560_topper_21_110_2_4_125_work__energy_and_power_up201506181308_1434613126_8274

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PHYSICS WORK, ENERGY AND POWER

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Work Energy and Power

Work

Work is any physical or mental activity which one does to perform daily tasks. However, in scientific

parlance, work is done when a force produces motion in an object. The amount of work depends on two factors:

The magnitude and direction of force applied to an object

The distance/displacement through which the object moves

The amount of work done by a force in moving a body is equal to the product of the force and the

displacement of the point of application of the force in the direction of force.

Work = Force× Displacement

W = F × s

Work is a scalar quantity.

Thus, the expression of work is

W Fscos

Thus, the amount of work done is the product of force, displacement and the cosine of the angle

between the force and displacement.

If the displacement is in the direction of the force, i.e. = 0, then the work done is W F s .

This work is maximum and positive.

If the displacement is normal to the direction of the force, i.e. = 90, then the work done is W 0 .

Thus, no work is done.

If the displacement is zero, then the work done is zero. This is the case when a body is performingcircular motion.

If the displacement is in the direction opposite to that of the force, i.e. = 180, then the work done is

W F s .

This work is minimum and negative.


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Work Done by Gravity

If a body of mass m moves down from a height h, then the force of gravity or weight acts on the body

through a displacement h.

Thus, the work done by the force of gravity is

W mg h

Similarly, if the body is thrown up to a height h, then the work done by gravity is

W mg h

The SI unit of work is newton metre (N m) or joule (J).

One joule of work is said to be done when a force of one newton displaces the body through a

distance of one metre in its direction.

The CGS unit of work is erg.

One erg of work is said to be done when a force of one dyne displaces the body through a distance of

one centimetre in its direction.

71 joule= 10 erg

Power: Rate of Doing Work

Power is defined as the rate of doing work or the rate of transfer of energy.

WP =

t

Power is a scalar quantity.

If displacement is at an angle , then the power is

W Fs cosθP = = = Fv cosθ

t t

Its SI unit is watt (W) or joule per second (J/s), and its CGS unit is erg per second (erg/s).

Another unit of power is kilowatt (kW).

1 kW = 1000 W

1 MW = 106 W

1 horsepower = 746 W = 0.746 kW


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Energy

We can define energy as the capacity to do work.

The amount of energy possessed by a body is the amount of work it can do when that energy is released.

Energy is a scalar quantity.

The SI unit of energy is the same as the unit of work, i.e. joule (J), and its CGS unit is erg. Another unit of energy is watt hour or kilowatt hour.

The commercial unit of electric energy is kilowatt hour (kW h), commonly known as unit.

61 kW h = 3.6×10 J = 3.6 MJ

Heat energy is usually measured in calorie. One calorie is the energy required in raising the

temperature of 1 g of water through 1°C.

1 J = 0·24 calorie

1 calorie = 4·18 J

1 kilocalorie = 1000 calorie = 4180 J

1 eV is the energy gained by an electron when it is accelerated through a potential difference of 1

volt

1 eV = 1·6 × 10−19

J

Mechanical Energy

The energy possessed by a body due to its state of rest or of motion is called mechanical energy.

The total mechanical energy of a body is equal to the sum of its kinetic energy and potential energy.

Kinetic Energy

The energy possessed by a body by virtue of its state of motion is called kinetic energy. It is denoted

by ‘K’. Suppose a body of mass m is moving with a velocity ‘v’. It is brought to rest by applying a constant

opposing force F. Let ‘a’ be the uniform retardation produced by the force, and the body travels a

distance ‘S’ before coming to rest.

Kinetic energy Work done by retarding force in stopping it

Retarding force displacement

F S

ma S

Thus, the kinetic energy is given as

1 2K = mv2

The kinetic energy and momentum are related as

p = 2mK


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Work –Energy Theorem

According to the work –energy theorem, the work done by a force on a moving body is equal to the

increase in its kinetic energy.

2 2W = mv - mu = K - Kif

1 1

2 2

W = Final kinetic energy – Initial kinetic energy

Thus, the work done is the increase in kinetic energy.

Forms of Kinetic Energy

The motion of a body in a straight line path is called translational motion, and the kinetic energy of the

body due to motion in a straight line is called translational kinetic energy.

