# Eenrgy (again)

1. Dec 29, 2003

### Thallium

I am very eager to understand what energy really is, thought no one really does.

Are there more than one definition of energy?

Is energy a property within all objects and thereby unifies all objects?

Is it true that every object has a potential energy?

2. Dec 29, 2003

### Arcon

You're right. Noone knows what energy is even today. This subject came up in the past several times in the past here. Since it takes some explaining I had to made a web page to get it correctly. Please see -- http://www.geocities.com/physics_world/mech/what_is_energy.htm

Please note that there is an error in this page that I have not gotten around to fixing. I incorrectly stated that the conservation of energy is also known as th first law of thermodynamics which is untrue.

3. Dec 29, 2003

### Staff: Mentor

There aren't multiple definitions of energy, but there are multiple TYPES of energy.

Energy is a pretty universal property, but I'm not sure what you mean by "unifies."

Any object CAN have potential energy because potential energy is something you define by choosing your reference frame. So for example, I have no potential energy with respect to my chair, but I do with respect to the floor.

4. Dec 29, 2003

### Thallium

I did not exactly know where I was going when I asked if energy is a property within all objects that unifies all objects. I think I meant if all objects have an energy. Of course they have.. Don't they?

How can you not have a potential energy to the chair but to the floor? Does that have to do with the distance? That there takes a distance to develop energy?

Thank you for the link Arcon! Very illustrative site!

5. Dec 29, 2003

### Mk

I don't belive in such a thing as energy anymore.

6. Dec 29, 2003

### Thallium

Striking thought really. Maybe we have created the idea that there is an energy. - a contrived philosophy that we fail to understand because we said something we actually are not capable of understanding - we made it all up. (..?)

7. Dec 29, 2003

### Jimmy

Energy is certainly an abstract concept. In the context of science, however, we understand what energy is simply because it has been arbitrarily defined. Any discussion outside of the scientific meaning of energy is philosophy.

Classically, energy is defined as the capacity to perform work. Work is the conversion of energy from one form to another. Work and energy are mathematically equivalent and are measured using the same units.

The most widely used example of work is the conversion of gravitational potential energy to kinetic energy. Consider an object of mass m suspended above the surface of the earth.

Gravitational potential energy is represented by the equation:

$$E_p = m a d$$

m is mass in Kg
a is acceleration in m/s^2. in this case a=g which is 9.81 m/s^2
d is the distance; the height above the surface of the earth in m.

Usually you will see w in place of Ep, w symbolizing work, but if the mass in question is being suspended, no work is being done at this time so I will use Ep to represent the potential energy.

The moment that the object is dropped, the potential energy decreases as the kinetic energy increases. This is work. The conversion of Egp to Ek. Kinetic energy can be calculated using:

$$E_k = \frac{m v^2}{2}$$

Neglecting air resistance, the kinetic energy of the object when it hits the surface will equal the original potential energy of the mass when it was suspended above the surface. Of what use is this? Well, if we know what the Ek is supposed to be when the object hits the Earth, we can calculate the velocity that mass will have at that time:

$$V = \sqrt{\frac{ 2 E_k}{m}}$$

This is just the equation for Ek arranged to solve for V. We could have used a simpler formula to calculate the velocity. Knowing the acceleration of gravity, the mass of the object(Edit: mass is not relevant here. Don't know why i mentioned it. ), and the distance between the object and the surface:

$$v = \sqrt{2 g d}$$

This would have given the same result, but it useful to examine the energy. In this problem, we have neglected the air resistance. In reality, the kinetic energy would not equal the potential energy. The velocity of the object will be lower than our original calculation and, consequently, the Ek will be lower as well. If the conservation of energy holds true, this tells us that not all the potential energy was converted to kinetic energy. We obviously did not take everything into account and we should try to examine what was missed. In this case, some of the original energy was converted into heat due to friction (drag) as the object fell through the atmosphere.

Energy, in physics, is a useful book keeping tool which allows us to keep track of certain facts about a system and also show us when our data is incomplete.

What energy really is outside of this definition does not fall within the realm of science.

Last edited: Dec 31, 2003
8. Dec 29, 2003

### Mike2

There is a mathematical definition of energy. See:
http://mathworld.wolfram.com/Energy.html

This seems to indicate that energy is the inner product of some space. But the inner product of two basis vectors of some space defined the metric of that space. So it would seem that energy is derived from the metric of space-time. This would be consistent with Einstien's formulation.

9. Dec 30, 2003

### pallidin

I've always thought that "energy" is the ability to do work, with work meaning "effecting a change"
Of course, those are my words, and I may be wrong, but it seems to sum it up nicely.
Potential energy is the potential of the ability to do work, meaning that the expenditure of energy is not yet actualized but established as possible under a given set of circumstances.
There are many forms of energy. Some are emmissive, or radiative in expression, while other forms of energy are non-emmissive. The reason for this duality is that energy is not a substance, or quantum anything, it is a relational concept; again, the ability to do work.

