Eren Posted October 13, 2017 Posted October 13, 2017 Hey everyone, I have a question that what is the pressure of perfect circle? I think we can think this in 2 ways; Physical properties and mathematical. If we look this in pysician view we should think about atoms, and the electron cloud. If we assume the circle is super solid that wont break we can think its on a electron cloud and its pressure should equal mass/diameter of electron. But we know that electron is fundamental and has no volume, so will it be infinite or mass/Planck's length? And if we look this in mathematician way thats virtual and doesn't contain atoms or any smaller particles we can guess Its interact point is the smallest measurement of all time. If we zoom in the interact point will become smaller and smaller. So is it infinite on mathematical way? I know a perfect circle is impossible on reality, but just imagine.
studiot Posted October 13, 2017 Posted October 13, 2017 (edited) 1 hour ago, Eren said: Hey everyone, I have a question that what is the pressure of perfect circle? I think we can think this in 2 ways; Physical properties and mathematical. If we look this in pysician view we should think about atoms, and the electron cloud. If we assume the circle is super solid that wont break we can think its on a electron cloud and its pressure should equal mass/diameter of electron. But we know that electron is fundamental and has no volume, so will it be infinite or mass/Planck's length? And if we look this in mathematician way thats virtual and doesn't contain atoms or any smaller particles we can guess Its interact point is the smallest measurement of all time. If we zoom in the interact point will become smaller and smaller. So is it infinite on mathematical way? I know a perfect circle is impossible on reality, but just imagine. Hello Eren, I don't want to get the wrong idea about what you are saying but I am puzzled as to why you have asked the question what is the pressue of and then answered yourself by saying that it is a mass? or a length? or a mass divided by a length? The dimensions of pressure are ML-1T-2, which means that you are missing the time component Can you explain further? Edited October 13, 2017 by studiot 1
Eren Posted October 21, 2017 Author Posted October 21, 2017 On 13.10.2017 at 10:32 PM, studiot said: Hello Eren, I don't want to get the wrong idea about what you are saying but I am puzzled as to why you have asked the question what is the pressue of and then answered yourself by saying that it is a mass? or a length? or a mass divided by a length? The dimensions of pressure are ML-1T-2, which means that you are missing the time component Can you explain further? Sir, imagine a perfect circle that is 1kg. Circle has same length from middle to its perimeter. Thats a perfect cricle. Then we put it on a hard surface that cant bend. We know pressure is mass/area of contact. It has 1 kg so it defines on its contact area. Does it 0, or should we think like it cant be smaller than planck lenght?
John Cuthber Posted October 21, 2017 Posted October 21, 2017 You need to distinguish between mass and weight. On the moon, you weigh less, but your mass is the same.
studiot Posted October 21, 2017 Posted October 21, 2017 (edited) 1 hour ago, Eren said: Sir, imagine a perfect circle that is 1kg. Circle has same length from middle to its perimeter. Thats a perfect cricle. Then we put it on a hard surface that cant bend. We know pressure is mass/area of contact. It has 1 kg so it defines on its contact area. Does it 0, or should we think like it cant be smaller than planck lenght? Edit Very Important The following is correct for 1kg sized objects, but it does not apply to electron sized objects. It sounds like you are asing about what we call 'Contact Mechanics' in Materials Science and related sciences. There are Elastic formula to this problem for the stress distribution in. The original developer of these stresses was Hertz, https://www.google.co.uk/search?q=hertzian+stress&ie=utf-8&oe=utf-8&client=firefox-b&gfe_rd=cr&dcr=0&ei=FTbrWeXhAc7A8geP6JrgDg although Coulomb previously offered solutions in Geology, Soil Mechanics and foundation engineering. https://www.google.co.uk/search?client=firefox-b&dcr=0&q=Coulomb+stress&oq=Coulomb+stress&gs_l=psy-ab.3..0i7i30k1l5j0l2j0i30k1l3.102840.105177.0.105721.7.7.0.0.0.0.124.756.2j5.7.0....0...1.1.64.psy-ab..0.7.749...0i7i10i30k1.0.DzRQlnNYh8c Development of this subject can be found in books on advanced elasticity, strength of materials, or mechnicas of materials. Most of these formula can be found in Roark: Formulae for stress and strain. https://www.google.co.uk/search?client=firefox-b&dcr=0&q=roark's+formulas+for+stress+and+strain&oq=Roark&gs_l=psy-ab.1.0.0i67k1l2j0l8.181493.182626.0.184564.5.5.0.0.0.0.123.567.1j4.5.0....0...1.1.64.psy-ab..0.5.560...46j0i131k1j0i46k1.0.dBx-cyoCbEU The subject also provides elastic solutions to the problems of contact area and max/min stresses and their location. https://www.google.co.uk/search?client=firefox-b&dcr=0&q=Fracture+Mechanics&oq=Fracture+Mechanics&gs_l=psy-ab.3..0l10.118752.122435.0.124577.18.18.0.0.0.0.173.2333.0j18.18.0....0...1.1.64.psy-ab..0.18.2322...0i131k1j0i67k1.0.DQugxEgc3v4 Here is the relevant page from Roark Modern treatments also include non elastic solutions from the subject of Fracture Mechanics. https://www.google.co.uk/search?client=firefox-b&dcr=0&q=Fracture+Mechanics&oq=Fracture+Mechanics&gs_l=psy-ab.3..0l10.118752.122435.0.124577.18.18.0.0.0.0.173.2333.0j18.18.0....0...1.1.64.psy-ab..0.18.2322...0i131k1j0i67k1.0.DQugxEgc3v4 Edited October 21, 2017 by studiot 1
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