[Eternal Student (OP)]

Hi everyone.
   This section of the forum has gone a bit quiet as of late.  Here's a question that should be open to everyone who has studied Physics at school level.  I'm interested in all answers and opinions.  You can talk about what you know from University if you wish but the main focus (for me) is on what I can say or present to a school-age audience.   What is the best way to answer questions like this from a child in school?

Background     When you were at school you may have studied some Physics.  How were you taught about gravitational potential energy?   Did it seem sensible to you?   You may have seen examples like the following:

    /\
 /  || \@
/   ||  \
    ||
 This thing is a tree.

@  <--- This thing is an apple in the tree.

What follows next is a beautifully animated diagram of the apple falling from the tree and gaining kinetic energy as it falls....
(You just have to imagine that part).

   It would have been said that the apple had gravitational potential energy while it was up high.  This potential is converted to kinetic energy as it falls.     OK, remember that?
   - - - - - -
Questions to focus on:
(i)  Were you taught that the gravitational potential energy was  IN THE APPLE ?
(ii)  Did you believe it?   (I did while I was at school).
(iii) Was there anything different about the apple when it was up high or just that it was up high?
(iv) If the energy was in the apple, then did it have more mass when it was up high?
(v)  You may have studied more physics since school.  Where do you now think the gravitational potential energy is located?
(vi) How would you go about explaining this concept to a school-age student, maybe one of your own children if you have them?  Suppose they ask directly   "where is the gravitational potential energy stored?"  - what will you tell them?

Thanks for your thoughts and opinions.  Best Wishes to everyone.

[Halc]

It would have been said that the apple had gravitational potential energy while it was up high.

I was taught that potential energy is negative, so it has greater magnitude negative energy after it falls to the ground.

Typically in early (7th grade) physics, concentration is on Earth-local environments where Earth is flat and the gravity is constant at all altitudes. In this environment, PE being negative has little meaning, but they still taught us that.

(Were you taught that the gravitational potential energy was  IN THE APPLE ?

I don't remember anybody trying to express it that way. The apple HAS potential energy, which is actually a relation between the apple and something implicit, but in the introductory phases, they didn't express it as a relation.

[/quote]Was there anything different about the apple when it was up high or just that it was up high?[/quote]Pretty much the latter.

If the energy was in the apple

It has negative energy up in the tree, and negativer (cool word!) energy sitting on the ground. That hardly seems like energy being in the apple.

then did it have more mass when it was up high?

This was introductory Newtonian stuff. Energy mass equivalence was quite a ways off still.
If you drag that in, then the energy/mass is constant all the way since the total energy never changes, so Newton or not, the falling apple doesn't lose mass on the way down.

You may have studied more physics since school.  Where do you now think the gravitational potential energy is located?

Relations don't have a location, but the apple has coordinate mass that is a function of its proper mass plus its potential relative to something, plus kinetic/thermal/chemical energy that contribute to coordinate mass, and that mass has a center of gravity which for all practical purposes serves as a location for that PE. Where else would it be? It seems a reasonable answer to give to students.

[Eternal Student (OP)]

Hi and thanks Halc.

 About negative p.e.:

Typically in early (7th grade) physics, concentration is on Earth-local environments where Earth is flat and the gravity is constant at all altitudes. In this environment, PE being negative has little meaning, but they still taught us that.

  7th grade in the US ≈ age 12-13 years  ≈ year 8  in the UK.
   I'm surprised.  We were not taught to consider a negative potential energy until year 12 ≈ age 16-17 years.
   None the less, it doesn't dodge the problem.   Consider an apple at rest in the tree and also the same apple at rest on the ground.   (The potential energy has been converted to heat and sound after the apple bounced about on the floor and that has definitely travelled away and left the apple).   Now with both apples at rest the difference is only the potential energy they have.  That difference in energy is not exhibited as a difference in mass of the apples.
   I agree that mass-energy equivalence may not be on the school syllabus but it's still a little deceitful to suggest that the apple has more or less energy depending on its height.  This is something that the students will have to un-learn later at university.

