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  1. Sure I will! But here is a question for you, engineer. Would not the swords (similar quality swords) produce resonance if clashed together, ie they are high grade metals (as such sonoric) with enhanced sonoric output due to achieving resonant frequency, ie the fundamental frequency of swords in this case? And in the case of the guy who is capabel of cladding the outside of his arm with a superhard substance, he blocks her attack such that she almost falls down from the direct impact (as such the sonoric output should be lower I imagine as the impact is more elastic than inelastic compared to clashing of the the swords, as such producing less vibratio of the air). She also imbues her sword with this substance in the clash, but the guy is simply far too capable of this and his arm is simply way harder, and he himself is physically stronger by far here. The wave speed is a function of metal stiffness and spring caracteristics. Spring steel is used for tuning forks for instance. When she strikes his arm, the sound output is actually higher (three exclamation points compared to two) in spite of the impact being such that it shouldn't lend itself well to sound production. As such, the loudness or sonority in this case is more due to the stiffness of the substance he clads his arm with which should be >>> Zoro's sword. Is that something you can dig it or is it a wrong way to look at it from a physics point of view (I see you like physics ;))?
  2. Anyone has any idea? The coating is harder than the swords, but it is only coated superficially, and it only envelops the hand and forearm. The density and the the elastic modulus is higher for the coating comapred to the swords, but there is no real resonance being formed here as the coated arm essentially stops her short. The metals cling so loud they're essentially clashing equally here, with their resonance building on one another, as in it forms a overtone or second harmonic (if that a correct way of describing it?). The difference with the coating here is that it's level of toughness and hardness is much higher. I'm not quite sure how this all effects the pitch and the frequency output
  3. Yes he tries to comply with the laws of physics and science, and for the purposes of this thread I want you to work under that assumption. If so, how would you judge the situation?
  4. Hi! I wonder if you guys could help me with applying some basic knowledge of accoustics to analyze these two situations. vs vs this is what happens in the very next chapter (meaning that the author I think wants to portray a difference in power between these two, but by how much is the question...? (And btw in japanese you read from right to left (if you were a bit confused by that) So we have a situation where two swords are clashing (two blades of extremely fine quality that are by far sturdier and tougher than regular swords), and in the other situation she is using the same blade to attack Vergo who is merely blocking and using a hard coating on the outside of his arm (as in just the outside of his arm is coated, not his entire arm) to defend against the strike. The sound from respective clashes are the same basically (and disregarding the difference in the size of the rooms they''re in, here I think the author focuses in on the sounds of the clashes themselves and not the acoustics of the room; as in the acoustics produced as a result of the material properties of the sword, Vergo's defensive coating, and the relative forces applied) SItuation 1: Zoro uses a lot of force (with one arm) but doesn't go all-out, and Tashigi just blocks rather casually in my opinion (she has no will to fight, as per his own statement). Sitution 2: Tashigi goes all out (in order to defend her subordinates that are being slaughtered by Vergo) and as such uses all her force, and Vergo just casually blocks by applying the coating, but also because he is just that much stronger physically he doesn't budge at all. The fact that the accoustics here are close to being very similar is very interesting, and certainly a hint from the author about how powerful they are in relation to one another (as these two instances are one chapter apart). But I'm just really unsure of how to judge this situatin from a purely accoustic point of view. Vergo's arm is thicker than the sword, but the coating is only applied on the outside, so that leaves me a ibt confused as to how that affects the sound output. Should use this formula for frequency (the same used to calculate the frequency of tuning forks) The answer relates to the difference in elastic modulus and the density between Vergo's coating and Zoro's sword, but I'm wandering in the dark here. How would you using your knowledge of how sound and accoustics work (and given the parameters I jsut described) evaluate this situation if your life depended on it? Appreciate any input here!
