My new favorite random fact is that it is physically impossible to exceed the weight limit on a USPS Priority Mail small flat-rate box.
Look it up.
Oooo, oooo, I’ll help! I’ve heard this before, but I’ve never seen the analysis, so lets do some physics!
For those not in the know, the United States Postal Service has a flat-rate shipping service if you use one of their standard boxes, A small flat-rate box is 8.625" x 5.375" x 1.625" on the inside. All flat-rate mail is limited to a maximum of 70 pounds per package. I’m going to convert this all to metric for my benefit.
Dimensions: 21.9 cm x 13.7 cm x 4.1 cm
Volume: 1235 cubic cm (cc)
Max weight: 31.7 kg
Anyways, you know what’s heavy? Water. Water’s pretty heavy. Water is right around 1 gram per cc (g/cc), so a box full of water is 1.235 kg. Hm. Unimpressive. We can do better.
What’s heavier than water? Stones sink in a lake, right? Let’s pick a fun one, say… granite. That’s a good stone. According to Wikipedia, granite is around 2.7 g/cc (coincidentally about the same as aluminium.) This comes out to 3.334 kg. Still pretty weak. We can do better.
You noticed I mentioned aluminum up there. Aluminum is a metal. Pretty well known for being a structural metal used when steel is too heavy. So what about steel? Steel has a density somewhere in the range of 8.7 g/cc, depending on which particular steel, but hey, close enough. This come out to 10.7 kg. Pretty heavy, but barely 1/3 of the way there. Can we do better?
Okay, let’s cut to the chase. Here’s some common elements that are more dense than iron:
Lead, 11.3 g/cc: 14.0 kg (pretty sure this falls under hazmat restrictions. Please don’t ship this through the USPS.)
Mercury, 13.5 g/cc: 16.7 kg (I’m POSITIVE this falls under hazmat restrictions. Definitely don’t ship this through the USPS.)
Gold, 19.3 g/cc: 23.8 kg (this is roughly $1.4 million market value, btw. The standard insurance isn’t even close to covering that should they lose it in transit.)
Okay, okay, okay, still only a little over 2/3 of the way there. Is there anything “less common?” The densest element on the periodic table is Osmium. It has about half the abundance in the Earth’s crust as gold and a density of 22.6 g/cc. Even at that density, that’s still only 27.9 kg. Close, but no cigar!
“But Rocket,” I hear you cry, “there’s got to be a way!” Not really! That’s the best we can do here on Earth. But if we go off of Earth and search the cosmos for one of the most ridiculous things to exist, maybe, just maybe we can pack more than 31.7 kg into a USPS small flat-rate box. If we ignore black holes, which are sorta infinitely dense, we find neutron stars. These are dead stars that were, in life, many times more massive than our own Sun. The reason that we can only fit so much mass into a given space is that atoms are mostly empty space! The protons and neutrons that are the “dense” part of the atom only take up a tiny fraction of the volume of the atom. The electrons whizzing around the outside of the nucleus have very little mass (~0.01%) of the nucleus, but they all have negative charges that make sure that the electrons of neighboring atoms don’t get close (relatively speaking) with each other. By this measurement, an atom is roughly 10,000 times bigger than its nucleus.
Now neutron stars, they sorta just…. ignore all that. At standard physical scales, the forces between electric charges swamps anything gravity could do by so many orders of magnitude it makes the mind spin. That’s why you can stick a static-y balloon to the ceiling and it just sorta hangs out there instead of falling to the floor. But neutron stars have so much mass that the gravitational forces actually overcome the force of the electrons keeping the nuclei of the various atoms apart! So that atom is now 1/10,000 as big as it was before, but it still has the same particles making it up… which means that it’s 1,000,000,000,000 (that’s 12 zeros) times more dense. (The actual number is more like 14 or 15 zeros, but that doesn’t really matter here.) The other interesting thing that happens is that since the electrons and protons are no longer separated from each other, they basically combine and become neutrons. So you have a giant ball of neutrons that is more dense than “normal” matter. Finally, our box now weighs somewhere in the neighborhood of 5x10^17 kg (that’s a 5 followed by 17 zeros). While this isn’t quite as much as the Earth (6x10^24 kg, a 6 followed by 24 zeros), it’s likely a million times more massive than the asteroid that killed the dinosaurs.
Only problem is that before you were able to scoop a bit of neutron star up with the box to prank the USPS, the atoms in the box would also turn into neutron star. Please don’t waste the USPS’s boxes, that’s a good service there! :P
I just paused the Great British Baking Show to read this out loud to Evie and Emet. Evie pointed out that your hand would also become a neutron star, so please only do this if you, too, want to be a neutron star.
If it makes you feel any better: you would not transform into Neutronium like some kind of science fiction Midas touch, but rather: you would collide with / splat against the Neutronium. Which would then absorb you like the earth does meteors.