It has negative energy up in the tree, and negativer (cool word!) energy sitting on the ground. That hardly seems like energy being in the apple.

   I'm not clear on where you thought the energy was,  or did you think that energy wasn't something that had to be located anywhere?   This isn't meant to be a silly or annoying question - it may be best not to worry about where energy is located and it may be best to teach children that energy doesn't always have a location in space.
- - - - -

Relations don't have a location, but the apple has coordinate mass that is a function of its proper mass plus its potential relative to something, plus kinetic/thermal/chemical energy that contribute to coordinate mass, and that mass has a center of gravity which for all practical purposes serves as a location for that PE. Where else would it be? It seems a reasonable answer to give to students.

   Where else would it be?    Well, for example, the potential energy could be stored in the earth rather than in the apple.   We know that the earth exerts a force on the apple but the apple also exerts the same force on the earth. 
   If you were able to hold the apple still rather than let it fall then the earth would eventually move to the apple's location.  The earth would have been the object that gained kinetic energy and seemed to lose potential energy in this case.  If you don't like the idea of holding the apple still then make a minor adjustment to the usual model:   We can imagine a really big planet-sized apple falling on to a very small apple-sized earth.
   What is special about the apple that allows you to say that the apple has the potential energy?  Even using your (Halc) complicated notion about everything being a relation based on positions - doesn't the earth also have that relationship, i.e. the earth also has the potential energy?
   OK... I think it's reasonable for a child to suggest that the potential energy is stored in the earth rather then in the apple.  If we make the situation more complicated then someone can suggest that the potential energy isn't stored in the apple or in the earth, instead it is stored in the field that exists between them.  This is like opening a whole new can of worms  (a colloquial phrase meaning - creating more problems as fast as any others are solved).
- - - - - - - -
More general discussion
    Thanks for your time Halc.  Anyone else have any views?  Have we been teaching children about something that isn't tied down to any location and quite possibly just doesn't exist anywhere?
    Is gravitational potential energy just a convenient book-keeping tool that allows for a conserved quantity (total energy) to be defined in simple mechanical systems?

Best Wishes.

[Halc]

Now with both apples at rest the difference is only the potential energy they have.  That difference in energy is not exhibited as a difference in mass of the apples.

Not in Newtonian mechanics, but in relativity, there very much is a difference in mass of the two.

I agree that mass-energy equivalence may not be on the school syllabus but it's still a little deceitful to suggest that the apple has more or less energy depending on its height.  This is something that the students will have to un-learn later at university.

I don't consider that un-learning any more than I had to un-learn how to add velocities when you do it the relative way. The approximations were enough to put a man on the moon. As an engineer, the apple still has the same mass in both places. As a physicist, they don't.

I'm not clear on where you thought the energy was,  or did you think that energy wasn't something that had to be located anywhere?

To reword, energy (like velocity) seems to be an abstract concept and abstractions don't necessarily have a location, but if it makes you comfortable to assign a location for the apple's energy (or velocity), what better place than the apple to assign it? But this is just for your own warm fuzzies. I cannot think of any part of physics where the location of energy needs to be entered into an equation to derive some physical description.

and it may be best to teach children that energy doesn't always have a location in space.

I agree with that. As I said, I cannot think of an instance where this location would be meaningful.

Where else would it be?    Well, for example, the potential energy could be stored in the earth rather than in the apple.

Touche.  PE is (usually) a relationship between two objects, so obviously if it could be in one object, it could also be considered to be located in the other. PE can also be a property of an object, but something like an apple has almost none of that, while Earth has plenty. It is the energy necessary to pull all the mass to zero potential relative to each other. I don't think a black hole has meaningful PE.

Even using your (Halc) complicated notion about everything being a relation based on positions - doesn't the earth also have that relationship, i.e. the earth also has the potential energy?

In relation to what? It has different PE relative to the apple, the moon, sun, or Betelgeuse.

OK... I think it's reasonable for a child to suggest that the potential energy is stored in the earth rather then in the apple.

