ASHAQ HUSSAIN BHAT
GL TEACHER SCHOOL EDUCATION
DEPARTMENT JAMMU AND KASHMIR
CHAPTER 3
WORK
ENERGY AND POWER
Introduction
In our day-to-day life, we talk about the term
work, energy and power. Out of them, energy is most important concept, since
all living things need energy to maintain life. The concept of work is closely associated
with the concept of energy. When we walk or run, we use the energy that we get
from the food we eat. The concept of power is also closely associated with that
of work. In our daily life, any physical activity In this blog, we shall discuss in
detail about these terms..
Work
Work is
said to done by a force on a body if the force applied causes a displacement in
the body or object. In other words, the conditions which must be satisfied for
the work to be done are
• a force
must act on the body and
• the body
must be displaced from one position to another position.
Examples:
(i) Work is done, when we hit a football. In this case, when we hit the football,
force is applied on the football and there is displacement for a fraction of second
by the force applied on football.
(ii) Work
is done when we lift a box through a height. In this case, the applied force
does work in lifting the box.
Factors
on which work done depends
·
Work done
by a force depends upon the following factors The magnitude of the applied
force: If a small force is applied on a body, less amount of work is done and
vice-versa. Thus Wα F, where F is the magnitude of force applied.
·
The
displacement of the body along the applied force: If a body travels large distance
on the application of force, large amount of work is done and vice- versa. Thus
W α s, where s is the magnitude of displacement.
Unit of
Work
The S.I.
unit of work is joule. One joule of work is said to be done on an object when a
force of one newton displaces it by one metre along the line of action of the
force.
1 joule =
1 newton x 1 metre or 1 J = 1 Nm
Bigger
units of work are kilojoule (kJ), megajoule (MJ) and gigajoule (GJ), i...
1
kilojoule - 10 J
1
megajoule - 10 J
1
gigajoule - 10 J
Work is a
scalar quantity, and it has only magnitude but no direction.
Work done
by a Constant Force
When a
constant force is applied in the horizontal direction: Let a constant E force F
be applied on a wooden block placed at position A on the smooth surface as shown
in figure. Suppose the block moves in the direction of applied force to the new
position 8 so that its displacement is s. Then, work done by the force is given
by
W=f x s
Thus,
work done on the block (or any other object) by a constant force is equal to
the product of the magnitude of the applied force and the distance travelled by
the body.
When
force is applied at an angle with the horizontal direction :
Let a
force F be applied on a wooden block at an angle with the horizontal direction
as shown in figure.
The
component of force Ƒ in the horizontal direction - FcosƟ.
The
component of F in the vertical direction - FsinƟ.
Let the
block moves horizontally and occupies a new position B so that it travels a
distances horizontally. Since, FsinƟ does not produce displacement in the block
in the upward direction, so the only force which displaces the block is FcosƟ.
According to the definition of work done,
W=force
applied x displacement of the body.
W=FcosƟ x
s= FscosƟ
W = Fxs
F-s is
read as dot product of F and s.
Thus,
work done on a body by a force is defined as the product of magnitude of
displacement and the force in the direction of displacement
Positive
work done: If force
is acting in the direction, of displacement, then displacement is positive so
the work done is positive. In this case 0 = 0° i.e., the force F acts in the
direction of displacement of the body.
Then W =
Fs cosƟ
W=f s ............ (cosƟ=1)
Example:
In a tug of war, the work done by a winning team is positive. The winning team
applies a force on the rope in the backward direction and the rope is also
displaced in the direction of applied force.
In this
case 0 = 90°
Zero work
done: If the
force is acting perpendicular to the displacement then work done is zero. In this
case 0 = 90°
i.e.,
force Facts at right angles to the displacement of the body.
Then W =
Fs cos90°
W = 0
(: cos 90º = 0)
i.e., no
work is done by the force.
Example: Work done by the force of
gravity on a box lying on the roof of a bus moving with a constant velocity on
a straight road is zero. In this case, force of gravity acts vertically
downward and the displacement of the box takes place horizontally.
Negative
work done : If the
force is acting in the direction opposite to the displacement then work done is
negative. If 0 = 180°
i.e.,
force F acts just opposite to the displacements of the body, then
W = Fs
cos180
W = - Fs ( cos180=
-1)
Thus work
done by force is negative.
