What Is the Connection Between Energy, Potential, and Work?

[nouveau_riche]

what is energy?
as much as i know "energy is the capacity/ability to do work"
if that is true then
what is potential ?

how can energy be positive or negative?
if the sign of work is the answer then it is just a matter of convention

 

[BruceW]

You are right, energy is capability to do work. Feynman explained energy like this: there is a child who has a certain number of toy blocks, and he keeps hiding them in different places, but the number of toy blocks always stayed the same.

So a good definition of energy is simply something which is conserved with time. Potential energy are all the forms of energy that are not kinetic energy.

In most situations, the actual value of the energy is not important, only that it doesn't change with time. The actual value of energy might be important in quantum field theories though.. I'm not sure

 

[Naty1]

There are many forms of energy...potential, kinetic, rotational, electrical,magnetic, nuclear,thermal,chemical, etc.


lots here:
http://en.wikipedia.org/wiki/Energy

and note "transformations" from one form of energy to another...


potential energy: see here:

http://en.wikipedia.org/wiki/Potential_energy

and see the "reference level" for positive/negative.
Potential also commonly applies to electrical potential which is another term for voltage.

In cosmology, gravitational energy is usually taken as a negative while nulcear reactions, such as fission and fusion in stars is positive. But that's a convention not an absolute.

 

[DrStupid]

You are right, energy is capability to do work.

And what is work?

 

[BruceW]

Work just means energy transferred from one system to another.

For example, I have chemical energy stored in my muscles. When I throw a bowling ball, I turn some of the chemical energy in my muscles into kinetic energy of the bowling ball. So I would say that I have done work on the ball.

Edit: also, in thermodynamics, work done on a gas usually means the gas is compressed. (Which requires transferring energy from some external source to the gas). In fluids, work can also mean something as simple as stirring the fluid. (Again, energy is transferred from an external system to the fluid, due to its increased kinetic energy).

 

[DrStupid]

Work just means energy transferred from one system to another.

That would mean energy is capability to transfer energy. Does anybody know a definition of energy or work without such an idem per idem construction?

 

[Dale]

That would mean energy is capability to transfer energy. Does anybody know a definition of energy or work without such an idem per idem construction?

Yes, there have been many threads on this topic. Just do a search for "what is energy". The threads usually get locked with one or more of the posters being banned.

 

[Dale]

what is energy?
as much as i know "energy is the capacity/ability to do work"
if that is true then
what is potential ?

Potential is energy divided by charge.

how can energy be positive or negative?
if the sign of work is the answer then it is just a matter of convention

Only differences in energy are important. So whether you say something has zero energy and falls to -10 J or whether you say that it has 10 J energy and falls to zero the physical result is the same.

 

[BruceW]

That would mean energy is capability to transfer energy. Does anybody know a definition of energy or work without such an idem per idem construction?

How about: 'the energy of a closed system does not change' and 'work done on one system by another is the exchange of energy of those two systems'.

 

[DrStupid]

How about: 'the energy of a closed system does not change' and 'work done on one system by another is the exchange of energy of those two systems'.

That's not sufficient because it applies not only to energy and work but to all conserved properties and their derivations with respect to time (e.g. momentum and force, angular momentum and torque, charge and current and so on). The definition should be specific for energy and work.

 

[BruceW]

Well, since the OP'er was asking basic questions about energy, I thought I should keep my answers suitable for a beginner in physics rather than go into detail.

 

[DrStupid]

Well, since the OP'er was asking basic questions about energy, I thought I should keep my answers suitable for a beginner in physics rather than go into detail.

If somebody ask me this question I usually give him the same answer. But I don't like it because I know that it is not a valid definition. That's why I am looking for an alternative that is not only handy but correct to.

 

[BruceW]

That's the thing with physics, often you need to sacrifice precise definition so that you can explain something intuitively to someone who is new to the subject.

For example, we are all taught that the electron orbits round the nucleus. But when we learn QM, we find that actually its much more complicated, since the electron doesn't take a particular path through space. And the s-orbital electrons have zero orbital angular momentum, so they're not even moving around the nucleus at all!