Seems confusing to me. We've a hydro-energy storage facility out here. When there is excess (cheap) energy available, water is pumped from the river into a storage lake at the top of a hill. At times of high demand, that stored PE is used to meet that demand in excess of the capabilities of local generation plants.
If Earth stored that PE, anybody could extract it. But if the PE is in the water, then only those in control of the water can use it. Just an example where the apple seems the more intuitive place to assign the location of the energy if you feel the need for such an assignment.

Location of energy does sometimes matter. When speaking of a closed system, we're in violation of it being closed if energy leaves the system, so maybe there's a case where the location matters. It's still abstract, since the delimiting of 'systems', closed or not, is an abstraction.

[Eternal Student (OP)]

Hi again.
   Thanks for your time, Halc.  Feel free to slow down and do something else.

Not in Newtonian mechanics, but in relativity, there very much is a difference in mass of the two

   You may need to explain that to me. 

In special or general relativity,  inertial mass = gravitational mass = rest mass = the only mass worth worrying about.

How does the position of the apple change its mass?
- - - - - - -

I cannot think of any part of physics where the location of energy needs to be entered into an equation to derive some physical description.

1.  You mention closed systems at the end of your own post.
2.   I can't think of many (or any) good school examples, however I can think of examples for university.  A momentum-energy tensor for General relativity.  To calculate the momentum-energy tensor for a continuous distribution of energy and momentum (e.g. an ideal fluid), you specify the various components of the 4-momentum flux at every point in space.  One of those components is the energy density at that point in space.   So, I would say you need to know where the energy is located and it certainly makes a difference - put the energy in a different place and you get a different tensor and then ultimately you will have a different system with its own evoution.
     I supose you have the same need to know the location of energy and momentum when you construct a stress-energy tensor for use in fluid dynamics (without needing to include General Relativity in your work).

(I could say more but it's boring and people really don't have to read it.  I'd be more interested in what others say).

Best Wishes.

[Halc]

Feel free to slow down and do something else.

To hell with that. You're making me think, which is a rare treat on this site.

How does the position of the apple change its mass?

It seems my comment was exceptionally poor in it wording. I said PE was a relation between two objects, and here I am giving the mass of that energy to one object and not the other.
Looking up some reliable (reviewed) sources, we have two systems: Earth with apple on tree, and Earth with apple on ground. The proper mass of both Earth and apple is the same in both systems, but the system mass of the former (as viewed from infinity) is greater than the system mass of the latter. That implies that any meaningful potential energy location is 'the location of the system' and not the location of the apple at all.
It also implies that the proper mass of Earth is less than the sum of the proper masses of all its components, the difference being the PE property of Earth.
See https://physics.stackexchange.com/questions/29570/does-the-mass-of-an-object-change-as-it-moves-away-from-the-earth

One of those components is the energy density at that point in space.

There you go. Nice example. Energy can have a location. Does an ideal fluid have a PE density?  I suppose it does if it is expressed as a deviation from the mean, but it is hardly a relation between discreet objects. The tensor arithmetic must be able to express that where the discreet relationship fails.

[alancalverd]

It was a long time ago, but AFAIK the notion of storage of potential energy wasn't mentioned in respect of gravitational p.e.

Not a serious omission. The potential energy of a spring is "stored" in the mechanical stress of the spring, and of the apple, in the tree that is holding it up. After all, the tree grew and raised the stuff needed to make the apple from the ground to the branch, so work was done that resulted in a downward stress on the branch.

[Eternal Student (OP)]

Hi again.

@alancalverd    Wow, I like that idea.   There is a mechanical stress or what might have been called elastic potential energy in the tree while the apple is hanging off it's branch.  You must have been a fairly smart child to think that gravitational potential energy was stored in the tree.  I wouldn't have done that and I've never seen it suggested before.

   Sadly, I think you could quash that idea if you tried:   When the apple does finally break off from the branch, that elastic potential is recovered in the branch (it moves about in something like damped harmonic motion for a short while).  Meanwhile, the gravitational potential energy is still available and the apple will soon convert this to kinetic energy as it falls.  You could go a bit further than this if you needed to:  Stop the apple falling (by holding it up with a stick for a while or something), just wait for the branch to stop waving about.   Now let the apple fall.   The apple seems to gain kinetic energy as usual (from what would have been described as gravitational potential) and the tree shows no changes as the apple falls.  You could fit stress gauges into the tree if you wanted to. Wherever the apple is getting it's kinetic energy from, it doesn't seem to be stored in the tree or dependant on stress in the tree.

