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digitalbusker posted a topic in MistbornI've been following the "Weight has nothing to do with allomantic Push/pull strength" thread for a while, and I think we're using the wrong model for framing physics questions related to Pushing and Pulling. What is the behavior observed in the books? If Coinshot A Pushes with allomantic strength B on coin C, we observe that both A and C will experience acceleration proportional to B but inversely proportional to their mass. So as long as C is not anchored, it will accelerate rapidly while A is barely affected, but when C hits the ground or a sturdy wall suddenly its effective mass is increased to the mass of the combined system (coin plus wall, or coin plus planet), and its acceleration drops way off while A's acceleration spikes. When we use F=ma, the problem that arises is that the acceleration a Coinshot experiences when Pushing a coin should depend only on the magnitude of the force applied, not on whether the coin is anchored. If we view the magic as a simple action/reaction between the Coinshot and their target, the behavior we observe in the books is not preserved. There is a well defined physics model that deals with two objects interacting in a way that changes their velocities to a degree that's inversely proportional to their masses: elastic collisions. If we reframe this situation in terms of an elastic collision, then the allomantic strength term becomes not force but kinetic energy. A given allomancer's push strength is the amount of kinetic energy they can add to the system. What happens to the velocities of the components of the system is then subject to conservation of (the new, higher) momentum. This preserves the behavior we see in the books. (Actually a person's Steelpush strength would be delta-kinetic energy per unit time, but integrating over time is left as an exercise for the reader.) If you'd like a pseudo-concrete framework for thinking about this, imagine that the blue lines you see while burning Steel are tangible to the things at either end of them. Normally they are happy to simply change length to remain in contact with their endpoints, but when Pushed or Pulled, an Allomancer pours some Investiture into them and makes them grow or shrink with some amount of power. The line doesn't care where its center winds up, or how long or short it winds up being, it just knows how hard to push, and the end that resists less will be moved farther than the other. So to bring this back around to the question of whether your Push/Pull strength depends on your mass: Yes and No. There's some innate Allomantic Strength term that's independent of your mass, but in practice the things you can do with Allomantic iron or Allomantic steel are influenced by both your strength and your mass. (When you're trying to move yourself it's better to be lighter, when you're trying to move other things it's better to be heavier.)
Nepene posted a topic in MistbornI was reading the alloy of law annotations and I read this. Then, I was, as a Chemistry degree holder, thinking of a way that this could play out and be considered relatively consistent and scientific. These are the challenges. 1. You have to be able to break things with your weight. 2. He has to be able to move about normally. 3. It has to focus on mass. 4. He can't be bullet resistant. I think I know a way he could do that and have the science remain consistent to all of the agreed upon conditions. This is a non spoilery quote from WoR Rather than storing mass, what if feruchemy stored the signal of mass? The agreement of mass between the tiny preservation and ruin building blocks of the world? Because it wasn't storing real mass when a human or a bullet under the influence of a human hit it, their innate investiture and spirit would resist the feruchemy, as it would resist an iron push, and they would feel the weight increase or decrease to a lesser degree. An object or the floor would feel the full influence of the iron feruchemy as it lacked much spirit and had no reason to think the person was lying about their weight. A bullet, shot from a human, would be filled with the human's intent to kill, perhaps a small part of their soul, and would resist the feruchemy increase in mass and kill. This could be scientifically tested in a future book.
