Julian Benali

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Mechanical energy

You made a change to our article on Mechanical energy – see your diff. Thank you for taking an interest in this article.

I reverted your edit because by changing the words “mechanical energy” to “kinetic energy” you made the sentence incorrect. Kinetic energy is never described as a conserved quantity. Total energy, mass, momentum and even mechanical energy are often described as conserved quantities because they remain constant even in highly dynamic situations. Other quantities, including kinetic energy and potential energy, only remain constant in static situations where nothing significant is changing. For example, Wikipedia has a topic devoted to conservation of mechanical energy: See Mechanical energy#Conservation of mechanical energy. In contrast, Wikipedia has nothing implying conservation of kinetic energy. As another example, notice that scientists never talk about conservation of weight, conservation of temperature, conservation of entropy etc. because none of these is a conserved quantity even though each one can sometimes remain constant with time - see Conservation law.

In your edit summary you wrote “Total mechanical energy may or may not be conserved during inelastic collisions.” I challenge you to describe an inelastic collision in which mechanical energy “may be conserved.”

You also wrote “See for example the pages on Elastic collision and Inelastic collision.” I have read those two pages carefully. Both contained errors in referring to “conservation of kinetic energy”. I have corrected the errors in both pages. See my diff related to elastic collisions and my diff related to inelastic collisions. (Both these articles mention conservation of momentum and conservation of total energy; I have no objection to these expressions because both momentum and total energy are conserved quantities.)

If you wish to reply, please do so here on your Talk page. I will add it to my Watchlist so I will see your reply. I will respond here also. Alternatively, if you wish to raise the matter at Talk:Mechanical energy you are welcome to do so. Dolphin (t) 14:34, 1 October 2020 (UTC)

Hello, and thank you for the feedback. I am not so sure that the pages elastic collision and inelastic collision were incorrect. All the sources I have encountered define or characterize an elastic collision as one in which the total kinetic energy is constant (aka is conserved). For example, in John Taylor's Classical Mechanics, he states "an elastic collision can be characterized as a collision in which two particles come together and re-emerge with their total kinetic energy unchanged." If you know of a source disagreeing with John Taylor's characterization, I would be interested to read it. For an example of an inelastic collision where mechanical energy is conserved, see problem 4.53 in John Taylor:

4.53** (a) Consider an electron (charge $-e$ and mass $m$) in a circular orbit of radius $r$ around a fixed proton (charge $+e$). Remembering that the inward Coulomb force $ke^{2}/r^{2}$ is what gives the electron its centripetal acceleration, prove that the electron's KE is equal to $-{\tfrac {1}{2}}$ times its PE; that is, $T=-{\tfrac {1}{2}}U$ and hence $E={\tfrac {1}{2}}U$. Now consider the following inelastic collision of an electron with a hydrogen atom: Electron number 1 is in a circular orbit of radius $r$ around a fixed proton. (This is the hydrogen atom.) Electron 2 approaches from afar with kinetic energy $T_{2}$. When the second electron hits the atom, the first electron is knocked free, and the second is captured in a circular orbit of radius $r'$. (b) Write down an expression for the total energy of the three-particle system in general. (Your answer should contain five terms, three PEs but only two KEs, since the proton is considered fixed.) (c) Identify the values of all five terms and the total energy $E$ long before the collision occurs, and again long after it is all over. What is the KE of the outgoing electron 1 once it is far away? Give your answers in terms of the variables $T_{2},r,$ and $r'$.

Indeed, mechanical energy is conserved in this scenario even though kinetic energy is not and the method for solving part (c) is to invoke conservation of mechanical energy (if you do not believe me, you can also see this in John Taylor's solution at the back of the book). Thus, the total mechanical energy may or may not be conserved in an inelastic collision.

Additionally, I do not understand your aversion to the word "conserved". The word is simply a synonym for "remains constant" with respect to time or some process. I see no issue with referring to temperature or entropy as being conserved in situations where their value remains constant. Obviously, there is no "law of conservation of kinetic energy" but this is very different than saying kinetic energy is conserved in a specific scenario. Your opinion about the reservation of the word "conserved" seems more like a semantic preference than a scientific consensus. Let me know what you think. Julian Benali (talk) 16:38, 1 October 2020 (UTC)

Thank you for your detailed and thoughtful reply. It is much appreciated. I will consider it carefully and reply later today. Dolphin (t) 22:13, 1 October 2020 (UTC)

I have examined one of my old Physics text books, Physics by Robert Resnick and David Halliday (1966), and I was disappointed to see that even these two eminent educators manage to successfully confuse students by writing "Collisions are usually classified according to whether or not kinetic energy is conserved in the collision. When kinetic energy is conserved, the collision is said to be elastic. Otherwise, the collision is said to be inelastic." (Section 10-4)

It has always been my understanding that the conserved quantities are well known - mass, energy, linear momentum, angular momentum, electric charge etc. Even mechanical energy can be described as a conserved quantity because in certain dynamic situations (no work done by non-conservative forces) the mechanical energy remains unchanging. It has always been my understanding that other quantities are never described as being conserved because the only situations in which they remain constant are static situations; when these other quantities are unchanging I would simply say they remain unchanged or remain constant. Alas, even Resnick and Halliday have been seduced into using the word "conserved" for these other non-conserved quantities. I wonder what Resnick and Halliday and others would make of a student referring to "conservation of weight" or "conservation of temperature". The potential confusion could be avoided simply by being willing to say "the weight remains constant" or "the temperature does not change" on the grounds that weight and temperature are not conserved quantities.

