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Why does kinetic energy increase quadratically, not linearly, with speed? (2011)

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Re: Why does kinetic energy increase quadratically, not linearly, with speed? (2011)

#21

Post by casey2 »

Agingcoder wrote: post #4

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…

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.

Re: Why does kinetic energy increase quadratically, not linearly, with speed? (2011)

#23

Post by [deleted] »

davidivadavid wrote: post #14
digdugdirk wrote: post #9

Earlier quoted context omitted.

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

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…

[deleted]

Re: Why does kinetic energy increase quadratically, not linearly, with speed? (2011)

#24

Post by cucumber3732842 »

throw0101a wrote: post #2

Fun little anecdote: A blue care is travelling along at 70 units, and a red car (exact same make and model) is catching up to it going 100. When they're both right beside each other a bend in the road reveals an obstacle blocking both lanes, so both cars brake at the same intensity and deceleration. The blue care stops right before the obstacle. Since the red car was going at a faster speed, and braked at the same ra…

>same intensity and deceleration.

It cannot be both. It mathematically cannot be both. They can brake at the same rate (acceleration) or intensity (conversion of kinetic energy into heat) but because they are traveling different speeds those two values cannot be the same for both cars.

The math you did was for intensity, not force/acceleration, which because of the ^2 in the KE equation exaggerates the difference. Whereas if you did the math based on force you'd get a mild, linear, difference.

> and braked at the same rate,

You're being a bit sly with word choice here. You're doing the math for conversion of KE into heat whereas in common parlance "rate" means force/acceleration.

Braking "at the same rate" [of energy conversion] is way less actual braking force for the faster car.

This is basically the same kinetic energy into heat math wherein you can descend a grade at a low speed, apply a force and be fine and descend the same grade at a higher speed and apply the same force and cook the brakes. Or you can apply less force, and get the same amount of energy conversion into heat (i.e. your wording trick in the proposed scenario)

You've taken what's basically the math behind trucks descending a grade (rate of energy conversion is actually limited by ability of brakes to shed heat, not friction) and re-framed it as cars stopping to create a trick question.

Re: Why does kinetic energy increase quadratically, not linearly, with speed? (2011)

#25

Post by [deleted] »

slicktux wrote: post #5
throw0101a wrote: post #2

Fun little anecdote: A blue care is travelling along at 70 units, and a red car (exact same make and model) is catching up to it going 100. When they're both right beside each other a bend in the road reveals an obstacle blocking both lanes, so both cars brake at the same intensity and deceleration. The blue care stops right before the obstacle. Since the red car was going at a faster speed, and braked at the same ra…

Cool anecdote! Couldn’t help but notice you misspelled car twice but only when talking about the blue car..

[deleted]

Re: Why does kinetic energy increase quadratically, not linearly, with speed? (2011)

#26

Post by JoshMandel »

Agingcoder wrote: post #4

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…

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.)

Re: Why does kinetic energy increase quadratically, not linearly, with speed? (2011)

#27

Post by joshAg »

davidivadavid wrote: post #7
Agingcoder wrote: post #4

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…

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…

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.

Re: Why does kinetic energy increase quadratically, not linearly, with speed? (2011)

#28

Post by AngryData »

This is also why splitting wood with a maul is way more work than using an axe. You can swing an axe at incredibly speeds which gives incredibly transfers of energy, but a maul is going to always have "meh" levels of speed because it is too much mass to accelerate over such a short distance as a swing. Also why you don't see framers using 3 lb hammers. You can put in more effort and get your lighter hammer swing to twice the normal speed, no way in hell you are doubling the speed of a 3 lb hammer though.

Re: Why does kinetic energy increase quadratically, not linearly, with speed? (2011)

#29

Post by esikich »

Agingcoder wrote: post #4

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…

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.
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