# Potential Energy

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Kinetic Energy seems easy to understand. For instance, if you throw a football, or any object, away from you. Your act of throwing, requires movement on your part. This movement is transferred to the object, which then itself starts moving.

As it moves, the distance between you and the object continually increases. This continually changing distance, reveals that the object has acquired extra (kinetic) energy. That's clear.

But I can't understand Potential Energy.

Suppose you don't throw the object, but just lift it up, and put it (say), onto the roof of your house.

Up there, it's supposed to have acquired extra (potential) energy. But once placed there, it's not in motion any more. Nothing is changing.

So has it really got extra energy, and how is that revealed?

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Kinetic Energy seems easy to understand. For instance, if you throw a football, or any object, away from you. Your act of throwing, requires movement on your part. This movement is transferred to the object, which then itself starts moving.

As it moves, the distance between you and the object continually increases. This continually changing distance, reveals that the object has acquired extra (kinetic) energy. That's clear.

But I can't understand Potential Energy.

Suppose you don't throw the object, but just lift it up, and put it (say), onto the roof of your house.

Up there, it's supposed to have acquired extra (potential) energy. But once placed there, it's not in motion any more. Nothing is changing.

So has it really got extra energy, and how is that revealed?

Kinetic energy is dependent on the frame of reference. Relative to you that football that you tossed has kinetic energy. But in the frame of the football it is at rest and you have kinetic energy.

Potential energy likewise depends on a choice of references. One can speak of a difference in potential energy between two states, but there is no absolute measure of potential energy. So if you put the football on the roof of your house, you apply a force over a distance, do work, to lift it from the ground to the roof, just as you did work to throw it and put it into a relative state of motion from a relative state of rest. In the case of the ball on the roof that work can be recovered and turned into kinetic energy if the football falls off of the roof back to the ground.

In either case the energy is associated with the work done to move the football from one state to another.

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I think you can look at potential energy as any situation in which energy can be released. When you throw a ball up in the air, you are adding potential energy to it that gets released when the ball accelerates downward after reaching its highest point. When you stretch an elastic band, you are adding energy to it that is released when you let it go and it snaps. When you compress a spring, you add energy to it that gets released when the spring re-expands. When you charge a battery, you are adding energy to it that gets released when you power an application. When you use energy to electrolyze water into hydrogen and oxygen, you can release that energy by igniting the gasses to recombine into water. Energy can't be created or destroyed but it can be stored and released, as well as converted from one form to another as you describe with the motion of your arm being converted into motion of a thrown ball.

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Kinetic energy is dependent on the frame of reference. Relative to you that football that you tossed has kinetic energy. But in the frame of the football it is at rest and you have kinetic energy.

Potential energy likewise depends on a choice of references. One can speak of a difference in potential energy between two states, but there is no absolute measure of potential energy. So if you put the football on the roof of your house, you apply a force over a distance, do work, to lift it from the ground to the roof, just as you did work to throw it and put it into a relative state of motion from a relative state of rest. In the case of the ball on the roof that work can be recovered and turned into kinetic energy if the football falls off of the roof back to the ground.

In either case the energy is associated with the work done to move the football from one state to another.

Thanks Dr Rocket. That seems clear, but could I just pursue your point about the frame of references. In the case of the thrown football, isn't it true that in any frame of reference, all observers would agree on one thing: relative position is continually changing - the football, and the person who threw it, are moving further and further apart. Whether you look at things from the point of view of the thrower, or the football, or from any outside viewpoint, you see relative movement occurring, and that's evidence of the kinetic energy.

However in the case of the football lying on the roof, I don't quite see where the evidence of the potential energy is. Both the football and the roof are static. There's no relative movement between them. Is it the height above the ground we're supposed to measure? But how do we know there is any ground? If we're standing on the roof, next to the football, and it's a very big roof, stretching to the horizon say, we don't know what's underneath. All we see is a flat plain.

Sorry if the above sounds a bit childish! I just can't help feeling that while kinetic energy is "real", potential energy seems somehow illusory.