But back to energy, I've found (over my time learning physics) that the precise meaning of energy depends on the branch of physics you are using it in.

For lagrangian mechanics, energy is a conserved quantity of the system as long as the potential of the system is not explicitly time-dependant.

In QM, the energy eigenstates are stationary states, meaning that if the entire system is an energy eigenstate, then a change in time only changes the state by a phase factor. (Which is due to the time dependant Schrodinger equation).

Energy/mass in Einstein's relativity is a generalisation of classical energy, such that it is a locally conserved quantity.

Energy in statistics is a useful concept, in that it gives us the distribution of the number of particles in particular energy states.

Energy density in electrodynamics, denoted u is given by the equation:
\frac{\partial u}{\partial t}=- \nabla \cdot S - J_f \cdot E

Application of Noether's theorem says that energy conservation is due to invariance with respect to time translation. So the energy conservation is due to this time symmetry, which is mathematically represented by some kind of group.

This last definition seems like the best and most general definition of energy. Unfortunately, I don't know much about the maths of groups, etc, so I can't tell you exactly what the group is or how it gives rise to a definition of energy conservation..

 

[Naty1]

BruceW: #13 post, very good!

 

[nouveau_riche]

That would mean energy is capability to transfer energy. Does anybody know a definition of energy or work without such an idem per idem construction?

as it appears energy can't be just transfer of energy,a system may have an energy but is not necessarily doing work

 

[nouveau_riche]

Potential is energy divided by charge.

Only differences in energy are important. So whether you say something has zero energy and falls to -10 J or whether you say that it has 10 J energy and falls to zero the physical result is the same.

well it is not the potential energy or kinetic,i was just only interested in definition of energy

 

[nouveau_riche]

Yes, there have been many threads on this topic. Just do a search for "what is energy". The threads usually get locked with one or more of the posters being banned.

it would be kind of you to provide the best link(the thread)

 

[nouveau_riche]

well no one actually gave me the difference between the energy and potential?

 

[BruceW]

The total energy is the sum of kinetic and potential energies. So if something is a form of energy and is not a kinetic energy, then it is a potential energy.

Edit: So, you could say a particular potential energy (ie gravitational potential energy) is a specific type of energy. Only the total energy is conserved, so we must add up all the types of energy in a system to get the total energy (which is a very useful quantity).

 

[nouveau_riche]

The total energy is the sum of kinetic and potential energies. So if something is a form of energy and is not a kinetic energy, then it is a potential energy.

what you brought up here is itself an energy not a potential
as you said it potential energy

 

[BruceW]

I see, you were asking 'what is potential'? Not 'what is potential energy'. Sorry, I got the two mixed up. Good question.

In physics, there are scalar and vector potentials which are fields in space. So generally, the word 'potential' has nothing to do with energy. But often there are potentials which are related to a form of potential energy.

One example is the (scalar) gravitational potential. If we have a mass in some gravitational field, then the gravitational potential of that field times by the mass is equal to the gravitational potential energy.

 

[DrStupid]

That's the thing with physics, often you need to sacrifice precise definition so that you can explain something intuitively to someone who is new to the subject.

Indeed, that's the problem. It seems to be the best compromise to give a simple answer first and if somebody claims that it is not correct to give him your summary of different definitions. Then he will have something to think about )

Sometimes I start with the definition of mechanical work as the line integral of a force over a path. This also has its limitations but it works for almost all mechanical problems.

 

[Dale]

i was just only interested in definition of energy

Energy is defined as the capacity to do work, as you already stated in your OP. I don't know why you are asking and re-asking a question to which you already know the answer.

 

[Dale]

well no one actually gave me the difference between the energy and potential?

I did, in post 8. Frankly, a statement like this is very irritating. If you didn't understand the answer, then ask follow-up questions, but to pretend like nobody answered is rude and makes me less interested in trying to answer further. Why should we bother if you are not even going to read the answers and will pretend that no answer was given.

