Physics conundrums
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Electric Sheep One
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written Tuesday, October 10 2006 22:18
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Non-physics conundrum: Could the plural really be 'conundra'? That sounds almost too good to be true. Anyway, here are some questions that I have asked a lot of physicists over the years, and mostly stumped them. I think I understand them myself to varying degrees, but few well enough to make me really happy. They're nothing very advanced, but they have a common feature that I think is really profound. 1) How do airplanes really fly? The answer must be in terms of molecules bouncing off the wings, and not in terms of hydrodynamics! Lots of people know some pat answer about Bernoulli's principle. That's not what I want. 2) What keeps clouds up? They're made of water droplets, not vapor, and water is heavier than air. So why don't clouds all fall? Actually, for a start I'd be happy for a hydrodynamic answer to this one. But ultimately I want a molecular story here, too. 3) Why does a tilted spinning top precess instead of falling over? Your answer must be entirely in terms of force and acceleration; you must not invoke angular momentum. In classical mechanics, angular momentum and all its properties are not fundamental, but derived; so everything must follow from Newton's Laws alone. 4) Related to 3), and a bit easier: Derive the 'law of balance' for the equilibrium of a lever, M1 L1 = M2 L2, in terms of force alone, without invoking torque or angular momentum. 5) The rule for a 'Newton's Cradle' is the number of balls swinging in is the number that bounce out. Explain why this is, after realizing that conservation of energy and momentum only works for the case of two balls. With as few as three balls, the conservation laws also allow additional solutions, which one does not see in reality. If anyone knows any further questions in this spirit, I'd be very happy to add them to my list. -------------------- We're not doing cool. We're doing pretty. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
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Shaper
Member # 7420
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written Tuesday, October 10 2006 22:33
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Do you want people to just throw up links that they googled? Because I could do that. Or are there actually physics experts on this board that can answer these? Edit: It's conundrums, I didn't have to google that. [ Tuesday, October 10, 2006 22:34: Message edited by: Emperor Tullegolar ] -------------------- You lose. Posts: 2156 | Registered: Thursday, August 24 2006 07:00 |
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...b10010b...
Member # 869
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written Wednesday, October 11 2006 00:05
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The original poster is a physics expert, and he's not the only one on these forums. Unfortunately, I'm not one of them. I know enough to understand why the questions are interesting, but not enough to answer them. [ Wednesday, October 11, 2006 00:07: Message edited by: Thuryl ] -------------------- The Empire Always Loses: This Time For Sure! Posts: 9973 | Registered: Saturday, March 30 2002 08:00 |
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Law Bringer
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written Wednesday, October 11 2006 01:05
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Interesting. I also thought I knew enough to explain at least a few of these, but a few sentences in I realized that I was partly repeating stuff I read but didn't understand, and partly making it up a la "instant expert". So I stopped to avoid making a fool of myself. Of course airplanes fly because the air pressure above their wings is lower than below. Of course this is because air that is in faster movement has a lower pressure. But why is that? -------------------- Encyclopaedia Ermariana • Forum Archives • Forum Statistics • RSS [Topic / Forum] My Blog • Polaris • I eat novels for breakfast. Polaris is dead, long live Polaris. Look on my works, ye mighty, and despair. Posts: 8752 | Registered: Wednesday, May 14 2003 07:00 |
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Infiltrator
Member # 1092
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written Wednesday, October 11 2006 04:35
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With number two, when it starts raining, thats when the clouds fall. -------------------- When you think you can't get any lower in life and hit rock bottom, God hands you a shovel. Why should I say somthin intelligent when idiots like you make me look intelligent in the first place. Posts: 615 | Registered: Friday, May 3 2002 07:00 |
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...b10010b...
