Law Conservation of Energy
Energy can neither be created nor be destroyed
Whenever the energy changes from one form to another form of
energy the total amount of energy remains constant.
Key Concepts
A fundamental principle of physics is that energy cannot be created or destroyed, although it can be converted from one
form to another.
• The sum of all forms of energy remains constant in any isolated or closed system.
• Interconversion of energy
The principle stating that energy cannot be created or destroyed, although it can be changed from one form to
another.
Interconversion of different Forms of Energy:
Now we discuss how it can be changed from one form to another Form .
Examples
When you switch on a bulb actually you are converting the electrical energy into light energy.
And what happens when you run, chemical energy (potential energy )of food changes into mechanical energy.
As all fuels like petrol, neutral gas and wood have chemical energy (potential energy) so when we burn these fuels energy I
mean potential energy or chemical energy changes into light and heat energy. And you can cook by using this heat energy
of fuels.Hydropower, here we can explain the energy conversion when the water is dropped from a certain height at this certain
height this water has potential energy ,but when you drop this water from that height ,now this moving water has kinetic
energy and this kinetic energy of water makes the turbines to run moving water this moving water makes the turbines to
run , and this turbine converts the kinetic energy of water in to mechanical energy and generator converts this mechanical
energy of turbines in to electrical energy this is how the energy is transformed.
How Energy remains constant
To understand this let’s discuss the phenomena of simple pendulum.
When you move the Bob of simple pendulum to extreme position from it’s mean position .At extreme positions the Energy
of the system is potential energy which is also total energy ,and here the kinetic energy is zero because the velocity at
extreme position is zero .so when you move from
Mean to Extreme position: kinetic energy is converted into potential energy and this potential energy is also total energy
Because
Total Energy =P.E + K.E here potential energy is Maximum but kinetic is zero so ,
Total energy =P.E +0
Total Energy = potential energy= constant
Total Energy is potential energy and is constant and .when you move the Bob of the pendulum from extreme to mean
position now the energy starts changing from potential to kinetic energy
Extreme to mean position: From extreme to mean the starts converting from potential to kinetic Energy and at mean it’s
total kinetic energy ,there is no potential energy at mean position ,mean zero potential energy at mean because of the
position of the Bob zero displacement here so.
Total Energy = P.E + K.E
Here in this case potential energy is zero so
P.E=0 Total Energy =0+K.E
Total Energy=K.E = constant
But when you move the Bob of the simple pendulum to a certain distance on either side of the mean position, then the
energy is partially kinetic and partially potential energy. So, At a certain distance from mean position : Energy is partially kinetic and partially potential energy
When the Bob come close to mean position it has more kinetic energy then potential energy because of the high velocity
and when you move away from the mean position the kinetic energy start decreasing and potential energy start increasing
and at extreme position there is a more amount of potential energy than the kinetic energy and near to mean position there
is a more amount of kinetic energy .But in both cases the total energy of the system remains constant.
As we have neglected all frictional forces in these cases .
This system also tells us the if there is a loss in form of Energy , same amount of energy is added to other form of energy ,
that’s how the total energy of the system remains constant.
Basic Forms of Energy
Energy is found in different forms such as light, heat, chemical energy we can put all the forms of energy into two
categories potential and kinetic Energy .
Potential energy
Potential energy is the energy that is stored in an object due to its position is called potential energy for example when we
stretch a rubber band or lift a stone to some high energy is stored in these objects this energy is called potential energy .
when you lift up a brick to some height or to a certain height energy is stored in that brick and when you release that brick
from that certain height this potential energy starts converting itself to kintic Energy.
Kinetic Energy
Energy in a body due to its motion is called kinetic energy a moving bus and running tap water possess kinetic energy it is
the amount of kinetic energy depends on the mass of the system and the object as well as the speed of the system. The train
has more kinetic energy than a car moving at the same speed this shows that if two objects have the same masses but have
different speeds then the then the object that has more speed will have more kinetic energy and if the two objects have the
same speeds but have different masses so the body with large amount of mass we’ll have more kinetic energy.
Key words
Energy , conservation of energy , potential energy , Kinetic energy . Simple pendulum etc.
Test your understanding
Why the kinetic energy is zero at extreme position?
What kind of energy stored when we put a stone in the sling of a catapult and stretch it’s rubber ?
When you cook food how the energy transforms?
Law Conservation of Energy
Energy can neither be created nor be destroyed
Whenever one form of energy changes into another from of energy the total energy of the system
remains constant.