  5. Btw this is an island in the middle of the ocean somewhere, so the stone is limestone most probably (just humour me here). So as such, it is more malleabe in fact. It's not as hard as other stones (ie easy to carve) so let's for the sake of argument say he uses soft and relatively malleable limestone for his flexors and tensors to move around, while having a harder stone exterior...?
  6. Just help me out in a purely hypothetical, how do we measure the cutting force? Like when he cuts the golem like this vertically (lets start with that) Do I have to take the shear modulus of stone into account here? It's not so easy so as to just say depth * length of the cut times the shear modulus (or shear strength) as the stone actually behaves differently once you've breached the shear strength, due to it being a crystalline material, when Zoro here applies an air projectile, when he breaches the shear strength of the stone, the cracks finds its way through the structure (same way a heated stone that rapidly cools down easily ruptures being that the cracks finds the "easiest way" through the crystals that the stone is composed of) and the stone gets significantly weakened by this. (same way the old guy can crack a stone in two with the chisel and how this is done in construction and stuff all the time with bigger boulders). @Ghideonyeah Pica somehow makes the stone more malleable and ductile as a softer core underneath to allow for his Golem to move, and supposing as Pica actually controls stone, that he can assimilate stone that is deeper underneath the crust where it's more pliable and ductile, he can assimilat this and make this as his flexors and tensors underneath the hard exsterior stone surface. That's just a suggestion (I'm sure Oda has some exemplary explanation for this lol and I'll get back to you when he does) But regardless of all of that, how would you calculate the cutting force? What way would you go about it supposing this was a real world scenario? I'm pretty much learning this stuff on the fly btw bc of "sheer" interest and I'm finding it to be veery interesting! Anyway, the shear modulus is usually something like 1/3 of the young's modulus, and the young's modulus is the thing we use to measure linear and normal forces (the act of cutting is a shear force). I don't know how exactly how much weaker a stone would get after you breach the shear stress of the stone, but from judging by several videos, such as this, my idea is that stone is jsut inherently weak to cuts.
  7. Yes, I understand that stone is brittle. The golem is actually a normal guy that has gained the ability to absorb, merge and assimilate with as well as control stone. If you can grant that premise, is there any way in which you can have a softer, more flexible core that allows for increased mobility (the stone golem does move increeedibly slow btw) but a harder core of stone (kind of like case hardened steel) jsut by altering its physical and chemical structure jsut a little bit, kind of how like you can make metallic glass that is flexible yet three times as strong as steel? I'm just spitting ideas here What's important to keep in mind is that this is a series that has been going on for 23 years, now and One Piece is the biggest manga in the world as of now the biggest selling manga in the world. This friday chapter 984 is out! Echiro Oda (the creator) has surely given this way more thought than you'd care to know, and I'm sure he has outside help to counsel him on areas where the science can get sketchy. Just so you know, this guy (Pica) who possess this abiltiy to assimialte with and control stone, the information on him is surprisingly scant, meaning that Oda probably wants to keep the mechanisms of this stone-controlling ability a secret until he divulges it at the proper moment (there are still a lot of unknowns in the story) Also, call it "magical" sword if you like, but just because you have a concept that is not really conceivable in our world (such as applying hardness to your body or weapon by channeling and applying the equivalence of tchi, ie it's called "haki" in One Piece) does not mean that every scientific law and principle are all topsy turvy. Just because you have this element in the story, does that not mean that the author just doesn't give a shit about how science work? For instance, it is known in science fiction and other similar genres that most lasers in fiction are not real or provable as real. Often they are supernatural in nature and do not function anywhere close to how real light should. Therefore, lasers/light beams are only accepted as real if they meet, at a minimum, a few of these criteria: The beam refracts in a new material, such as a liquid or... The beam reflects off a material that it can be expected to, such as a non-magical mirror The beam is called lightspeed by reliable sources It is stated to be made of photons or light itself, again by a reliable source It has its origin at a realistic source of light, such as a camera Furthermore, there are a few criteria which show a beam is NOT real light: It is shown at different speeds in the same material It is tangible and can be interacted with physically by normal humans They do not travel in straight lines (unless you can prove refraction/reflection) In several science fiction - The Lazers were never said to move at light speed - True light can be reflected. - They create explosions thus interacting with people. Here are examples of sonic booms and I don't know what you're getting at. Doesn't the manga author display the sonic boombs such as this and why is it so different? Zoro is durable enough to withstand it apparently (though I'm actually curious as to how the heating effects build up differently to the titanium or other metal that has higher thermal conductivity)