Scriptorian posted a topic in MistbornI read the mistborn series while taking a class on calculus-based Newtonian physics, so I couldn't help but formalize a theory on how steel/iron allomancy would actually work. There has already been a topic on how weight is related to the strength of push/pulls, and you can read it here http://www.17thshard.com/forum/topic/3307-weight-has-nothing-to-do-with-allomantic-pushpull-strength/?hl=%20allomancy%20%20mass%20%20weight. But I want to introduce a new theory (with a bit of math) that I think clears up a lot of the confusion. I'm not incredibly physics-savvy, so I explain something terribly wrong, I apologize. (For the sake of efficiency, when I say allomancy, I am referring specifically to Iron and Steel) The Force of Pushes and Pulls First, I am operating under the assumption that weight is only tangentially related to the force an allomancer can exert. Instead, it is actually the mass involved that is important. Weight is the force exerted on an object by the planet equal to the mass of the object multiplied by the acceleration due to gravity. Most people (including the mistborn characters) probably mean mass when referring to allomancy. So I came up with an inverse-squared formula to determine the force an allomantic push/pull can exert. F= (A x (m1 x m2))/(r2), where F is the resultant force, A is the coefficient of Allomantic strength (I'll get into this later), m1 is the mass of the allomancer, m2 is the mass of the object, and r is the distance between the two masses. (The force is positive for Lurchers, and negative for Coinshots). I based this off of the Newton's Law of Gravitation since the principles involved appear very similar to me. When the earth pulls on an object, the object is actually pulling on the earth with the same force. However, the earth has so much more mass than the object so it effectively doesn't move. If a much larger object, like another planet, were to come near the earth, then both it an the other planet would move towards it at noticeable speeds. And again, if a much more massive object, like the sun, where to come near the earth, you wouldn't see the sun move,, just the earth. This is very similar to how a Coinshot can send a coin flying, but be pushed into the air by a much heavier object. The coefficient of allomantic strength accounts for the varying levels of power between different allomancers. This variable changes depending on how hard the allomancer is pushing/pulling (i.e. by flaring). In this way, both the mass and strength of the allomancer are important to the amount of force he/she can exert. Both the allomancer and the object are affected by the same force, but the less massive object accelerates much faster. The force also decreases quadraticaly as the distance between the object and allomacer increases. So I did some math the figure out about what this coefficient of allomanctic strength would be...and kept doing things wrong. At first I made the mistake of assuming a coinshot was pushing on a coin in free space, which resulted in a Coinshot strong enough to move planets. Then I tried having him push against the mass of the planet, which came out to him being ridiculously weak. I finally realized that when you are pushing off of a coin, your effectively pushing off a certain amount of ground, not the entire planet. I have no idea how you would calculate the mass of the ground however, so my formula is now un-provable without some more concrete measurements of allomancy . Feruchemical Iron This theory requires some pretty weird physics concepts. There's been a lot of discussion about what is actually stored with Feruchemical iron, but I think this theory coveres it pretty well. Basically, there are two different measures of mass: gravitational mass and inertial mass. Gravitational mass affects the gravitational field exerted by an object, and also how it is affected by other fields of gravity. Inertial mass is how much an object resists changes in motion. So far as we know, the two values are the exact same for any object and are functionally the exact same concept, in the real world. However, in the Cosmere, it appears you can change one without changing the other. I propose that Feruchemical iron merely stores the feruchemist's inertial mass. This means that nearly every force will affect the feruchemist as though they had gained more mass when the feruchemist is tapping, and vice-versa for storring. Gravity, however, affects the feruchemist the same as normal. The difference is, say when the feruchemist jumps while storring, the force of the jump affects him much more, with gravity affecting him the same, resulting in a much higher jump. Similarly, while falling, drag affects the feruchemist much more, resulting in a slower fall. This also solves the issure of the feruchemist suffering not crushing themselves while tapping, because their atoms become more resistant to motion in direct correlation with the increase of inertial mass. This increase in inertial mass would also factor directly into my above equation for allomancy. Since the force is directly proportional to the mass of the allomancer, tapping iron results in a greater force, both on the allomancer and the object. However, the increased force accelerates the allomancer the same as normal force the allomancer is now proportionately more resistant to motion. Now a potential hole in my theory is that the reverse should also be true. Decreasing your inertial mass would make forces affect you more, but would also reduce the strength of your Push/Pull. In the AoL, Wax is more affected by Pushing while storing Iron, and I can't figure out how to account for this mathematically... I wanted to have a bunch of physics and math extrapolated from this...but most of my calculations were really flawed.... Anyway, thoughts? Criticism? Any real physicists who wants to tell me I explained this all wrong?