Key Point
Fundamental law of Physics is that energy can not be created or destroyed although, it can be
converted from one form to another.
• Sum of all forms of energy remains constant in any closed or isolated syestem.
• Conservation of Energy , Mechanical Energy conservation
• How this law relates with Newton motion law
• First law of thermodynamics .
What is principle of conservation of Energy?
Basic concept of this principle is conservation so first we should know what is the meaning of
conservation in Physics, The meaning of conservation in physics something which does not
change . The variable quantify in an equation remains constant over time, it has the same value
before and after an event. It’s not only the energy which is conserved in mechanics also
momentum and angular momentum are conserved quantities in mechanics. We are talking about
Energy but total Energy as the body move around over time energy associated with this body
like potential , kinetic , heat might change forms but if energy is conserved then total Energy will
remain the same .
But , why we are saying that if Energy is conserved then total will remain the same it means there
are some conditions where energy is conserved and also this shows that some of the things
where we can’t say that energy is conserved. Yes it’s true, let’s discuss where Energy is conserved
and what are the things which does not obey law of conservation of energy .
A Ball rolling across the Floor : A rolling ball across the Floor does not obey this law of
conservation of Energy Because when the ball rolls across the floor it is not isolated from the
floor and there is a friction between floor and ball and the floor will do work on ball by using this
friction . But if we talk about both ball and floor together then we can say the energy is conserved,
but only for ball energy is not conserved .But in case of ball floor syestem energy is conserved .
Generally in mechanics we , deal with. Kinetic , potential , elastic potential energy etc.
Sum of initial Energy = sum of final Energy
So here we conclude that Conservation of energy only applies to isolated syestem .
When we talk about syestem it means it’s collection of objects , but some time considering the
objects for our need in our equation we often ignore some things and first thing that comes to
our mind is environment which is often ignored by the physicst. Because it may effect the
accuracy level. So , being a good physicst you should have an Idea of ignoring the interaction ,
mean a good physicst always ignores those interaction which he knows will not effect the overall
calculation of the equation.
For Example, A person is making a bungee jumping from a bridge , so what are minimum objects
should be included , I think the person , earth and bungee should be the minimum objects to be
chosen for our equation and if you further want to include you can include air as he as it will not
work on jumper via drag force , and further if you want to include you can include the bridge and
it’s foundation but we know that if we ignore the bridge it will not effect because the bridge is
much heavier than person , so we can safely ignore this so you should keep in mind that what
are the interaction you are going to ignore in your calculation.
Conservation of Energy , Mechanical Energy
To understand conservation of Energy first we should know mechanical Energy
What Is Mechanical Energy And how it conserved ?
Mechanical Energy is the sum of kinetic Energy and potential Energy .
Mechanical Energy= Kinetic Energy + Potential Energy
If you are going to discuss the Conservation of Mechanical Energy then you should know that the
mechanical Energy Conservation is only applies to conservative forces and should have an idea
of conservative forces to understand this concept of mechanical Conservation because
Conservation of mechanical Energy is very important for easy calculations in physics .
Conservative forces and Non conservative forces
Remember that conservation of mechanical Energy is only applies to conservative forces where
you can get back the energy you have provided to a system because the work done by
conservative forces along a closed path is zero For example Force of gravity is a conservative
force, spring force is also a conservative force where the energy mechanical Energy is conserved.
And non conservative forces like force of friction or drag force are those forces where it’s difficult
to recover the energy that you have provided to a system, mean the energy transferred by non
conservative forces how ever it’s difficult to recover and the reason for that we can not recover
it easily because it often ends up in the form of heat or other form of energy which is typically
outside the syestem in others words you can say energy is lost to the Environment. So
Conservation of me mechanical Energy is only applies when all forces are conservative and luckily
in many cases the non conservative forces are negligible which makes our calculations easy.