Resnick and Halliday have written that an elastic collision is one in which kinetic energy is conserved. They have not stated so explicitly, but clearly they are referring to a collision which takes place entirely on a horizontal plane so that there is no exchange of potential energy and kinetic energy. As you know, when an object moves in a plane that is not horizontal, there is an exchange of potential and kinetic energies so that mechanical energy remains constant but kinetic energy does not.

You have written that the word conserved "is simply a synonym for remains constant". I disagree, although Resnick and Halliday might agree with you. A quantity remaining constant is a necessary condition for that quantity to be conserved, but it is not a sufficient condition. If a bronze statue has not moved for 100 years its kinetic energy and potential energy have been constant but that doesn't convince me the potential and kinetic energies of the statue should be described as having been conserved. It would be trivial to say that, in a static situation, nothing is changing so everything is conserved. My understanding of the word "conserved" is that it is reserved for those remarkable quantities that remain unchanging in dynamic situations when everything else is changing around them. For example, even in highly dynamic situations like explosions and the conversion of heat into useful work, total energy remains unchanging. This is one of those astounding discoveries of science so it has become known as the law of conservation of energy. I think the concept of conservation of energy is diminished if scientists and others are willing to say "weight and temperature and kinetic energy and everything else is also conserved some of the time" and then to justify their statement by saying "conservation is nothing more than something remaining constant for a period of time." Conservation of energy is so much more profound than simply "remaining constant for a period of time." Similarly for conservation of momentum etc. Conservation of weight and temperature and kinetic energy should be expressions that no scientist is willing to use. If these things remain constant for a period of time scientists should be willing to say they are constant or unchanging. It is unnecessary to make them look more important than they are by describing them as conserved.

Wikipedia has an article about conserved quantities. Unfortunately it is written from a mathematical perspective and is not immediately helpful in our present dilemma. However, my reading of the article is that it does not support the notion that every quantity that remains constant, at least for a short time, is a conserved quantity. It associates conserved quantities with the laws of physics, rather than with anything that remains constant for a short time. Unless the unchanging nature of a quantity is assured by one of the laws of physics, that quantity is not a conserved quantity. Dolphin (t) 14:30, 2 October 2020 (UTC)

I understand what you are saying. It seems that most of what you are arguing is a semantic opinion. You want to reserve the word "conserved" for quantities which obey a law of conservation because doing otherwise might confuse students and seemingly undermines the significance of conservation laws. I personally do not find these reasons significant enough to bar the word "conserved" from being used except in the case of conservation laws, but again, that's just my semantic opinion. You also refer to the article on conserved quantities as justification for your opinion, but the article only defines it in the context of dynamical systems. There are plenty of scenarios (e.g. collisions) which cannot be modeled by a dynamical system due to a lack of differentiability with respect to time of the quantities being measured. Nonetheless, if you want to edit the wording of Wikipedia articles to avoid the word "conserved" except in the case of conservation laws, I won't stop you since that is just a matter of semantics, but I won't say I would make the changes myself since I have yet to encounter a physicist or physics author who insists that the word "conserved" should be reserved in such a manner.

You claim that Resnick and Halliday are "referring to a collision which takes place entirely on a horizontal plane so that there is no exchange of potential energy and kinetic energy", but I don't think this assumption is necessary. Indeed, on page 142 of his Classical Mechanics, John Taylor proves that the total kinetic energy sufficiently long before and after an elastic collision is the same even if there is a nonconstant potential energy. This leads to the real issue and the reason that I made the edit to Mechanical Energy in the first place.

There is an inconsistency between some of the physics articles here on Wikipedia. The article on Mechanical Energy states "In elastic collisions, the mechanical energy is conserved, but in inelastic collisions some mechanical energy is converted into thermal energy" whereas the article on Elastic Collision states "An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies remains the same". One of these two claims must be untrue. If the collision described in problem 4.53 of Taylor is elastic, then the latter claim is untrue, but if the collision described in that problem is inelastic, then the former claim is untrue. The fact that Taylor referred to the collision in his problem 4.53 as inelastic and the fact that no other Wikipedia article I could find agrees with the claim in Mechanical Energy is what lead me to conclude that the claim "In elastic collisions, the mechanical energy is conserved, but in inelastic collisions some mechanical energy is converted into thermal energy" is untrue. Thus, I edited that claim and will edit it again to correct it unless there is sufficient evidence that it is John Taylor and the claims from the other Wikipedia articles that are incorrect. Julian Benali (talk) 16:31, 2 October 2020 (UTC)

Thank you again for your thoughtful and persuasive response. I will re-examine my edits in the light of your explanations and revert those that aren’t consistent with Taylor, a Resnick and Halliday etc. I would like to leave an explanation on the relevant Talk pages to serve as clarification of what we have decided here and why I am making the reversions so please give me a day to make my changes. Dolphin (t) 23:02, 2 October 2020 (UTC)

No problem, and thank you very much for your work. No rush. Also, thank you for welcoming me. If you need/want any more input from me feel free to contact me. Julian Benali (talk) 02:01, 3 October 2020 (UTC)

Please see Talk:Mechanical energy#Inelastic collisions. Dolphin (t) 12:25, 5 October 2020 (UTC)

@Julian Benali: Today I received an Alert saying "Julian Benali sent you an email". I haven't received an email from you yet. I have checked my email address registered with Wikipedia and it is correct. I don't know of any reason why your email hasn't reached me. Perhaps you could try again or send your message to my Talk page. I look forward to reading it. Dolphin (t) 05:14, 6 October 2020 (UTC)