How would one go about calculating the following?
The speed necessary for a 10kg mass to hit an object with the comparable energy output of a 1kiloton explosion?
or is it two non comparable energy types?
This question popped into my head due to the threads on Kinetic energy and Nuclear bunker-busters that are doing the rounds.
Got to wondering if it were possible to just do kinetic strikes from space (you know, setting aside accuracy issues and other piddly details 
)
Well…if you are up for the math perhaps you can figure it out from the info below (noting of course that “nuclear weapon” is a pretty broad definition in terms of destructive power as they come in a wide range of explosive yield).
1 kiloton TNT is about 4E12 Joules. For a 10kg projectile, this gives a small enough speed (though substantially faster than we expect meteors to be traveling) that the nonrelativistic KE formula K=mv[sup]2[/sup]/2 is reasonably valid.
From Wikipedia, [url=“http://en.wikipedia.org/wiki/Kiloton”]1 kiloton = 4.2 * 10[sup]12[/sup] Joules (I can never remember that figure). Kinetic energy is E = 1/2 mv[sup]2[/sup], and m is 1 kg. So v = sqrt(2E/m) = 2.9*10[sup]6[/sup] m/s, or about 1% of the speed of light, which is unattainable with current technology for a 1 kg object.
Well, I did a bit of calculating and the rounded answer I came up with is that a 10kg object would have to be going 52,740 miles per hour to release 1 kiloton of energy.
Fixed link, and I misread the OP as 1 kg instead of 10. That brings my calculation down by a factor of about 3, but it’s still too fast for current technology.
You can’t.
The 10KG mass would have to hit every square inch of the object. Recalling from an actual DoD manual my boss had at my first job (in Civil Engineering), a nuclear (and with the exception of radiation any explosion really) produces three things:
-blast force
-heat
-radiation
obviously the heat and radiation part can’t be simulated by the weight.
the blast is a pressure differential radiating from the center of the explosion. At the origin it travels 1000s mph or more IIRC, rapidly loosing speed.
When that wave hits an object, it essentially high speed wind that applies a crushing pressure to the entire object. It’s also directional so it blows it away from the source of the blast.
Wouldn’t a kinetic missile produce all three? Granted it does not have chemical or nuclear explosives but upon impact wouldn’t the force imparted convert to heat, blast force and (by virtue of the heat) radiation? I do not think “Rods from God” simply drill a nice little hole and that’s the end of it.
As for the rest I would think someone could calulate the force imparted per in[sup]2[/sup] (or whatever) and for a nuke and compare that to the force imparted over the same area by a Rod from God.
From my link above the “Rod from God” is going about 24,500 miles per hour so about half what you posted but then a Rod from God sounds like it’d weigh a lot more than 10kg. Not sure where it all balances out.
Uh, yeah… a tungsten rod 20 feet long and 1 foot in diameter would weigh a metric shitload. I really don’t want to calculate how much, suffice it to say my barber when I was a kid had a chunk of tungsten that was a brick about 4" by 6" by 3" and would bet guys that they couldn’t hold it for one minute with their fingertips. It was Heavy, I think he very very rarely lost that bet.
Rod from God: isn’t that where we got Jesus?
It’s easier to remember as 1000 calories per gram! This is not coincidence - TNT varies between about 900-1100 calories per gram due to impurities from the synthesis. If you’re going to use TNT for comparison purposes, may as well pick a round number.
I make the required impact velocity as 917 km/s, the same as Chronos after applying his 10[sup]1/2[/sup] correction.
msmith537 is partially right - the high KE impact won’t give identical effects to a nuclear explosion. But there certainly will be a considerable blast - the impact releases a hell of a lot of energy in a small volume, effectively turning the projectile and a fair chunk of the target into a high-pressure plasma. Take a peek at Arizona crater, or photos after the Tunguska event, (1908 Siberian comet impact) to see evidence of blast from high KE impacts.
I was under the impression you wanted to fire your mass against an object to simulate the forces of the bomb.
I know this thread is old but i want to see if i could get someone to retry the calculations. Retry the calculation with the mass at 8712.5 kilograms. Everything else is the same, still want it to equal up to the output of a 1 kiloton explosion
Do your own homework.
Look at post #4, and plug your numbers into the formula.
Are we questioning the plot of “The Moon is a Harsh Mistress” ??? :-o
If the original poster for this thread sees this again that number was for an actual bombardment based on the weight of tungsten rods that are 20 feet long and 1 feet in diameter. A real kinetic strike’s Kinetic Energy would be 1.3*10^10 joules if we had the technology to perform such a strike. The dimensions used were reported dimensions from 2003. He’s the link to a wiki that mentions it. Kinetic bombardment - Wikipedia
In reply to my last post, it’s actually 3.66360625e+19 joules. I forgot to convert kilograms to grams.