When a body rotates about an axis, the motion is called rotational motion, and the kinetic energy of the

body due to rotational motion is called rotational kinetic energy or simply rotational energy.

When a body moves to and fro about its mean position, the motion is called vibrational motion. The

kinetic energy of the body due to its vibrational motion is called vibrational kinetic energy or simply

vibrational energy.

Potential Energy

The energy possessed by a body by virtue of its specific position or changed configuration is called

potential energy. It is denoted by ‘U’.

The potential energy possessed by a body due to its position relative to the centre of the Earth is

called its gravitational potential energy.

Larger the distance of the body from the centre of the Earth, greater is its gravitational potentia

energy.

The potential energy possessed by a body in the deformed state due to change in its configuration iscalled elastic potential energy. It is equal to the amount of work done in deforming the body or in

changing the configuration of the body.

Gravitational Potential Energy

The gravitational potential energy of a body at a height above the ground is measured by the amount

of work done in lifting it up to that height against the force of gravity.

Let a body of mass m be lifted from the ground (or Earth surface) to a vertical height h. The work W

done on the body in lifting it to a height h is

W = Force of gravity (mg) x displacement (h) =mgh

This work is stored in the body when it is at a height h in the form of its gravitational potential energy

Thus, gravitational energy is U = mgh.

Thus, when a body is thrown vertically upwards, its potential energy increases. Similarly, when a body

is dropped from a height, its potential energy decreases.

Potential energy changes into kinetic energy whenever it is put to use.

When the string of a bow is pulled, some work is done which is stored in the deformed state of the

bow in the form of its elastic potential energy. On releasing the string, the potential energy of the

bow changes into the kinetic energy of the arrow which helps to move it forward.


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Different forms of Energy

The energy radiated by the Sun is called solar energy.

Several devices are available to use solar energy. These devices are solar panels, solar furnaces,

solar cells etc.

The energy released on burning coal, oil, wood or gas is heat energy.

Light energy is the form of energy which helps other objects to be seen. The Sun is the natural source of light energy. The moon reflects light from the Sun.

Other sources such as fire, candle, tube light, bulb etc. provide light energy.

The energy possessed by fossil fuels such as coal, petroleum and natural gas is called chemical

energy or fuel energy.

The energy possessed by running water is called hydro energy. It is used to generate electricity in

hydroelectric power stations.

When two dry bodies are rubbed together, they get charged due to the movement of free electrons

from one body to the other. Thus, they possess electrical energy. An electric cell is a source of

electrical energy.

The energy released during the process of nuclear fission and fusion is called nuclear or atomic

energy.

The energy released in nuclear disintegrations in the interior of the Earth gets stored deep inside

the Earth and is called geothermal energy. This energy heats up the underground water to produce

natural steam.

The energy possessed by fast-moving air is called wind energy. This energy is used in driving a

wind mill.

A vibrating body possesses sound energy. It is sensed by our ears. When the disturbance

produced in atmospheric air layers by a vibrating body reaches our ears and produces vibrations in

the ear membrane, sound is heard.

The energy possessed by a magnet due to which it can attract iron filings is called magnetic

energy. An electromagnet has magnetic energy.

The energy possessed by a body due to its state of rest or of motion is called mechanical energy.

A body at a height, a moving body, a stretched bow etc. have mechanical energy.

Sources of Energy

A source of energy is one which provides adequate amount of energy over a long period.

A source of energy supplies energy which is needed to do work. Thus, a good source of energy is one

which would:

a. Do a large amount of work per unit volume or mass

b. Be easy to transport from one place to another

c. Be easily accessible

d. Be economical


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Renewable or Non-conventional Sources of Energy

A natural source providing us energy continuously is called a renewable source of energy.

These sources of energy can be used again and again and will not get exhausted. They are also

called non-conventional sources of energy.

The Sun is the most powerful source of radiation energy.

The solar energy reaching unit area at the outer edge of the Earth’s atmosphere exposed

perpendicularly to the rays of the Sun at an average distance between the Earth and the Sun is known

as solar constant.

Its value is approximately equal to 1.4 kJ per second per m2 or 1.4 kW/m

2.

The large mass of flowing air is called wind. It possesses kinetic energy due to its motion, and this

energy is called wind energy.

The kinetic energy possessed by flowing water is called hydro energy.

Hydro energy also comes indirectly from the Sun. Solar energy is responsible for the water cycle in

nature.

