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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)

#181

Post by AngryData »

gorfian_robot wrote: post #88
AngryData wrote: post #28

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 t…

have you ever had to split wood?

Ive split wood by hand my entire life to use for heat. Have you?

A practiced arm with an axe beats a maul any day of the week. That's why splitting mauls are a modern device and splitting axes have existed since forever. Plenty of information on it online and on youtube, and why there are dozens of expensive specialty handmade splitting axes to buy and just cheap mauls for the rest.

Also this post is the physics behind it. Kinetic energy scales faster with speed than mass.

Splitting mauls are for people who either lack any experience or physically can't swing an axe that well. An axe is for people who got shit to do and don't have time to waste.

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

#182

Post by mistercow »

ThoAppelsin wrote: post #174
freehorse wrote: post #117

Earlier quoted context omitted.

The effort to move a piece of furniture from 1st to 2nd floor is the same as the effort to move it from the 2nd to the 3rd. We have good intuition for this by our experience, which derives a linear relationship. The effort to move a piece of furniture up two floors is double the effort of moving it up one floor (ie you have to put the same effort twice, assuming enough rest). I would not say we have the same intuitio…

Scale up the numbers in you example: The effort to move a piece of furniture from 10,000th to 20,000th floor is NOT the same as the effort to move it from the 20,000th to the 3rd. The reduced gravity will help you.

If you're talking about intuitions, you have no firsthand intuitions about lifting effort decreasing with distance to the Earth. We can intuit about constant gravity, and the math of constant gravity works fine for this description.

And while the real situation at scale is more complicated, the math is going to come out to the same answer, albeit with extra terms muddying everything up.

If someone says that something true can be illustrated intuitively with a thought experiment, "sure, but what if we take that to a scale where our intuitions fail" is a sort of odd place to take the discussion unless you're genuinely curious how the math is going to shake out.

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

#183

Post by nkrisc »

ThoAppelsin wrote: post #174
freehorse wrote: post #117

Earlier quoted context omitted.

The effort to move a piece of furniture from 1st to 2nd floor is the same as the effort to move it from the 2nd to the 3rd. We have good intuition for this by our experience, which derives a linear relationship. The effort to move a piece of furniture up two floors is double the effort of moving it up one floor (ie you have to put the same effort twice, assuming enough rest). I would not say we have the same intuitio…

Scale up the numbers in you example: The effort to move a piece of furniture from 10,000th to 20,000th floor is NOT the same as the effort to move it from the 20,000th to the 3rd. The reduced gravity will help you.

What intuitive understanding do you have of moving furniture up 10,000 floors? None.

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

#184

Post by johanyc »

SyzygyRhythm wrote: post #36

Cheat answer: velocity is a vector, and can be negative, while KE is a scalar and has to be positive. Therefore you have to square v to get rid of the minus sign. Why not take the absolute value? Nature hates those, probably because the derivative is undefined at 0. So squaring it is.

That's mnemonic not intuition.

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

#185

Post by xlayn »

because we need quadratic energy increase to increase speed linearly, that's why a 200hp car is not twice as fast as a 100hp one. Gee let me elaborate a bit more... if the 100hp car has a top speed of 100mph, a 200hp car will have maybe 130mph of top speed (assuming all other things the same) because you are fighting friction of an inmense amount of things that want to stop that movement. Anecdote... this famous US plane made with this titanium allow, I remember reading that at the speeds it was able to reach, the pressure of the air hitting the surfaces is so much that it will cause other metals to fail. Imagine the amount of energy you have to spend to heat the whole surface of the plane while traveling through cool air!

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

#186

Post by econ »

perilunar wrote: post #151
6510 wrote: post #118

Earlier quoted context omitted.

Nice bit of camera trickery. He says "both drivers react and a moment later they break", but the cars are still side by side. It (apparently) takes drivers 1.5 seconds to respond, the 5 km/h speed difference cuts the distance by 2 meter. Which apparently is a big deal. Rough estimate breaking distance: 5 km/h = 0.13 meter 30 km/h = 4.5 meter 60 km/h = 14 to 18 meter 65 km/h = 21 to 24 meter The +5 km/h adds 6 to 7 me…

"Breaking distance": how much shorter the car is after the impact.

Haha, this auto completely technology needs some distance too.

In Dutch its remweg (something like brakeway) and my mind was occupied not finding the English word for it.

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

#188

Post by ChadNauseam »

tcoff91 wrote: post #155
hyperhello wrote: post #46

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.

To me the simplest way to understand it is through calculus. Kinetic energy is the integral of momentum so You go from p = mv to k = 1/2mv^2

That just pushes it back one level for me, because I never got why kinetic energy is the integral of momentum w.r.t. velocity

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

#190

Post by ThoAppelsin »

mistercow wrote: post #182
ThoAppelsin wrote: post #174

Earlier quoted context omitted.

Scale up the numbers in you example: The effort to move a piece of furniture from 10,000th to 20,000th floor is NOT the same as the effort to move it from the 20,000th to the 3rd. The reduced gravity will help you.

If you're talking about intuitions, you have no firsthand intuitions about lifting effort decreasing with distance to the Earth. We can intuit about constant gravity, and the math of constant gravity works fine for this description. And while the real situation at scale is more complicated, the math is going to come out to the same answer, albeit with extra terms muddying everything up. If someone says that something…

I’m not talking about intuitions; I’m talking against them. The intuition about carrying something 1st to 2nd then to 3rd floor is clearly wrong as evidenced by the example I gave; it is less wrong in smaller scales, but it still is wrong.

If the floors were as high as the radius of the Earth, the first one would be three times as hard as the second one. The math doesn’t come out the same. It’s not at all linear, it’s the inverse square; that’s much more than just _extra terms muddying things_.

Calling this relation linear by just looking at the intuitions of tiny humans is akin to hyper-zooming an exponential graph and calling it linear. It is “approximately true” locally, but hey, the same is also true for velocity vs kinetic energy!

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