  8. Thanks for the detailed answer! But you're approaching this as if this is a world of magic where the author throws scientific laws to the wind and is all willy nilly with science - and that's not at all what this series is about! At the clip I will show below for reference, the guy being hit is made out of smoke (you need to imbue your weapon with a special coating in order to be able to hit him which is what the balck stuff is) but just because there are these elements in the story doesn't mean that he bends the overall laws of science.This is a series where powerscaling (the activity of assigning power levels to characters based on their showings) is a BIG THING! This wouldn't be possible or consisent if the author was inconsistent and messy with the science. I am working under the assumption that the author has insight into and is trying to follow physics as best he can, as he is trying to create a consistent and coherent world, and here the laws of physics aren't different from ours: it's just that the parameters are diferent. Such as (1) people in this verse are stronger and more durable, and as such Zoro (at the hgher echelon of superhumans trength) here is durable enough to withstand the heating effects of the air (that would result from what can be seen from the trail of sonic booms as supersonic flight. and (2) the guy throwing him is physically strong enough to launch him at such a speed that he has (despite not being perfectly streamlined like an airfoil) he is actually flying at such a high speed that the lift is generated is enough to counter gravity; and of course Zoro's speed is slowed down, it's just that his launch speed is incredibly high (see again the manga panels I posted when he is thrown vs when he is flying in the air; see the difference in the inital speed vs the speed when he is approaching the Golem) (btw this Golem is about 200m from the waist up where he cuts, so maybe it would be something like on the order of 1 megaton in weight (stone weighs 1,6 tons per m^3, and you imagine compressing his upper body down to a cylinder, I'd say it comes down to maybe 1 or at msot 2 megatons in weight) Thing is, this feat of cutting the golem and lifting it like that, people are saying that this is purely due to his own strength; but I'm trying to say here is that (1) Him being thrown with that momentum and (2) there wasn't a huge drag right in front of him because of the Bernouilli's principle which actually reduces the air pressure right above him There is also the fact that stone is very easy to cut through in fact. Just like this old man is showing us here, if you hammer down on the chisel along a ridge and the stone form cracks that will eventually break the stone in two. This just goes to show that stone can be easily sliced through with enough power, but to actually break through stone with blunt force takes unproportionally more force. The shear strength is closely related to the tensile force, and here is a good example why stone is easier to cut through (compressive force is much higher than the tensile force, and as shown in the video below, that once the cracks forms the material gets significantly weakened) https://www.engineeringtoolbox.com/compression-tension-strength-d_1352.html Again, you have people want to blow this stone cutting feat out of proportion. With the objections I raised (and therefore I want to check with you guys how you think my arguments make sense) I don't think his stone cutting feat is that much greater (or greater at all) than this feat shown below. Here the guy has no momentum (unlike Zoro) and just swings around his weapon with one arm, and that creates a shockwave powerful enough to dent a wall made of what could be highly reinforced concrete (some extremely tough material against compression at any rate being that this is a facility that houses radioactive material; and actually the engineering in this world is very much simialr to our own; this is a world government facility and they have technology that is far higher than the civilian world) and he just follows through with the swing casually. He is mortally wounded by the way in this scene, so his actual strength output would be signficantly higher if he was at full health. See how he has put a lot of effort into damaging his opponent, so when he follows through with his swing (with just one arm) he has no momentum or torque, so this all comes to pure arm strength. Again, Zoro slashing through stone is very easy (as shown in the clip) but this is applying compressive force against a material that is extremely tough against compression)
  9. When he cuts the stone golem, can I say he is applying a shear force (it has no counteracting force as in support from a wall or anything like that) so am I correct in saying it is a shearing force that would be proportional to the speed of the deformation (ie as in Hooke's law)? The act of him cutting the Golem is a shearing force at any rate?