Example:
In a tug of war, the work done by the losing team is negative. The losing team applies a rope in the backward direction but
the rope is displaced in the forward direction.
Work done
in lifting a body against gravity
The earth
attracts every object (or body) towards it. The force with which the earth
attracts a body towards its centre is called its weight. The weight of a body
is thus a force acting on it due to the gravitational attraction of the earth.
So, if a body is to be lifted up from the surface of the earth, a force equal
to the force of gravity (weight) must be applied to the body. Then, the work
done in lifting a body through a certain height (h) from the surface of the
earth is given by,
Work done
in lifting a body = Force of gravity x Height
= Weight
of the body x Vertical displacement
W= m x g
x h
where, m
is the mass of the body, g is the acceleration due to gravity, and h is the
vertical distance through which the body is lifted.
Thus,
when a body of mass m is lifted to a height h above the ground, work equal to
mgh is done on the body. Since the body is moved against the force of gravity,
hence the work W = mgh, is commonly called the work done against the gravity.
It is always positive.
Energy
Energy is
defined as the capacity to do work and it is measured by the total quantity of
work it can do. When a car runs, the engine of the car generates a force which
displaces the car. In other words, work is done by the car. This work is done
at the expense of fuel. Fuel provides the energy needed to run the car.The
conclusion is that, if there is no source of energy, no work will be done.
Unit of
Energy: The S.I. unit of energy is joule (J). The C.G.S. unit of energy is erg.
Other unit of energy are electron volt (eV), calorie (cal), kilowatt hour
(kWh).
1eV 1.6 ×
10-19 J, 1 cal = 4.186 J.
Kilowatt
hour is the commercial unit of energy.
1 kW h =
1000 W x 1h
We know, 1W=1JS-¹
1 h = 60
x 60 s = 3600 s
So, one
can write
1
kilowatt hour = 1000 W x 1 h=1000 × 1 ] s¹ × 3600 s
So, 1 kWh=3,600,000
J=3.6 × 106 J
Therefore,
1 kilowatt hour (1 kW h) is equal to 3.6 × 10° joules.
Examples:
(1) A man
or a horse does work when they pull a load.
(ii) A
moving body can set other bodies into motion when it collides with them.
(iii)
Compressed air in a cylinder causes the motion of the piston in it and thus
performs work. artificially are as follows:
Our
lifestyle demands energy in various forms. Some forms of energy available naturally
or created artificially are as follows;
·
Heat or Thermal Energy: The energy possessed by a body due to its
temperature is known as heat or thermal energy.
·
Chemical Energy: The energy released in chemical reactions is known as chemical energy.
·
Sound Energy: The
energy of a vibrating body producing sound is known as sound energy.
·
Electrical Energy: The energy of moving electrons in a conductor connected with a battery
is known as electrical energy.
·
Nuclear Energy: The energy released when two nuclei of light elements combine with each
other to form a heavy nucleus or when a heavy nucleus breaks into two light
nuclei is known as nuclear energy.
·
Solar Energy: The
energy radiated by the sun is known as solar energy.
·
Mechanical Energy: The energy possessed by a body because of its speed or position or
change in shape is called the mechanical energy. It is the sum of kinetic
energy and potential energy of a body. In this chapter our focus will be on
mechanical energy.
Kinetic
Energy
The
energy possessed by a body by virtue of its motion is called kinetic energy. So
a moving body can do some work due to its kinetic energy. The faster a body is
moving, the greater is the its kinetic energy. If a body is at rest, its
kinetic energy is zero. Kinetic energy is a scalar quantity.
Examples:
A high speed bullet, a fast moving cricket ball, a stone thrown with a high
speed, flowing wind, and flowing water.
Expression
for Kinetic Energy
Consider
a body of mass m lying at rest on a smooth floor. Let a force F be the force
applied on the body so that the body attains a velocity v after travelling a
distance s.
Work done
by the force on the body, W = Fs……………….....(i)
Since the
velocity of the body changes from zero to v, so the body is accelerated. Let a
be the acceleration of the body. Then according to Newton's second law of
motion, F = ma Substituting the value of
F=ma in equation (i), we get
W = m a s
Now,
using v ²-u²=2as, we get
v²-0=2as
or s=v2/2a……………………(iii)
Substituting
the value of s from equation (iii) in equation (ii), we get
W=max
v2/2a =½mv2
This work
done is equal to the kinetic energy of the body.