 

[Dale]

it would be kind of you to provide the best link(the thread)

https://www.physicsforums.com/showthread.php?t=507345
https://www.physicsforums.com/showthread.php?t=498497

Both threads were locked, and both resulted in the ban of one or more of the participants. By going through the existing threads you can probably find the information you need without risking getting banned yourself.

 

[nouveau_riche]

Energy is defined as the capacity to do work, as you already stated in your OP. I don't know why you are asking and re-asking a question to which you already know the answer.

I did, in post 8. Frankly, a statement like this is very irritating. If you didn't understand the answer, then ask follow-up questions, but to pretend like nobody answered is rude and makes me less interested in trying to answer further. Why should we bother if you are not even going to read the answers and will pretend that no answer was given.

in spite of the fact that i already know the answer i raise this thread to highlight the similarities between energy and potential,when you talk about potential energy or potential difference you are only taking in account the transformation in energy not the ability to give that energy

 

[sanzefor]

hello,
some interactive animations that speak of energy http://physiquecollege.free.fr/physics_chemistry_middle_high_secondary_grammar_school_higher_education_academy_co.uk.us.en/mechanics_interactive.htm" .

 

[mounith]

"energy is the capacity to do the work" that's correct.. and the word POTENTIAL ENERGY means this has a capacity to do work STILL.. i mean the potential energy is the energy in static state.. all other forms of energies get converted from one to the other in no time.. like kinetic energy of electrons to light energy, light energy to heat energy, and this heat energy to radiations and this further hits a surface and converts to kinetic energy of electrons through the photoelectric effect and so on... But the POTENTIAL ENERGY is one which still has potential to do work and waiting for a chance to do work...

and the signs of energy are just conventions which shows the direction of flow of energy towards or outwards a system or with respect to a system..
The sign is not for the magnitude of the energy...
all the magnitudes of physical quantities are relative to something.. so if the value is zero joules, it doesn't mean it doesn't contain any energy...

 

[Dale]

i raise this thread to highlight the similarities between energy and potential

Clearly potential and potential energy are similar. They are proportional to each other, by a factor of charge.

when you talk about potential energy or potential difference you are only taking in account the transformation in energy not the ability to give that energy

What do you mean by this?

 

[nouveau_riche]

Clearly potential and potential energy are similar. They are proportional to each other, by a factor of charge.

in that case potential=energy*k
k being some constant of proportionality and that's all i was interested in

What do you mean by this?

in simple way-what gives charge the energy contained in its potential energy as you like to say it?

 

[Dale]

I wouldn't say that the potential energy is in the charge, I would say that it is in the system. Then what gives the system the energy is the configuration of the different parts of the system.

 

[nouveau_riche]

I wouldn't say that the potential energy is in the charge, I would say that it is in the system. Then what gives the system the energy is the configuration of the different parts of the system.

so how would justify that configuration for a particle say electron?

 

[Dale]

An electron, by itself, doesn't have a potential energy.

 

[nouveau_riche]

An electron, by itself, doesn't have a potential energy.

but have the potential to give potential energy
so how does electron gets this potential?

 

[BruceW]

Its all about the system man. For example - if we had two massive bodies, then the gravitational potential energy is a property of the system. It isn't a property of one body or the other.

If we had an electron in some external electromagnetic field, then the potential energy is dependant on both the electromagnetic field and the electron.

Another way of thinking is like this: a charged particle gains some kinetic energy. So this energy must have come from somewhere. We realize that it came from the potential energy of the system.

 

[Dale]

but have the potential to give potential energy
so how does electron gets this potential?

Again, not by itself, only as part of a system. Then it is the configuration of the whole system that determines the potential energy.

 

[nouveau_riche]

Again, not by itself, only as part of a system. Then it is the configuration of the whole system that determines the potential energy.

well if that is true then the charge of an electron should be the property of system not some constant value like 1.6x10^-19

 

[Dale]

Why is that? I don't get your logic here. Potential energy is not a property of a particle, but why would that lead you to believe that charge is not a property of a particle?

