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Relation among energy types

The expression of mechanical energy of the “Earth – satellite” system is typical of two body system in which one body revolves around other along a circular path. Particularly note the expression of each of the energy in the equation,

E = K + U

G M m 2 r = G M m 2 r G M m r

Comparing above two equations, we see that magnitude of total mechanical energy is equal to kinetic energy, but different in sign. Hence,

E = - K

Also, we note that total mechanical energy is half of potential energy. Hence,

E = U 2

These relations are very significant. We shall find resemblance of forms of energies in the case of Bohr’s orbit as well. In that case, nucleus of hydrogen atom and electron form the two – body system and are held together by the electrostatic force.

Importantly, it provides an unique method to determine other energies, if we know any of them. For example, if the system has mechanical energy of - 200 X 10 6 J , then :

K = - E = 200 X 10 6 = 200 X 10 6 J


U = 2 E = - 400 X 10 6 J

Energy plots of a satellite

An inspection of the expression of energy forms reveals that that linear distance “r” is the only parameter that can be changed for a satellite of given mass, “m”. From these expressions, it is also easy to realize that they have similar structure apart from having different signs. The product “GMm” is divided by “r” or “2r”. This indicates that nature of variation in their values with linear distance “r” should be similar.

Energy plots

Plots of kinetic, potential and mechanical energy .vs. distance

Since kinetic energy is a positive quantity, a plot of kinetic energy .vs. linear distance, “r”, is a hyperbola in the first quadrant. The expression of mechanical energy is exactly same except for the negative sign. Its plot with linear distance, therefore, is an inverted replica of kinetic energy plot in fourth quadrant. Potential energy is also negative like mechanical energy. Its plot also falls in the fourth quadrant. However, magnitude of potential energy is greater than that of mechanical energy as such the plot is displaced further away from the origin as shown in the figure.

From plots, we can conclude one important aspect of zero potential reference at infinity. From the figure, it is clear that as the distance increases and becomes large, not only potential energy, but kinetic energy also tends to become zero. We can, therefore, conclude that an object at infinity possess zero potential and kinetic energy. In other words, mechanical energy of an object at infinity is considered zero.

Gravitational binding energy

A system is bounded when constituents of the system are held together. The “Earth-satellite” system is a bounded system as members of the system are held together by gravitational attraction. Subsequently, we shall study such other bounded systems, which exist in other contexts as well. Bounded system of nucleons in a nucleus is one such example.

The characterizing aspect of a bounded system is that mechanical energy of the system is negative. However, we need to qualify that it is guaranteed to be negative when zero reference potential energy is at infinity.

Questions & Answers

what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
How can I make nanorobot?
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
how can I make nanorobot?
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Gravitation fundamentals. OpenStax CNX. Sep 26, 2007 Download for free at http://cnx.org/content/col10459/1.2
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