Steelpush Mechanics

[Moogle]

From the previous thread:
 

 

 

(Slightly unrelated, but Mistborn are actually kinda OP when compared to other characters throughout the Cosmere. Seriously. They dodge/block coins on reaction without Atium. When you take into account how fast those coins could be flying (based on the average weight of a person, because Mistborn have to be able to Push with at least that much force to lift off the ground, the mass of the coin, and 1 meter of acceleration from a constant push, and you've got near bullet speeds) and how often Mistborn react to them (not aim-dodging or precognition, just flat *oh there's a coin headed my way* *Push/Dodge*) and you've got really superhuman reflexes and reaction speed.

 
Not to derail this, but this probably isn't how Pushing works - just because Vin can lift her hundred pounds or whatever off the ground does not necessarily mean she can put one hundred pounds of force on a coin. If she could, she'd be basically accelerating it past the speed of sound and disintegrating it mid-air.

 

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Well, Sanderson has said in WoB* that he wanted Allomancy to make some sense within physics. It is most logical (to me, at least) to accept that Pushing/Pulling, pretty much the most recognizable part of Allomancy, follows this precedent, rather than assuming it is the exception to that rule. Unless Sanderson comes out with a statement refuting this, I have no reason to make assumptions that make Allomancy inconsistent. 
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I highly doubt that the coin would disintegrate in mid air. I mean, bullets don't. And bullets are propelled by a sudden and violent explosion, not a smooth, uniform Steelpush, sending them flying out at over twice the speed of sound, in some cases. What are bullets made of? Lead, or lead with copper sheathing. They handle these stresses just fine; they don't just disintegrate in mid air. 
V
Making the assumption the lowest denomination coins commonly used by Mistborn are made of common metals like tin, copper or bronze, which makes sense, considering the plentiful supply of those metals in the books. This is further supported by the fact that the lower value coins in Medieval eras here on Earth were made of these types of metals. Plus it's said in the books that silver/gold coins exist in the Final Empire, if I recall correctly, but the small coins are used because of their lack of value, suggesting they are made of a more common metal. 
V
Bronze, copper, and tin are fairly tough when compared to lead. Based on the Brinell scale, which measures the ease with which the metal can be punctured, lead scores 5 MPa. Of the metals probably used in Scadrian coins, tin is the lowest with 350 MPa. Copper is next with 874. I couldn't get a number for bronze, but it's apparently multiple times tougher than copper, so you get the idea.  According to the Mohs scale of hardness, which measures how difficult it is for a material to be scratched by another material, lead is again the lowest, though admittedly tied with tin. 
V
So bullets are made of a softer metal, suffer more violent acceleration methods, and are accelerated to a higher speed than the coins. Bullets don't disintegrate, so I doubt the coins would either. 
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Sorry for the long post, and I apologize if I sound offensive in this, or like I'm belittling your opinions. I just wished to explain fully why I believe this theory of the mechanics of Allomancy and why I don't think your rebuttal will change my opinions. 
 
*

http://theoryland.com/intvsresults.php?kw=allomancy+physics

 

Because this was going to derail the thread, I've started this thread over here.

 

I disagree with a few of your assumptions.

 

Vin can lift herself (ie. put out around a hundred pounds of force) from quite the distance away - she can levitate in the air from 5-10 feet up, if not more, and this is a sustained Push. You're modeling coin Pushes as like a bullet - a violent force put on the coin temporarily at the start of its flight, speeding it up like a bullet. I disagree with this - there's no reason for a Mistborn to stop Pushing on a coin as they fling it out.

 

If Vin can put out more than a hundred pounds of force (she leaps violently into the air) at the start of her Push, and can put out a hundred pounds of force or so around 5-10 feet away (which she'd have to be able to to levitate), we're looking at an absolutely massive sustained Push over ten-twenty feet (and because duralumin is applied nigh-instantly, things get more awful). The acceleration would be ridiculous, to the point where it would be speeding far, far faster than a bullet does, and would likely disintegrate in the air, to say nothing of what duralumin would do.

 

If Vin is applying this 100 lb. force to the metals she pushes, little specks of metal would become a deadly, terrifying weapon.

 

So, I don't think it makes sense for Vin to be Pushing on coins with 100lb.+ forces. This thread (highly highly recommend) has a compelling model which deals with adding kinetic energy to the system, rather than Vin applying a constant force.

[Dunkum]

the lovely thing about physics is that we know how it works, and can apply equations to things.  to wit: F=ma and therefor a=F/m; v_f=v_i+at; d=1/2at²+v_it so t=(-v_i+(v_i²-4(1/2a)(-d))^1/2)/a giving v_f=(v_i²-4(1/2a)(-d))^1/2) so v_f=(v_i²+2(F/m)(d))^1/2  so this last equation is the relevant one for the final velocity of a coin, given inputs for the force, mass, distance, and initial velocity.  Also, initial veloocity can be assumed to be 0, if it is a coin she is holding, meaning we just get: v_f=(2(F/m)(d))^1/2.  If Vin is 50kg (~110 lbs) and exerts an average force of  about 1.5x her body weight on the object (about 750 N, assuming scadrial gravity is about the same as ours), is about 5 meters (16ish feet) away from the target, the mass of the coin is about 10 grams (.01kg) then the final velocty of the coin should be ~850 meters per second, which is way more than, say, a musket, but less than most modern small arms (if the wiki page on muzzle velocity is to be believed).

 

*Edited to correct a math mistake*

Edited January 9, 2015 by Dunkum