  10. Because it's a question that is science related The clip is the anime, I can post the manga itself (should've done that instead) Here in the actual manga he does not make backflips in the air nor does he spin around his blades like that (I suppose that's the laws of Newtons you referred to as being broken). Disregarding the fact that the guy can turn into a golem (and Zoro possessing superhuman durability to withstand the heating effects of the air), how would you view the cutting feat from the perspective of drag and Bernouilli's principle? Would there be a reduction in the air pressure because of the speed of the streamflow that is created when he is flung at that immense speed (and would the imparted momentum help in the cutting, or, as others posit, just result in drag force that he would need to act against in order to cut the golem)? Would you say the cutting here can be defined as a shear force or how would you characterise the force applied? Can I say the force applied = area of the cut times the shear strength of stone? Is this a shearing force (there is no counter force in the opposite direction so I'm not sure what to call this force) Source https://www.physicsforums.com/threads/shearing-force-cutting-force.783346/ Source https://www.physicsforums.com/threads/shearing-force-cutting-force.783346/
  11. This clip right before he cuts the stone golem, would you say he is experiencing more drag or does he in fact experience less drag where he applies his cut because of the Bernouilli's Principle? "A wing provides aerodynamic lift through the camber (curvature) of its surfaces. Because the upper surface is more highly cambered than the lower surface, the air moving over the top surface is forced to move more quickly. This results in a lower pressure on the upper surface as compared with the lower surface and results in aerodynamic lift (Bernoulli's Principle)". The claim among some of his fans is that he acted against drag and as such had no help when he was launched (see how he is thrown). I don't exactly how how legit this argument from mine is, but I said that there is going to be a boundary layer where the air pressure is much lower, as there is a streamflow that is created from Zoro's fast flight which would in theory result in lower pressures above him, and because he was thrown he had extra momentum on top of lower air pressure where he cuts it. In the clip you see at 1:52 sonic booms following in his track, and in the manga (which is the primary canon) you see the sonic booms really clearly so how fast would you say in Mach is he travelling here? How would you judge this feat from a physics standpoint? Did his being thrown and the Bernouillis principle aid in cutting the stone golem, or was it a hindrance due to drag build up? Grateful for any input!
  12. Hehe yeah, as long as they take some liberties with the science in instances where you want to create more suspenseful moments, as with the battle at the Death Star how fun would it be if the laser never sounded But here I want to seriously debunk the notion that Zoro is so much more impressive as I don't think he is.Here if we compare the compressive vs tensile strength of materials, one can see how much more force it takes to crush or dent stone vs actually cutting it. Am I right? https://www.engineeringtoolbox.com/compression-tension-strength-d_1352.html Vergo unleashes an attack wherein all the torque and momentum is exerted onto damagin Smoker, and the result of him just following though his swing, that is enough to cause that amount of damage; Vergo has taken a counter shock and many hits before this, meaning he is extremely bad off at this point, again, perhaps even mortally wounded. Mortally wounded Vergo dents a wall of reinforced conrete with his shockwave that's just a result of him following through with his swing vs Zoro cutting through 200m stone golem with his air slash. You ask majority of people Zoro is the better, but I think they're seriosly underestimating Vergo. I'm not sure mysekf which is why I'm asking for outside opinions
  13. No lol, this is not a homework I am a fan of this manga and I'm genuinely curious who is stronger of the two. I want some outside opinion on this Sorry, I don't get what you're trying to say. Are you talking about shockwaves here? (I'm not familiar with those terminologies)
