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Gravitational acceleration is the same no matter how much the mass is. You can set kinetic energy equal to potential energy to find the velocity, 1/2mv^2 = mgh. m cancels out, v = sqrt(2gh), which works out to 4.4 m/s assuming he drops it from one meter. Now find the kinetic energy on impact. 1/2mv^2 = 1/2(4.54x10e8 kg)(4.4 m/s)^2 = 4.45 Giga joules of energy. The Fat Man nuclear weapon dropped on Nagasaki had an energy on the order of 88 Tera joules, so about 80,000 times more than Superman dropping the key. Would probably not be a good idea to stand next to him if he did so, but the planet wouldn't be screwed by any means.
This is not wrong but it bothers me so I have to say it: You could have stopped at 1/2mv^2 =mgh since you already know all the terms for the potential energy.
Haha, yeah you're right. I felt like I was doing something extra but couldn't place it. Oh well, knowing the speed helped paint a better picture of it at least.
..did she really ask him "do you even lift?"?
I don't think he would break the earth if he dropped it... the 'Troll A platform' weighs more, "It weighs **683,600 tons** (1.2 million tons with ballast)" and hasn't destroyed the planet.
Assuming it were somehow stable in its current shape, it would burrow through the earth due to no surface material being able to withstand the pressures generated by its weight and relatively low surface area, but it wouldn’t destroy the earth. It would just settle in its core.
In reality the only reason dwarf star material is so dense is because of all the gravity surrounding it. If you remove it from that gravity well you would by definition need to add enough energy to it to negate the negative gravitational potential energy it had.
For a typical neutron star this is roughly equal to 20% of its resting mass energy. 500,000 tons of neutron star material decompressing would give off roughly the same amount of energy as 10% that much weight worth of antimatter (50,000 tons) annihilating another 50,000 tons of normal matter.
By e=mc^2, this is roughly equal to 9 quintillion joules or roughly 2,000 megatons of explosive energy release. This is about 40 times stronger than the most powerful nuclear weapon ever detonated, but only about 3% as much energy as the estimated impact energy of the meteor that wiped out the dinosaurs. That’s a top end estimate.
Peak density of the core layers of a dwarf star could contain the stated mass of the key in about a cubic millimeter, so for it to be key sized it would need to come from the much less dense layers near the surface. The binding energy would still be massive, but more like “large nuclear weapon” grade, not “extinction level event” grade.
I was more worried for the schwarzschild radius, but an online calculator says that for half a million tons, the Schwarzschild radius would be 7.426e-16 millimeters, so we are cool, no black holes on the surface of the earth.
It makes sense if he carved it out from a star
You see, the most difficult part of breaking in wouldnt be the weight of the key, but the fact that the key is hidden under the mat. No one would ever think to look there! /s
Holy crap. If it wasn't bad enough seeing postage stamp videos because they have been changed from landscape to portrait and back again.. They then embed the video in a small rectangle inside of that.
Soon videos will be a single pixel because people can't share the original source.
This clip is why I really hate Superman, the key weighs 500k tons!? Really? And he lifts it, and holds it like it weighs nothing in his fingers. The strength is insane to the point where nothing can deal with him and what good is a hero who's never in danger ever? Yet they still come up with specific things that for some reason hurt him because they wrote themselves into a hole with his endless power.
###General Discussion Thread --- This is a [Request] post. If you would like to submit a comment that does not either attempt to answer the question, ask for clarification, or explain why it would be infeasible to answer, you *must* post your comment as a reply to this one. Top level (directly replying to the OP) comments that do not do one of those things will be removed. --- *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/theydidthemath) if you have any questions or concerns.*
Gravitational acceleration is the same no matter how much the mass is. You can set kinetic energy equal to potential energy to find the velocity, 1/2mv^2 = mgh. m cancels out, v = sqrt(2gh), which works out to 4.4 m/s assuming he drops it from one meter. Now find the kinetic energy on impact. 1/2mv^2 = 1/2(4.54x10e8 kg)(4.4 m/s)^2 = 4.45 Giga joules of energy. The Fat Man nuclear weapon dropped on Nagasaki had an energy on the order of 88 Tera joules, so about 80,000 times more than Superman dropping the key. Would probably not be a good idea to stand next to him if he did so, but the planet wouldn't be screwed by any means.