 

[MrNerd]

I think he means that an electron has an electric field around it. This is what the potential is. Inserting another charge into the field gives the particle potential energy, at the expense of another form. You can't just pop energy into existence(That would make the existence of energy impossible, though. But unless you're doing some uber-crazy mad scientist on meth type of stuff that hasn't been thought of yet, energy will not change. That's not the point though). I don't think work is the ability to use the energy. I believe it means that energy is transferred from one form/place to another, high to low.

Back to the second charge. It's now in the electric field. But it took work to move it there, as given by the equation W = Fd. Since work is a change in energy between two differing sources, it therefore requires a transfer of energy.

Think of it like a scifi forcefield that you can penetrate if you push hard enough. If you don't push, you don't get through, or maybe even pushed back. But if you push hard enough, and perform work, you can get closer to the source.

If you're wondering about the definition of energy, I don't think there is a perfect answer to it. I just consider it "stuff" that is existence. Without energy, there is no existence. So perhaps one could define it as existence.

 

[galtsgulchb]

Defining energy looks like it should be simple but is not. The best way to understand the concept “energy” is to get familiar with it in many different contexts (often by solving homework problems or doing labs). Once you are familiar with the concept of energy you can then appreciate a nice tidy definition of energy. That said, I will take a whack at defining energy.

The first clue to the answer is to realize that energy is not a separate entity; it is property of an entity. (Therefore, you should not imagine little blobs of energy.) In order to avoid the circular definitions pointed out above, you might define energy this way:

energy: a property of entities that makes things happen.

Of course, if you were not already familiar with the concept energy in the real world you would ask, “Wait! Make what happen?” By "happen" I mean to move a thing or change the state of a thing. This is where you need real world experience so you can imagine examples, “Ah, yes, I can move a block and compress a piston.”

In summary, do not worry too much about a tidy definition of “energy” at the beginning; that is putting the cart before the horse. It is better to get familiar with the concept of energy in real world examples in the beginning. Leave the tidy definition to the end.

 

[Dale]

Defining energy looks like it should be simple but is not.

It is simple. In Newtonian mechanics, "Energy is the capacity to do work." Easy, done.

I don't know why people think that energy is so difficult. See:

https://www.physicsforums.com/showthread.php?t=507345
https://www.physicsforums.com/showthread.php?t=498497

Both threads were locked, and both resulted in the ban of one or more of the participants. By going through the existing threads you can probably find the information you need without risking getting banned yourself.

 

[galtsgulchb]

It is simple. In Newtonian mechanics, "Energy is the capacity to do work." Easy, done.

I don't know why people think that energy is so difficult.

I agree this is a good start. The difficulty comes when the new student is told, "Work is the amount of energy transferred to a body."

 

[MrNerd]

I agree this is a good start. The difficulty comes when the new student is told, "Work is the amount of energy transferred to a body."

That doesn't seems too bad. Energy is the ability to do something. Work is the amount of something done.

Think of it like this:

A job is an ability to earn money. A wage/salary is merely a measure of how much one earns.

Change it to:


Energy is the ability to change something. Work is merely a measure of the amount of change.

 

[nouveau_riche]

It is simple. In Newtonian mechanics, "Energy is the capacity to do work." Easy, done.

I don't know why people think that energy is so difficult. See:

https://www.physicsforums.com/showthread.php?t=507345
https://www.physicsforums.com/showthread.php?t=498497

Both threads were locked, and both resulted in the ban of one or more of the participants. By going through the existing threads you can probably find the information you need without risking getting banned yourself.

it is not about an easy or difficult definition,it's about the unclear context

suppose there is wall i am trying to push,it requires 20 N of force to displace it,i push it with 10 N for the first time,according to you there will be no energy in this case(it will be better if you for a moment will put aside the perception of seeing me,u can only perceive the wall)
so at the end you will not take me in existence(considering you cannot see me)

but 2 seconds later you find that the wall is moving(this time i applied the force of 30N)
so you count my existence

 

[MrNerd]

it is not about an easy or difficult definition,it's about the unclear context

suppose there is wall i am trying to push,it requires 20 N of force to displace it,i push it with 10 N for the first time,according to you there will be no energy in this case(it will be better if you for a moment will put aside the perception of seeing me,u can only perceive the wall)
so at the end you will not take me in existence(considering you cannot see me)

but 2 seconds later you find that the wall is moving(this time i applied the force of 30N)
so you count my existence

There should still be energy at the 10 Newton mark. There just won't be any work done.

