# Potential energy = BS?

1. May 2, 2005

### michael879

I never really thought about this until the other day when someone asked me why something accelerating towards a planet doesnt make the planet lose mass. It makes sense according to conservation of mass/energy right? the object gains energy (speed) therefore the planet must lose energy or mass. I know that potential energy explains this energy gain, the object gains kinetic energy while losing potential. But doesnt this seem like some theory made up just to make conservation of energy work?

2. May 2, 2005

### cepheid

Staff Emeritus
No, it exists. Gravitational potential energy is a property of an earth/ball system in which the ball is initially a distance r away from the centre of the Earth, for example. If r > R, the latter being the Earth's radius (which is a fancy way of saying, if the object is above the ground, lol), the ball will begin to fall. How much work was needed to get it there in the first place? You would have to do work on the ball against gravity to get it there. That is how much potential energy is stored in the system. The energy exists by virtue of the presence of the gravitational field.

We're dealing with gravitational potential energy, which I underlined. Conversion of mass to energy, on the other hand, occurs when nuclear forces binding nuclei together are overcome. That's a whole different ball game.

3. May 2, 2005

### michael879

well actually, Im pretty sure mass and energy are basically the same thing (E=mc^2), but any way I get what your saying. However, what if the ball was never put there. What if the ball has never been on earth, it started on the other side of the universe. What about when it starts to accelerate towards earth. why would it have potential energy in this case?

4. May 2, 2005

### juvenal

This is more of a philosophical question, I believe. Pretty much any quantity is "made up" into order to make a theory work.

5. May 2, 2005

### michael879

not rly, kinetic energy exists, we can feel it whenever something hits it. But never mind I answered my own question: the potential energy comes from the big bang, when the ball and the earth were in 1 place.

6. May 2, 2005

### juvenal

One cannot measure an absolute potential energy. It's only useful to talk about the difference in potential energy between two points.

7. May 2, 2005

### juvenal

You feel something. In principle, I think one could formulate a theory of mechanics that never used the concept of kinetic energy.

8. May 2, 2005

### michael879

Im not talking about absolute potential. I was talking about two points very far apart that were "never" together. However they were right before the big bang.

I misphrased that, the reason a baseball thrown at you hurts is because of energy. Also, our bodies live off energy which definately exists. And how can you deny heat?

9. May 2, 2005

### Hessam

because it takes work/energy to place the ball in its location...

the entire universe is conducting through entropy and ethalpy... disorder and lowest potential state..

if you think about it, it makes sense... a ball has a tendency to be on the ground... so to lift it up 5 meters you need to apply a force, thus giving it potential energy

10. May 2, 2005

### juvenal

I'm not denying anything. Kinetic energy and heat are defined by a theory used to explain physical phenomena, i.e. classical mechanics and thermodynamics. There is no external meaning.

11. May 2, 2005

### michael879

ok what I was trying to say is that this ball wasn't lifted by anyone, it just popped into existance far away from earth. However it would still have potential energy right? so the whole work theory doesnt rly apply here.

12. May 2, 2005

### cepheid

Staff Emeritus
*Sigh*...yes, of course. But how do we harness that energy? The point I was trying to make is that we can only convert mass directly to energy in nuclear reactors. You need to blow up nuclei, or fuse particles together to form them. For example, if I remember right, two hydrogen nuclei and two neutrons when considered separately have a total mass greater than that of a helium nucleus, despite the fact that a helium nucleus consists of just those very same four particles, bound together! So where did the extra mass go? It was converted to energy in the process of fusion. That's what happens in the sun (well, to simplify things).

What I was saying is that plain simple everyday MOTION in a gravitational field is does not involve the conversion of mass to energy (and I'm not sure where you got the idea that it ought to). It involves the interchange of energy between only two forms: kinetic and potential. We generally call this total "energy of motion" (when gravitational fields are involved) mechanical energy. In a conservative field, in the absence of other forces (non conservative forces such as friction), mechanical energy is conserved. We say that gravity is a conservative force. The energy is not "lost" (note the quotes), i.e. converted to other non - mechanical forms such as heat, light, etc.

