources”.

Some nonrenewable sources of energy are given below:

1) Fossil Fuels:

We use fossil fuels such as coal, oil and gas to heat our houses and run industry and transport. They are usually hydrocarbons (compounds of carbon and hydrogen).

Chemical Reaction:

When they are burnt, they combine with oxygen from air. The carbon becomes carbon dioxide; hydrogen becomes hydrogen oxide called water; while energy is released as heat. In case of coal;

Carbon + Oxygen carbon dioxide + heat energy

Hydrocarbon + Oxygen carbon dioxide + water + heat energy

Fossil Fuels are Non-renewable:

The fossil fuels took millions of years for their formation. They are known as non-renewable resources. We are using fossil fuels at a very fast rate. Their use is increasing day by day to meet our energy needs. If we continue to use them at present rate, they will soon be exhausted. Once their supply is exhausted, the world would face serious energy crises.

Future Crises of Energy:

Thus, fossil fuels would not be able to meet our future energy needs. This would cause serious social and economical problems for countries like us. Therefore, we must use them wisely and at the same time, develop new energy sources for our future survival.

Harmful Effects Produced By Burning Fossil Fuels: (LHR 2017)

Moreover, fossil fuels release harmful waste products. These wastes include carbon mono-oxide and other harmful gases, which pollute environment. This causes serious health problems such as headache, tension, nausea, allergic reactions, and irritation of eyes, nose and throat. Long exposure of these harmful gases may cause asthma, lungs cancer, heart diseases and even damage to brain, nerves and other organs of our body.

2) Nuclear Fuels:

In nuclear power plants, we get energy as a result of fission reactions. During fission reaction, heavy atoms, such as uranium atoms, split up into smaller parts releasing a large amount of energy. Nuclear power plants give out a lot of nuclear radiations and vast amount of heat. A part of this heat is used to run power plants while lot of heat goes waste into the environment.

RENEWABLE SOURCES OF ENERGY

Definition:

“The sources of energy that reproduce quickly and do not have chances to run-out in future are called renewable energy sources.”

Example:

Sun light and water power are the renewable sources of energy. The will not run out like coal, oil and gas.

Sources of Renewable Energy:

Some renewable sources of energy are given below:

Energy Form Water:

Energy from water power is very cheap. Dams are being constructed at suitable locations in different parts of the world. Dams serve many purposes. They help to control floods by storing water. The water stored in dams is used for irrigation and also to generate electric energy without creating much environmental problems. Energy stored in the water of dams is used to run power plants.

2) Energy From Sun:

Solar energy is the energy coming from the sun and is used directly and indirectly. Sunlight does not pollute the environment in any way. The sunrays are the ultimate source of life on the Earth. We are dependent on the Sun for all our food and fuels. If we find a suitable method to use a fraction of the solar energy reaching the Earth, then it would be enough to fulfill our energy requirements.

Solar energy is most preferred form of energy due to following reasons:

It is easily available and it is the most cheapest form of energy

It can easily be converted into other forms of energy

It is pollution free form of energy.

Wind Energy:

Wind has been used as a source of energy for centuries. It has powered sailing ships across the oceans. It has been used by wind mills to grind grain and pump water.

Wind Turbines:

More recently, wind power is used to turn wind turbines. When many wind machines are grouped together on wind farms, they can generate enough power to operate a power plant. In the United States, some wind farms generate more than 1300 MW of electricity a day. In Europe, many wind farms routinely generate hundred megawatts or more electricity a day.

Geothermal Energy: (GRW 2017)

In some parts of the world, the earth provides us hot water from geysers and hot springs. There is hot molten part, deep in the Earth called magma. Water reaching close to the magma changes to steam due to high temperature of magma. This energy is called geothermal energy.

Electricity From Geothermal Energy:

Geothermal well can be built by drilling deep near hot rocks at places, where magma is not very deep. Water is then pushed down into the well. The rocks quickly heat the water and change it into steam. It expands and moves up to the surface. The steam can be pipes directly into houses and offices for heating purposes or it can be used to generate electricity.

5) Energy From Biomass: (GRW 2015, 2017)

Biomass is plant or wastes that can be burnt as fuel. Other forms of biomass are garbage, farm wastes, sugarcane and other plants. These wastes are used to run power plants. Many industries that use of forest products get half of their electricity by burning bark and other wood wastes. Biomass can serve as another energy source, but problems are there in its use.

