Work, Energy and Power

Work done by a constant force

 Work is said to be done only when the force is applied on a body makes the body move
 The amount of work done by a force is equal to the product of the force and the
displacement of the point of application of the force in the direction of force
 W = F × S, it is a scalar quantity
Note:
 The amount of work done by a force depends on, the magnitude and direction of the force
& displacement it produces, if a force acts on a body and the body does not move, no work
is done
Expression of work
 Work done W = force × component of displacement in the direction of force,
W = F × S cosθ
 If the displacement is in the direction of the force i.e., θ = 0°, then cosθ = cos0° 1,
W = F × S, the work done is maximum and positive
Different conditions
 Condition for the work done by a force to be zero
 When there is no displacement i.e., S = 0, force i.e. = 90°
 If the displacement is in a direction opposite to the force, i.e., θ =180°
 W = F × S cos 180° = – F × S, Work done is negative
Work done by the force of gravity
 W = F × S = mgh
 The work done by the force of gravity is the same whether a man comes down from a
certain height (h) using a staircase or along the slope or he comes down from the same
height using a lift or elevator
Unit of work
 S.I. unit of work is newton metre (Nm) or joule (J)
  1 J is the amount of work done on an object when a force of 1N displaces it by 1m along
the line of action of force
 C.G.S unit of work is dyne centimetre or erg, 1 J = 107 erg
Power:
Power is defined as the rate of doing work or the rate of transfer of energy
𝑤
P = ⇒ P = F × v = force × average speed
𝑡
𝐽𝑜𝑢𝑙𝑒
The S.I. unit of power is watt and its symbol is W, 1 watt = 1 or 1W = 1J𝑠 −1 ,
𝑆𝑒𝑐
1 H.P. = 746 W = 0.746 kW
The C.G.S unit of power is erg per second (erg 𝑠 −1 ), 1W = 1J𝑠 −1 = 107 erg 𝑠 −1
Factors on which power spent by a source depends on:
 The amount of work done by the source.
 The time taken by the source to do the said work.
Difference between work and power:

Work Power

𝑤
W=F×S P=
𝑡

It does not depend on time It depends on the time in which work is done

S.I. unit of work is joule (J) S.I. unit of power is watt (W)

Energy:
 The energy possessed by an object is measured in terms of its capacity of doing work
 Like work, energy is also a scalar quantity
 The unit of energy is, therefore, the same as that of work, that is, joule (J)
 1 J is the energy required to do 1 joule of work
Unit of energy:
The energy used in households, industries and commercial establishments are usually
expressed in kilowatt hour
kW h = 1 kW × 1 h = 1000 W × 3600 s = 36,00,000 J
Difference between energy and power:

Energy Power

It is the capacity to do work It is the energy spent by a body in 1 s.

It does not depend on time It depends on the time in which work is done

S.I. unit of work is joule (J) S.I. unit of power is watt (W)

Mechanical Energy:
The energy possessed by a body due to its state of rest or of motion is called the
mechanical energy.
The two forms of mechanical energy are;
 Kinetic energy
 Potential energy
Kinetic energy:
The kinetic energy of a body moving with a certain velocity is equal to the work done on
1
it to make it acquire that velocity, 𝐸𝑘 = 𝑚𝑣 2 J
2
The kinetic energy possessed by an object of mass, m and moving with a uniform
velocity,
Example: A fast moving stone has the capacity of breaking a window pane on striking it
and thus it has the kinetic energy.
Work-energy Theorem
Work done to change the velocity of an object of mass m from
1
 𝑊 = ∆𝐸𝑘 = 𝐸𝑘𝑓 − 𝐸𝑘𝑖 = 𝑚(𝑣𝑓2 − 𝑣𝑖2 ) 𝐽
2
Relationship between kinetic energy and momentum:
1
 P = √2𝑚𝐸𝑘 , is the momentum = mv, 𝐸𝑘 = 𝑚𝑣 2
2

Forms of kinetic energy

 Translational kinetic energy: The kinetic energy of the body due to motion in straight line
 Rotational kinetic energy: The kinetic energy of the body due to rotational motion
 vibrational kinetic energy: The kinetic energy of the body due to vibrational motion
Potential energy
 The potential energy possessed by the object is the energy present in it by virtue of its
position or configuration
 It is denoted by the symbol U
Example: A body placed at a height above the ground.
Forms of potential energy
 Gravitational potential energy: The potential energy due to changed position
 Elastic potential energy: The potential energy due to changed configuration
 Potential energy = work done on the object, of mass m, against gravity to raise it through
a height h
𝐸𝑝 = Force × displacement = mg × h = mgh J

Different forms of energy:

