Here’s another physics post which empirically makes real physicists say “hmmmmmmm”.
Beth Barnes asks why animals can run around for so long after eating such a small amount of food. I think the answer is roughly “because the sky is far away”.
(This answer is obviously going to involve some kind of aggressive approximations. I wrote all of it up to the hyphens before I actually looked up any facts about metabolism.)
The median molecule in the atmosphere is traveling at around 300m/s, and its altitude (roughly 10km) is roughly the altitude which a ball would get to if you threw it upwards with the same vertical velocity as a median molecule (which is a bit less than 300m/s, because on average molecules are going kind of diagonally rather than straight up or down).
Our bodies are made up of molecules which are apparently resistant to collisions which are as energetic as being hit by a nitrogen molecule going at 300m/s. In fact, they’re apparently resistant to collisions much more energetic than that, because we can withstand not just an average collision but even unusually energetic ones. So apparently the molecules that we’re made from have bonds with a bond energy which is noticeably bigger than the kinetic energy of a N2 molecule at 300m/s. (In fact, covalent bonds have something like 100x that energy.)
Metabolism involves harvesting energy from a chemical reaction. How much energy does a chemical reaction release? Well, I don’t know exactly, but it’s probably around the same scale as the energy of a chemical bond, which as we’ve said is definitely bigger than the energy of that average air molecule. So probably if you do a chemical reaction which involves changing a chemical bond, you’ll generate more energy than would be required to lift up the atoms involved up to the median height of the atmosphere.
Metabolism is probably kind of inefficient, which would suggest that metabolism is worse than this analysis suggests, but also covalent bonds are more energetic than “barely more energetic than the average air molecule”, which would make it better. Hopefully these errors kind of cancel out.
Therefore, if you metabolize your body weight, you’ll be able to jump something kind of like 10km into the air. Inasmuch as you usually jump less high than that, you will only metabolize a small proportion of your body mass with every jump.
Okay, so that’s the “theory”, but how does it compare to reality? I wrote all of the above and then shared it with Damon Binder, who googled “how many kilojoules of food would you get from eating someone” and found this article on cannibalism which claims that a 145lb (=65kg) human body has about 500 thousand kJ in it. Lifting a 65kg object 10km in the air takes about 6500kJ. So actually you’d have to metabolize only about 1% of a human body to lift it up to the representative height of the atmosphere. I think that this is because of covalent bonds having an energy scale 100x greater than the atmosphere energy scale, and because metabolism is actually really efficient. Note that muscles are only like 40% efficient, so actually climbing that many stairs or whatever will take a bit more energy than this.
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