Electricity From Biomass:

When animal dung, dead plants are dead animals decompose, they give off a mixture of methane and carbon dioxide. Electricity can be generated by burning methane.

SOLAR HOUSE HEATING SYSTEM

Introduction:

The use of solar energy is not new. However, it’s use in houses and offices as well as for commercial industrial purposes is quite recent. Complete solar house heating system are successfully used in area with a minimum amount of sunshine in winter.

Construction:

A house heating system consists of:

A collector

A storage device

A distribution system

Working:

The above figure shows a solar collector made of glass panels over blank metal plates. The plates absorb the sun energy which heats a liquid flowing in the pipes at the back of the collector. The hot water can be used for cooking, washing and heating the buildings.

Solar energy collected through this system is used in solar cookers, solar distillation plants, and solar power plants.

SOLAR CELLS AND SOLAR PANELS

Solar Cell:

Solar energy can also be converted directly into electricity by solar cells. A solar cell also called photo cell is made from silicon wafer. When sunlight falls on the solar cell, it converts the light directly into electrical energy.

Use:

Solar cells are used in calculators, watches and toys.

Solar Panels:

Large number of solar cells are wired together to form a solar panel.

Uses:

Solar panels can provide power to telephone booths, light houses and scientific research centers.

Solar panels are also used to power satellites.

Several other methods to trap sunrays are under way. If scientists could find an efficient and inexpensive method to use solar energy, then the people would get clean, limitless energy as long as the Sun continues to shine.

MASS ENERGY EQUATION

Einstein predicted the Inter-conversion of matter and energy. According to him, a loss in the mass of a body provides us a lot of energy. This happens in nuclear reactions.

Equation:

The relation between mass m and energy E is given by Einstein mass – energy equation.

E = m c²

Here c is the speed of light (3 x 10⁸ ms^-1). The above equation shows that tremendous amount of energy can be obtained from small quantity of matter. It appears that matter is highly concentrated form of energy.

Energy on Sun and Stars:

This process of getting energy from our nuclear power plants is based on the above equation. This process is taking place on the sun and stars for the last millions of years. Only a very small fraction of the sun energy reaches the earth. This very small fraction of the sun energy is responsible for life on the earth.

ELECTRICITY FROM FOSSIL FUELS

We are using electricity in houses, offices, schools, business centers, factories and in farms. We have different ways of generating electricity. Most of the electricity is obtained using fossil fuels such as oil, gas and coal. Fossil fuels are burnt in thermal power stations to produce electricity. Various energy conversion process involved in producing electricity from coal are described in Block diagram.

ENERGY AND ENVIRONMENT

Environmental problems such as pollution that consists of noise, air pollution and water pollution may arise by using different sources of energy such as fossil fuels and nuclear energy.

Pollution:

“Pollution is the change in the quality of environment that can be harmful and unpleasant for living things.”

Pollutants:

All things, chemicals or substances that cause pollution in our environment are called Pollutants e.g. Co₂ and So₂ are air pollutants.

Thermal Pollution:

A temperature rise in the environment that disturbs life is called thermal pollution. Thermal pollution upsets the balance of life and endangers the survival of many species.

Air Pollution:

Air pollutants are unwanted and harmful. Natural processes such as volcanic eruptions, forest fires and dust storms add pollutant to the air. These pollutant, rarely build up to harmful levels. On the other hand, the burning of fuel and solid wastes in homes automobiles, and factories releases harmful amount of air pollutants.

Nuclear Pollution:

All power plants produce waste heat, but fission plants produce the most. The heat released into a lake, a river or an ocean upsets the balance of life in them. Unlike other power plants, nuclear power plants do not produce carbon dioxide. But they produce dangerous radioactive waste.

CONTROLLING POLLUTION

It is not easy to control environmental pollution; however mutual efforts can reduce its rate as:

Government Laws:

In many countries, governments have passes laws to control air pollution. Some of these laws limit the amount of pollution level that, power plants, factories and automobiles are allowed to give off. To meet these conditions for automobiles, new cars have catalytic converters these devices convert some polluting gases. The use of lead free petrol has greatly reduced the amount of lead in air. Engineers are working to improve new kinds of cars that use electricity or energy sources other than petrol and diesel.

Individual Efforts:

Many individual communities have laws which protect their areas from pollution. Individuals can help to control air pollutions simply by reducing the use of cars and other machines that burnt fuel. Sharing rides and using public transportation are the ways to reduce the number of automobiles in use.