To understand this concept we take an example of simple harmonic oscillator when it oscillates
between kinetic energy and potential Energy but it’s total Energy remains constant
Potential Energy
When Force F = KX is applied to a mass m attached to the end of spring. It displaces distance x and
restores P.E which is elastic potential Energy in spring and this force is given by this equation
Elastic potential Energy = 1/2 kx^2
At mean position which is O in that figure here x is zero
At mean position : x=0 so U= 0 so potential energy is zero at mean position
At Extreme position : X = maximum
Due to this Maximum distance from mean position the elastic potential Energy becomes Maximum
Kinetic Energy
As we know kinetic energy is the energy due to motion of a body
So it’s equation is
K.E = 1/2 mv^2
It is depending on mass as well as velocity of the object so mass is conserved in this case which is not
changed in this case velocity is variable here so more will be the velocity the more Kinetic Energy will be
possessed by the body
So At Extreme position :Velocity of the object will be zero so that’s why kinetic Energy of the body will
be zero at extreme position which is point m which is our Right extreme here the velocity of the object
will be zero so
V=0 so Kinetic Energy according to formula will become zero
K.E=0
At mean position: the velocity of the object is maximum so
V= maximum
Due to this Maximum velocity Kinetic Energy of the object will be maximum
K.E = maximum
K.E= 1/2 mv^2 (maximum)
Total Energy (Mechanical Energy)
Total Energy =P.E+ K.E
By solving the equation we concluded that
T.E = 1/2 kx^2
Where here x is representing maximum displacement so
Energy of harmonic oscillator oscillates between kinetic energy and potential energy at mean position
energy is wholly kinetic energy add potential energy is zero at extreme positions energy is wholly
potential energy and kinetic energy is zero in between mean position and extreme position at any
displacement from mean position energy is partly kinetic and partly potential energy but total energy
remains constant.
You can understand how the total Energy remains constant by examining this table so this table shows
that while moving between mean position and extreme positions the energy transforms but total Energy
of the system remains constant. Here point O represent mean position and x positive is right extreme
and x negative is our left extreme .
So, here we concluded that how mechanical Energy is conserved and this also proves that spring force is
a conservative force.
Laws of Motion and Conservation of Energy
I think Newton second law of motion which is F=ma explains very well the law of conservation of energy
and this Newton second law of motion proves that energy Conservation law is true. According to
statement of law of conservation of energy total Energy of an isolated system remains constant this is
the indication of all parts of the system I think the whole system is obeying certain motion laws. And
also this shows that energy of the system should not be changed after interaction or collisions and for
this the laws of motion be such that after interaction energy should remain constant.
And in case of Everlasting and perpetual motion
In case of perpetual or everlasting motion by listening this word first thing that comes to our mind is
perpetual machine , where no reduction in it’s speed no and this continues it’s motion for er because it
is designed such that but I think it’s impossible to have such machine in reality. Because if you want this
type of machine which would run forever you should have a complete isolated system andthst system
subject to conservative forces only then there is a possibility that you can run this machine fire er , but in
real you can not completely isolate a system from Environment. And energy can never be consevrd in
that machine .
Our Earth
I think our Earth is the best example to understand this concept of machine as we know that our Earth is
moving around the as well as the earth is roasting on its axis In space with the speed of 1700 km/h and
completes it’s one rotation in 24 hours and formation of days and night are the result of this rotation
and also Earth is revolving in anti clock wise direction from west to east around the sun with a speed of
107,000km/h and completes it’s one revolution in 365 days and 6 hours . So what do you think our
Earth speed is gradually decreasing or not? Yes our Earth speed is gradually decreasing because it
interacts with moon as well as other celestial Bodies and also tidal friction .
This means our Earth day
time is increasing with the passage of time and that’s why scientist have to add leap seconds after every
couple of years to account with the variation in the length of day. And it also shows that if you go back
to past on early earth at that I think there would be small length of the day on earth because at that
time it was a start and according to scientist 4.5 billion years ago the duration or length of the day on
earth was only 6 hours . So you can imagine how this interaction can effect the movement of the objects
.from this point of view it’s impossible to design such a machine which is everlasting or perpetual which
can conserve energy. Today lots of effort are made to make such flywheel which work in space whichhas very low effect of friction actually this kind of flywheel work in space to conserve energy but stillthey lose energy so it’s impossible to have such machines that can conserve energy completely.
First law of thermodynamics
First law of thermodynamics, which is in any thermodynamics process , when heat is added to a system
,this heat energy appears as an increase in the internal energy of the system plus the work done by the
system on its environment.
This statement shows that how the energy transferred from one system to other and how it remains
constant mean how total Energy remains constant
Q=∆U+W where
Q is the amount of heat added to that system which appears as change in internal Energy not the system
∆U and the work done on the system w and that’s how energy is conserved and this shows that first law
of thermodynamics is the law of conservation of Energy.
Test your knowledge
• How the tidal friction effect the earth motion?
• Is it possible to make an engine or machine which can conserve energy completely if no then why?
• Prove that how Newton second law of motion proves that energy Conservation law is true.