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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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.
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 :)
> What makes this intuitive?
20 million years of evolution hard-wiring it into our primate brains on a genetic level, from every thrown rock and fall from a tree. That's what made it intuitive. But not everyone gets the same batch of genes, I guess..,
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.
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.
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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 intuition for kinetics. Increasing walking/running from 0 to 5 km/h doesn’t feel the same as than moving from 5 to 10, which does not feel the same as moving from 10 to 15. I don’t think we have an experience of linear relationship between running speed and effort, or other types of speed/energy types of relationships.