@Halc   I'll reply more later and examine that link you gave.  I have some annoying things to do in the real world first   

Best Wishes and thanks for everyones time.
 

[evan_au]

(i)  Were you taught that the gravitational potential energy was  IN THE APPLE ?
- I was taught that it was in the separation between the apple and the surface of the Earth (although it would be greater if you had a convenient nearby deep mine shaft):
- "E=mgh"; E=Potential energy, g=gravitational acceleration, h=height above ground (or wherever it was going to end up)
- Where it was assumed that g was the same all the way down (and up)

(ii)  Did you believe it?   (I did while I was at school).
- Yes, although I also knew about the inverse square law for gravity.
- Assuming constant g makes the calculations easier, especially before learning how to do calculus

(iii) Was there anything different about the apple when it was up high or just that it was up high?
- Not for apples
- But for other things, like experiments where we carried weights up to the next floor and dropped them, work went into the weight to lift them up high.
- And with the traditional museum demonstration of orbits (roll a coin into a plastic "gravitational well"), the interplay between kinetic and potential energy was visible (until friction swallowed your coin... )

(iv) If the energy was in the apple, then did it have more mass when it was up high?
- I did not worry about that
- although I was aware of the equivalence of mass and energy.
- E=mc² only makes a measurable difference in hydrogen fusion (at least, potentially measurable by a High School student).

(v)  You may have studied more physics since school.  Where do you now think the gravitational potential energy is located?
- The gravitational well of the apple merges more closely with the gravitational well of the Earth when it falls.
- The gravitational well is a map of force or potential energy (depending on the units used)

(vi) How would you go about explaining this concept to a school-age student, maybe one of your own children if you have them?  Suppose they ask directly   "where is the gravitational potential energy stored?"  - what will you tell them?
- I like the museum gravitational well: unlike the apple, it is (partially) reversible, showing the return of kinetic energy back into potential energy.
- The total energy of the system is conserved (if you account for sound and heat).

Q: If an apple tree falls in the forest and no-one is there to hear it, does it make a noise?
A: Yes. After the event, you can see the broken branches and scattered leaves. The energy of the falling apple tree is turned into broken branches, wind which tears off the leaves, plus heat and sound.

[Eternal Student (OP)]

Hi again.

OK, I've looked at Halc's reference.
 

Looking up some reliable (reviewed) sources, we have two systems: Earth with apple on tree, and Earth with apple on ground. The proper mass of both Earth and apple is the same in both systems, but the system mass of the former (as viewed from infinity) is greater than the system mass of the latter. That implies that any meaningful potential energy location is 'the location of the system' and not the location of the apple at all.

    I'm surprised at you Halc.  You nearly always rush to say something is only a co-ordinate effect or that something is co-ordinate dependant - but you haven't done it here.  If "system mass" depends on the observer and their reference frame then why are you concerned about it?  Have some faith that the best theories (like my favourite - GR) was built with tensors to be as co-ordinate independent as possible.

1.   I'm not entirely sure that a "system mass" is a useful concept.  It seems like an attempt to return General Relativity to a Newtonian way of thinking about gravity.  They (the people on your stack-exchange site) seem to be implying that a ray of light that passes close to this earth-apple system experiences a gravitational effect (e.g. takes a curved path) that is due to this "system mass".   It's OK as far as it goes, if you must think of gravity in Newtonian terms then I suppose this "system mass" is required and is definable.
    Meanwhile, General Relativity is not a blunt tool - it has no need to know or care about this "system mass".  The location of the apple is information that is already known and made available to the theory of General relativity.  The location of the apple is encoded in the stress-energy tensor since the distribution of mass has changed slightly if the apple is on the tree or on the ground.  Just change the stress-energy tensor by inputting the new distribution of mass-energy.   Then "turn the handle" on the machinery of General relativity and it will correctly tell you about the path taken by light as it passes close to the earth.  It will be (ever so slightly) different when the apple is located in the tree rather than on the ground.   You cannot and indeed must not input any extra mass anywhere - just change the distribution (location) of the masses.   Any attempt to input some extra mass because the apple was up high in the tree will break the validity of your stress-energy tensor.
   This may be worth phrasing another way... see item 2. below.

