I didn’t think this was that weird. When you double your speed you are also going to be going twice as far in the same time, not just twice as fast, and they both have the effect of work.
That made it trigger for me intuitively. Thanks
Why does kinetic energy increase quadratically, not linearly, with speed? (2011)
101–110 of 231 posts
Re: Why does kinetic energy increase quadratically, not linearly, with speed? (2011)
#102Earlier quoted context omitted.
Because if the one falling 20ft lands on a seesaw, the other side of it will toss two balls each of the same mass 10ft up.
Then 20ft should not be used in the explanation. They should just have one ball going at 2x speed hit the seesaw and have 4 of those balls go up at 1x speed.
That ends up begging the question, because the next step is "how high do you have to drop it from so that it's travelling twice as fast?" and you're immediately going round in circles.
Re: Why does kinetic energy increase quadratically, not linearly, with speed? (2011)
#103It's easiest to visualize in terms of conversion from potential energy. We know intuitively that a ball atop a 20ft ladder has twice the potential energy of a ball atop a 10ft ladder. And we also know when they fall, by the time they reach the ground and all the potential energy has been converted to kinetic energy, the previously higher ball will have twice the kinetic energy too. But a twice higher ball won't have…
> We know intuitively that a ball atop a 20ft ladder has twice the potential energy of a ball atop a 10ft ladder. What makes this intuitive? The foundation of the asker’s question is that it seems intuitive that kinetic energy would increase linearly with speed, but that turns out to be wrong.
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Re: Why does kinetic energy increase quadratically, not linearly, with speed? (2011)
#104Ron Maimon uses an argument that relies purely on symmetry, which circumvents the standard explanations, including many in this thread. In some sense, this is the simplified version of Noether's theorem (as far as I understand it). As an aside, I believe Ron Maimon's account was suspended after he challenged the character of someone who was soliciting votes for a moderator position. Ron Maimon's stance was that if so…
It wasn’t “prescient”, StackExchange sites have always been among the most hostile communities on the Internet.
Today they are additionally weighed down by increasingly erratic management decisions desperately trying to extract as much monetary value as possible before AI completely obsoletes SE, but the amount of aggression and hostility on the network was unbearable from the start.
I remember dozens of occasions where I looked up something on StackOverflow, intending to be in and out in 10 seconds, and ending up spending several minutes just staring in disbelief at the comments showing how people treat each other on that site.
Re: Why does kinetic energy increase quadratically, not linearly, with speed? (2011)
#105Earlier quoted context omitted.
That's a good question, and I suppose the mgh formula isn't a suitable answer, so my answer would be something like: if you lift an object to some height, and then you repeat that action (lifting it from there to twice the height), you've done twice the work, and doing twice the work requires twice the caloric intake.
Okay but that depends on the intuitions the question is trying to justify, which makes it circular. We also know, for example, that the body uses more than twice as much energy to do twice as much work (because of fatigue on the muscles or whatever the right term is here). In fact it takes positive energy just told a weight at a fixed height, doing zero mechanical work! So you’re actually appealing to even weaker int…
At some point you just have to shut up and calculate.
Re: Why does kinetic energy increase quadratically, not linearly, with speed? (2011)
#106Fun 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…
> The blue car, using ½mv², shed (~70²=) 4900 units of energy (we'll hand wave away the constants). So the red car, which had (100²=) 10000 units of kinetic energy to start, also shed 4900 units, which means it had 5100 units of energy when it collided, and so was going (√5100~) 71 But if the cars produce downforce this is no longer true because you brake harder (more friction available) at higher speeds! This is how…
While it is true that some cars can brake harder due to downforce etc, the point from GP was that both cars brake/ decelerate at the same rate. Regardless of how exactly that deceleration is achieved.
Re: Why does kinetic energy increase quadratically, not linearly, with speed? (2011)
#107Ron Maimon uses an argument that relies purely on symmetry, which circumvents the standard explanations, including many in this thread. In some sense, this is the simplified version of Noether's theorem (as far as I understand it). As an aside, I believe Ron Maimon's account was suspended after he challenged the character of someone who was soliciting votes for a moderator position. Ron Maimon's stance was that if so…
It wasn’t “prescient”, StackExchange sites have always been among the most hostile communities on the Internet. Today they are additionally weighed down by increasingly erratic management decisions desperately trying to extract as much monetary value as possible before AI completely obsoletes SE, but the amount of aggression and hostility on the network was unbearable from the start. I remember dozens of occasions wh…
Really? Most hostile? I’ve only ever contributed to the comp sci topics on stackoverflow and visited the ones for math/physics and sysadmins. Were some replies a bit pedantic, yes. But I’ve also seen a lot of very extensive answers and helping out people. Maybe I’ve been lucky to use it in the golden age.
Re: Why does kinetic energy increase quadratically, not linearly, with speed? (2011)
#108It's easiest to visualize in terms of conversion from potential energy. We know intuitively that a ball atop a 20ft ladder has twice the potential energy of a ball atop a 10ft ladder. And we also know when they fall, by the time they reach the ground and all the potential energy has been converted to kinetic energy, the previously higher ball will have twice the kinetic energy too. But a twice higher ball won't have…
I agree that this feels intuitive, that potential energy should increase linearly with height.
But in the end, it's all up to the units/quantities we choose to measure, no? If we, say, decided to measure "Squenergy" in Sqoules, with 1Sq² = 1J, then suddenly, squenergy does increase linearly with speed! The formula for kinetic Squenergy becomes sqrt(m/2)v.
Of course this complicates other stuff, like potential Squenergy becoming sqrt(MgH), it not being additive, etc.
Re: Why does kinetic energy increase quadratically, not linearly, with speed? (2011)
#109Physics 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 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.
Re: Why does kinetic energy increase quadratically, not linearly, with speed? (2011)
#110Earlier quoted context omitted.
Then 20ft should not be used in the explanation. They should just have one ball going at 2x speed hit the seesaw and have 4 of those balls go up at 1x speed.
That ends up begging the question, because the next step is "how high do you have to drop it from so that it's travelling twice as fast?" and you're immediately going round in circles.
Nothing of the sort. The seesaw can be in space far from gravitational influences. Potential energy is extraneous in this explanation.