  14. Hello everyone! This is my first post about something that I can't really make heads or tails about and I would really appreciate any input or thoughts from you people! It concerns a manga called One Piece in which you have a lot of different characters with varying qualitites, and a big thing is to try to assign these individuals correct strength levels based on their showings. There are different variables that go into this, but in this case the question is solely in terms of their respective power outputs with their respective attacks with two different modes of action in this case: one is a guy named Vergo who uses a bamboo stick and uses blunt force (guess I cal call it concussive force for the purposes of this thread) to strike down his enemies, and the attack in question sends out a powerful shockwave; Zoro uses cutting (shearing force) with his swords, and the attack in question sends out a powerful air slash. I am of the opinion that Vergo is the better of the two whereas the wide majority think Zoro has a better showing. I will try to explain all the factors and circumstances that go into this as best I can for you to get a better grasp of the situation to assess their different power levels. All this is provided that the author himself has a good idea of who of these two are the strongest and have done a rough estimate/calculation and all that's left for us is to come to a correct conclusion based on what we've seen. Demon Bamboo, Vergo vs Pirate Hunter Roronoa Zoro Fast forward to 2:44. Here Vergo with his bamboo stick breaks through his opponent's, Smoker, defence, destroys his weapon and crashes into his body, and just by swinging through with his bamboo, sort of the after effect of the attack itself, that carries enough force to dent a thick wall of what I would presume to be very high grade steel or reinforced concrete (in this world the engineering is very much similar to our own and this is a facility that houses radioactive material, hence why the walls would be built of such a high quality material; feel free to come with any ideas). The weapon of Smoker is hardened with the black stuff (same as Vergo's bamboo) by something called haki. Armament haki is a physical manifestation of one's willpower that one can use to harden one's own body or weapon. Smoker's weapon (a jitte) I would venture to say is as hard as very hardened steel, while Vergo who was described as having much better armament haki would have a much harder weapon than Smoker. Now for you to better understand the context, here you might wonder why Smoker is, well, smoke? Smoker has a special ability called logia (which I'm sure some of you know is greek for element) which allows the user to completely alter their form into a natural element and manipulate it at will: the element being smoke in this case. As such he is intangible for the average Joe and they can try punch and throw stuff at him, but will just pass right thorugh him. That is to say that he is a normal human with muscles and all, with the only exception that he can turn into smoke (and back) at will. However, this is all irrelevant as the application of armament haki nullifies all intangibility of logia users (hence why Vergo can hit him and in the end destroy him). Now how durable is Smoker to begin with? We actually don't have a baseline for saying how physically durable this guy is really as outside of this battle, so here I am making as an assumption: that Smoker (based on his rank and overall portrayal - we'll roll with this one) is about 10-20% as durable as the fishman Hody Jones (a hybrid of whiteshark and human) takes a lot of beatings from this guy that destroys the midsection of this ship, Noah (yes as you can tell by now the authour likes throwing in biblical and other religious references). This is a ship that has been resting on the ocean floor 10,000m below sea level for over 800 years, having been able to fully withstands the 1000 atmospheric pressure of those depths (the wood here is a special kind of wood called Adam's woods, again a little biblical reference there) that is extremely hard and tough material, a vaunted material in the world of shipbuilding. The reason why Luffy, the protaginist here, is alive is because the ship is enveloped in a special kind of bubble that is able to withstand the outside water pressure, and as the bubble has been oxygenated they both can breath (as a fishman he can breath underwater, naturally, as well). Also, the protagonist is made of rubber, as such when you see him attack he uses the elasticity of the rubber as the means of attack, using Hooke's law and the springback effect to cause damage. Fast forward to 2:20 where the attack begins Hody Jones takes an insane amount of beating here (actually you see him floating out of the bubble but in the manga this does not happen in the manga, meaning that he was just lying in the rubble of this destruction and taking all this insane beating - and he could actually cling to his conscious