Would it be valid to make an analogy with "real" centripetal force, and centrifugal force - which (as I understand it) is also a kind of illusion?

Will greatly appreciate any further comments.

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However in the case of the football lying on the roof, I don't quite see where the evidence of the potential energy is. Both the football and the roof are static. There's no relative movement between them.

Could the force with which the ball is pushing against the roof be considered potential motion, i.e. if the roof wasn't pushing back against the ball with an equal and opposite reaction? Many people will tell you that potential energy depends on how you frame it, but I tend to think of it as an inherent propensity to work due to an something's state or position. I.e. it is energy that can be expressed but isn't at present, hence it is "potential (future) kinetic energy."

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Thanks Dr Rocket. That seems clear, but could I just pursue your point about the frame of references. In the case of the thrown football, isn't it true that in any frame of reference, all observers would agree on one thing: relative position is continually changing - the football, and the person who threw it, are moving further and further apart. Whether you look at things from the point of view of the thrower, or the football, or from any outside viewpoint, you see relative movement occurring, and that's evidence of the kinetic energy.

It is only evidence of kinetic energy of the football relative to the thrower or of the thrower relative to the football. There is no such thing as absolute kinetic energy.

However in the case of the football lying on the roof, I don't quite see where the evidence of the potential energy is. Both the football and the roof are static. There's no relative movement between them. Is it the height above the ground we're supposed to measure? But how do we know there is any ground? If we're standing on the roof, next to the football, and it's a very big roof, stretching to the horizon say, we don't know what's underneath. All we see is a flat plain.

Potential energy is only meaningful relative to some reference. That is the point.

Gravitational potential energy relative to the round is one natural choice, but not the only choice. To make sense of potential energy a choice of "ground state" is needed, and that can be arbitrary.

Potential energy and kinetic energy are not absolute. Energy is relative.

Even in relativity, while speed of a photon is the same in all reference frames, the frequency depends on the frame, and energy is proportional to frequency.

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Potential energy is only meaningful relative to some reference. That is the point.

Gravitational potential energy relative to the round is one natural choice, but not the only choice. To make sense of potential energy a choice of "ground state" is needed, and that can be arbitrary.

Potential energy and kinetic energy are not absolute. Energy is relative.

Can't potential be empirically tested by inciting the release of potential/stored energy? I.e. If you can't get any energy out of something, then it didn't have any potential (energy), right? Conversely, if you CAN trigger a release of energy, then that energy must have been potential/latent in the system that released it, no?

Even in relativity, while speed of a photon is the same in all reference frames, the frequency depends on the frame, and energy is proportional to frequency.

But doesn't frequency shift directly correspond to the rate of apprehension of the energy (waves)? Only since the waves can only be measured at the same speed regardless of motion relative to the source, the doppler effect registers as a stretching or contracting of the wave instead of as a change in its speed. So the amount of energy that a given star emits during its lifespan is the same no matter whether it is measured in a shifted frame or not, right?

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Can't potential be empirically tested by inciting the release of potential/stored energy? I.e. If you can't get any energy out of something, then it didn't have any potential (energy), right? Conversely, if you CAN trigger a release of energy, then that energy must have been potential/latent in the system that released it, no?

Yes, but so what ?

But doesn't frequency shift directly correspond to the rate of apprehension of the energy (waves)? Only since the waves can only be measured at the same speed regardless of motion relative to the source, the doppler effect registers as a stretching or contracting of the wave instead of as a change in its speed.

??????????

So the amount of energy that a given star emits during its lifespan is the same no matter whether it is measured in a shifted frame or not, right?

no

Don't thoink about the complex processes involved in nuclear reactions and radiation. Just note that the total energy (aka relativistic mass times c^2) of the star is dependent on the reference frame.

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Yes, but so what ?

So potential energy is empirically present or absent, not just frame-relative.

??????????

