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Lets suppose we have a material that is not equal affected by gravity as everything else,I don't care how, anything from dark matter to fairy dust works, but the point is that the weight formula for this material is

w = m * g * d

Being d a value between -1 and +1

This material has mor or less the same properties as iron and alloys are posible, so you can make a "steel" sword.(When alloying lets suppose d do not change)

Now we have four different materials:

The first one(A) has all iron/steel properties but d=0.5

The second(B) is 10 times dense so ten times mass and is of course has ten times toughness, hardness etc... (and yes It can be work in a forge because of the fairy thing)in this case d=0.05

The third(C) is the same 100 times everything d=0.005

The forth(D) ... d=0.0005

Time to swing that swords! But, what will happen?

Test 1

Broadsword made of material A 1m long 1700g*0.5=850g

I'ts a light sword but when you swing it feels somehow heavy.

Test 2

Same sword but made of material C I'ts a light sword but when you swing it it feels very heavy, hit like a truck and if not hit anything maybe trough you to the floor.(Please grip it well or it will hurt someone)

Test 3

Same sword but made of material C

Here I suppose that you barely can move the sword

Test 4

Same sword material D but you have super strength(balanced whit the sword mass) but with the average human weight

So you are swinging the equivalent of a truck (And this literally hit like a truck)

Finally here are the questions:

Can you explain what will happen in Test 4? Will you fly away?

In addition

If g is gravity acceleration, anything made of this material should fall at d times speed right?Then, there is a logical way to implement this with the same falling speed? Like(I hope this is clear enough )

w = (m * g )* d (forget about math rules here just focus on the idea)

Feel free to point any unsuspected behave in the other test or even make extra ones if you like(This is not required for the answer as it may be considered too abroad)

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  • $\begingroup$ What do you mean by d ? As far as I know weight=mass x gravity ? $\endgroup$ – Planarian Aug 15 '16 at 13:30
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    $\begingroup$ @Planarian d is just a made up value to multiply the weight with the same mass ex: if d=0.5 mass is the same but weight is the half $\endgroup$ – Westside Tony Aug 15 '16 at 13:33
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    $\begingroup$ Breaking my brain trying to figure this out. Closest I can think of is Thor's hammer in Marvel canon. $\endgroup$ – Azuaron Aug 15 '16 at 13:40
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    $\begingroup$ I think the funniest part about this, is that it would still have the same fall rate as everything else (everything falls at the same speed minus air resistance, but a sword doesn't fight much air resistance). So the most effective use of these weapons would probably be to drop them off tall buildings onto your targets. Once moving fast, really hard to slow down. $\endgroup$ – Azuaron Aug 15 '16 at 15:02
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    $\begingroup$ Ignoring air resistance (a physicist's favorite phrase), a paperclip and a Boeing 747 will fall at the same rate. The gravitational force relevant to "falling" is the attractive force of the Earth + the attractive force of the object. Since the Earth is so big, unless the "object" in question is on the planetary scale, the relative difference between a paperclip and a 747 is negligible, so they will fall at the same rate. $\endgroup$ – Azuaron Aug 15 '16 at 15:18
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You have indirectly stumbled across the equivalence principle of General Relativity.

Mass can have two quite different meanings, depending on the situation.

The first occurs in Newton's second law:$$ F = ma$$

The second occurs in the Law of Universal Gravitation:$$F = \frac{G{m_1}{m_2}}{r^2}$$

If the body referred to in the first equation (m) is the same one referred to in the second (let's say ${m_1}$) does m equal $m_1$?

This is not entirely obvious, but the Equivalence Principle says yes.

The first equation deals with what we commonly call inertia, and physicists and other purists call simply mass. It refers to how hard it is to get something moving or, once it's moving, how hard it is to stop it. The second equation relates mass to weight. The more mass a body has, the harder the earth pulls on it (well, and how hard it pulls on the earth).

In the real world, as far as anyone can tell, the two effects of mass are identical. You, on the other hand, are trying to separate them. In effect, you are changing m while leaving $m_1$ unchanged. While friction usually causes massive bodies to be hard to move, this is not always the case.