2.  Conceptually, General Relativity is not a strap-on addition for Newtonian gravity, rather it is a total replacement of the Newtonian theory.
   You have no model of gravity until AFTER the stress-energy tensor has been calculated and then the Einstein Field Equations can be applied.  Therefore, you have no way of calculating gravitational anything (e.g. gravitational potential energy) until after the stress-energy tensor has been determined.   Einstein was kind enough to make sure that gravitational potential energy was not a form of mass-energy that needed to be included in the stress energy tensor.  Yes, it was likely that the distance between two masses  would be important or more generally the spatial distribution of mass would be important but that information was directly captured by the stress-energy tensor.
    [gravitational potential energy is not needed in the stress energy tensor  ---> this is close to suggesting gravitational potential energy is fundamentally not required but I'll leave that for another day and another post].
- - - - - - -

  I'm over-running again and should stop talking.  I'm sorry for not liking your peer-reviewed information sources about system mass.  It also looks like someone else has added a post and I'm interested to see what they learnt about gravitational potential energy.

Best Wishes.

[Eternal Student (OP)]

Hi @evan_au
  Thanks for your reply.

I was taught that it was in the separation between the apple and the surface of the Earth

   That is interesting.  The gravitational potential energy wasn't said to be in or any object  and/or it wasn't implied that the gravitational potential energy was possessed by an object in some way.

The next section almost contradicts this:

Was there anything different about the apple when it was up high or just that it was up high?
- Not for apples
- But for other things, like experiments where we carried weights up to the next floor and dropped them, work went into the weight to lift them up high.

   Force was applied at the object and this was moved through some distance.  I think everyone would agree that work was done at the object's location.  If I've understood what you've said then it seems the teacher presented the common view that this work (or energy) went into the object.
   So the teacher gave you two different possible locations for the energy and everyone just went along with that?  It was put into the weight (I'm going to call this "the object") you carried up one flight of stairs but it was stored in the space (the separation) for the apple.   For example, they could have said that work was being done against the gravitational field and implied that the energy was being stored in the field or in the separation between the object and the floor as you progressed - but they didn't do that - they implied the work went into the object.

- - - - - -
Stopped,  sorry I have to do some tasks for an elderly relative.   I'll write more later and I need to re-read the section about the gravity-well merging idea.   Bye for now.

[alancalverd]

School physics is all about frictionless pulleys and weightless elephants, and even Evan's recollection of lugging weights up the stairs to drop them on unsuspecting newbies, ignores the weight of the slaves.

Likewise Newton's apple tree was infinitely stiff so didn't bend as the apple grew.

Sorry to play the grumpy engineer in this, but you may recall one of the problems of laying undersea cables or dropping hydrophones to great depth is that you can't ignore the weight of the cable - it stretches as you drop it and whilst you can ignore the elastic energy of a fly fishing line, a deep trawl cable contains a lethal load of joules.

[Eternal Student (OP)]

Hi again.

Where do you now think the gravitational potential energy is located?
- The gravitational well of the apple merges more closely with the gravitational well of the Earth when it falls.
- The gravitational well is a map of force or potential energy (depending on the units used)

   This is an unusual and somewhat oblique description of where you now think gravitational potential energy is located.  It seems that you only loosely associate a location to gravitational potential.   The well is a map of potential and this is important.   I think you're implying that the potential is in the field somehow and spread out in space a little but mainly centred around each object.  (You could be suggesting that location just doesn't matter but I've discussed that later in this post).

   You seem to have thought about gravitational potential in every way here Evan_au (that's obviosuly good).

