CHAPTER
2 WORK,ENERGY & 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 = Fscosθ
• 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. θ = 0o, then the work done is W = F X s . This work is
maximum and positive.
• If the
displacement is normal to the direction of the force, i.e. θ = 90o, 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 performing circular motion.
• If the
displacement is in the direction opposite to that of the force, i.e. θ = 180o, then the work done is W = – F x s.
This work is
minimum and negative.
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 x h
• Similarly, if the
body is thrown up to a height h, then the work done by gravity is W = – mg x 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.
• 1 joule =107 erg
Power: Rate of Doing Work
• Power is defined
as the rate of doing work or the rate of transfer of energy.
P = W / t
• Power is a scalar
quantity.
• If displacement
is at an angle θ, then the power is
• 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
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.
• 1 kW h =3.6×106 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 x
displacement
= F x S
= ma x S
• Thus, the kinetic
energy is given as
• Thus, the kinetic
energy is given as K = 1 / 2 mv2
• The kinetic
energy and momentum are related as P
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.
• 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
potential energy.
• The potential
energy possessed by a body in the deformed state due to change in its
configuration is called 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.
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.
Conversion of One form of Energy into Another
• In a hydroelectric
power station water stored in a dam has potential energy which is converted
to kinetic energy while falling and then this mechanical energy is
converted to electrical energy by the generator.
• In an
electric motor, the electrical energy is passed through the coil which is
freely suspended between the poles of a magnet. This causes the coil to
rotate converting the electrical to mechanical energy.
• In a
loudspeaker electrical energy is converted to sound energy.
• When a
candle burns the chemical energy inside the wax gets converted to light energy.
• In a
photocell, light energy incident on gets converted to electrical energy.
• In
automobiles, the chemical energy of petrol is used to run the engine and
convert to mechanical energy of the vehicle.
Many more such
conversions are possible, viz. Heat to electrical, sound to electrical,
electrical to chemical, light to chemical, heat to mechanical, etc.
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.
K + U = Constant: Theoretical Verification
• Consider a body
of mass m freely falling under gravity from a height h.
At position A: Total energy = K + U = mgh
At position B:
Kinetic energy is
Potential energy is
= mg (h – x)
Hence, total energy
= K + U = mgx + mg(h -x) = mgh
At position C:
Kinetic energy is
Potential energy is
0.
Hence, total energy
= K + U = mgh + 0 = mgh
• Thus, the
mechanical energy always remains constant. Hence, mechanical energy is
conserved.
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.
1) Difference
between Work and Power
|
Work |
Power |
|
Work
is a scalar quantity. |
Power
is a scalar quantity. |
|
The
SI unit of work is Joule (J). |
The
SI unit of power is Watt (W). |
|
The equation to calculate work is Work = Force ×
Displacement. |
The equation to calculate power is Power = Work/Time |
2) Difference between Energy and Power
|
r.no |
Energy |
Power |
|
1. |
Energy is defined as the capacity to do some work.
It is the power which is integrated over time. |
Power is defined as the rate at which specific work
is done or which the energy is transmitted. |
|
2. |
The unit used to measure energy is joules or
watt-seconds |
The unit used to measure this is watt or joules per
second |
|
3. |
‘W’ is the symbol which denotes energy |
The symbol used to denote power is ‘P’. |
|
4. |
Energy changes from one form to another |
Power cannot be transformed from one type to another |
|
5. |
Energy is a time quantity or component |
It is an instantaneous quantity |
|
6. |
Various types of energy are kinetic, thermal,
potential, gravitational, sound, electromagnetic, light, elastic, etc |
Different kinds of power are electric power, optical
power, human power, etc. |
|
7. |
Energy is known to be stored, which can be used in
the future |
Power quantity is not storable or cannot be stored |
|
8. |
Energy is used in moving a car, heating a home,
lighting at night, flying an aeroplane, etc. |
Power finds its uses in mechanical applications,
electrical applications, heat applications, etc. |
3) Difference Between Kinetic and Potential Energy
|
Sr.no |
Kinetic Energy |
Potential Energy |
|
1. |
Kinetic energy is the kind of energy present in a
body due to the property of its motion |
Potential Energy is the type of energy present in a
body due to the property of its state |
|
2. |
It can be easily transferred from one body to
another |
It is not transferable |
|
3. |
The determining factors for kinetic energy are Speed
or velocity and mass |
Here, the determining factors are Height/ distance
and mass |
|
4. |
Flowing water is one of the examples of kinetic
energy |
Water present at the top of a hill is an example of
potential energy |
|
5. |
It is relative with respect to nature |
It is non-relative with respect to nature |
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