Water in oceans, rivers, lakes etc. absorbs solar energy, and it then evaporates to form clouds. The

clouds move due to air currents, and water ultimately returns to the Earth in the form of rain and snow.

Waste and dead parts of living beings such as plants, trees and animals are called biomass. Biomass

contains carbon compounds. The chemical energy stored in the biomass is called bioenergy.

Biogas is a mixture of gases produced during the decomposition of biomass in the absence of oxygen.

The main constituent of biogas is methane (65%), and the rest is a mixture of carbon dioxide,

hydrogen and hydrogen sulphide.

The energy possessed by rising and falling water in tides is known as tidal energy.

Water in oceans possesses energy in two forms—ocean thermal energy and ocean (or sea) wave

energy.

The energy available due to the difference in temperature of water at the surface and at deeper levels

of the ocean is called ocean thermal energy (OTE).

Ocean or sea waves because of their high speed carry tremendous amount of kinetic energy. Thus

the kinetic energy possessed by such fast-moving ocean (or sea) waves is called ocean (or sea) wave

energy.

At some places, rocks below the surface of the Earth are very hot. Such places are called hot spots

The heat energy possessed by such rocks inside the Earth is called geothermal energy.

In the processes of nuclear fusion and fission, the origin of energy is the loss in mass (or mass

defect), i.e. the sum of masses of the products of the reaction is less than the sum of masses of the

reactants, and this loss in mass is converted into energy according to the Einstein's mass –energy

equivalence relation E = mc

2

, where c is the speed of light and m is the loss in mass. This energy iscalled nuclear energy.


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Non-renewable or Conventional Sources of Energy

The sources of energy which have accumulated in nature over a very long period and cannot be

quickly replaced when exhausted are called non-renewable or conventional sources of energy.

Coal is a non-renewable substance made of complex compounds of carbon, hydrogen and oxygen

along with some free carbon and compounds of nitrogen and sulphur.

It is found in deep mines under the surface of the Earth. Petroleum is a dark-coloured viscous liquid also called crude oil. It is a non-renewable source of

energy which is found under the Earth’s crust trapped in rocks. It is called petroleum because

petroleum means rock oil.

It is a complex mixture of many hydrocarbons with water, salt, earth particles and other compounds of

carbon, oxygen, nitrogen and sulphur.

The process of separating useful components from crude petroleum is called refining, and it is done by

fractional distillation.

Petroleum gas liquefied under pressure is called liquefied petroleum gas (or LPG) which is used in

domestic gas stoves as fuel for heating purposes.

Natural gas is a non-renewable source of energy which is found deep under the Earth’s crust eitheralone or above the petroleum reservoirs.

The main component of natural gas is methane (up to 95%) along with small quantities of ethane and

propane. It easily burns to produce heat.

Judicious Use of Energy

Fossil fuels such as coal and petroleum should be used only for limited purposes when no other

alternative source of energy is available.

Wastage of energy should be avoided.

Cutting of trees must be banned, and more trees should be planted.

Techniques should be developed such that we may make use of renewable sources such as solar

energy, wind energy, hydro energy, bioenergy, ocean energy etc. as much as possible to meet our

requirements.

Efforts must be made to obtain nuclear energy by the controlled nuclear fusion of deuterium nucle

present in heavy water available in the sea. This will then become an endless source of energy.

Production of Electricity from Solar Energy

The Sun is the most vast and direct source of energy. The energy obtained from the Sun is called

solar energy.

The device which converts solar energy directly into electricity is called a solar cell. A solar heatingdevice is also used to generate electricity from solar energy. This is called a solar power plant.

Solar cells are usually made of semiconductors such as silicon and gallium.

To increase the efficiency, a large number of such cells are arranged over a large area so that they

can collect a large amount of solar energy to produce sufficient electricity. Such an arrangement of

solar cells is called a solar panel.


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Advantages of Using Solar Panels

They do not require any maintenance and last over a long period.

The running cost is almost zero.

They are most suitable for remote, inaccessible and isolated places where electric power lines cannot

be laid.

They do not cause any pollution in the environment.

Disadvantages of Using Solar Panels

The initial cost of a solar panel is high, whereas the efficiency of conversion of solar energy to

electricity is low.

A solar panel produces DC electricity which cannot be directly used for many household purposes.

