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Yes, this question has been asked a few times, and will be downvoted to hell, but I still haven't seen a good answer.

Qmechanic
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Matt
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  • The derivation here is not enough? What principle bothers you? https://en.wikipedia.org/wiki/Kinetic_energy – Augusto Matteini Aug 10 '21 at 21:46
  • I don't think so, no! I think this comes down to what David Deutsch considers a 'good explanation'. There is a reason that very few people find that explanation satisfying. – Matt Aug 10 '21 at 21:48
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    What is a good answer? What are you after? Have you interpreted the vector of force times time? – Cosmas Zachos Aug 10 '21 at 21:50
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    I don't think that there can be a better one than the wiki one. What is wrong with it? – mike stone Aug 10 '21 at 21:50
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    Kinetic energy is not $F \times d$. That's work. Remember that in the absence of any force, things in motion stay in motion and do not lose any kinetic energy no matter the distance they move. – DKNguyen Aug 10 '21 at 21:55
  • oh yes, I know that part, my question was just poorly worded, I have edited it – Matt Aug 10 '21 at 21:59
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    Because your suggestion is the change in momentum. – J.G. Aug 10 '21 at 22:04
  • I think people ask this question because they don't have a clear idea of what KE actually is, I think very few people actually do, you can throw logically consistent math at people all day but if they don't feel the truth of it they are going to keep asking the question. I'm just trying to figure out what answer qualifies as 'truth' for me. I guess this is a bit of a meta-question. I think there may be a good answer though. – Matt Aug 10 '21 at 22:05
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    It is unclear what you expect as an answer to this question, given that force times time doesn't even have units of energy and so can't be equal to any energy, kinetic or otherwise. – ACuriousMind Aug 10 '21 at 22:08
  • @ACuriousMind Stop closing these questions too early. Most interesting questions look foolish to start off. It's overmoderation – Matt Aug 10 '21 at 22:17
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    @Matt This post might be helpful to you: https://physics.stackexchange.com/a/14752/174766 – Vincent Thacker Aug 11 '21 at 01:53
  • @VincentThacker thank you, this is much closer to the kind of think I'm thinking of. – Matt Aug 11 '21 at 03:24

1 Answers1

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We define concepts which are useful.

If you take force times time, you get the concept of momentum, which is conserved, and useful, as made evident by all the physics problems you can solve by considering conservation of momentum.

Imagine no one forced you to define kinetic energy as force times distance.

But you notice that many of the forces in nature depend on distance. Gravity, electric fields, springs. You notice that many forces are conservative. Moreover, you find that you have the option of doing path integrals of the form $F \cdot dr$, and these path integrals end up not depending on the path, but only on the endpoints. This (I hope) is starting to seem very useful to you (both in this reality, and in the imagined reality wherein we do not yet have such a thing as energy), as it gives you knowledge about a situation which only depends on the start and endpoints, and not on what's happened in between.

One day, sitting in a bath, eureka. What does $F \cdot dr$ make you think of? Let's consider time, now. $dr = v dt$. $F = \frac{dp}{dt} = m\frac{dv}{dt}$. These integrals we were playing with, the ones that seemed to have so much potential to be useful, can be written in another form. $\int F \cdot dr = \int m\frac{dv}{dt}vdt = \int \frac{1}{2}m\frac{d}{dt}v^{2}dt = \frac{1}{2}mv^{2} |_{start}^{end}$. This is essentially the derivation here.

After noticing how useful a construct like this might be, you start applying some names to them, since $F \cdot dr$ and $\frac{1}{2}mv^{2}$ is a mouthful. So you call one the potential energy, the other the kinetic energy, and you notice that the two combined are conserved, which has proven to be a very useful definition.

Alwin
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  • Thank you. Yeah, this feels like the reason most people use KE. It just seems to introduce so many problems when you try to link it back to your intuitive mental physics simulator though. Thank you for the answer. – Matt Aug 10 '21 at 22:08
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    When you find it more useful to think of momentum, use momentum :) when you find situations where energy might be useful, then you'll use it instead. As an example, to calculate the speed of an object tied to a spring at position x, you would have to figure out how much time it took to reach position x in order to use momentum. Or, you could just use the difference in position, and use energy instead. With practice, your intuitive mental physics simulator will learn to use the new tool. – Alwin Aug 10 '21 at 22:10
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    This is just a guess, but perhaps you are noticing how the tools don't necessarily have to be reality. We define the tools (all math is definitions and their logical outcomes) to make predictions for reality, and you do not have to choose to believe that this is how reality truly works underneath. Energy is no different from defining imaginary numbers, quantum wavefunctions, even momentum, gravity, or anything else you find intuitive. Our biology makes some things seem intuitive too, but that's just math hardwired into our neurons. It's okay if everything is an illusion. – Alwin Aug 10 '21 at 22:18
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    I look forward to when you are able to articulate what that is :) – Alwin Aug 10 '21 at 22:23
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    I don't mean to be stupid or disagreeable here -- thank you for taking this seriously! – Matt Aug 10 '21 at 22:24
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    @Matt, I taught high school physics for 13 years and I noticed a pattern. Most students had incorrect intuitive preconceptions of how the world worked. Those incorrect concepts were VERY difficult for students to unlearn and it led to errors on tests. You would be well advised to diligently work on discarding such misconceptions when they are shown to you, and it would be wise to learn the correct concepts even though they don't make "common sense". In other words, don't try to "link back to your intuitive mental physics simulator", as this is a dead end. – David White Aug 11 '21 at 00:31
  • Removed unkind exchange of pleasantries. Everyone is entitled to their opinions and can choose their way of thinking and learning however they like, especially on the internet. Downvoting and commenting are a way to express one's dissent. Please keep this in mind and keep the conversation respectful and civilised. – SuperCiocia Aug 11 '21 at 02:55
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    A number of further comments removed. If you are considering leaving a "zinger" of a comment to have the last word in the discussion that went off the rails, please instead look at a different website for a while. Be kind, folks. – rob Aug 11 '21 at 04:09
  • I'm glad you found an example that made sense. Next time people ask you "what a good answer for you" would be, you can tell them you are looking for illustrative examples, toy models, concrete examples, or compelling examples. Just some sample key words I think might be useful in finding the answers you are looking for. – Alwin Aug 11 '21 at 05:39
  • Everyone has a unique brain and so some models are more compatible with a person than others. So asking for many diverse examples of models is a great way to find the one that clicks with you :) – Alwin Aug 11 '21 at 06:04