Ooh a challenge!
Most cloth is a mixture of cotton and polyester, luckily, those have super close melting points, 250° C approximately. Keep in mind, that's the melting point. You wanted to ATOMIZE it, which I'll generously presume doesn't mean actual molecular breakdown but a change from a liquid into a gaseous or plasma state. Those molecules both basically break down into the same things, the hardest of which to liquify is carbon. Carbon is that black stuff that remains when you burn other stuff.. and it's also really hard to burn up itself. It begins liquefying at temperatures of over 3550° Celsius.. and that allows us
a lot of heat friction.
So, how much mass do we actually expel that's relevant. Let's use polyester with a better defined atomic mass to make this easier on us, and cheap shirts are mostly polyester or something comparable anyway. We have:
Molecular Formula:C27H38O14Molecular Weight:
586.587 g/mol
now the H and O's all turn into water vapor, molecular mass is 16 for Oxygen, 1 for Hydrogen, 6 for carbon. So, now we need the weight of a T'shirt, ask google:
So, a small Fruit Of The Loom Budget t-shirt weighs
128 grams /
4.5oz. A medium Gildan Softstyle t-shirt weighs
138 grams / 4.86oz. And an XL American Apparel t-shirt 50/50 weighs 156 grams / 5.5oz. So, an average t-shirt will probably weigh about 130 grams to 150 grams.
Let's go with 140 grams. Almost there, now we do some chemistry math!
27 x 6, 14 x 16 +38
162, 224 and 38. now this differs from the actual molecular weight because the Polyester chains have different lengths.. and yes, the benzole group also would be harder to burn up due to its strong enthalpic bonds, but lets cast all that aside, we're looking at pure yield potential here, plus ignoring all chemical bondaging means we are looking at a more minimum yield yet.
What we can tell is that the rough amount of carbon in here is 150 : 250, or a bit over a third, a sum that'd suprise no one knowing organic chemistry.
So we are looking at, to round down again, 37% of 140, or a round 50 gram of carbon from the burned up T-shirts.. Now, we look at the mass of a Bullet, because that, together with the pointyness, does the damage. The point of force is half irrelevant here.. skin and flesh is not that resistant to impact damage as a material and we can impart almost any velocity as per your specifications, as long as we don't vaporize our carbon.:
Depending on the gun, the mass of a bullet usually ranges between 0.02 kilograms and 0.04 kilograms. The mass of a bullet depends on the caliber and type of gun used. A bullet can be fired from a revolver, pistol, rifle, machine gun or other weapon.
So, for those that didn't pay attention to metrics, our T-shirt bullet with 0.05 Kg is above most normal bullets in weight of pure carbon. If that mass hits you at the right velocity, you're in trouble.
BUT AIR FRICTION! Doesn't matter at all, you can completely ignore air-friction, we're at this point dealing with a rough sphere of burned up carbon, sure, the resistance is going to deform it.. into its most aerodynamic shape. there's some opposing force from the air, of course, just like there is on bullets.
Now we know the velocity at which a bullet can do damage, that means, all that's left is for us is to be dense, or rather, look at the density of carbon vs lead (What bullets are primarly made off ofc), the denser a material the heavier it is per surface area, meaning the more damage I can do. We have a rounded 2 for Carbon vs an 11 for lead, or a 1 to 5.5 ratio.
So. to simplify, a 50 gramm bullet of carbon does the same damage, at the same velocity, as a lead bullet of about 9 gram weight. Can that do damage?.. Well, it's still heavier than the lighest gun shell around. So yes.
But! We are not talking average velocity, you see, the melting point of lead is only ~330 °C. Carbon is, we recall, at ten times that amount just to MELT And lead bullets do not vaporize into nothing in thin air, So, while our Carbon payload faces over five times more resistance due to it's lower density, it can handle over ten times the acceleration force without melting.
So, we're doing, at bare minimum, the same damage as 90 gram of lead, spread over a larger area of impact, but so are shotguns. Now, Shotgun shells are weighted in nonsensical nonmetric american units like gauges and grains and their weight varies heavily, but even using heavy rounds, I reckon that'd still be several
@shotgungunshot 's. Completely ignoring the molten stuff coming at you, yes, this would do damage.
Now keep in mind, there are realistic objections to this, but most are waved away by Slicer stating I could use 'any means' to turn the t-shirt into a projectile, to, I presume impart Velocity, that means I can choose a barrel that wouldn't melt up itself first, I don't have to worry about the shooter and Newton's laws (aka, recoil), or the energy source used to power our higly impractical shotgun.
TL/DR: NEVER understimate the physics of energy working on objects.