A solar power plant is a device in which the heat energy of the Sun is used to generate electricity.

The Sun’s rays after reflection from a large concave reflector get concentrated at its focus. The rays

have sufficient heat energy which can boil water if it is placed at the focus of the reflector.

Production of Electricity from Wind Energy The Sun’s rays falling on the Earth heat the different areas of the Earth unequally.

Due to (i) unequal heating of different areas of the Earth, (ii) rotation of the Earth and (iii) loca

convection currents, we have different wind cycles.

The electric power generated by a single wind mill generator is small. So, to generate enough electric

power, a large number of such wind generators are arranged over a big area called a wind farm.

At present, India generates more than 1025 MW electric power by this technique in the coastal areas

of Gujarat and Tamil Nadu.

Wind energy does not cause any kind of pollution. It is an everlasting source.

Production of Electricity from Hydro Energy

Water at a height has potential energy stored in it. When this water falls down, its potential energy is

converted to kinetic energy.

Hydro power plants use this kinetic energy to generate electricity.

Advantages

Hydroelectric energy is a renewable source of energy as the water on the Earth will keep flowing for a

very long time.

Environmental pollution is not caused as the energy is obtained from flowing water.

Construction of dams on rivers helps in controlling floods. It also aids the irrigation process.

Disadvantages

Dams can be constructed only in certain areas as flowing water is not available everywhere.

Large areas of agricultural land and human settlement need to be sacrificed, as they get submerged in

the reservoir formed by dams.

Large ecosystems are destroyed.

Submerged vegetation rots under anaerobic conditions and gives rise to large amounts of methane—a

greenhouse gas.


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Production of Electricity from Nuclear Energy

Nuclear energy is generated in a process called nuclear fission.

In this process, the nucleus of a heavy atom when bombarded with low-energy neutrons can be spli

into lighter nuclei.

This releases a large amount of energy due to mass defect. Mass defect occurs because the mass of

reactant nuclei is slightly greater than the sum of the masses of product (daughter) nuclei.

In a nuclear fission, the difference in mass m between the original nucleus and the product nuclei getsconverted to energy E at a rate governed by Einstein’s equation E = m c

2.

At present, only about 3% of the total electrical power generated in India is obtained from nuclear

power plants.

Advantages of Using Nuclear Energy

A very small amount of nuclear fuel (such as uranium-235) can produce a tremendous amount of

energy.

After the nuclear fuel is loaded into a nuclear power plant, it continues to release energy for severalyears.

Limitation of Use of Nuclear Energy

It is not a clean source of energy because very harmful nuclear radiations are produced in the

processes which are highly energetic and penetrating.

They cause ionisation, and hence, they are very harmful to the human body.

The waste obtained from nuclear power plants causes environmental pollution.

Law of Conservation of Energy

According to the law of conservation of energy, energy can neither be created nor be destroyed. It

only changes from one form to another.

The total mechanical energy of an isolated system at any instant is equal to the sum of its kinetic

energy and potential energy.


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Application of Law of Conservation of Energy to a Simple Pendulum

At the resting position, the bob of the pendulum has zero potential energy. When the bob is displaced

from its resting position, it gets raised by a vertical height h, so its potential energy increases by mgh if

m is the mass of the bob.

On releasing the bob from a height, it moves back to its initial position. Its vertical height decreases

from h to zero, so its potential energy decreases from mgh to zero, and it gets converted into kinetic

energy,

i.e. ½ mv2 = mgh.

Velocity of the bob = v 2gh

At an intermediate position, the bob has both kinetic energy and potential energy, but the sum of both

remains constant throughout the swing.

Energy Degradation

According to the law of conservation of energy, the total energy of the universe remains constant.

While transformation, the entire energy does not change into the desired form, but a part of it always

changes to some other form which is not useful.

This conversion of energy to the undesirable (or non-useful) form is called dissipation of energy.

The gradual decrease of useful energy due to friction etc. is called degradation of energy.

Examples:

When we light a bulb by using electricity, less than 25% of electrical energy is converted to light

energy. The remaining energy changes into heat in the filament and other invisible radiations.

In transmission of electricity from the power generating station, a lot of electrical energy is wasted in

the form of heat energy in the line wires used for transmission.

All machines have efficiency less than 1, which implies that only a fraction of input energy is used for

doing useful work and the rest of the input energy is wasted.

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