alt Hacker News> 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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Because things like energy are relative. So if you label the ground 0, and go up 10 feet, you get x energy. Going up another exact same x from your 10 foot ladder spot you could now call 0 again, would mean you gain x energy again. Since they're both the same height, and you gained the same energy, you could infer double the height has double energy.
Because physical movement is intuitively transitive. Going from A to B then B to C is the same as going from A to C.
The journey from Y to Z might feel more tiring than the journey from A to B, but only if you do them all in one day :)
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.
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.