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Going so far as to reduce the shirt to it's atoms (honestly he could have just wrapped it around a canonball if he was really lazy) and sling them through god knows what sort of acceleration device.
Something with magnets propably, that's where you get the real speed out of, ask Hadron.
gun - safely above 2700 joules of energy
human punch - 300-700 joules of energy
Air gun - could easily produce 1500 joules of energy
T-shirt weighs around 135g, if we assume it has 300m/s, then that shirt will hit you with 400 joules of energy. In reality, it will probably be much more, but I am limiting it to 300m/s because most ASG don't go above that. Even with only that... 400 joules, how much is a punch by averages?
And your point being? You know, Slicer never disputed that it could hurt. He disputed that it'd do serious damage. Even before fact-checking your numbers, you say that something with at best the surface of a human fist, will punch you about as hard as a good human fist and thus would do a bit of damage? Well, yeah, the mascot was down, that was never in dispute. But I don't feel human fist is good enough. But besides that.
You used genuine numbers and math which I can fact check, even if you used a derived unit. Then again, Joules is just (Kg x m²)/s² or Newton metre. Your number for Joules for weapons seems off, I found smaller, with similiar calibre, but oh well, lets give you that.
But they are not doing the same. A 6 mm plastic ball has just that diametre. A T-shirt is far lager. I'll show you exactly why this is a false comparison.:Most air guns are limited by law. ASG with limit of 20 joules during pellet barrel release will be enough to hurt and leave a mark. Now, instead of 6mm plastic ball, you have a rolled up shirt doing the same.
Alright Yoshi, I'ma do you a solid and pretend that every time you messed up velocity you ment not m/s but m/s², make this a little less brutal on you, k? I mean.. unless you insist on using a speed calculation in an impact-velocity scenario, in that case, you're beyond help though. Just go look up why Velocity is a Vector and Speed is a linear function, and yes, by now we're not in basic high school physics anymore.Now, if you want some math. T-shirt weighs around 135g, if we assume it has 300m/s, then that shirt will hit you with 400 joules of energy. In reality, it will probably be much more, but I am limiting it to 300m/s because most ASG don't go above that. Even with only that... 400 joules, how much is a punch by averages?
The energy your projectile can impart is dependant on more factors than just 20 joules on barrel release.
Any gunowner with a bit of experience will tell you about ammunition that, the greater it's weight, the lower it's velocity and vice versa. How does that work?
Well, you are putting 20 Joules not into a small plastic ball, but into 135 gramms of T-shirt, trying to accelerate it, somehow, to 300 m/s². Almost immediatly this should feel wrong. You lift a weight with 10 kg, and then lift a weight with 135 kg, exerting the same force, which one can you lift higher? (With the 10 gramm comparison I'm highballing the ~2.5 g air gun pellets taken from this source
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and not even considerign classical airsoft pellets, which I think you refer to,
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) It doesn't add up. Here's the math to prove your math wrong:Now, what are we actually dealing with here, formula wise. NEWTON HELP!
Force equals Mass times Acceleration. Newtons second law can help us here as what we want is to check Yoshi's claims about acceleration and
We have the mass of the T-shirt, and the Force working on it, 20 Joules, so our formula would look like this:
20 (N/m)= 0.135 Kg x X m/s²
Physically savy people will realize we need to get that one m away to properly do my calculation. So now we need the barrel size of a T-shirt gun. Luckily, there are build it yourself instructables that state you need 36 inch length and 2 inch diametre or 91,44 and 5,08 cm.
Now we need to calculate the volume of our cylindre, radius x radius x height.
First, divide 5.08 by 2, that gives you the radius of 2.54 . 2.54 x2.54 = 6.4516
91.44 x 6.4516 = 589.92 for the total volume of our T-shirt gun, as this was in cm, we're at 5.89 metres.
That's 20N/5.89 m tells us we got only 3.1 Newton working on our pellet. Can that be right? Let's solve for a pellet to make sure! For a 10 g pellet, just to see if our calculations fall in the ballpark of the expected acceleration. 10 gramm makes 0.01 kg, using our above formula, Newton equals kilogram times velocity
3 N = 0.01 kg X m/s²
Solve for X
3 N/0.01 Kg = X m/s² Divide and add all the things on one side:
X N/kg = 300 m/s² Our Formula is not just a bit correct. It's flawless within the speed margin Yoshi presented earlier. Neato!
WAIT! The physics guys among you say. You got all these units here pervy, what about them? No I don't! I got N/kg and m/s², let me wizard all of that away by dividing! N/kg is another derived unit i can wizard away using the SI unit conversion:
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X m/s² = 300 m/s², Dividing either side by m/s² is the same as multiply with s²/m, leaving you with nothing but X= 300, tada! We just did physics together folks! Always remember to carry the annoying units, they should all disappear in the end if you did your calculations right. (Of course, the physics cracks already knew the units would disappear, this is Newtons second after all)
By the by, I am aware that military or hunting weaponry can reach faster velocity, but that's the difference you have comparing a rifle ment for shooting things dead vs shooting t-shirts at a crowd, I'd presume.
Now. After checking our calculus to be sure, we can do the same for mass = 135 g and have the units equal out one another immediatly.:
3 = 0.135 X
3 / 0.135 = X
X = 22. About what I'd expected, ballpark wise.
So! No, we wont be moving at 300 m/s T-shirt vs pellet with just 20 Joules of power, even in a best case scenario, We'll be moving at 22 m/s. all discounting Air resistance, impact zone damage and whatnot, your very math is wrong, because you got some basic physics wrong, quite daring from someone that snidely demanded others go back to school. All it would have taken not to make this mistake would be a quick look up on what Joules actually are. Of course your subsequent conclusion on actual energy imparted is also wrong. I mean, hey, I'm certainly no expert, infact I suck at advanced math stuff, so feel free to double check my math, I'd be suprised if you found me wrong and amazed if you managed to do that and act like an adult, but I think the calc is solid.
You, whoever upthumbed him? Think about what units can mean, don't be tricked. Joules, Kcal and Newton are among the most interesting units, in my opinion, they are involved in food, in explosions, they are often involved in weird science scams too though, for some further watching for those interested:
So, in the end we learn that the T-Shirt wont be like the punch of a karate master, more like a slight slap. A slap at close up range on your genitalia will hurt and take you out shortly.. about enough to still wave at the audience, which is exactly what happened, I'd guess, in addition with the malfunction possibly increasing the psi of the damage.
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