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Definition of potential energy

Having decided the universal zero reference, we are now in position to define potential energy, using the expression obtained for the change in potential energy :

Δ U = U 2 U 1 = W C

If we set initial position at infinity, then U 1 = 0 . Let us denote potential energy of a system to be “U” for a given configuration. Then,

U 0 = W C

U = W C = 0 F C r

Hence, we can now define potential energy as given here :

Potential energy
The potential energy of a system of particles is equal to “negative” of the work by the conservative force as a particle is brought from infinity to its position in the presence of other particles of the system.

We should understand that the work by conservative force is independent of path and hence no reference is made about path in the definition. This work has a unique value. Hence, it gives a unique value of potential to the system of particles.

Distribution of potential energy

There is a peculiar aspect of the definition of potential energy, presented above. It defines potential energy of the system of particles in terms of work on a “single” particle. This peculiarity can be explained as it defines work in the presence of other particles and as such accounts for the forces operating on the particle due to their presence.

This definition, however, is not clear about how potential energy is distributed among the particles in the system. The value of potential energy does not throw any light on this aspect. As a matter of fact, it is not possible to segregate potential energy for the individual constituents of the system. Potential energy, therefore, belongs to all of them – not to any one of them.

Potential energy and external force

The potential energy is defined in terms of work by conservative force and zero reference potential at infinity. It is equal to the “negative” of work by conservative force :

U = W C = 0 F C r

Can we think to express this definition of potential energy in terms of external force? In earlier module, we have analyzed the motion of a body, which is raised by hand slowly to a certain vertical height. The significant point of this illustration was the manner in which body was raised. It was, if we can recall, raised slowly without imparting kinetic energy to the body being raised. It was described so with a purpose. The idea was to ensure that work by the external force (in this case, external force is equal to the normal force applied by the hand) is equal to the work by gravity.

Since speed of the body is zero at the end points, “work-kinetic energy” theorem reduces to :

W = K f K i = 0

W = 0

This means that work by “net” force is zero. It follows, then, that works by gravity (conservative force) and external force are equal in magnitude, but opposite in sign.

W = W C + W F = 0

W F = W C

Under this condition, the work by external force is equal to negative of work by conservative force :

W F = F C r

where “ F C ” is conservative force. It means that if we work on the particle slowly without imparting it kinetic energy, then work by the external force is equal to negative of the work by conservative force. In other words, work by external force without a change in kinetic energy of the particle is equal to change in potential energy only. Equipped with this knowledge, we can define potential energy in terms of external force as :

Questions & Answers

how does Neisseria cause meningitis
Nyibol Reply
what is microbiologist
Muhammad Reply
what is errata
Muhammad
is the branch of biology that deals with the study of microorganisms.
Ntefuni Reply
What is microbiology
Mercy Reply
studies of microbes
Louisiaste
when we takee the specimen which lumbar,spin,
Ziyad Reply
How bacteria create energy to survive?
Muhamad Reply
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Muhamad
they make spores
Louisiaste
what is sporadic nd endemic, epidemic
Aminu Reply
the significance of food webs for disease transmission
Abreham
food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.
Mark
explain assimilatory nitrate reduction
Esinniobiwa Reply
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
Elkana
Examples of thermophilic organisms
Shu Reply
Give Examples of thermophilic organisms
Shu
advantages of normal Flora to the host
Micheal Reply
Prevent foreign microbes to the host
Abubakar
they provide healthier benefits to their hosts
ayesha
They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!
Mark
what is cell
faisal Reply
cell is the smallest unit of life
Fauziya
cell is the smallest unit of life
Akanni
ok
Innocent
cell is the structural and functional unit of life
Hasan
is the fundamental units of Life
Musa
what are emergency diseases
Micheal Reply
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
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Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
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Heyy Lubega hussein where are u from?
_Adnan
en français
Adama
which site have a normal flora
ESTHER Reply
Many sites of the body have it Skin Nasal cavity Oral cavity Gastro intestinal tract
Safaa
skin
Asiina
skin,Oral,Nasal,GIt
Sadik
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How can Commensal Bacteria change into pathogen?
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all
Tesfaye
by fussion
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what are the advantages of normal Flora to the host
Micheal
what are the ways of control and prevention of nosocomial infection in the hospital
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what is inflammation
Shelly Reply
part of a tissue or an organ being wounded or bruised.
Wilfred
what term is used to name and classify microorganisms?
Micheal Reply
Binomial nomenclature
adeolu
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Source:  OpenStax, Physics for k-12. OpenStax CNX. Sep 07, 2009 Download for free at http://cnx.org/content/col10322/1.175
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