I’m not a science-y person, but I love sci-fi. In a novel I read near a decade ago (Larry Niven’s Known Space series), he mentions occasionally kinetic weapons. I’ve seen this online as well with tungsten-based projectiles being discussed. So my question is how does mass and velocity affect the amount of damage? If I had a nickel-sized object, how fast would it need to go to cause city-wide devastation (would it be possible or would the damage output be capped based on either size or velocity)? Conversely, If I launched something at the speed of sound, would the damage output be the same if it were different-sized objects?
In: 5
Howdy! Others have pointed out the equations for this, but here’s the application.
Take and object (piano, bowling ball, grain of sand) and throw it. The energy it carries to hit something depends on the mass (lets say How Heavy and leave it at that) of the object and how fast it’s moving. But — Double the speed, quadruple the energy. Double it again and now it’s Sixteen times the energy. So that tiny grain of sand moving way way fast can do enormous damage when it hits something.
First Problem – After getting your piano up to speed on your Acme Co Catapult Mark II, it’s likely in the atmosphere, so it has to push air out of the way on it’s trip to that horrible bird. BTW, launching it at double or quadruple the speed to get more energy means more energy in to do it!. Meanwhile, Air. The faster it goes, the more drag (air friction) holding it back. The bowling ball has a better shape to let the air slip by, so less drag. Grain of sand? Much less friction, but because it weighs nearly nothing, any drag will get in the way in a hurry.
Second Problem – If you’re going fast enough, the friction from drag will heat up the air, and the thing (lets go with bowling ball) it’s touching. Supersonic aircraft have to deal with this. And the rules change some once you hit the Sound Barrier. Think of a tugboat in the water chugging off to do tugboat things. It’s usually pushing a big hump of water ahead of it as it goes. This is called a Bow Wave, and it’s the water equivalent of a air Shock Wave. You actually use shock waves all the time! It’s called Hearing. Drop the bowling ball, not on your foot, please, and it goes Thump on the ground. Or drum your fingers on the desk. Whatever.
The air pushed away (suddenly!) makes an itty bitty shock wave, and so do the vibrations from whatever got hit by the ball (or fingers). Your ears detect this and…. Hearing! This waves, with their small energy, wiggle the eardrum, then magic pixies do their stuff and you can suddenly speak Swahili. Or something. The point it a wave moved through the air and your heard it.
Once at or past the Speed of Sound, the bow/shock wave can’t move away from the front of the object — they touch — because the object is moving faster than the sound can get out of the way. So, lots of friction, lots of drag, and lots of heating. This is where them 1 2 4 8 16 etc (increasing powers of two) progression really, really gets in the way.
The piano is probably a lost cause at this point, but the bowling ball has the best chance to really get some speed (and therefore energy) behind it. The grain of sand could do as well if you remove the air, and BTW the piano would still be a player in that environment.
Now I can finally get around to your ELI5 about how much devastation can you pack into a nickel? A lot but limited in the atmosphere, and insane amounts in the vacuum of space. Throw a piano at the Space Station at Mach 25, and the Blue Danube will never be the same.
A side point is the damage caused by gunfire. Just about all modern pellet projectors have enough oomph to get that 1/4 to 1/2 (hey — I’m winging it here) ounce bullet up past Mach 1 (about 1000 Feet Per Second) into the 2000 Fps range. The shape and density of the bullet get around much of the drag issue with decent aerodynamics. And here the mass plays directly into the speed part of the equation. When it hits, you have not just punched a hole into something, that supersonic shock wave (bullets passing near you can be heard as a Snap, not so much a whizz) is now inside your body, stretching and tearing things. It’s not the .45 you’ve been shot with — that’s an itty bitty hole (painful, yes) that not even 1/2 inch across. It’s the orange to grapefruit sized shock following the bullet as it moved through, ah, umm …. you. Well, somebody deserving, anyway.
So you can’t toss a penny off the Empire State Building and crush skulls. Air drag stops that (called terminal velocity), but in a vacuum it would be dangerous, because all the pedestrians below would be dead. Don’t bother throwing pennies at them you sick freak!
And as for your opening thoughts, a very heavy and dense tungsten telephone pole screaming (in space, no one can hear you….) down from 200 miles above only has a few miles of air to puncture before it arrives in Central Park. The front end would be very hot, even partially melted maybe. When it hit the dirt at Mach 25, the shock wave would do a lot of urban renewal in the nearest mile or two circle, and you’ll have to get your frappuccino from some other coffee shop. The Tic Tok videos would be spectacular, though!
Hope that helps!
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