DIFFERENTIATION

Renewable and nonrenewable energy sources can be differentiated as:

FUNCTIONS OF TIMES

Dams serve many purposes.

They help to control floods by storing water.

The water stored in dams is used for irrigation and also to generate electric energy without creating much environmental problems.

Energy stored in the water of dams is used to run power plants.

PRODUCTION OF ELECTRICITY

Geothermal well can be built by drilling deep near hot rocks at places, where magma is not very deep. Water is then pushed into the well. The rocks quickly heat the water and change it into steam. It expands and moves up to the surface. The steam can be pipes directly into houses and offices for heating purposes or it can be used to generate electricity.

POLE VAULTER

A pole vaulter uses a flexible vaulting pole made of special material. It is capable to store all the vaulter’s kinetic energy while bending in the form of potential energy. The vaulter runs as fast as possible to gain speed. The kinetic energy gained by the pole vaulter due to speed helps him/her to rise up as the vaulter straightens. Thus he attains height as the pole returns the potential energy stored by the vaulter in the pole.

FLOW DIAGRAMS

In an energy converter, a part of energy taken (used up) by the system is converted into useful work. Remaining part of the energy is dissipated as heat energy, sound energy (noise) into the environment. Energy flow diagram given below shows the energy taken up by an energy converter to transform it into other forms of energy.

Some flow diagrams of energy converters are given below:

EFFICIENCY

Definition:

“Efficiency of a system is the ratio of required form of energy obtained from a system as output to the total energy given to it as input”.

Example:

Electric motors may be used to pump water, to blow air, to wash clothes, to drill holes, etc. for that they use electric energy. How good a machine is, depends how much output we obtain from it by giving certain input. The ratio of useful output to input energy is very important to judge the working of machine.

Mathematical Form:

Efficiency =

Or % Efficiency =

Unit:

Efficiency is a ratio between two similar quantities so it has no unit. It is measured in percentage.

IDEAL SYATEM

Definition:

An ideal system is that which gives an output equal to the total energy used by it. In other words, its efficiency is 100 %. People have tried to design a working system that would be 100 % efficient. But practically such system does not exist.

Reason For Not Existing 100% Efficient System:

Every system meets energy losses due to friction that causes heat, noise etc. These are not the useful forms of energy and go waste. This means we cannot utilize all the energy given to working system. The energy in the required form obtained from working system always less than the energy given to it as input.

POWER

Definition:

“Rate of doing work with respect to time is called the power.”

Formula:

Formula for power is given below:

Thus,

If we represent power by ‘P’, work by ‘W’ and time by ‘t’, then

P =

Quantity:

Since work is scalar quantity so power is also a scalar quantity.

Unit of Power:

In System International, the unit of power is watt (W).

Watt:

“The power of a body is one watt if it does work at the rate of 1 joule per second (1Js^-1)”.

Bigger Units:

Bigger units of power are kilowatt (kW), megawatt (MW) etc.

1 KW = 1000W = 10³ W

1 MW = 1000000 = 10⁶ W

1 horsepower = 1hp = 746 W

Given Data:

Mass of athlete = m = 40 kg

Time taken by athlete to climb= t = 10 s

Height of ladder = h = S = 10 m

To Find:

Power of athlete used for climbing = P = ?

Calculations:

As we know that Force = weight = w = mg = 40 x 10 = 400N

Work = W = FS = 400 x 10 = 4000 J

As we know that Power = P = W/t

So, Power = P = 4000/10 = 400 W

Result:

EXAMPLE 6.5

Given Data:

Useful work done by the cyclist = Output = 12J

Energy used by the cyclist = Input = 100J

To Find:

Efficiency of cyclist = ?

Calculations:

We know efficiency is measured in percentage as:

Putting the values,

Result:

EXAMPLE 6.6

Given Data:

Force used in lifting the load = F =200N

Time taken by M₁ to do the job = t₁ = 80 s

Distance covered by the body = S = 10m

Time taken by M₂ to do the job = t₂ = 10 s

To Find:

Power of M₁ = P₁ = ?

Power of M₂ = P₂ = ?

Calculations:

As the work done by both men is same i.e.

