# Energy ,potential and work

1. Sep 23, 2011

### 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

2. Sep 23, 2011

### 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

3. Sep 24, 2011

### 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.

4. Sep 24, 2011

### DrStupid

And what is work?

5. Sep 24, 2011

### 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).

6. Sep 24, 2011

### DrStupid

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?

7. Sep 24, 2011

### Staff: Mentor

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.

8. Sep 24, 2011

### Staff: Mentor

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.

9. Sep 24, 2011

### BruceW

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'.

10. Sep 24, 2011

### DrStupid

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.

11. Sep 24, 2011

### 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.

12. Sep 25, 2011

### DrStupid

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.

13. Sep 25, 2011

### 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..

14. Sep 25, 2011

### Naty1

BruceW: #13 post, very good!!!

15. Sep 25, 2011

### nouveau_riche

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

16. Sep 25, 2011

### nouveau_riche

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

17. Sep 25, 2011

### nouveau_riche

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

18. Sep 25, 2011

### nouveau_riche

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

19. Sep 25, 2011

### 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).

20. Sep 25, 2011

### nouveau_riche

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