# B Potential energy and conservation of energy

Tags:
1. Mar 8, 2016

### Ryan Bruch

When a particle (or any objects) accelerates when acted upon by fundamental forces, what is happening to the amount of energy in that particle? A large example would be an asteroid in space caught by earth's gravity and accelerates toward earth as a result.

The fundamental forces here can be electromagnetism, gravity, strong force, and weak force.

If a particle accelerates because of gravity or electromagnetism, does that mean it is gaining energy? How does that make sense with the conservation of energy (first law of thermodynamic)?

Potential energy is defined as the energy that an object has due to its position in a force field, but where does that potential energy, whether it be gravitational or electric, come from in the first place?

I have heard of gravitational energy being negative energy, but what does that mean exactly?

2. Mar 9, 2016

### Staff: Mentor

The energy isn't contained within the object, it is a property of the system containing the object. In this example the asteroid has a certain amount of potential energy by virtue of being in Earth's gravitational field. As it accelerates, this potential energy is transformed into kinetic energy. However, the total mechanical energy (TME) of the system remains the same. Mathematically this would be written something like TMEi=TMEf, where TMEi is the total initial mechanical energy of the system and TMEf is the final. TME itself can be broken down into TME = PE + KE, where PE is potential energy and KE is kinetic energy. So PEi + KEi = PEf + KEf.

Typically it means that you're converting potential energy into kinetic energy or vice-versa.

It's an inherent property of the position of the objects within the system. It arises because objects within a system can be acted upon by forces.

I believe it comes around because we commonly choose the zero point of gravitational potential to be an infinite distance away. An object being pulled towards Earth moves from a region of space with a higher potential (less negative) to a region with a lower potential (more negative), leading to the formula for gravitational potential energy, U = -GMm/r. But I'm not 100% sure on that.

3. Mar 9, 2016

### Simon Bridge

When an object accelerates, it gains kinetic energy. This means something else is losing energy... in the kinds of interactions you are thinking of, the energy is lost from the potential of the force-field: so the gain in kinetic energy is equal to the loss in potential energy.

The potential energy of an object in a certain position is the amount of work that has to be done to move the object to that position from some reference point.
For instance, to lift a mass m to a shelf h meters above the ground costs mgh energy ... so the potential energy of height h is mgh. This energy is considered to be stored in the gravitational field ... but we often say the mass has that energy as a shorthand.

What is means by "negative energy" for gravity depends on who is talking. Where did you hear this?

4. Mar 9, 2016

### Ryan Bruch

I heard it from Wikipedia articles "Gravitational energy" and "Negative energy." Both articles cite Alan Guth's The Inflationary Universe.

5. Mar 9, 2016

### Ryan Bruch

I can trace the energy preserved in a stretched elastic rubber to those from my arm muscle, can I do the same with an asteroid accelerating towards Earth?

6. Mar 9, 2016

### Staff: Mentor

I'm not quite sure what you're asking. Can you elaborate?

7. Mar 9, 2016

### Simon Bridge

In that case, they are referring to gravity as opposed to mass energy - trying to answer the question of how something can come from nothing in a way the average person can grasp.
Sort of - you didn't hoist the asteroid up into space by muscle power however, it is the same sort of thing as putting a rock on a high shelf and letting it fall to a lower one: the kinetic energy gain is the difference in potential energies: only here you can feel the potential energy because of the effort it took to lift it in the first place. You can imagine you just found the rock on a shelf, and saw it fall ...

For the space example, the configuration that has the asteroid farther from the Earth has more potential energy that the configuration that has the asteroid closer. The kinetic energy it gains is the same as the difference in potential energy between these two configurations. The asteroid got to be in a higher energy configuration by whatever mechanism put it there... we usually don't know exactly what the process was.

8. Mar 9, 2016

### Ryan Bruch

I was asking about the fact that a rubber gains energy when stretched and an asteroid gains energy when accelerated by earth's gravity. I know the source of energy of the former but not the latter.

Last edited: Mar 9, 2016
9. Mar 9, 2016

### Staff: Mentor

Unfortunately I think that gets into some subtle discussion on what energy is that I'm not qualified to answer.

10. Mar 12, 2016

### Simon Bridge

Not really - the source of the energy in both cases is work of some kind... it will not always be obvious what did the work etc. i.e. what is the source of the energy in muscles?

Ultimately the source of all the energy is whatever process brings the Universe into existence... which is currently under investigation.
So: we don't know. But we do know that if we do the maths this way - it works. It works really really really well.