10. Dec 30, 2003

### Arcon

The problem with that definition is that it's too vague. In fact it has come to mean different things to different physicists.

For example: Consider the text Classical Dynamics of Particles & Systems - 3rd Ed., by Marion and Thornton. On page 72 the authors write
Now consider the notes at
http://blueox.uoregon.edu/~courses/dlivelyb/ph161/L5.html

These authors define "energy" as the capacity to do work. Here we have the same definition meaning two different things since we know that energy is not the same thing as potential energy.

Here we have that kinetic energy is the capacity to do work
http://oregonstate.edu/instruct/exss323/Work_Power_Lab/indexa.htm

Once again - kinetic energy is not potential energy nor is it energy

11. Dec 30, 2003

### Mike2

Re: Re: Eenrgy (again..)

What's wrong with posing that energy is the curvature of spacetime? We have F=ma, where acceleration is a curvature in the path in spacetime. E=Fd=mad so that the more curved your path in a given distance, then the more energy was involved. And Einstien's general theory of relativity equates the curvature of spacetime to the mass in the system where mass is equivalent to energy. And the faster strings vibrate in spacetime, the greater the mass and therefore the energy of the particle. So in string theory we can exchange an overall curvature of a particle's path with the curvature associated with the vibrational mode along the string. This occurs when a particle gains or loses kenitic energy and speed or slows its velocity.

There then is the question of the curvature in various dimensions and the mechanism of exchange between them. And it would seem that the tighter the curvature the more the energy. At the big bang, the universe was curled up into a singularity and the energy was near infinite. Then the universe expanded. One question is in the conservation of energy implemented. Does the universe expand only if the curvature can be incorporated into submanifolds of the overall space time?

12. Dec 30, 2003

### Staff: Mentor

Arcon, thats simply two different types of energy. The standard definition "capacity to do work" applies to both. Kinda like water and oil being two different types of liquid.
Thats a verbal description. Mathematically, the definition is exact.

13. Dec 31, 2003

### Thallium

Oh really Scientists all over the world wonder what energy really is so I cannot say I agree with you here. Otherwise thank you for the descriptions. I have allready learned of Ek and Ep, but was not familiar with the non-air resistance formula.

14. Dec 31, 2003

### Thallium

Is this definition equal to saying that energy is the capacity to move an object?

15. Dec 31, 2003

### Jimmy

What I'm saying is that energy has been given a specific definition. Scientists may wonder what energy really is as anyone may wonder. Is that necessarily science?

What do you mean by non-air resistance formula?

Edit:

You must mean the $$v = \sqrt{2 g d}$$

That is just a simple kinematic equation that represents a change in velocity, given a constant acceleration over a specified distance. It really has nothing to do with air resistance.

It can be derived from these two equations:

$$d = \frac{v t}{2}$$ and $$d = \frac{a t^2}{2}$$

Last edited: Dec 31, 2003
16. Dec 31, 2003

### Jimmy

No.

Edit: Actually, I need to think on that for a bit. I was a bit hasty in my answer.

I would have to say no; Energy is not the capacity to move an object. That description is too vague.

Energy is the capacity to accelerate a mass through a distance. As I think about about that though, it seems that definintion might not cover all forms of energy. IF work has been performed, has a mass been moved? Also, can all forms of energy be utilized for work?

Last edited: Dec 31, 2003
17. Dec 31, 2003

### Jimmy

Thallium,

I found a web page that might interest you.

http://home.pacifier.com/~ppenn/whatis2.html

18. Dec 31, 2003

### Arcon

Re: Re: Re: Eenrgy (again..)

Mike2 wrote
That is pretty vauge definition. Note that at a given poing in spacetime near a gravitational source it is possible for there to be no spacetime curvature and yet a particle may have energy. Unless you want to say refer to the mass-energy of the particle that is. Otherwise you can have energy in the absence of spacetime curvature.
That is not spacetime curvature. That is a different kind of curvature.
True. But that only demands that there is energy a the location of the mass. It does not demand that there is energy at other points. At other nearby points the spacetime may be flat.

russ_waters wrote
Correct. That is why the different forms of energy are well defined but energy itself is not defined.
Yes. Potential energy, as with all the forms of energy, are well defined. But energy itself is not. That's why Feynman states that nobody knows what energy is. To understand the reasoning behind that statement I suggest reading the Feyman lectures and read Feynman in its totality on this point.

Thallium wrote
That is what I referred to in the link I gave above, i.e. in
http://www.geocities.com/physics_world/mech/what_is_energy.htm

19. Dec 31, 2003

### Mike2

Re: Re: Re: Re: Eenrgy (again..)

I'm thinking that once a string particle has been accelerated by force and travels with a faster constant velocity, then the string vibrations curl more tightly with the same number of space oscillations in a shorter period of time. Of course, this increased kinetic energy is transfered via other particles. So I am talking about how the curvature of one particle can add to another in an interaction. But if energy is transfered by particles only, then where does that leave potential energy due to distance only?

20. Dec 31, 2003

### Thallium

What are the last two equations for? And what do the letters mean?