Work = Force x distance. In order to perform work, you need energy. Admittedly, there is no work done in the example. However, if the wall were to stop exerting the force on you(I mean not move as a result,it will always exert an equal and opposite reactionary force), the wall would then move. The impeding forces are generally from things like friction and being bolted down. So if the impeding force is eliminated, then the wall would move, and thus work would be done, meaning energy has been exchanged.

Energy must be present if a force is to be applied. I don't know about the things like the strong and weak forces, though, but just in general, a force requires energy.

 

[nouveau_riche]

There should still be energy at the 10 Newton mark. There just won't be any work done.

Work = Force x distance. In order to perform work, you need energy. Admittedly, there is no work done in the example. However, if the wall were to stop exerting the force on you(I mean not move as a result,it will always exert an equal and opposite reactionary force), the wall would then move. The impeding forces are generally from things like friction and being bolted down. So if the impeding force is eliminated, then the wall would move, and thus work would be done, meaning energy has been exchanged.

Energy must be present if a force is to be applied. I don't know about the things like the strong and weak forces, though, but just in general, a force requires energy.

i guess you didn't read what i was saying,i told you to forget about the perception of seeing me,how will you say there is energy?

 

[galtsgulchb]

it is not about an easy or difficult definition,it's about the unclear context

I agree. Often, when solving homework problems or understanding what awriter means by 'energy', the context is not well spelled out. Do you think you understand what energy is now or do you still have any unresolved questions?

FYI- I found a wonderful discussion of energy here:
http://www.ftexploring.com/energy/energy.html

 

[russ_watters]

Energy must be present if a force is to be applied.

No!

...

 

[russ_watters]

i guess you didn't read what i was saying,i told you to forget about the perception of seeing me,how will you say there is energy?

What you wrote - and what your point in this thread is- is very unclear.

 

[MrNerd]

i guess you didn't read what i was saying,i told you to forget about the perception of seeing me,how will you say there is energy?

I can ignore see you, but you still exert a force. IF you weren't there at all, there wouldn't be a force, anyway, aside from the obvious like air pressure and gravitational. I suppose since I am only a freshman at college, I'm not an expert to back my ideas up. If a comparison can be made where a compressed gas cylinder is pushed against the wall instead of you, it may be easier to explain.

The compressed gas cylinder is held up against the wall. The cylinder has a piston on the wall side that will enable it to push out when it has higher than outside pressure inside it(kind of like those things under chairs than enable the height to be changed). The piston, because the pressure is higher inside the cylinder, pushes on the wall with 10 N of force. This is the same situation as before, except the compressed gas cylinder has replaced you. The cylinder does indeed have energy(potential energy) stored in the compressed gas. Allowing the piston to pull out is the same as doing work. W = p\Deltav, where W is work, p is pressure, and v is volume. The +/- change in the volume matters, too.

If the piston is to push the wall out, it must have energy stored in the compressed gas. Say we compress it to the point it pushes out at 30 N. It will make the wall move, work happens, and energy is transferred. Now say we only compress it to the point it exerts 10 N. The gas doesn't provide enough force to push the piston to make the wall move. BUT it does still have potential energy. I believe this is what you were trying to say it doesn't have.

Forces result when an object with high energy has the ability to transfer it to one with low energy if the conditions are met. Your arm has the high energy in the arm/wall example above. However, it is not high enough to overcome other forces resulting from high/low imbalances. Friction is an electromagnetic force. The electric part repels the atoms if they get too close, unless they're bonding. But because the surface is all uneven, they sometimes have to get closer to other atoms, or go around them entirely by going backwards.This takes energy to overcome. If an insufficient amount of energy is supplied by the object, it can't overcome the friction, and doesn't move.

If we still disagree, I'm going to assume that either one of us is wrong but just can't figure it out, or we're having a communication difficulty. We should probably get a more experienced person to help decide this, then.