1.  It could be in the field,  or in the space between objects.
2.  It could be in the object.
3.  It's location may not matter.  It's just a store of energy.
- - - - - - - -
 

How would you go about explaining this concept to a school-age student, ......
- The total energy of the system is conserved (if you account for sound and heat).

   Well I agree that this is important and it's got to be taught to school-age children.  It's also on most examination syllabuses so there really isn't a choice about teahing this.
    It also links with comments and ideas presented by many physicists.
Energy could be just a book-keeping tool.   It doesn't represent anything real or tangible in the universe and it does not have to be located at a definite position in space.   It just so happens that in all the best theories  (Newtonian Mechanics, Quantum Mechanics, Special Relativity etc.) there is some quantity which can be identified and it seems to be conserved.
    It is important to realize that in physics today, we have no knowledge of what energy is.   -  From The Feynman lectures, vol. I Chapt. 4,   circa. 1963.    (To put that quote in context - Feynman went on to say that the conservation of energy is just about all we do know about energy).   
    Please note that I don't agree with everything that was just said, I'm just sumarising one view about energy as a book-keeping tool or abstract quantity only.
- - - - - -
    In Britain, schools have been changing the way they teach about Energy in physics over the last 10 years.  We are not encouraged to suggest that energy has different forms.  Instead the approach of suggesting that energy is just a book-keeping tool should be used.  You don't talk about "transforming" energy anymore.  Instead you just identify different stores of energy (but sometimes you just can't say where exactly the store is physically located -  e.g.   gravitational potential energy) and then talk about transferring this energy from one store to another.   It may seem like just a change of terminology but it isn't.   There is the suggestion that we have incredibly little understanding of energy and it's fundamentally wrong to suggest that it exists as a real thing like a "form of energy" in our universe.  Instead our understanding should be based on the principle of conservation of energy, i.e. that energy is just an abstract quantity that is conserved in all physical changes and in all models of science.

    Anyway, why does this matter to me (and hopefully other people)?  It's because one of my younger children is caught in the midddle of this transition over how energy is taught in school.  They have one older teacher who is still pushing the old teaching method with forms and transforming  and another  going down the new route with  stores and transferring.  Meanwhile, I need to unpick and unscramble what often seems like junk that they come home with while trying not to say anything myself that would directly contradict what the new teaching method suggests.
@alancalverd --->  I appreciate that school was a long time ago and it's not all that important what was done back in the day BUT I am stuck in this sitation where I do have to re-enagage with the way things are presented in school. 

     How are they teaching about energy in schools in your area (country) these days?  Do you know?     Forms of energy and Transforming      OR        Stores and Transferring        OR   something else?

Best Wishes.

[Eternal Student (OP)]

Does an ideal fluid have a PE density?

   Sorry, Halc,  I just spotted this and realised it could have been a question you wanted to discuss.
The use (or rather the lack of use) of gravitatonal potential energy when constructing the stress-energy tensor for General relativity was discussed in reply #9.
    Obviously you can say something else or even start a new thread if you want more discussion (but you're a mdoerator and you know this better than I do).
Best Wishes.

[evan_au]

So the teacher gave you two different possible locations for the energy and everyone just went along with that?  It was put into the weight (I'm going to call this "the object") you carried up one flight of stairs but it was stored in the space (the separation) for the apple.

I didn't see it as different or contradictory until I saw some of the discussion in this thread.

I never studied tensors at university, so I didn't have to think much about "the energy density of a point in space" - or in this case "the energy density of a path in space".

For a pre-calculus high school student, it's easiest to calculate the potential energy based on the difference in height before and after dropping the object, and ignore everything in between (but definitely clear the area of newbies before starting the experiment!).
 
With calculus, you could consider a force being applied to the object over a certain distance as you lug it up the stairs, which produces exactly the same answer as you get before calculus. I expended that energy over a certain distance, but I after I have passed, you can't actually see the energy in the zig-zag pattern as I trekked up the stairs (unless you have a sensitive infra-red camera or some such..). However, if you can see a 1kg lump of iron sitting on the balcony of the building, you can see the separation, and easily calculate the potential energy.