Ok, a rocket ship leaves a star and travels to Earth and registers a certain amount of energy from the star en route. Another rocket ship leaves Earth and travels to the star. Both ships depart and arrive simultaneously. The first ship will register the star's energy as redshifted and the second blueshifted, correct? Yet both must register the same amount of energy getting emitted from the star since their departure and arrivals were simultaneous?

Don't thoink about the complex processes involved in nuclear reactions and radiation. Just note that the total energy (aka relativistic mass times c^2) of the star is dependent on the reference frame.

Because energy decreases as time goes faster? But isn't the total amount of energy the same, only spread out over a longer period or compressed into a shorter one?

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So potential energy is empirically present or absent, not just frame-relative.

Wrong.

It is not even just frame relative. It is relative to a choice of ground point within a frame.

Ok, a rocket ship leaves a star and travels to Earth and registers a certain amount of energy from the star en route. Another rocket ship leaves Earth and travels to the star. Both ships depart and arrive simultaneously. The first ship will register the star's energy as redshifted and the second blueshifted, correct? Yet both must register the same amount of energy getting emitted from the star since their departure and arrivals were simultaneous?

Why ? If one of them is moving fast enough, relative to the star, the energy in any single photon can be made arbitrarily large (blue shifted) by making that speed sufficiently close to c.

Because energy decreases as time goes faster? But isn't the total amount of energy the same, only spread out over a longer period or compressed into a shorter one?

no

Where are you getting this stuff ? Just making it up as you go along ?

I give up.

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Wrong.

It is not even just frame relative. It is relative to a choice of ground point within a frame.

Maybe in terms of measuring it as a specific quantity of energy. But it could still be the case that an object measured as having one quantity of potential energy within a chosen frame will have yet more potential energy to release at the point of maximum entropy within that frame, right? So it's not like you can say that once an object expresses all its potential within a given frame, that its potential energy has reached 'absolute zero.'

Why ? If one of them is moving fast enough, relative to the star, the energy in any single photon can be made arbitrarily large (blue shifted) by making that speed sufficiently close to c.

But doesn't the same amount of energy get emitted by, say, the sun in one Earth year regardless of how much time is measured by a traveling observer? The energy could get blueshifted, but then the amount of time would decrease so that the total amount of energy would be the same as if they were in orbit with Earth.

Where are you getting this stuff ? Just making it up as you go along ?

This is my understanding of redshift/blueshift. I.e. that the wave gets expanded or compressed but so does the amount of time elapsed so that conservation of energy doesn't get violated. I don't see how frequency of light can shift in a way that adds or subtracts energy from the total amount emitted +/- the amount the vehicle adds with its own speed. It's like if a train moving in one direction runs into a train going in the opposite direction, except with photons, the speed can't be added to the speed of the receiver so the frequency blueshifts instead - but how can more energy be gained than that of the light plus the speed of reception?

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This is my understanding of redshift/blueshift. I.e. that the wave gets expanded or compressed but so does the amount of time elapsed so that conservation of energy doesn't get violated. I don't see how frequency of light can shift in a way that adds or subtracts energy from the total amount emitted +/- the amount the vehicle adds with its own speed. It's like if a train moving in one direction runs into a train going in the opposite direction, except with photons, the speed can't be added to the speed of the receiver so the frequency blueshifts instead - but how can more energy be gained than that of the light plus the speed of reception?

Conservation and invariant refer to two different things. "X is conserved" means that it will not change value in a reference frame. "X is invariant" means that it will not change values in a transform to another reference frame. Energy is conserved. It is not invariant. Once you involve a second frame of reference for comparison, you are not talking about conservation.

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Maybe in terms of measuring it as a specific quantity of energy. But it could still be the case that an object measured as having one quantity of potential energy within a chosen frame will have yet more potential energy to release at the point of maximum entropy within that frame, right? So it's not like you can say that once an object expresses all its potential within a given frame, that its potential energy has reached 'absolute zero.'

But doesn't the same amount of energy get emitted by, say, the sun in one Earth year regardless of how much time is measured by a traveling observer? The energy could get blueshifted, but then the amount of time would decrease so that the total amount of energy would be the same as if they were in orbit with Earth.