W = FS

Putting values

W= (200)(10)

W= 2000J

Now we find power of M₁ as

Putting the values

Now we find power of M₂ as

Putting the values

Result:

EXAMPLE 6.7

Given Data:

Mass of water = m = 70 kg

Height at which the water has been lifted = h =16 m

Time taken in lifting the water = t = 10 s

To Find:

Power of the pump (hp) = ?

Calculations:

We know,

In this case work done will be converted into P.E. of the body so

Putting the values

Conversion in hp:

We know

1hp = 746 watts

Result:

WORK

Definition:

Work is done when a force acting on a body displaces it in the direction of a force.

Mathematically:

Work is equal to the product of force and distance covered in the direction of force.

Work = Force x Displacement

W = FS

Unit of Work:

In System International, its unit is Nm that is also called as joule (J).

Joule:

“The amount of Work done will be one joule if a force of one Newton displaces a body through a distance of one meter in the direction of the force.”

Bigger Units:

Joule is a smaller unit of work. Commonly bigger units of work are also in use.

1 kilo joule ( kJ) = 1000 J =10³J

1 Mega Joule (MJ) =1000000J = 10⁶J

Quantity:

Work is a scalar and derived quantity.

ENERGY

Definition:

A body possesses energy if it is capable to do work.

OR

Ability of a body to do work is known as energy.

Quantity:

It is a scalar quantity

Unit:

Joule (Nm) is the unit of energy same as that of work.

Types of Energy:

Energy exists in various forms such as mechanical energy, heat energy, light energy, sound energy, electrical energy, chemical energy and nuclear energy etc.

MECHANICAL ENERGY

Definition:

The energy possessed by a body due to its motion or position is called mechanical energy.

Examples:

Water running down a stream

A moving car

A lifted hammer

A stretched bow

A catapult or a compressed spring

Types of Mechanical Energy:

Mechanical energy possessed by a body is of two types:

Kinetic Energy:

“The energy possessed by a body due to its motion is called kinetic energy”

Formula:

It is denoted by K.E. and its formula is given below:

K.E. = ½ m v²

Potential Energy:

“The energy possessed by a body due to its position is known as potential energy.”

Formula:

Potential energy is denoted by P.E. and its formula is given below:

P.E. = m g h

See Q. no.1 Long Question TOPIC 6.2

See Q. no.2 Long Question TOPIC 6.3

See Q. no.2 Long Question TOPIC 6.6

DEVICES NAMES

Following devices convert electrical energy into mechanical energy:

Electric Motor

Electric Fan

Elevator

Drill machine

Grinder

Electric sewing machine

EFFICIENCY

Definition:

“Efficiency of a system is the ratio of required form of energy obtained from a system as output to the total energy given to it as input.”

Example:

Electric motors may be used to pump water, to blow air, to wash clothes, to drill holes, etc. for that they use electric energy. How good a machine is, depends how much output we obtain from it by giving certain input. The ratio of useful output to input energy is very important to judge the working of machine.

Mathematical Form:

Efficiency =

Or % Efficiency =

Unit:

Efficiency is a ratio between two similar quantities so it has no unit. It is measured in percentage.

POWER

Definition:

“Rate of doing work with respect to time is called the power.”

Formula:

Formula for power is given below:

Thus Power =

If we represent power by ‘P’, work by ‘W’ and time by ‘t’, then

P =

Quantity:

Since work is scalar quantity so power is also a scalar quantity.

Unit of Power:

In System International, the unit of power is watt (W).

UNIT OF POWER

In System International, the unit of power is watt (W).

Watt:

If a body does a work of one joule in one second then its power will be one watt.

1 W = 1 Js^-1

Bigger Units:

1 KW = 10³ W

1 MW = 10⁶ W

Long question #1 topic 1

NEED OF ENERGY

We need energy to do different types of work in our daily life. When we say that body has energy, we mean that it has the ability to do work.

Examples:

Energy is required to move.

Energy is required to stop the moving objects.

NONRENEWABLE ENERGY SOURCE

The fossil fuels took millions of years for their formation. They are known as non-renewable resources. We are using fossil fuels at a very fast rate. Their use is increasing day by day to meet them at present rate, they will soon be exhausted. Once their supply is exhausted, the world would face serious energy crises.

MOST PREFERRED FORM OF ENERGY

Solar energy is most preferred form of energy due to following reasons:

It is easily available and it is the most cheapest form of energy

It can easily be converted into other forms of energy

It is comparatively pollution free form of energy.

DEVICE NAME

Electric Generator is a device which is used to convert mechanical energy into electrical energy.