So, whether you call it a form of energy, or a store of energy, it is easier to see where it is now, rather than work out how it got there, especially for pre-calculus students.

Changing terminology can be a pain, and using the wrong terminology can cause lose you marks in the exam. Maybe just show your child how the two systems are equivalent (for a pre-calculus student, or an examiner assuming the student is pre-calculus). Encourage the student to use the terminology that the examiner is expecting.
 
I frequently find myself on the wrong side of a terminology change around mass, rest mass and relativistic mass.... The answers are the same, but the terminology has changed

[alancalverd]

I have sought guidance from an actual current  physics teacher and will forward the Party Line as soon as I have it.

Meanwhile here's my own twopennorth. As Feynman probably said it first, you can call it two cents' worth.

Mass and velocity are intuitively obvious. A weighs more than B, cars go faster than buses. Now multiply some numbers together and define acceleration, and you have all you need to analyse and predict classical mechanics. 

Energy should always and only be taught as "a conserved scalar", along with momentum as "a conserved vector". If you like, just call them "conserved quantities" and just note that momentum involves both  speed and direction. This is entirely sufficient for all newtonian mechanics and stresses the importance of conservation when analysing any physical event.

This approach makes sense of gravitational acceleration, ballistics, and all the other idealised mechanical interactions including pendulums. The mechanical equivalent of heat is fun to demonstrate, as is the use of electrical energy, and you can start asking the "engineering" questions about frictional losses or transducer heating if you always assume conservation.   

A skeptical note. A teacher is someone who understands something and phrases it so a pupil can understand it. An educationalist is someone who thinks he knows something and phrases it so nobody can understand it. Storage and transformation of energy seems like the language of the latter.

[Eternal Student (OP)]

Hi @evan_au  and thanks for your reply.

Changing terminology can be a pain, and using the wrong terminology can cause lose you marks in the exam. Maybe just show your child how the two systems are equivalent (for a pre-calculus student, or an examiner assuming the student is pre-calculus). Encourage the student to use the terminology that the examiner is expecting.

   I'm not sure it is just terminology.  Let's take this question as a simple example:

What is energy?  If you were walking down the street and found something, how would you know it was energy?

Possible answers (under the old system):  Energy exists in only certain forms.  Just run a test for each of those forms.  Is it sound energy?  Is it a source of electrical energy ?  etc. etc.

(Under the new system):  There is no easy way to know or describe what energy is.  The only way to know that what you have found is energy is to observe the ability to use it to transfer value to a known store of energy.   Sadly, even if you can't transfer value to a known store of energy it doesn't show that this thing is definitely not energy - just that you haven't found a way to transfer it to another store yet.

(Ignore the system being taught in school and just free-style the answer):   The usual definition of energy is something like this:
Scientists define energy as the ability to do work      -  taken from U.S. Energy Information Administration website.
    So the typical example of an energy source is a really hot thing (like burning coals in a power station).  This has a high temperature or a lot of internal kinetic energy.  As the energy flows out of the hot thing into the surrouding environment, we can extract useful work.  So that's OK, our definition works - energy is the ability to do work and we can say that the coal has a high energy content.
    Now, you probably realise that our ability to extract useful work actually depended on temperature differences and the concepts of heat flow as described by thermodynamics.  Let's assume that global warming has become such an issue that our surrounding environment is at hot as the burning coals anyway.  Now we can't extract any useful work from the burning coals.  Has the energy gone?  Is there no energy in coal any more?  Also what about really cold stuff?  We can quickly reverse the engineering in our power station.  Replace the burning coals with some really cold thing you brought in from our solar system.  Now the heat will flow out of the environment into the cold thing and we can extract useful work while that is hapening.  So the cold thing now seems to have a high energy content - we have the ability to do a lot of useful work with it.  Do cold things have a higher energy content than warm things?  Do things change their energy content when you change their environment?  Is it better to say that energy was never an intrinsic property of the thing to begin with?

