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Posted by ProxyTracer 22 hours ago

Why does kinetic energy increase quadratically, not linearly, with speed? (2011)(physics.stackexchange.com)
330 points | 174 commentspage 4
charlie90 14 hours ago|
If you are in a space ship that is accelerating, your available fuel energy also goes up (since it increases its own kinetic energy).
Agingcoder 20 hours ago||
Physics is an endless source of frustration to me. It feels like a mix of random tricks, most of which I don’t understand.

I find math and compsci reasonably understandable, can read research papers in both fields ( and have published papers) etc. There’s something specific about physics I don’t get but I’ve never been able to figure out what. The main symptom is that most cause -> consequence in such demonstrations , which are seemingly obvious to everyone, make no sense to me.

Am I the only one ? Are there good resources to learn it?

esikich 19 hours ago||
Weird, I always loved physics because I felt like I didn't have to straight up memorize everything. In a pinch (years ago) I felt like I was able to pretty much derive everything I needed if I couldn't remember the exact formulas. It's all just forces and vectors.
davidivadavid 20 hours ago|||
More than twenty years ago, I quit a program that taught math/cs/physics (the notorious French "classes préparatoires") ~almost precisely over this: I felt like I was being taught physics like it was an axiomatic system where the tricks should not be questioned, they just work so "shut up and calculate" (and you don't even need to be doing quantum mechanics for that).

I just felt like we never got to the heart of the matter of why the models work and how to approach developing them, it was all about learning a bag of tricks.

Meanwhile, math and CS being a lot more axiomatic by nature, they also made a lot more sense to me.

That being said, that specificity of physics, the unbridgeable gap between reality and the models we build to describe it, in retrospect, is what makes it more interesting to me today (it's not just a "closed" system in the sense that math is — of course the relationship between math and physics is itself fascinating but that's yet another topic), but I still feel like I haven't found the right pedagogical approach to make it fit my mindset.

joshAg 20 hours ago|||
Your issue with physics but not with math reminds me a little of Hume's law. The difference that has always made that difference "make sense" to me is that math rules, even the axiom we use, are entirely chosen by the people using them, but the rules of physics are only useful if they match/predict what happens in the real world. For math we get to pick the ones that happen to be useful at a given time for a given problem (my go-to example of "it's all made up and the points don't matter" is why 1 isn't considered prime). For physics we're constrained to pick what best describes the real world. It probably helped that nearly all the physics course I had in high school/university had lab components focused on experimentally validating those rules/using those rules to predict results.
davidivadavid 19 hours ago||
I think what it boils down to is that in my experience physics education lacks a clear historical component about how the current state of the art is a gradual process of proposing new models and rejecting old ones and figuring out the gaps between reality and the model. Instead, it feels like a God-given set of equations (that lots of people consider "the truth" for some reason), that you apply to cookie-cutter problems you must learn by rote. Though I understand the practical concerns (but then let's call it "physics for engineering"), as far as I'm concerned, you couldn't treat physics in a worse way.
joshAg 19 hours ago||
that (edit: the way you were taught) sounds like an altogether awful way to learn any hard science
lazide 20 hours ago|||
The world just is, regardless of what we think about it. Physics is our best attempt so far to understand and predict it at a low level, but it will always be incomplete.

Maths (and especially compsci!) are constructions by and for humans.

Is it any wonder it is as you describe? It would be odd if it was any other way.

davidivadavid 20 hours ago|||
My point is precisely that I was often taught physics as if it was mathematics, where there is in fact a profound ontological difference between the two.
davidivadavid 20 hours ago|||
Also, physics (the discipline) is also a construction by and for humans.
lazide 16 hours ago||
To find tools applicable to reality. Not to construct reality.
gucci-on-fleek 13 hours ago|||
> I find math and compsci reasonably understandable, can read research papers in both fields ( and have published papers) etc. There’s something specific about physics I don’t get but I’ve never been able to figure out what. The main symptom is that most cause -> consequence in such demonstrations , which are seemingly obvious to everyone, make no sense to me.

Math and CS are mostly human-made, so most of the theorems/proofs/axioms are either straightforward or elegant—there are infinitely many possible axioms with no objective way to choose between them, so people generally choose to work with the ones that are the easiest for humans to reason about. You certainly could define a complicated set of axioms with dozens of special exceptions, but unless there are some external reasons why these axioms are important, nobody will want to work with them.

Conversely, physics exists to model the real world, so unlike math and CS, physics doesn't have the privilege of being able to choose the most convenient/elegant/simplest axioms to work with. Given the constraints of the real-world data, physicists will still choose the most elegant possible model, but sometimes a wacky model is the only way to accurately model the universe.

Nobody is really happy about this though, so physics textbook authors love to make their equations/derivations look simple/obvious/elegant, but this is often completely misleading, since often the rules of the universe are so weird that nobody would ever guess them without having ran the experiments first. But textbooks tend to downplay actual experiments in favour of post-hoc explanations, which tend to make the readers think that they're missing something.

> Physics is an endless source of frustration to me. It feels like a mix of random tricks, most of which I don’t understand.

Your feelings are correct, since physics really is mostly a set of random rules that nobody truly understands. But the important thing is that these random rules correctly model nearly everything in the universe to within a few hundredths of a percent, so they're not completely arbitrary.

> Are there good resources to learn it?

The annoying/inconvenient answer is to do lots of lab work. This is actually fairly accessible though, since a measuring tape, a scale, and a slow motion camera (present on any modern phone) is all that you need for most kinematics/mechanics experiments, and a multimeter, a 9V battery, some resistors, and some magnets are enough for most electromagnetics experiments.

digdugdirk 20 hours ago|||
It seems that we're exact opposites! But if mathematics is your thing, it might be interesting for you to explore trying to learn things from a lagrangian perspective first?