Bank vault doors (typically weighing about one ton per inch of thickness, and 12–16 inch doors were the norm) have really excellent hinges, and when I worked as an installer of such things, the mark of a good installation was that you could open a vault door by pushing on it with the point of a pencil and not break the lead. Of course, you had to go very slowly, but the point is that such things do happen.

One such installation had the vault door in a brick alcove, and one morning the bank VP opened the vault for a couple who were major bank customers. He showed how smoothly the door operated, and kept pushing it faster. As it approached full open, he realized he should slow it down, and braced his elbow on the wall of the alcove and waited. When the door reached his hand, of course, it did not even slow down, but sheared off the door stop and telescoped his forearm into the brick wall. Ouch. The customers were impressed.

This is an extreme version of what you are proposing. The greater the difference between inertial mass and gravitational mass, the slower but more irresistible the swing becomes. And it's not actually easy to lift the sword, since any change in motion is resisted by the increased inertial mass, but the effort to hold it steady at a given height is unchanged.

In the case of a ×100 differential, let's start with an average broadsword, weighing about 3 pounds. Swinging it will be the equivalent of swinging a 300 pound sword which rolls on really good ball bearings. Its impact will be close to irresistible, but the swing will be ungodly slow and easily dodged.

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  • $\begingroup$ See my edit. Homonyms are getting more creative! $\endgroup$ – JDługosz Aug 15 '16 at 18:24
  • $\begingroup$ Something got messed up in the second sentence of the paragraph starting with "If a broadsword runs about 3 pounds...". That 2nd sentence includes part of one sentence and all of another sentence. $\endgroup$ – BrettFromLA Aug 15 '16 at 19:10
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    $\begingroup$ What I'm getting out of this is that swords: ineffective due to necessary quick changes in momentum, but something where you could use slower, incremental momentum shifts would be vastly more effective. Like thrown weapons (think more hammer-throw instead of javelin). You could carry tons of these things, essentially iron golf balls on a silken rope, and slowly add energy to it to hurl it with massive momentum. Due to the immense force involved once it's up to speed, we may have to get some creative multi-human slings to distribute the tension across. $\endgroup$ – Delioth Aug 15 '16 at 19:12
  • $\begingroup$ +1 for inertia. I recall seeing some cool videos along these lines of astronauts in space. $\endgroup$ – Joel Harmon Aug 16 '16 at 0:25
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So as I understand your question, the different materials increase mass like normal, but specifically the force of gravity is reduced to the percentage expressed by d.

I'll also assume we're talking about the European longsword, which historically massed 1 kg - 1.8 kg.

So the decrease in gravity will make these swords no harder to pick up, but the human arm still won't be able to increase the velocity, as they're still tackling x2, x10, or x100 the mass. All things being equal these three swords will all reach the same velocity, but will take x2, x10, and x100 as long.

As soon as you reach 10x the mass and have normal human strength the sword becomes impractical as a weapon. We're now dealing with a beast that is at a minimum 10 kg. Even the massive Zweihänders topped off at 3.2 kg, but this monster (again, on the smaller end for longswords) is just over 3 times that massive. Trying to swing this would be ridiculous, as your swings would be monstrously slow.

When we reach 100x the mass, we're dealing with 100 kg. Of course since the weight hasn't been changed we can still lift up the weapon... but it stops there. Swinging this weapon would be so slow a child could maneuver around and stab you with his incredibly mundane sword.

So let's go 1000x the mass of a normal sword but you have super strength, enough strength where we can wave aside this acceleration problem. As you swung the sword you and the sword would create something of a line. The center of mass would be almost exactly at the balance point of the sword (generally closer to the hilt), not particularly affected by your own weight. You wouldn't go flying off, but you would swing around something like a top (for as long as you could hold on or keep your balance). You'd certainly not be using the sword like the any smith down the ages envisioned.