1. Solar energy
2. Heat energy
3. Light energy
4. Chemical or fuel energy
5. Hydro energy
6. Electrical energy
7. Nuclear energy
8. Geo thermal energy
9. Wind energy
10. Sound energy
11. Magnetic energy
12. Mechanical energy
Characteristics of a source of energy:
 A source of energy should be such that it can provide an adequate amount of useful energy
at a steady rate over a longer period of time.
 It should be safe and convenient to use.
 Economical and easy to store and transport.
Classification of Sources of energy
 Renewable or non-conventional resources: A natural source providing us energy
continuously is called a renewable source of energy
 Non-renewable or conventional resource: The sources of energy which have accumulated
in nature over a very long period and cannot be quickly replaced when exhausted are called
the non-renewable or conventional source of energy.
Difference between Renewable resources and Non-renewable resources:

Renewable Energy resources Non-renewable Energy resources

These are Energy resources which can These are resources which cannot be
be utilized continuously over a very long utilized continuously over a very long
period of time period of time

They are the non-conventional resources They are the conventional resources

These are the natural resources which

These are the natural resources which
would soon deplete if they are consumed
will not get exhausted
indiscriminately

These resources can be regenerated These resources cannot be regenerated

Examples: air, water, sunlight etc. Example: Coal, mineral oil etc.
Solar power plant:
 The device which converts solar energy directly into the electricity is called a solar cell
 A solar heating device is also used to generate electricity from the solar energy
Advantages of solar panels:
 They do not require any maintenance
 They last over a long period of time
 Their running cost is almost zero
 They are most suitable for the remote places and do not cause any pollution in the
environment
Disadvantages of solar panels:
 The initial cost of solar panel is high
 The efficiency of conversion of solar energy to electricity is low
 A solar panel produces D.C. electricity which cannot be directly supplied for household
purposes
Production of electricity from wind energy:
Wind energy is used in a wind generator to produce electricity by making use of a windmill
(or wind turbine) to drive a wind generator.
Advantages of using wind energy:
 It does not cause any pollution in the environment
 It is an everlasting source
Limitations of using wind energy:
 The establishment cost is expensive
 A large area of land is needed
 The wind farms can only be established where wind blows at a speed not less than 15 km/h
Production of electricity from water energy:
 The kinetic energy possessed by the flowing water is called the water (or hydro) energy.
 The electricity obtained by hydro energy is called Hydroelectric power.
Advantages of using water energy
 It does not cause any pollution in the environment
  The dams constructed over rivers helps in irrigation and control of floods
Limitations of using water energy:
 The flowing water is not always available
 The ecological balance in the downstream areas of rivers gets disturbed
 Due to construction of dams over the rivers, plants and animals of that place get destroyed
or killed
Production of electricity from nuclear energy:
 When a heavy nucleus is bombarded with slow neutrons, it splits into two nearly equal
light nuclei with the release of a tremendous amount of energy. This process is called
nuclear fission.
 The electricity is produced by a controlled chain reaction of nuclear fission of a radioactive
substance in a set up called nuclear power plant.
Advantages of using nuclear energy:
 A very small amount of nuclear fuel can produce a tremendous amount of energy
 If the nuclear fuel is loaded into a nuclear power plant, it continues to release energy for
many years
Limitations of using nuclear energy:
 Harmful radiations are produced in the process
 The waste obtained causes environmental pollution

Conservation of energy: It is the principle that energy is not created or destroyed; it only moves
from one place to another – from one type of energy to another.
Energy Degradation: In all energy transformations some energy is lost to surroundings which is
not useful for any productive work.
Conservation of resources:
 Conservation of resources means such a management of natural resources for all living
beings by which not only the needs of the present generation is fulfilled, but also there may
remain all possibilities of nurturing the future generations.
 Efficient use of energy is to reduce the amount of energy required to provide us the various
products and services.
Example: Insulating a home allows a building to use less heating and cooling energy to achieve
and maintain a comfortable temperature.
Disadvantages of building large dams for generating hydro-electric power:
 The natural ecosystem in the surrounding forest areas gets disturbed
 The plants aquatic ecosystem and animals’ life get disrupted
 The people get displaced on a large scale
Law of Conservation Energy
According to the law of conservation of energy, energy can only be transformed from one form
to another. It can neither be created nor destroyed. The total energy before and after the
transformation always remains constant.
Energy degradation:
The gradual decrease of useful energy due to friction, heat due to resistance etc. is called the
degradation of energy
 All machines have efficiency less than 1, which implies that only a fraction of input energy
is used for doing useful work and rest of the input energy is wasted
 When electrical appliances are run by electricity, the major part of electrical energy is
wasted in the form of heat energy.