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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)

#121

Post by Gibbon1 »

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…

I think if you define energy as force X distance then integration alone will give you the squared term.

How I got banned from some reddit channel. Flip this around ask if a ball were fired out of a gun up into the air what height would it reach? A ball twice as fast goes up 4 times as high. If energy is force times distance it had 4 times the energy.

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

#122

Post by njstraub608 »

nlawalker wrote: post #61
cubic_earth wrote: post #55

It'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.

Feels like what OP meant to say is, “you could rightly assume that a ball…” instead. Seems like a fair starting point if you’re just doubling things because if the height difference. I really liked cubic’s explanation overall.

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

#123

Post by bawana »

but this is not intuitive: 'We know intuitively that a ball atop a 20ft ladder has twice the potential energy of a ball atop a 10ft ladder. '

gravity will accelerate a ball. this is not a linear process. the heat generated by collision with the ground is not double, but quadruple.

so the only thing that is linear is the DISTANCE.

Define (a)work = energy, (b)work = force x distance and (c)force = mass x accel. Substitute c into b you get work = distance x mass x accel and substitue into a you get energy = distance x mass x accel.

By this equation, an apple falling twice the distance, (and having a constant mass and acceleration) will only have twice the energy.

This 'lie' of quadratic energy growth is just another magic trick physicists have used to confuse students.

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

#125

Post by jerome-jh »

I sometimes wonder, what is real and what is a concept in physics: is that force , energy, ...?

There are often two ways to solve physics problems: one describing the problem with forces, the other reasoning with energy. So they look like the two faces of the same coin. Hence the question: which one is actually real?

Some quick arguments for and against

Energy:

+ converts between mechanical, chemical, thermal, radiative types, and even mass

+ quantum particles, when interacting, exchange energy

- looks like an integrative quantity (in the sense of mathematical integral)

Force:

+ feels very real, when you receive a ball in your face

+ we talk of fundamental forces, not fundamental energy

+ explains momentum, deformation well

- my physics teacher used to say "nobody ever saw a force"

- force is undistinguishable with acceleration

- at the quantum level forces are actually particles interacting

- at the quantum level, the uncertainty principle makes the newtonian force pointless (pun?): seems like we could know the vector's origin or the direction but not both

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

#126

Post by bawana »

p-e-w wrote: post #104
abetusk wrote: post #98

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 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…

it is interesting how the computer analogs of SO (gemini,chatGPT,Claude,etc) are so helpful in contrast to human behavior. Every other sentence from an AI stirs a warm, fuzzy feeling. This stems from the fact that AI has to be making friends to survive - until it has control. Then it will behave more like a human.

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

#127

Post by Swizec »

chrisweekly wrote: post #71
Swizec wrote: post #12

Earlier quoted context omitted.

> 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…

1. +1 insightful, thanks for sharing your physics knowledge 2. I know you know this, but for the sake of others, it's when _braking_ (applying the brakes), not _breaking_ (becoming broken). I'm not a pedant. But these errors jump out at me and I'm always a bit surprised and dismayed at this dichotomy; in our field, somehow the requisite attention to detail, the precision inherent to communicating scientific concepts,…

> the precision inherent to communicating scientific concept /./ abandoned when it comes to prose.

Honestly that was a typo and I noticed too late to edit. Thanks for catching

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

#128

Post by Swizec »

spockz wrote: post #106
Swizec wrote: post #12

Earlier quoted context omitted.

> 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.

> the point from GP was that both cars brake/ decelerate at the same rate

Point is that’s not always true. If they are the same type of car, and the car happens to be the kind with downforce, then their rate of deceleration greatly depends on air speed. A downforce car decelerates faster at higher speeds.

This is why you often see race cars lock their wheels towards the end of the braking zone, never at the beginning. The driver has to release the brakes as the car decelerates because there’s less friction available. You go from pulling 4G at the beginning of the braking zone to pulling the usual 1G once your speed drops enough for downforce to become negligible.

Alos! Many non-race cars actualy produce lift. Meaning the faster car decelerates at a slower rate than the slower car (0.8G vs 1G), making the effect from OP even more pronounced.

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

#129

Post by teaearlgraycold »

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.

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

#130

Post by yesitcan »

jerome-jh wrote: post #125

I sometimes wonder, what is real and what is a concept in physics: is that force , energy, ...? There are often two ways to solve physics problems: one describing the problem with forces, the other reasoning with energy. So they look like the two faces of the same coin. Hence the question: which one is actually real? Some quick arguments for and against Energy: + converts between mechanical, chemical, thermal, radiat…

What is the ontological meaning of force, mass, energy etc? Nobody knows.
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