# True or False: energy is conserved in all collisions [closed]

Using introductory physics, how would you answer this question? (I have a disagreement with my instructor and I’m curious to hear your input)

One of us says true because the question doesn’t specify “kinetic energy,” or a “system” and all energy is always conserved. The other says false because “only perfectly elastic collisions conserve energy. Otherwise energy will be lost to sound or light”

• This is really a question about the psychology of test writers, not physics. I would guess that the test writer thought that the student who said false should get a green check mark and the student who said true should get a red X. Both students' reasons for their answers are correct. – g s Jul 17 at 6:39
• @gs That's a good comment, but I've left an answer with a somewhat different spirit, if only to provide some hopefully helpful broader context. – J.G. Jul 17 at 6:42
• @gs, ambiguous test questions are very easy to write. The posted question is a bit ambiguous, but I have seen (and written) worse. – David White Jul 17 at 15:54
• Probably the "safe" way to answer the question would be to write an explanation about kinetic energy vs other types of energy, perfectly elastic collisions, and so on, to show that you understand both the question and the ambiguity inherent in its wording. Of course that's only possible to do if there is room on the page for the necessary text... :) – Jeremy Friesner Jul 18 at 17:44
• This is funny because it is exactly one of the break-throughs giving birth to modern physics what we are discussing here, a mere 180 years ago: The equivalence of heat and kinetic energy. Exactly that, counter-intuitively, nothing is lost in an inelastic collision. I mean, we named a unit after the guy. We better do him honor and get this right. – Peter - Reinstate Monica Jul 19 at 1:32

The correct answer is that energy is conserved. It is not pedantic, but simply correct, to insist that if the questioner meant kinetic energy, or mechanical energy, which would be conserved only in an elastic collision, then they should have said so. The conservation of energy is such a fundamental property of nature that any wording which risks confusing a student's understanding of it should be strictly avoided.

As you already noted, the pedantic answer is "true", while the likely expected answer is "false". The meaning of the question is key. It's context-dependent, because courses differ in what they ask you to assume "goes without saying". I don't know whether your instructor (or, if they didn't write this question, the syllabus) has done a good enough job of that; if they haven't, the question may be badly worded (or it could be trying to catch people who insert their own assumptions, in which case the pedantic answer is intended).

This kind of thing happens all the time. In biology, "how much energy is produced?" can have a nonzero answer, because the term references phosphorylation rather than conservation violation. In sociology, "gravity" refers to trade volume's dependence on geography. Ultimately, we have to adapt language to what's useful in a given context. If we're talking about collisions for a while, having to say "kinetic" and "for this system" and so on all the time is wasteful.

• This is not a pedantic answer, this is a fundamentally true answer. How much energy is a collision is lost to sound or light? Oh yea, you can calculate it from conservation of energy, so is it conserved or not? I have not yet seen a physics question or course that would that would brush it under "obvious context". Even OPs explanation of "false" answer is wrong, if there is a confusion the answer should spell "The kinetic energy is conserved in perfectly elastic collisions." What you call pedantism here, from my experience in academia, separates a right answer from a wrong answer. – luk32 Jul 19 at 11:40
• @luk32 Maybe calling it pedantry was unhelpful. As you put it, one answer is fundamentally true, while another one is only true with the right assumptions implicitly added. – J.G. Jul 19 at 14:06

If this is a school/test question, the "correct" answer to put down on the test is whatever the teacher said in that particular class. That's what they're going to be expecting, and looking for, as the test is to test you on how well you've done in their course. If they are taking the idea that at this stage, the only forms of energy in play are kinetic and potential energy, then you have to put "no" even if you "know better" already.

However, for the underlying physics, energy is indeed almost(*) always conserved, and in these cases that conservation involves additional forms of energy such thermal and acoustic (sound) energy for which in an introductory mechanics course adequate theoretical machinery has not yet been laid out.

(*) Let's not get into relativistic cosmology.

• +1, I think this is the right answer on both fronts (and I chuckled since I was indeed thinking about cosmology as a counterexample and your footnote made me realize how much unnecessary baggage would be needed to even to explain in what regime that caveat applies) – Andrew Jul 18 at 14:29
• I was not aware that cosmologically energy is not conserved. Is it annihilated or produced? An answer likely doesn't fit in a comment -- I could ask a question about it. – Peter - Reinstate Monica Jul 19 at 1:26
• @Peter-ReinstateMonica When a photon is red-shifted from Hubble expansion, it "loses" energy, but the energy isn't "annihilated". And I put "loses" in quotes because it's a bit of a simplification to say it loses energy. The frame of reference that we're observing it in, and the one we're backwards extrapolating it to have come from are in some sense different frame of references. – Acccumulation Jul 19 at 3:55

In any situation you will encounter, most notably using mere introductory physics, it is "true".
Energy is always conserved, but gets quite handily transmuted between different forms. As a last resort, energy becomes simple thermal heat. But it is still energy, and is conserved.