FINDING EFFICIENCY OF A SYSTEM

Efficiency of a system is the ratio of required form of energy obtained from a system as output to the total energy given to it as input.

Mathematically, it can be calculated as:

Efficiency =

Given Data:

Force applied = F = 300 N

Distance moved by cart = S = 35 m

To Find:

Work done by the man = W =?

Calculations:

As we know that,

W = F x S

By putting the values, we have

W = 300 x 35

W = 10500 J

Result:

Given Data:

Weight of the block = W = 20 N

Distance moved vertically upward = h = 6 m

To Find:

Potential energy of the block = P.E = ?

Calculations:

As we know that

W = F x S

By putting the values, we have

W = 20 x 6

W = 120 J

Result:

Given Data

Weight of car = w = 12 kN

Speed of car = v = 20 ms-1

To Find:

Kinetic energy stored in car = K.E = ?

Calculations:

As we know that

K.E = ½ mv²

By putting the values, we have

K.E. = ½ x 1200 x (20)²

K.E. = ½ x 1200 x 400

K.E. = 240000 J

K.E. = 240 Kj

Result:

Given Data:

Mass of the stone = m = 500 g = 0.5 kg

Velocity of the stone = v = 15 ms^-1

To Find:

P.E. at its maximum height = P.E. = ?

K.E. when it hits the ground = K.E. = ?

Calculations:

As we know that

Potential energy at maximum height = kinetic energy while throwing

Potential energy at maximum height = ½ mv²

By putting the values, we have

Potential energy at maximum height = ½ x 0.5 x (15)²

Potential energy at maximum height = ½ x 0.5 x 225

Potential energy at maximum height = 56.25 J

Also we know that

Kinetic energy while hitting the ground = Potential energy at maximum height

As Potential energy at maximum height = 56.25 J

So Kinetic energy while hitting the ground = 56.25 J

Result:

Given Data:

Speed of the cyclist = v = 1.5 m^s-1

Height of slope = h = 6 m

Mass of cyclist and bicycle = m = 40 kg

To Find:

Kinetic energy of the cyclist = K.E. = ?

Potential energy of the cyclist = P.E = ?

Calculations:

As we know that

P.E. = mgh

By putting the values, we have

P.E. = 40 x 10 x 6

P.E. = 2400 J

Also we know that

K.E. = ½ mv²

By putting the values, we have

K.E. = ½ x 40 x (1.5)²

K.E = ½ x 40 x 2.25

K.E. = 45 J

Result:

Given Data:

Speed of the motor boat = v = 4 ms^-1

Water resistance acting on boat = 4000 N

To Find:

Power of the engine of motor boat = P = ?

Calculations:

As we know that

P = F x v

By putting the values, we have

P = 4000 x 4

P = 16000 W ( 1000 = 1 kilo)

P = 16 KW

Result:

Given Data:

Force applied on block = F = 300 N

Distance covered by the block = S = 50 m

Time taken = t = 60 s

To Find:

Power used to pull the block = P = ?

Calculations:

As we know that

By putting the values, we have

Result:

Given Data:

Mass of man = m = 50 kg

Height of each step = h = 16 cm = 0.16 m

Number of steps = n = 25

Time taken = t = 20 s

To Find:

Power of the man = P = ?

Calculations:

Since

F = w

= mg

= (50) (10)

= 500 N

Height reached by man = h = 0.16 × 25

= 4 m

As we know that

By putting the values, we have

Result:

Given Data:

Mass of the water = m = 200 kg

Height attained = h = 6 m

Time taken = t = 10 s

To Find:

Power of the pump = P = ?

Calculations:

Since

F = w

= mg

= 200 × 10

= 2000 N

Given Data:

Power of the motor = P = 1 hp

Time taken by pump = t = 10 mins = 600 s

Capacity of the tank = v = 800 liters

Height of the tank = h = 15 m

To Find:

Work done by the motor = W = ?

Efficiency of the system = ?

Calculations:

As we know that

P = So W = P x t

By putting the values, we have

W = 1 hp x 600s

Or W = 746 w x 600s = 447600 J

Now Output = W = mgh

By putting the values, we have

Output = 800 x 10 x 15

Output = 120000 J

We also know that

% Efficiency =

By putting the values, we have

% Efficiency =

% Efficiency = 0.268 x 100

So, % Efficiency = 26.8%

Result: