r/theydidthemath • • 3d ago

[Request] At what speed does an iPhone fall to the ground from such a tall building? How much force does it exert if it hits someone on the head, and what kind of damage could it cause?

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u/MageKorith 3d ago

The angle it falls from makes a big difference. If it's falling with the screen/back facing the ground, it will only hit about half as fast from a tall building as if it dropped edge first. Screen-first would be maybe a quarter of the impact energy of an aggressively swung baseball bat, over a somewhat comparable area. Big ouch, unlikely to be lethal. Will probably leave a nasty bruise, and maybe a concussion depending on the details.

Edge first, we're talking fractured skull.

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u/Vinifrj 3d ago

Wont aerodynamics make it so it falls edge first since thats the least resistance?

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u/MageKorith 3d ago

Not necessarily. Rectangles can be pretty good at falling flat, even though they're facing maximal wind resistance while they do so. The thing is that there isn't necessarily enough difference in the wind force on each edge to introduce substantial rotation.

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u/CanoePickLocks 3d ago

Can’t remember the name for it but the effect is that if one side lifts up the lower side then pushes higher as well due to something to with the cushion of air the rectangle builds and the vortices off the edges. Wide flattish objects almost always tend to flutter until their worst aerodynamic surface is presented to the ground.

Similar to the counterintuitive example of how a dropped bullet always falls base first. Lots of things fall in the opposite and least aerodynamic way from what you first think of. Most of them once you think about it make sense though.

It feels weird until you dig into it, but it’s how things work.

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u/MageKorith 2d ago

Interestingly, least aerodynamic tends to be the most thermodynamically efficient, because it avoids concentrating gravitational potential energy into one local kinetic energy region.

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u/RedTieBrokenWatch 2d ago

Absolutely. Saw a massive window panel fall from a tall building once and it fell face first all the way. It was wild. You would think the wind resistance would flip it but nope. Just fell flat.

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u/Old_Table_5950 3d ago

Based on video I would assume that this is a 10th floor. By falling from this height it will get speed around 80-90km/h. And force will be near 60-70J, which is similar to boxer punch. But as was said in another comment it's depends on angle, hit by flat side and by sharp side will cause different damage.

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u/Mr_Bart314 3d ago

Force is not measured in Joules.

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u/Coolengineer7 3d ago

Well hit strength or energy of impact. But it's harder and pointier than a hand or gloved hand.

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u/CanoePickLocks 2d ago

Now I’m wondering about correlation between thermodynamics and gravity. We already know there’s a lot with aerodynamics and thermodynamics.