..
Kinetic energy, K.E.= ½mv2
Thus,
K.E. =½ mass of body x(speed of body)2
Relationship
between kinetic energy and momentum
We have,
KE=½mv2
=½mv2 =m/m=mv2/2m p2/2m (Ƥ=mv) KE= p2/2m.
Potential
Energy
Energy
possessed by a body by virtue of its position, (e.g., height above the ground)
or configuration (e.g., shape) is called potential energy. There are two types
of potential energies. These are as follows:
Gravitational
Potential Energy: The potential energy of a body by virtue of its height above
ground level is called gravitational potential energy. Example, the energy
stored in a body held at a certain height from the ground is gravitational
potential energy.
Elastic
Potential Energy: The potential energy of a body by virtue of its configuration
(or shape) is called elastic potential energy. Example, the potential energy
stored in the coiled spring of a clock is elastic potential energy.
Examples:
(i) Water stored in an overhead tank possesses gravitational potential energy
by virtue of its position (height above ground level).
(ii) A
raised hammer possesses gravitational potential energy by virtue of its height
above the ground level.
Expression
for gravitational potential energy
Suppose a
body of mass m is raised to a height h above the surface of the ground The force applied just to overcome the
gravitational attraction is
F= m x g……………………………(.i)
where g =
acceleration due to gravity
As the
distance moved is in the direction of the force applied, work is said to be
done. The object gains energy equal to the work done on it. Let the work done
on the object against gravity be W, so
Work done
= Force x Displacement
W=f x h………………………………(.ii)
Substituting
the value of F from equation (i) in equation (ii), we get
W= m x g x
h
Work done
on the object against gravity = Gravitational potential energy
Gravitational
potential energy (P.E.) = m x g x h
The
expression shows that potential energy depends on
(i) mass
m
(ii)
height h from ground
(iii)
acceleration due to gravity
Transformation
of Energy
Life on
the earth depends on the energy received from the sun. Hydrogen nuclei
(protons) fuse together to form helium nuclei in the sun's core. In this
process, energy of the nuclei is converted into heat energy. This heat energy
is absorbed by the atoms at the surface of the sun, and a part of it is
converted into light and other radiations. These radiations travel through
millions of kilometres of empty space to reach the earth. On receiving
radiation from the sun, the land and air get heated. This, as you know, causes
wind. This means that heat energy gets converted into kinetic energy. The
energy from the sun also heats up the water of oceans. Water evaporates from
ocean and rises up to form clouds. This is a case of conversion of kinetic
energy into potential energy.
Efficiency
of a device: In a
device, we supply a particular form of energy as input and we get a particular energy
as output. For example, in an electric heater, we supply electrical energy and
get heat The electrical energy form of is not into heat energy. Some energy
gets Converted in light energy. The percentage of electrical energy converted
into heat energy is called the efficiency of the electric heater.
Efficiency
ŋ, = out put energy/input energy = output power/input power
Conservation
of Energy
According
to law of conservation of energy, energy can neither be created nor destroyed,
it can be converted from one form to another. The law of conservation of energy
holds universally, i.e., it is valid in all situations and for all kinds of
transformations.
Verification
of Law of Conservation of Energy
Let m be the mass of a body held at a position A and at a height & above
the ground.
.
At position A
Kinetic energy of the body, K.E. =0
(the body is at rest at A)
Potential energy of the body P.E. -mgh
the body is lifted to a height h)
Total mechanical energy at A, M.EA = K.E. + P.E.
.=0 + mgh = mgh
Let the body be allowed to fall freely under the
action of gravity. In free fall, let the body reach the point
B with a velocity v1 where AB= x.