Consider an analogy: I want to assemble a system of electric charges. The system includes two unlike charges separated by a distance r. In order to separate them, I need to do work, because there is an attractive force trying to keep them together. So are you surprised that when I take away whatever is keeping them separated, they shoot back together? Do you ask, where did the energy come from? No, because you saw me put in a lot of work to painstakingly assemble this system. The mere existence of this system of two charges and their associated fields, separated by a distance, means that there is certain amount of energy stored in it, equal to that work. We usually associate this energy "with the electric field", because knowing the strength of the total electric field of this system of charges, we can calculate the electrostatic energy. What if I want to move my charges really far apart? Your first impulse would be to say that I'd have to do a hell of a lot of work to separate them this huge distance. But remember that the attractive force between them diminishes, the farther away they get. So if the second charge starts out* really far away in the first place, is there some potential at that far away point (essentially, "at infinity") due to the field of the first charge? Yes. Is it small enough to be considered essentially zero? Yes. Will the second charge accelerate towards the first if they are separated by this vast distance? No. But the potential due to the Earth's/source charge's field at intermediate points between the earth and the ball is higher, so if it somehow ends up at those intermediate points (closer to the earth), its potential energy will increase.

*I know what you're going to ask about, that's why I starred it. How might the two charges "start out" that far apart in the first place? Well, consider what you are asking me. We were talking about assembling a system of masses (or charges). Then what did you do? You went and extended that "system" to include...

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................THE ENTIRE KNOWN UNIVERSE :yuck:

And now you are asking me: Where did the energy come from to "assemble" this system?!?!? I.e., why does matter exist, and why are objects in their current locations/how did they get there/what is their entire history since the beginning of time? Sorry, not qualified to answer that. :tongue2: If you're satisfied with "big bang", then fine.

Last edited: May 2, 2005
13. May 2, 2005

### michael879

Im just responding to the first part of ur post. I get that we cant harness the energy by converting mass to energy. But whenever something loses energy it loses mass since they are the same thing. This wasnt rly part of my question but I was saying that (and I know this is wrong) if a ball gained energy from a planet as it accelerated towards it, it would also gain mass while the planet loses mass. The mass would be negligible since Mlost = E/c^2 however, there would be a mass loss whenever energy is lost.

14. May 2, 2005

### cepheid

Staff Emeritus
Not true. You have to be careful how you interpret E = mc^2. Mass and energy are not the same thing. This equation simply states that it is possible to get one from the other, i.e. that they are interchangeable. Possible under the circumstances I outlined.

15. May 2, 2005

### michael879

exactly, so that when there is an energy loss, there is also a much smaller loss of mass.

16. May 2, 2005

### cepheid

Staff Emeritus
You're not really listening. That's exactly what I said is NOT true.

17. May 2, 2005

### michael879

o I thought you were saying something else. are you sure that isnt true? because Im pretty sure there is a way to get free energy if it isnt.

18. May 2, 2005

### Hessam

well w/ hypothetical situations that are not possible, a lot of stuff can occur that can make your head spin

what i'm saying is plain and simple... gravity is a force... it pulls on the ball... so, for the ball to stay stationary it would require another force of equal magnitude

because this force is necessary to stay stationary there is some form of energy on the ball, which we label as "potential energy"

the force theory however does apply, because you do need a force to keep it stationary

so you ask yourself... why is this ball spontaneously falling towards a planet?

spontaniety of a process is caused eitehr by enthalpy or entropy

in this case enthalpy, reaching lower potential... the ball wishes to reach lower potential, thus its gravitational potential energy is converted into kinetic energy and is launched towards the earth

19. May 2, 2005

### HackaB

My copy of Halliday and Resnick does not have this as a boxed eqn, so my guess is the answer is no.

20. May 2, 2005

### michael879

haha ok I give up, I got my answer thx