In the typical teacher's mind, the answer is "false". Because the average teacher will state that kinetic energy is lost in an inelastic collision. It is, but only as kinetic energy. What actually happens is that the energy just puts on a different nametag.

Like all the others, I agree: terrible question. The real answer is to hang the test writer by their toes until they apologize. However, that won't help is going forward. The reality is that English is quite often an ambiguous language. We rely on context, and that is not always written context.

So how can we approach this problem in a way that will help going forward?

The real question is "what energy are they talking about?" Often you will find papers just talk about "energy" in general, and trust that you know enough to provide the context.

If I may put words in the mouths of those who are saying "energy is conserved," this implies that they think "energy" is the total energy of the system. The idea that "total energy is always conserved" is a easy to repeat meme that many people hear. And it's true for isolated systems. But it has its limits. If a system isn't isolated, energy isn't conserved. (And, when you get into university level cosmology, some of these concepts regarding energy conservation start to get murky due to effects like curvature of space.)

The other group saying "energy is not conserved" are focusing on either

• A specific subset of the total energy of the system (i.e. "Kinetic energy")
• The total energy of a non-isolated system. (i.e. "Energy of the two colliding objects")

In the former case, energy is not conserved because we were only looking at one small subclass of energies: kinetic energy. It's ignoring others. In the latter case, energy is not conserved because the system is not isolated -- energy can leave the system in the form of heat and sound.

So who is right? Well, it doesn't matter. Its words. However, we can talk about consistency. What happens when you write the equations for energy before and after? If you write

$$PE_{before} + KE_{before} = PE_{after} + KE_{after} + HeatAndSound$$

then what you have done is consistent with the "total energy" way of thinking. On the other hand, if you write

$$PE_{before} + KE_{before} \ne PE_{after} + KE_{after}$$

then what you have done is consistent with the other ways of thinking.

Now I notice you cleverly don't state which opinion the instructor has and which one you have. That does a good job of blinding our answers (like a real scientist, good job!). As such, I have to suggest two possible reasons for the disagreement, depending on which opinion the instructor is holding.

• The instructor could be a purist who is looking to drill into your head that "energy is always conserved." (The scientist in me is typically in this camp)
• The instructor could be someone who has had too many students write $$PE_{before} + KE_{before} = PE_{after} + KE_{after}$$ on their tests without first checking to see if the collision was elastic or not. If you make this mistake, you get a whole big pile of messy contradictions and wrong answers. They may be trying to focus you towards the particular system which is needed to solve these problems. Remember, their job is to teach a lot of students how to do physics. (The engineer in me is typically in this camp)

Yes it is conserved, and this does not depend on the course level. The tricky part it can still be transferred to parts of the system that are not the colliding objects.

Energy can escape the system of colliding particles via sound or heat, converted to mechanical work resulting in a permanent deformation of the colliding particles, be converted to internal energy if the bodies are not strictly rigid, etc.

Sooooo… it’s a matter of what is included (or allowed) in your definition of energy, and what you are allowed to ignore as forms of energy. Every possible form of it or limited to one or more specific form of energy, like kinetic energy?

The question is worded ambiguously, and any "correct" answer will be determined by psychology not physics - namely what interpretation of the ambiguous question was in the test-setter's mind. There is no way to answer it purely based on coursework or accurate knowledge of the topic, because there will always be that guess element regarding the ambiguity.

This happens disappointingly often in tests, and you kind of have to ride it and accept when it does. I tend to write in margins so its on my answer the basis and critique of the question and answer, so I can show I knew my topic. You don't get scored for it, but you pick up "moral win" points, and maybe a good examiner will reflect and award if you show them afterwards.

From an introductory physics perspective, the answer is True. Energy is energy, whether as heat, sound, kinetic energy, potential energy, mass, et cetera. The only reason that the concept of 'energy' exists is because it is a conserved quantity. If Energy is not conserved then what is meant by "energy"? What quantity does it refer to? This is unclear.

Technically speaking, energy is only conserved on average since quantum transitions happen between states with differing energies. Quantum decoherence of energy eigenstates results in a probabilistic choice of energy outcomes. Those outcomes conserve energy on average, but not individually.