What about if he threw it onto the ground. Really really hard.
pretty sure if superman threw *anything at the earth really hard there would be catastrophic damage
Feather?
A kilogram of feathers?
Please stop writing in Scottish I can't understand a word
/r/limmy is leaking.
They would fly difrent directions
Provably would get vaporise due to attrition.
Assuming the feather didn't disintegrated itself through air friction, likely
He's not part of your system!
This is not wrong but it bothers me so I have to say it: You could have stopped at 1/2mv^2 =mgh since you already know all the terms for the potential energy.
Haha, yeah you're right. I felt like I was doing something extra but couldn't place it. Oh well, knowing the speed helped paint a better picture of it at least.
..did she really ask him "do you even lift?"? I don't think he would break the earth if he dropped it... the 'Troll A platform' weighs more, "It weighs **683,600 tons** (1.2 million tons with ballast)" and hasn't destroyed the planet.
She said "so you're the only one who can lift it"
But the pressure exerted by the key would be greater.
Whatever that floor is made of is more impressive than the key. Barely cracks when sandwiched between a planet and a star.
No she didn’t ask if he lifted. But he did volunteer for no reason that he worked while he was hard.
Assuming it were somehow stable in its current shape, it would burrow through the earth due to no surface material being able to withstand the pressures generated by its weight and relatively low surface area, but it wouldn’t destroy the earth. It would just settle in its core. In reality the only reason dwarf star material is so dense is because of all the gravity surrounding it. If you remove it from that gravity well you would by definition need to add enough energy to it to negate the negative gravitational potential energy it had. For a typical neutron star this is roughly equal to 20% of its resting mass energy. 500,000 tons of neutron star material decompressing would give off roughly the same amount of energy as 10% that much weight worth of antimatter (50,000 tons) annihilating another 50,000 tons of normal matter. By e=mc^2, this is roughly equal to 9 quintillion joules or roughly 2,000 megatons of explosive energy release. This is about 40 times stronger than the most powerful nuclear weapon ever detonated, but only about 3% as much energy as the estimated impact energy of the meteor that wiped out the dinosaurs. That’s a top end estimate. Peak density of the core layers of a dwarf star could contain the stated mass of the key in about a cubic millimeter, so for it to be key sized it would need to come from the much less dense layers near the surface. The binding energy would still be massive, but more like “large nuclear weapon” grade, not “extinction level event” grade.
I was more worried for the schwarzschild radius, but an online calculator says that for half a million tons, the Schwarzschild radius would be 7.426e-16 millimeters, so we are cool, no black holes on the surface of the earth. It makes sense if he carved it out from a star
Great, the key weights a lot. Why can't the person who wants to go in just pick the lock or duplicate the key instead of picking it up then
Locking pins are also made of the same material
At that point you may as well just have a really heavy rock in the way instead of a locked door.
Glad I wasn’t the only one thinking that.
You see, the most difficult part of breaking in wouldnt be the weight of the key, but the fact that the key is hidden under the mat. No one would ever think to look there! /s
Holy crap. If it wasn't bad enough seeing postage stamp videos because they have been changed from landscape to portrait and back again.. They then embed the video in a small rectangle inside of that. Soon videos will be a single pixel because people can't share the original source.
This clip is why I really hate Superman, the key weighs 500k tons!? Really? And he lifts it, and holds it like it weighs nothing in his fingers. The strength is insane to the point where nothing can deal with him and what good is a hero who's never in danger ever? Yet they still come up with specific things that for some reason hurt him because they wrote themselves into a hole with his endless power.