some odd 30min later or so later). See here how much damage it has done to the ship on this panel here Hody Jones remains conscious yet heavily damaged after this. Now, working under the assumption that Smoker is about 10-20% as durable as Hody Jones, here Smoker's entire defence gets taken out by one blow and he is left squirming on the floor from Vergo's attack Now an extremely important factor in all of this is this attack that precedes Vergo's fight with Smoker is this attack that Vergo tanks with his own durability Now I'm sure you probably know what a counter shock is, ie the same thing as defibrillation, Medical Definition of countershock. : a therapeutic shock of electricity applied to a heart for the purpose of altering a disturbed rhythm (as in chronic atrial fibrillation) delivering a life-saving countershock within seconds of an arrhythmic episode Now we know that extremely low currents can kill, and right about 12 miliamperes does you in if it goes through your heart which can induce a cardiac arrest. Law here can control his output of current in an extremely controlled manner with a clear intent to kill. This is a lethal dose of electicity applied to the heart (supposedly) yet Vergo doesn't die from this lol The extremely impressive thing here is that we see an electrical arc being created; meaning that this attack is so high in electrical potential it actually ionises the air around Vergo and creates an arc blast, as in it causes the air to become conductive due to the strong electrical field he produces (same principle used for things such as plasma torch welding). The heat output of that thing is several thousands of degrees, but that's not the impressvie thing but the amount of current that is delivered into him. This is an insane feat to survive and I can guarantee few if any people should be able to survive from this, even by the standards of the One Piece world where you have a lot of strong people. As such Vergo was one could argue mortally wounded from this attack and still kept going (he is a monster!) so his power and stamina was severely drained when performing that attack. So now that you have everything you need to know to judge Vergo's feat, let's compare it to Zoro: It is this clip I want you to look at Here Zoro gets thrown and as such has imparted onto him incredible amounts of force needed to cut through this golem that is entirely made up of stone, as at 1:52 you can see there are sonic booms following in his trails, so he is going waay past the speed of sound here, such that with this momentum he actually lifts the golem from its waist (the golem is not symmetrically built, but it has been estiamted to be around 200m from the waist up where he cuts). But I don't think that's a fair comparison as Zoro actually gets help here, and you might also add (don't know if this is a valid argument from a physics standpoint) that owing to his immense speed and the bernoulli's principle, the air resistance actually gets lowered above him such that he can better perform his cut. At any rate, he gets help here and Vergo had no momentum when he performed his attack. I'd really want to know your thoughts on this feat! As such this is a better and the real comparison I wanted to make. Fast forward to 1:00 where he proceeds with attacking the Golem and here he makes a vertical cut that slices the Golem in two. This is by dint of his own strength with no help from outsiders, and here he sends out a powerful air slash that slices he 200m of rock in two! So there we have it: A Vergo that is heavily wounded (let's say even mortally wounded) creates a powerful shockwave just from the after effect of his attack (the bulk of the force has been transferred and imparted onto damaging Smoker, where the denting is due to him just swinging through with the bamboo rather casually) that is strong enough to buckle and dent a thick layer of high-grade reinforced concrete https://makeagif.com/gif/vice-admiral-smoker-vs-vergo-final-one-piece-hd-67-ql4GJJ vs A fully healthy Zoro who with his vertical air slash cuts through 200m of thick stone https://gfycat.com/likablelavishblackwidowspider In terms of pure strength output, I'd say Vergo with his full attack smashes through Zoro, but the majority of the fandom says Zoro busts through Vergo. I'm apparently in a clear minority, so I just wanted to see how people with no bias and merely objectively looking at this situation judge their respective feats all things considered. Would Vergo be able to match Zoro or does he in fact do better? Appreciate all and any effort as this is a question I'm rally stuck on Thanks! 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