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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)

#91

Post by hibernator149 »

SilasX wrote: post #89
hunter2_ wrote: post #63

Earlier 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…

All intuitions are wrong, but some are usefull. You have to do the experiment, discover the formula, and then adapt your intuitions accordingly.

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

#92

Post by drivebyhooting »

c1ccccc1 wrote: post #53
drivebyhooting wrote: post #44

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.

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 ene…

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.

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

#93

Post by G_o_D »

Don't think about numbers double quadraple etc.

Think of simple notion. Why more energy is needed to accelerate moving object compared to still?

Kinetic energy possesed by any object is equal to work/effort needed to be made by an external force to accelerate it from present state to stated velocity.

If object is already moving, and i am that external force, first i had to catch up with that object, for that i had to do work make effort until i am moving at same speed as object, even after catching up, at the momennt if i try to push object, i am distracting myself engaging into 2 activity maintaining my speed same as object and trying to push so that will definetely reduce my speed, so i first had to gain slighly more speed than object before i give it a push and transfer all my momentum to object so it accelerates.

Thus i needed more effort or work to do, to accelerate moving object compared to stationary one.

That work done is kinetic energy object posses when it was accelerated from 1 to 2 and its more than when moving object from 0 to 1.

That simply explains the fact. Now how much more energy triple or quadraple that comes down to practical established formulas.

In my understanding OP was confused as when talking about,op was simply thinking if object is already moving it would take less force to move it as it already has gain momentum against all odd of nature and resistive forces, so now only work needed is to accelerate it and it doesn't include loss against resistive forces.

But to accelerate moving object the applier of force whether human or another object also needs to catch up

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

#95

Post by koolala »

esalman wrote: post #58
ajross wrote: post #16

Earlier quoted context omitted.

Actually, it is momentum, sorta. Galilean 3D momentum isn't conserved under special relativity. The energy-momentum four-vector, however, is, under all lorentz-transformed frames. So in some sense energy is momentum in the time direction (though it's not a Euclidean 4D space, so beware of assumptions). For an object at rest, this becomes its E=mc² equivalence. Kinetic energy is just a straightforward "rotation" of th…

Original comment is correct, it's not momentum. Work (hence, energy) is integral of force over distance, momentum is integral over time. There's not "sorta" about high school physics.

You can't cover distance without time.

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

#96

Post by dguest »

symian wrote: post #34
11101010010001 wrote: post #22

read Ron Maimon.

He has interesting perspectives in math which is an area I know about. I assume the same for physics. People should read his answers.

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

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

#97

Post by sumolessons »

Assuming the Newtonian framework F=dp/dt, p=mv, dW=Fdx, as well as constant mass, then Fdx=dpdx/dt=mvdv and integrating both sides gives deltaW=1/2mvf^2-1/2mvi^2+constant. So the amount of work to move the object from x1 to x2 is proportional to the difference of the square of the initial to final velocity squared up to a constant. This we define to be the change in kinetic energy.

But as others have mentioned this is only as intuitive as F=ma, or p=mv.

In my view, at least classically it's just a matter of definitions then. If our definitions of energy differ, the only thing we will experimentally agree on is the equation of motion, and even then up to a frame transformation.

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

#98

Post by abetusk »

Ron 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 someone was running for an elected position, discussing their character was valid. The SO site had/has a strict challenge-the-question-not-the-person policy, which the moderators used to ban him permanently.

At the time, I remember seeing some posts by Ron talking about how the SO sites were corrupted by their policies and that it was a matter of time before they ceased to provide value. I think this was late 2000s or early 2010s. Looking back it's hard not to feel like his stance was prescient.

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

#99

Post by imtringued »

casey2 wrote: post #6

Mikes' answer is the most intuitive, but he rephrases the question in a possibly non intuitive way. Odd that nobody mentioned power, which scales linearly with speed. Of course if you add linear increasing amounts of power to the system the energy will increase quadratically. Power scaling linearly is more intuitive because doubling your speed requires twice the power to maintain the same force, why does it require t…

This is basically it. If power is linear with respect to velocity, then it becomes illogical for kinetic energy to be linear with respect to velocity.

The energy of the object is simply the integral of power over time and that happens to be a quadratic function.

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