At position B
From the
equation of motion
v2-u2 = 2as
v2/1-0=2gx
v2/1=2gx …………….i
Kinetic energy of the body, K.E. =1 ⁄2 mv2/1………….ii
Substituting the value of v2/1 from equation (i) in equation (ii), we get
KE=
Height of the body at B above the ground = CB=
(h-x)
Total mechanical energy at B (M.EB) = K.E. + P.E. = mgx + mg(h-x)
At position C
From V²-U²= 2as
V2-0= 2gh
V2 =2gh……………………..iii
Kinetic energy of the body, K.E. =½ mv2…………………..iv
Substituting the value of v² from equation (iii) in equation (iv), we get
KE ==½ m(2gh) = mgh
Potential energy of the body at C, P.E. = mgh= mg (0) = 0 (the body is on
ground h=0
Total mechanical energy (M.Ec) = K.E. + P.E. = mgh
+0= mgh
(M.Ec) =mgh
Thus, we find that
MEA = MEB = MEC = mgh
Thus, the total mechanical energy (i.e., sum of kinetic energy and potential energy) always remains constant at each point of motion of a body falling freely under gravity and is equal to mgh (initial potential energy at height h). As the body falls, its potential energy decreases and kinetic energy increases. The potential energy changes into kinetic energy. At A, the energy of the body is entirely potential energy and at C, it is entirely kinetic energy. At B, the energy is partly kinetic and partly potential. Total mechanical energy remains constant (i.e., mgh) throughout. This proves the law of conservation of mechanical energy.
Conservation of Energy in case of a Simple Pendulum
A small metallic ball (called bob) suspended by a light string (thread) from a frictionless, rigid support is called a simple pendulum. When the bob of the pendulum is displaced to B, through a height h, it is given P.E. = mgh, where m is mass of the bob. On releasing the bob at B, it moves towards A.P.E. of the bob is being converted into K.E. On reaching A, the entire P.E. has been converted into K.E. The bob, therefore, cannot stop at A. On account of inertia, it overshoots the positions A and reaches C at the same height h above A. The entire K.E. of the bob at A is converted into P.E. at C. The whole process is repeated and the pendulum vibrates about the equilibrium position OA. At extreme positions B and C, the bob is momentarily at rest. Therefore its K.E. = 0. The entire energy at B and C is potential energy. At A, there is no height and hence no potential energy. The entire energy at A is in the form of kinetic energy. The swinging pendulum finally comes to rest due to friction at the support and friction of the air.
Power
The rate at which energy is transferred by an object is called the power delivered by that object, or rate of doing work is power.
If a force does work W in time t, the average power delivered by the force is
ρ＝ W/t
If the force does work at a constant rate, the average power is the same as the power at any instant during the time the work is being done.
By definition, Power ＝Work done/Time taken
Units of Power
The unit of power depends upon the units of work done, and of the time taken. The 5.1 unit of work done is joule (J), while that of time is second (s).
Unit of power = Unit of work/Unit of time =1 joule (J)/1 second(s) =1js-1
The unit of 1 J s¹ is called watt (W). So, the S.I. unit of power is watt (W). or 1W=1JS-¹
Thus, when a body works at the rate of 1 J per second, then its power is 1 watt (W).
Generally, bigger units called kilowatt (kW), megawatt (MW) and gigawatt (GW) are used.
1 kilowatt, 1 kW = 1000 watt
or
1 megawatt = 1 MW - 106 W
1 gigawatt = 1 GW -109 W
The unit of power in the British engineering system is horse power, denoted by hp.
1 hp=746 W -0.746 kW
To express large quantities of energy, joule is found to be very small and as such an inconvenient unit. For this purpose, a bigger unit of energy, called a kilowatt hour (kWh) is used.
One kilowatt hour is the amount of energy consumed (or work done) by an agent in one hour working at a constant rate of one kilowatt. Clearly,
1 kW h=1000 W x h
= 1000 (J s-¹) × 3600 s (1 W = 1Js¹)
= 3600000 J = 3.6 × 106 J = 3.6 MJ
A kW h, also called BOTU (Board of Trade Unit) or simply a unit, is used in households, industries and commercial establishments for measuring electric energy consumption. For example, if an electric heater of 1kW power is used for 2 hours, it consumes 2 kWh or 2 units of electric energy
Power in terms of energy
We know that, energy is the ability of a body to do work. Power is the rate of doing work. So, for doing a particular work, an equivalent amount of energy is supplied or transferred, so
Work done = Energy supplied
So, the rate of energy supplied by a body is called its power,
i.e., Power = Energy supplied/time taken =E/t = fxs/t = fxv
where v is the velocity of the body.
Average power
It is defined as the average amount of work done by a body per unit time,
i.e., Average power = Amount of work done/Time taken
In terms of energy, Average power =Amount of energy supplied/Time taken
Since power is the ratio of energy to time, both being scalar quantities, power is also a scalar quantity.
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