This is my understanding of redshift/blueshift. I.e. that the wave gets expanded or compressed but so does the amount of time elapsed so that conservation of energy doesn't get violated. I don't see how frequency of light can shift in a way that adds or subtracts energy from the total amount emitted +/- the amount the vehicle adds with its own speed. It's like if a train moving in one direction runs into a train going in the opposite direction, except with photons, the speed can't be added to the speed of the receiver so the frequency blueshifts instead - but how can more energy be gained than that of the light plus the speed of reception?

" That's not right - that's not even wrong” – Wolfgang Pauli

Where in the world are you getting such ideas ?

You desperately need to read a physics book. Try The Feynman Lectures on Physics.

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Conservation and invariant refer to two different things. "X is conserved" means that it will not change value in a reference frame. "X is invariant" means that it will not change values in a transform to another reference frame. Energy is conserved. It is not invariant. Once you involve a second frame of reference for comparison, you are not talking about conservation.

That makes sense. My point is that it doesn't matter what frame of reference an observer measures energy from a star, however redshifted or blueshifted, the total amount of energy emitted is what it is. It's only relative to the rate of time. In other words, if you control for the speed of time, the amount of energy, whether blueshifted or redshifted, doesn't change. Is that not correct?

" That's not right - that's not even wrong" – Wolfgang Pauli

Where in the world are you getting such ideas ?

You desperately need to read a physics book. Try The Feynman Lectures on Physics.

That's not a reason I'm wrong. That's not even a reason

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That makes sense. My point is that it doesn't matter what frame of reference an observer measures energy from a star, however redshifted or blueshifted, the total amount of energy emitted is what it is. It's only relative to the rate of time. In other words, if you control for the speed of time, the amount of energy, whether blueshifted or redshifted, doesn't change. Is that not correct?

No. The total energy released will depend on who is doing the measurement. If the star moves toward me or away from me at some speed the time dilation will be exactly the same, but my measurement of the energy will not.

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No. The total energy released will depend on who is doing the measurement. If the star moves toward me or away from me at some speed the time dilation will be exactly the same, but my measurement of the energy will not.

I know, but if you control for the time dilation and the speed between source and receiver, the amount of energy must remain the same. You couldn't, for example, use a rocket to reach a speed where you could capture more solar energy than you would be able to capture from Earth orbit. I.e. if you were flying around at high speed with hyper-dilated time, you would capture and store the same amount of energy the sun emitted to a non-dilated receiver that aged longer while you were accelerated, right? Only the light-energy you captured was received at a higher-frequency for a shorter period of time (by your clock).

Edited by lemur
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I know, but if you control for the time dilation and the speed between source and receiver, the amount of energy must remain the same. You couldn't, for example, use a rocket to reach a speed where you could capture more solar energy than you would be able to capture from Earth orbit. I.e. if you were flying around at high speed with hyper-dilated time, you would capture and store the same amount of energy the sun emitted to a non-dilated receiver that aged longer while you were accelerated, right? Only the light-energy you captured was received at a higher-frequency for a shorter period of time (by your clock).

wrong

Now go read a physics book.

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wrong

Now go read a physics book.

Dr. Rocket, how many posts are you going to criticize me uncritically before explaining why I'm wrong? How can the amount of energy contained in a given amount of radiation change because of the time rate of the receiver? I can see how moving toward a source can add energy to the received radiation because the added energy comes from the motion of the observer. How else can energy amounts vary in the way you're suggesting?

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Dr. Rocket, how many posts are you going to criticize me uncritically

I have not accomplished this seemingly impossible feat.

explaining why I'm wrong? How can the amount of energy contained in a given amount of radiation change because of the time rate of the receiver? I can see how moving toward a source can add energy to the received radiation because the added energy comes from the motion of the observer. How else can energy amounts vary in the way you're suggesting?