Then there is the matter of curved space-time, in which even classically (not quantum) energy is not conserved. So if you're talking about the collision of massive celestial bodies, I imagine (not 100% sure) that there is no "energy" quantity which is conserved. (Recall: energy only has meaning as this special quantity which is conserved through time! It also has other properties)

The point is whether or not the student understands the problem in context. Neither the teacher nor student should get embroiled in technicalities if it is clear that the student does/does not understand the answer to the question. The teacher should not withold marks if it is clear the student understood, and neither should they award them if it is clear the student is winning on a technicality that they don't even understand. (As above, you can massage the answer to "true" or "false" depending on context).

However there are also issues of equity. Suppose the teacher marked the student as wrong, but the student did in fact understand the true answer. The teacher cannot determine for certain whether this student is genuine about their understanding. If they award them marks, maybe other students who are less honest will attempt the same. Furthermore, what about the test records showing that one student received marks for a given answer while another did not?

The solution to all of this is either to abandon standardised testing (fat chance) or for the teacher to be clear and explicit about the context of problems, and any assumptions made. The teacher should have made a disclaimer at the start of the test:, i.e. "All questions are asked in the context of classical Newtonian mechanics.". However, in the absence of such a disclaimer, I think it's fair for them to expect students to answer based on the level of physics taught in their course. I assume you are not being taught quantum physics or general relativity, in which case the reasonable answer to the question is True, energy is conserved in a Newtonian collision between bodies.

Note how I was clear about my answer being contingent upon Newtonian physics? I used to make such clarifications in my schooling because I frequently encountered the situation you've described here. I understood the answer but did not understand the question. I have concluded that such a situation is invariably the teacher's responsibility. They should award marks if you understood but the question was poorly phrased, despite the equity issues above. It is worse to rob a student of marks than to award extraneous ones. Robbing marks affects your grades and future prospects in a very real sense, if you have ambitions of higher education.

In my experience, teachers and professors were understanding of these issues and usually did award marks when I pursued the matter. However sometimes the teacher (and on rare occasions the professor) actually does not understand the answer themselves, in which case it's up to you whether you feel it's worthwhile to pursue a formal appeal process.

Saying "energy is conserved" in an inelastic collision is a bit like saying "a painting is conserved" when running it through a shredder because the results have the same weight as before and consist of the same material. The total level of energy remains the same, but it stops being a tangible entity.

The question is just what meaning to attribute to such a statement and what kind of insight one hopes to reflect. Tests are not usually trying to reward smartassery. Unless they are. They need to be scored, and so it is sort of of an additional chore for those who "know to much" to judge which kind of answer expresses an insight appropriate for the course level and the expectations of the teacher covering the class material, and which kind of answer could be considered "formally right" but not in a manner the teacher/grader would be interested to hear.

Physics class isn't law school, and even in law, judges interpret the laws according to their intent rather than to the letter when push comes to shove.

I will presume the test question was precisely True or False: energy is conserved in all collisions.

In my opinion,

The comment "Using introductory physics" is not relevant. It does not add context to the how the question was asked, and presents as a control to direct the responses you may receive.

The arguments about Kinetic Energy, System, and Elastic Collisions are equally not relevant. If they were not included in the question or in a specific directive on how to answer the test, we should not assume any of them were implied. Whether the Collision causes the energy to transform into light, sound, or a different state of Kinetic energy, or (ad nauseum) the energy still has not been lost, though it may need to be measured in a different way.

The answer to the question as posted, True or False: energy is conserved in all collisions, is True.

Though some answers here suggest you should yield to an instructor that seems to be teaching something that appears different from what is generally accepted, I submit that as an opportunity to appeal the response and present valid arguments as to why it is incorrect.

Suppose no energy is lost to heat and sound. The perspective of the writer is to focus on elastic versus plastic impacts. If the impact is elastic, then the total mechanical energy is conserved. If the impact has some plasticity, then mechanical energy is not conserved. Some of it is lost to damage energy, the energy needed to plastically deform the bodies.

This is reflected through the coefficient of restitution.

Key point is "Using introductory physics".

Using High school Physics, energy is not always conserved. It needs the elastic collision. Using University level, it is always conserved (except dark energy).

Just listen to your teacher. "Only in the elastic collisions" is right if you are in high school.

• I think even in high school it is possible to understand that total energy in all forms is always conserved, but kinetic energy is not. Listening to your teacher is good, but developing a habit of independent thought is even better. – gandalf61 Jul 17 at 8:23