Not sure if it'll help you with gaining an intuitive understanding, but at least it'll be interesting!

https://en.wikipedia.org/wiki/Lagrangian_mechanics

davidivadavid 20 hours ago||
Lagrangian / Hamiltonian mechanics, the principle of least action, always seemed neat, in L&L and other places I encountered it, until I tried doing exactly what you're saying: gaining an intuitive understanding. At that point it just never made sense to me and seemed like a gratuitous deus ex machina that happens to work beautifully but for no apparent reason. You won't be surprised to learn I dropped out of my STEM program shortly after, though I keep a keen interest in the topic.
symian 19 hours ago|||
Same for me. I wanted to major in physics and I quickly realized that I have no intuition for physics. Math made sense to me and I went to graduate school in math and still don’t understand anything in physics. Differential geometry, no problem. Electromagnetism makes no sense to me.
JoshMandel 20 hours ago|||
I identify with this perfectly. (I mean, was able to get by in physics but it never crystallized into intuition for me the way math and CS do.)
casey2 20 hours ago|||
Physics? Yes. Feynman Lectures On Physics and Computation. Landau & Lifshitz. If you like SICP you might like SICM. Nielsen & Chuang's Quantum Computation and Quantum Information then Faulkner's Modern Quantum Mechanics and Quantum Information

General advice take a look at the references in works you've recently read and look for lower level topics that interest you, after repeating a few times you'll find your way to physics or chemistry and you can use the above as reference works. The best resource is the one you actually use. If https://www.youtube.com/learning works better for you then use it.

rustyhancock 20 hours ago||
What's the problem exactly? Could you not follow the example in the text?

The standard text to build understanding in physics is University Physics by Sears & Zemansky.

It's worth remembering you're quite far from the ground in physics, and it's mostly taught with "neat" cases that give insight into physics. I.e. the thought experiment to show why kinetic energy must scale quadratically with velocity is carefully designed to show that conclusion. You shouldn't expect to have come up with it off the cuff.

drivebyhooting 19 hours ago||
I don’t find the answer convincing. It assumes one can measure heat at a distance and it is a conserved quantity between reference frames.

Energy is actually not a conserved quantity in Galilean relativity.

c1ccccc1 18 hours ago|
Energy is conserved in Galilean relativity. The thing you're trying to say is that it's not invariant across reference frames.

The answer linked above actually takes advantage of the fact that energy is not the same in different reference frames in order to make the argument work.

I think you are overthinking the heat thing. If you have a train car full of hot water and you slow the train down (extracting kinetic energy from it) until it stops, the water in the train car does not change temperature at all, other than a bit of sloshing around and loss of heat to the surroundings.

drivebyhooting 15 hours ago|||
Yes that is what I meant. It’s not the same across reference frames.

I don’t find the OP a convincing argument. What is temperature, why can you assume it didn’t change and the measurement also didn’t change commensurately? Why should kinetic energy be convertible with thermal energy? Chemical energy?

It’s very hand wavy and introduces many assumptions.

Kinetic energy is a book keeping trick. The real mystery is explaining how it relates to other forms of energy and how to tie it together.

itemize123 16 hours ago|||
thinking aloud here - so it seems like 2 things are taken as intuitive here:

a) energy is conserved in any frame of reference. b) energy can vary in 2 frame of references.

but then what it feels like is that when you reference the energy as mE(v), the v is actually not the only variable, and it will be more like mE(v, v_moving_reference)?

so we also must take intuitive that c) E(v, v_moving_reference) == E(v - v_moving_reference)

laszlojamf 12 hours ago||
walking into a wall slowly doesn't hurt much, but you really don't have to speed up a lot for it to a hurt a whole lot more.
microgpt 7 hours ago||
RIP Stack Exchange
netbioserror 5 hours ago||
I recently learned, through visual intuition, how the relative perception of time between two subjects changes as relative speed between them changes. It's because they are observing each other from an "angle" in the time dimension. And in that time dimension, angles do not trace circles, they trace paraboloids.

If I'm remembering correctly, this is also why the energy required to "reach" the speed of light for subjects with mass parabolically goes to infinity. I'm also guessing it can directly trace a proof down to why kinetic energy increases quadratically.

teaearlgraycold 11 hours ago||
Here’s my attempt:

Assume you have a fan sitting still. You smack it and it’s now rotating with 1m/s angular velocity. If you want it to go faster you can’t smack it at the same speed. You have to hit it faster else you’re just tickling it and it stays the same speed. So you smack your hand twice as hard and now it’s going even faster. Then three times as hard, four times, etc.

If you sum the smack energy it will be 1+2+3+4, which starts to build out a right isosceles triangle if you graph it. Such a triangle is half of a square, ie: 1/2*v^2.

11101010010001 20 hours ago||
read Ron Maimon.
symian 19 hours ago||
He has interesting perspectives in math which is an area I know about. I assume the same for physics. People should read his answers.
dguest 15 hours ago||
Also his profile on Stack Exchange [1]

    This account is temporarily suspended network-wide. The suspension period ends on Mar 18, 2292 at 16:28. 
Note the "temporary" suspension end date, 250 years in the future.

[1]: https://physics.stackexchange.com/users/4864/ron-maimon

koolala 15 hours ago||
It doesn't make sense to me. Why split it into heat and motion and combine them to make 2 + 2 = 4 as if that solves the question? They are not the same units of energy.
jacknews 17 hours ago||
The first example only tells me that the energy is dependent on your frame of reference, since the collision seen from the train appears to have more energy than the head-on collision, simply due to the moving viewpoint, whereas they must be the same.
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