It has been explained to you several times, by several people, precisely why you are wrong. I have no intention to continue to attempt to explain physics to someone who is so blatantly proud of his state of ignorance and who refuses to learn either the subject itself or the language (mathematics) in which it is spoken.

Either acquire a physics book and learn something about the subject, or remain in your present state. It is your decision.

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It has been explained to you several times, by several people, precisely why you are wrong. I have no intention to continue to attempt to explain physics to someone who is so blatantly proud of his state of ignorance and who refuses to learn either the subject itself or the language (mathematics) in which it is spoken.

Why is it so hard for people who like math to acknowledge how much of science involves non-mathematic ideas and concepts?

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Why is it so hard for people who like math to acknowledge how much of science involves non-mathematic ideas and concepts?

Perhaps it's because these concepts are inherently mathematical, and what you are using are watered-down analogies based on the concepts, not the concepts themselves. Why is it so hard to accept that all of the actual scientists who post here and say that science is inherently mathematical actually know what they are talking about? And that all of the people who claim that math isn't necessary (or they don't "do" math) invariably turn out to not be scientists?

Strictly speaking, I think we do acknowledge how much of science involves non-mathematic ideas and concepts. It's a small amount. I don't see a single scientific concept in this thread that isn't mathematical in nature. What I do see are several misunderstandings presented where math comprehension is lacking.

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Strictly speaking, I think we do acknowledge how much of science involves non-mathematic ideas and concepts. It's a small amount. I don't see a single scientific concept in this thread that isn't mathematical in nature. What I do see are several misunderstandings presented where math comprehension is lacking.

Math does what it does. Dealing with specific issues/questions determines what is relevant, whether math or other forms of reasoning. The issue of potential energy involves the concept, imo, that energy can be differentiated into active expressions and inactive (potential) expressions. The primary method is to look at a mechanical system and identify what energy is doing in that system, the paths it takes, and where/how it becomes inactive until a later moment in which it is once again activated. This is qualitative reasoning/description, but I believe it explains the basic logic behind dividing energy into kinetic and potential variations. I'm not arguing that it's useless to measure energy quantitatively or that various types of mathematical modeling don't allow you to describe and predict mechanical systems in a more accurate way. I'm just saying that when people are confused about why potential energy is different than kinetic energy, or what constitutes potential or kinetic energy, that it makes sense to analyze and identify what energy is and what makes it kinetic or potential in the first place, at a qualitative level. I'm not in competition with math. I lament my lack of math skills and I try to understand math-references when I can. I just don't appreciate being told that I'm an idiot and nothing I think can be grounded or have truth-value without math. It's just not the case. There is more to physics/science than just math. The ration of math to non-math is also irrelevant. 90% of science can be math but that doesn't mean that the other 10% is any less important. It comes down to specific questions/issues and what is specifically necessary to address them.

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Math does what it does. Dealing with specific issues/questions determines what is relevant, whether math or other forms of reasoning. The issue of potential energy involves the concept, imo, that energy can be differentiated into active expressions and inactive (potential) expressions. The primary method is to look at a mechanical system and identify what energy is doing in that system, the paths it takes, and where/how it becomes inactive until a later moment in which it is once again activated. This is qualitative reasoning/description, but I believe it explains the basic logic behind dividing energy into kinetic and potential variations. I'm not arguing that it's useless to measure energy quantitatively or that various types of mathematical modeling don't allow you to describe and predict mechanical systems in a more accurate way. I'm just saying that when people are confused about why potential energy is different than kinetic energy, or what constitutes potential or kinetic energy, that it makes sense to analyze and identify what energy is and what makes it kinetic or potential in the first place, at a qualitative level. I'm not in competition with math. I lament my lack of math skills and I try to understand math-references when I can. I just don't appreciate being told that I'm an idiot and nothing I think can be grounded or have truth-value without math. It's just not the case. There is more to physics/science than just math. The ration of math to non-math is also irrelevant. 90% of science can be math but that doesn't mean that the other 10% is any less important. It comes down to specific questions/issues and what is specifically necessary to address them.