Perhaps the entire language or nature of the original question is a problem:  Maybe energy isn't a physical thing you can find as you walk down the street.  Energy is abstract and does not exist as a thing in the universe, there just are some stores of it.  The only thing that you can find as you walk down the street is an "outlet" or an "intake" for these stores.  You can find a thing with which you can interact to access a certain store of energy.  This may be a lump of coal you can burn or an object with mass that you can lift up.  However it is just an intake or outlet for a store, the energy was never IN the object?  I don't know - just throwing out some discussion for a quiet evening.  I reckon we ought to think about things like this since you're going to end up teaching it to someone. In your case (Evan_au) you have readers on this forum and you're a moderator, you could be teaching this to someone tomorrow.
     ------
OK, I've probably talked enough and this isn't really the chat section of the forum.  Thanks for your time and best wishes to you.

[Eternal Student (OP)]

Hi again.

Thanks for your time and effort @alancalverd
  You do know that you can slow down and do something else with your time.  Also let's get some basic admin covered:  This discussion may be becoming more like general chat and I have no objection to any moderator moving the thread.

A skeptical note. A teacher is someone who understands something and phrases it so a pupil can understand it. An educationalist is someone who thinks he knows something and phrases it so nobody can understand it. Storage and transformation of energy seems like the language of the latter.

     I agree.  Sadly, teachers also have to follow a school syllabus.  I'm suspicious that physics teaching will revert back to something more like the old system but in the meantime it's an awkward marriage of government recommendations and multiple teacher preferences.
     Also, we've got to be open minded.  We (the collective group of all scientists) have been telling certain things to pupils for years and some of them are being challenged by modern science and not just educationalists.
(For examples - see threads where Noether's theorem is mentioned and conservation of energy may not apply;  threads discussing Cosmology;  or the awkward truth about thermodynamics you've always known where "the ability to do work" should really be a description only of Free Energy and not a definition of "Energy" as it often used).

Best Wishes.

[alancalverd]

This may be a lump of coal you can burn or an object with mass that you can lift up.  However it is just an intake or outlet for a store, the energy was never IN the object? 

This shows the inadequacy of energy being "stored in the object"! You can't squeeze or shake heat out of a lump of coal, nor can you burn it in an atmosphere of nitrogen.  When you think about the origin of coal, it is obviously a tree that has had all the life squeezed out of it, so is in almost the lowest energy state of elemental carbon (I don't advocate igniting diamonds to measure the difference). 

What you can say is that the tree used solar energy to convert carbon dioxide and water into useful structural materials and oxygen, then geological energy extracted various gases and left us with a lump of carbon which we can return to its oxide with the release of heat energy. It happens that the oxidation of carbon always involves the release of the same amount of energy as is required in the reduction of carbon dioxide. The intermediate chemical processes are very complicated, particularly in the forward direction (photosynthesis generates PhD theses by the score) but the physics is straightforward (energy is conserved in every interaction) so provides us with a trail of breadcrumbs through the chemistry and the means by which I can follow biochemistry research presentations!

[evan_au]

Replace the burning coals with some really cold thing you brought in from our solar system.  ... Do cold things have a higher energy content than warm things?  Do things change their energy content when you change their environment?

For the last question: Yes.
- If you take an object to the building balcony, it has a certain amount of potential energy.
- Now, if you build up a mound of dirt to the same height as the balcony, there is effectively no potential energy (the separation drops to zero). The potential energy changes when you change the environment
- Now, mound the dirt even higher, and it will consume energy to get it off the balcony (the separation becomes negative)
- So it is fair to say that you measure energy content relative to some reference level

Thermodynamics has some similarities:
- If two bodies have the same temperature & pressure, you can't extract useful energy - the potential energy in this closed system is zero
- The special case for thermal energy (as developed by Carnot) is that there is a limit to the amount of energy you can extract, and the extractable fraction increases with the difference in temperature.
- The fraction is also better with an "infinite" heat sink (ie able to absorb all the heat from the hot body, without a detectable change in temperature)

There is a somewhat similar situation with electrical charges.
- You can't extract electrical energy from two objects at the same voltage
- The extractable energy increases with the difference in voltage
- The extractable energy is also better with an "infinite" current sink: "Earthed" (ie able to absorb all the current from the charged body, without a detectable change in voltage)