# B What is energy?

#### BeedS

And I need to look into my understanding of work and energy.
Energy = current motion (Since everything is moving, energy is the current motion caused by previous work done)
Work = change of motion (result of changing a objects energy through KE)

Is this better?

#### lomidrevo

And we should not forget about the rest energy $E = m c^2$. Quite a good example of a energy not associated with a particle's motion.

#### BeedS

The object with potential is still created by things moving internally(sum of the objects scaled energy(its mass)). PE is potential motion, the PE object is still moving (KE) and has a potential to change that motion through work done.

#### A.T.

the PE object is still moving (KE)
What about two opposite charges at rest? They have PE without moving.

#### BeedS

What about two opposite charges at rest? They have PE without moving.
At rest relative to what? Only to the object itself and something with the same motion as the object?. The charges are still moving with the charged objects. The charges are considered part of the objects mass (PE)? Charges do contain mass? Charges do move with the object they are bound to?

#### jbriggs444

At rest relative to what?
Yes, every object that is at rest in one frame is moving in another. It does not follow that energy is motion or that rest is a meaningless concept.

Edit: You do realize that energy is a frame-relative concept? If we are talking about energy being present in an object at rest, we are working in a frame of reference within which the energy is non-zero and and the object is at rest.

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#### A.T.

At rest relative to what?
Relative to the reference frame in which you calculate the energy.

#### folkethefat

What is mass?
The dimension of time might be related to energy?

In E=MC2, what does it mean? The energy bound in mass?

#### lomidrevo

What is mass?
In relativity, it is a property of an object - a quantity which is invariant for all observers. But mass can be defined in different ways too: https://en.wikipedia.org/wiki/Mass

The dimension of time might be related to energy?
No idea what do you mean by your question.

In E=MC2, what does it mean? The energy bound in mass?
I think this short video provides a nice introductory explanation:

#### Kavorka

It really is just easiest to think about it as "the capacity to do work". Essentially, work is measured in terms of energy (work and energy have the same units). This is because energy by itself doesn't mean much, it is in reference to what is it able to physically do that matters. For example, it means little to say you have a certain amount of potential energy relative to 20 feet underground below you. You certainly could possess this capacity to do work, but it is meaningless in the context of the physical situation - you are not able to fall through the ground. Because energy can only be transformed and not destroyed, you can think of any context of energy in terms of this definition.

#### A.T.

It really is just easiest to think about it as "the capacity to do work".
Having energy around doesn't mean you can do work. When you dissipate energy, there is still the same amount of energy in the from of heat, but it cannot by itself be used to do work.

#### folkethefat

Is this correct then?
Time is measured by the ordering of events. "Events" always involves a change in energy. Energy is driving the change. So energy seems to be driving that which we measure as time?

#### jbriggs444

Is this correct then?
Time is measured by the ordering of events. "Events" always involves a change in energy. Energy is driving the change. So energy seems to be driving that which we measure as time?
I do not agree. An "event" is simply a location in four dimensional space-time. It does not involve a change in energy. How could it, since "energy" is a conserved quantity?

In particular, energy is the conserved quantity associated with time translation symmetry by Noether's theorem.

#### Mister T

Gold Member
While I was doing some practice questions it hit me "what is energy".
There's no definition that will help when the concept is being refined and used in different contexts. After a while the different contexts provide you with enough experience that you feel comfortable with the concept of energy. Like how we feel comfortable with the concept of money.

I also don't understand how the formulas for potential and kinetic energy were derived. Was it due to their definitions or is there some reason behind their respective formulas.
Any college-level introductory physics textbook would have good explanations of those things.

#### BvU

Homework Helper
I also don't understand how the formulas for potential and kinetic energy were derived. Was it due to their definitions or is there some reason behind their respective formulas.
Perhaps it's nice to add that in real life the concept of 'force' is much more vivid. Force has something to do with to the change in energy

Some force fields are conservative, hence the introduction of a potential (energy) with somehing like $\Delta {\rm PE} = \vec F \cdot \Delta \vec x\$.
From $$\vec F = {\Delta\vec p\over \Delta t} \Rightarrow \quad \vec F \cdot \Delta \vec x= m{\Delta\vec v\over \Delta t} \cdot \Delta\vec x = m\;\Delta\vec v \cdot {\Delta\vec x\over \Delta t} = m\;\Delta\vec v \cdot \vec v = \Delta \left ( {1\over 2 }m \vec v^2 \right )$$ comes the formula for kinetic energy.

It's all differentiation and integration -- which makes math so useful !

 hehe if you do it right

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#### folkethefat

I do not agree. An "event" is simply a location in four dimensional space-time. It does not involve a change in energy. How could it, since "energy" is a conserved quantity?

In particular, energy is the conserved quantity associated with time translation symmetry by Noether's theorem.
Ok! i see, i was confused about the definition of "event" in a physics context. I thougt it implied a change in the energycontent in a location in space, a defined volume.

#### folkethefat

There's no definition that will help when the concept is being refined and used in different contexts. After a while the different contexts provide you with enough experience that you feel comfortable with the concept of energy. Like how we feel comfortable with the concept of money. /
But to ask what "money is" except that its nice to have lots of, , is a legitimate question and there are many theoretical answers for it.
The question about if energy is something more fundamental than the different types of energy, leads beyond the standard model and thats the problem. I Think?

#### sophiecentaur

Gold Member
I do not agree. An "event" is simply a location in four dimensional space-time. It does not involve a change in energy.
Strictly, yes perhaps but an 'event' is a word used colloquially to describe 'something happening' and that does imply change because that sort of event has to be observable - which involves some change of Energy state.
I used to use the form of words "Energy is needed for anything to happen" in lower school introductions to Science. It was interesting to note that 'they' would always try to argue with that and to bring up examples that didn't fit. I always managed to explain away their examples. 'Death' would always be one of them.

#### folkethefat

Can all sorts/types of energy translate into some other kind? Heat for example.
Is there a hierarchy in this "translation"? Is heat the lowest form or state of energy?

"What is energy?"

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