"Mathematics is the study of any kind of order that the human mind can recognize" -- Pasquale Porcelli, Professor of Mathematics.

Your problem is that, like most people who are ignorant of mathematics, you fail to recognize what mathematics really is. Very little of mathematics is equations. Logical qualitative arguments ARE mathematical arguments.

No one has said that you are an idiot. You have admitted to being ignorant of mathematics. Ignorance and idiocy are not the same thing. One might, however, be of the opinion that proclaiming understanding while simultaneously admitting ignorance is a bit idiotic.

Mathematics and physics are two completely different things. But mathematics is the language in which physics is expressed. It is illogical to think that one can understand a subject while remaining illiterate in the language in which it is developed and recorded. Your "10%" is illusory.

"To summarize , I would use the words of Jeans, who said that ‘the Great Architect seems to be a mathematician’. To those who do not know mathematics it is difficult to get across a real feeling as the beauty, the deepest beauty, of nature. C.P. Snow talked about two cultures. I really think that those two cultures separate people who have and people who have not had this experience of understanding mathematics well enough to appreciate nature once." – Richard P. Feynman in The Character of Physical Law

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"Mathematics is the study of any kind of order that the human mind can recognize" -- Pasquale Porcelli, Professor of Mathematics.

Your problem is that, like most people who are ignorant of mathematics, you fail to recognize what mathematics really is. Very little of mathematics is equations. Logical qualitative arguments ARE mathematical arguments.

No one has said that you are an idiot. You have admitted to being ignorant of mathematics. Ignorance and idiocy are not the same thing. One might, however, be of the opinion that proclaiming understanding while simultaneously admitting ignorance is a bit idiotic.

Mathematics and physics are two completely different things. But mathematics is the language in which physics is expressed. It is illogical to think that one can understand a subject while remaining illiterate in the language in which it is developed and recorded. Your "10%" is illusory.

"To summarize , I would use the words of Jeans, who said that 'the Great Architect seems to be a mathematician'. To those who do not know mathematics it is difficult to get across a real feeling as the beauty, the deepest beauty, of nature. C.P. Snow talked about two cultures. I really think that those two cultures separate people who have and people who have not had this experience of understanding mathematics well enough to appreciate nature once." – Richard P. Feynman in The Character of Physical Law

My shortcoming is in decoding the meaning of equations expressed in variables and symbols. Simple formulas like W=FD, F=MA, Power=WT, acceleration=speed change T, P=MV, etc. are just shorthand for expressing analogical relationships in my mind. I do think about relationships between such things in a quasi-mathematical way, but I don't think in exact relationships between variables in the sense of processing a mathematical proof. For example, I get confused when thinking about the relationship between energy, power, work, force, time, etc. because I am simultaneously trying to think in terms of empirical situations and logical relationships between terms. I suppose you could say I think mathematically in a way, but I just don't respect my own 'mathematical' thinking the way I respect people who can explicitly represent and manage their thought-process in terms of precise balances between two sides of an "=." However, instead of giving up completely, I try to maintain the more constructive attitude that my methods of thought aren't totally worthless and so I enjoy thinking about physical/mechanical issues in my way and discussing what I come up with with people who think using more formal mathematics or other approaches. I view diversity of thought-approaches as a constructive process, although in practice it does sometimes lead to confounding miscommunication. I do have to admit that I usually get more out of discussions with highly math-literate people than with math-illiterates without rigorous reasoning abilities. Some of the most interesting thoughts can come from such people, or those with some reasoning, but such people are an elite among many more people who are just playing in sandboxes trying to develop rigorous reasoning. Of course, it's also important for them to develop so I can't denigrate their efforts too much.

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I hope this is the correct place to post this:

How is gravitational potential energy stored?, because all the other energy I know about is kinetic (like an electron that moves faster has more energy than other that is slower) or in form of mass (E=mc^2). But I don't see any of them doing something there.

Off of topic, my native language isn't English so tell me if you don't understand what I'm trying to say.

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