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    $\begingroup$ A quick comment: you couldn't pick it up "just fine", since lifting it still requires moving it. You could lift it in the same monstrously slow manner you could swing it. $\endgroup$ – Azuaron Aug 15 '16 at 14:48
  • $\begingroup$ What about an ascendant swing in test 4; holding the sword with the tip on the ground our super knight draws a circle trying to hit something above his head ending pointing the floor again but in the oposite direction the floor is also hard enough, in some point should loose his toehold, there is any way to predict when? $\endgroup$ – Westside Tony Aug 15 '16 at 14:49
  • $\begingroup$ @Azuaron Okay, fair enough. It would lift slower, but you wouldn't have to fight (at least very much) gravity trying to accelerate it back down, like we normally have to do with massive objects. $\endgroup$ – Nex Terren Aug 15 '16 at 14:49
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    $\begingroup$ @WestsideTony So he'd only continue to accelerate while he could maintain his footing (and thus able to push himself around in his swing). Once he starts skidding or trips the acceleration he applies to the sword would stop. I'm not sure how to predict that, though, as it's as much a matter of skill and foot speed than anything else. Ever grabbed hands and spun around with somebody else as a kid? You'd be doing something of the same thing, except you're what's moving the other person and keeping you both upright. $\endgroup$ – Nex Terren Aug 15 '16 at 14:52
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Swinging a space-station about its tail

What you have done is just to mess about gravity, and the mass of the sword. This will not be of any use.

That you can lift a massive (in the sense: with a lot of mass) sword more easily from the ground, does not mean you can swing it more easily.

Let us say you have a sword made of ultrastrong paper, that has the weight of 1 gram (that is 15.4 grain for SI-impaired imperialists). But you have increased its mass to the point where its mass like the International Space Station. As you surely can imagine, a single astronaut cannot swing the ISS about its tail.

It does not matter that the weight of the ISS is the equivalent of 0 while in orbit, with a mass of 419,455 kg / 924,740 lb, the astronaut cannot swing it about.

The reason is simple: $Acceleration = \frac{Force}{Mass}$

You arms can only output so much force. And so as the mass increases, the acceleration decreases. Which means that even though you work yourself blue in the face tugging at your superheavy sword, you will not be able to put any great speed into it.

Now granted a sword that has little weight would be a boon, because you do not fatigue yourself lugging it about, or holding it level. That would be quite nice. But the force with which you swing it about and impact stuff will not be greatly affected by this.

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    $\begingroup$ I believe @WestsideTony recognizes this, which is why "...but you have super strength..." is part of the statement. The assumption is that you do have the strength to swing the ISS... but what's that going to do when you swing it? Will you accidentally fly across town with every swing? I imagine stopping the sword, for a super-strong person, will be a much more difficult problem than starting the sword. $\endgroup$ – Azuaron Aug 15 '16 at 14:26
  • $\begingroup$ If my math is right the test 1 sword is like an aluminum one but harder no big deal, then in the example 4 you the equivalent mass of 1.7 tons and super strength so you can swing it PD: since in the space there are almost no friction any force applied to the ISS has nothing but inertia to oppose so it may take a year but in theory eventually the astronaut will move it $\endgroup$ – Westside Tony Aug 15 '16 at 14:30
  • $\begingroup$ @WestsideTony And in that year his opponent in the duel will have chopped him up into tiny little bits, watched them decay, gotten bored and gone home to celebrate his victory. $\endgroup$ – MichaelK Aug 15 '16 at 14:37
  • $\begingroup$ @MichaelKarnerfors XD sure thing $\endgroup$ – Westside Tony Aug 15 '16 at 14:41
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    $\begingroup$ @WestsideTony That was no joke. While the mass increases the impact when you finally get the sword up to speed and do hit, this is of little use if the sword has so much mass you cannot track the opponent. $\endgroup$ – MichaelK Aug 15 '16 at 15:08
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So, you've neutralized the vertical component but the mass is unaffected. Conservation of momentum means what force you apply generates an equal momentum in the opposite direction. You might lift the sword but swinging it isn't going to be possible, because YOU are lighter than the sword.

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