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written Wednesday, October 11 2006 05:39
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quote::rolleyes: All you've done is change the question to "why doesn't it rain all the time instead of just some of the time". -------------------- The Empire Always Loses: This Time For Sure! Posts: 9973 | Registered: Saturday, March 30 2002 08:00 |
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Off With Their Heads
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written Wednesday, October 11 2006 06:01
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quote:This now bugs the heck out of me. I looked this up, and apparently "conundrum" was a word that was invented to sound like Latin (hence an old alternative spelling, "quonundrum"), and the original meaning and usage is now entirely unknown. No writer cited in the OED ever pluralized it as "conundra," though, since it wasn't ever Latin to begin with. My best guess is that it was a play on "unde," which means "whence," or in real English, "from where," and "quo," which means a whole heck of a lot of things, including "by which," "where," "to where," "because," and "in order that." Or maybe it's some sort of play on "undecumque," which means "whencesoever" ("from wherever"), since "cum" was in some Medieval texts spelled "con" (presumably by influence from Spanish). Either way, it wasn't Latin at all, so the plural ought to be "conundrums." As for the physics, well, that's much harder. I'll check back in when I've had time to think a bit more. EDIT: Typo. [ Wednesday, October 11, 2006 20:28: Message edited by: Kelandon ] -------------------- Arancaytar: Every time you ask people to compare TM and Kel, you endanger the poor, fluffy kittens. Smoo: Get ready to face the walls! Ephesos: In conclusion, yarr. Kelandon's Pink and Pretty Page!!: the authorized location for all things by me The Archive of all released BoE scenarios ever Posts: 7968 | Registered: Saturday, February 28 2004 08:00 |
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Raven v. Writing Desk
Member # 261
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written Wednesday, October 11 2006 07:13
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quote:Heh. I like that pluralization! -------------------- Slarty vs. Desk • Desk vs. Slarty • Timeline of Ermarian • G4 Strategy Central Posts: 3560 | Registered: Wednesday, November 7 2001 08:00 |
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Guardian
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written Wednesday, October 11 2006 07:30
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By SoT: quote:(Resists urge to write a story about two friendly molecules separated by a cruel airplane wing, where their love for each other is so great that they rush to meet again at the other end of the wing.) -------------------- Yes, I'm bored. Posts: 1509 | Registered: Tuesday, January 10 2006 08:00 |
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Law Bringer
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written Wednesday, October 11 2006 07:48
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Trying to answer physics questions to a physicist makes me a little nervous, but why not? 1. My very rough understanding is that it's a matter of Newton's third law/conservation of momentum. Air hits the wing and is deflected downward, so the wing and the plane are deflected upward. It's a lot more complicated than that, which is why we have aeronautical engineers. I think. 2. Hot air rises and cold air sinks for reasons that I think I'll leave alone for now. Hot air rises and hits bits of water in the sky. If the force of air going up is enough to oppose gravity, you get clouds that stay more or less stationary. If there's no hot air, you get suddenly falling clouds that we call rain. 3-5. A wizard did it. —Alorael, who thinks he could probably work through Newton's cradle eventually. Ah, hubris! He'll leave it as an exercise for the reader instead, though, because it builds character. Posts: 14579 | Registered: Saturday, December 1 2001 08:00 |
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Electric Sheep One
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written Wednesday, October 11 2006 09:48
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About 1 I'm afraid I'm not really any better than Aran's and Alorael's answers. Yes, it must be that molecules hit the bottom of the wing harder than the top, and presumably this is because the plane is moving. But I'm pretty sure there's more to efficient aerodynamic lift than just being a kite. Wings have a particular shape, and this is supposed to be important. I should really sit down to think about this properly sometime. About 2, the best answer I ever got was from an army officer who immediately answered, "Suction!", and then escaped while I was still stunned. The water droplets that make up clouds are very small, and have a very low terminal velocity, so they don't fall very fast. Updrafts and downdrafts are probably a bigger factor in the vertical motion of clouds than gravity. This is hand-waving, though. I believe the comparatively enormous amounts of energy involved in water condensation and evaporation can have huge effects on air temperature and pressure, so the hydrodynamics of clouds is formidable. Someday I'll get time to read a proper atmospheric physics text, and become happy. 4 and 5 I actually believe I understand, and I have some idea what the answer to 3 should look like. All of these are questions that many people do understand, of course; but they are a small minority even among physicists. The central issue in all of them is the role of what is called an effective theory. The fundamental theory is known -- in these cases, Newtonian mechanics -- but explaining things in these terms can be long and involved, like writing a program in machine language. From it people have derived higher level theories, which are powerful in the sense that they compress long explanations into short ones. The problem is that some kind of information is always lost in going to the higher level explanation. Richard Feynman pointed out long ago that the ultimate higher level explanation is simply the equation "U=0", where U is the "unreality". This is very compact, but it's obviously a lousy explanation. Just what's lousy about it, though, is sort of hard to state clearly. What I want to say is that it conveys no understanding, but since I can't explain what understanding is, this is really not much better than just calling it lousy. An objective measure of what gets lost with effective theories, though, is simply that hardly any physicists can explain why a spinning top precesses, without using the words 'angular momentum'. Yet all trained physicists know that angular momentum is a derived quantity in classical mechanics, so that any statements about angular momentum and torque are in principle reducible to statements about linear momentum and force. They just can't actually perform the reduction, though they should be able to and know they should be able to, in the practical case of a spinning top. This seems to me to be an interesting case study for the philosophy of science. -------------------- We're not doing cool. We're doing pretty. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
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Law Bringer
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written Wednesday, October 11 2006 10:28
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I think that's more or less the key to 2. There's a lot of air and not that much water. As long as the air is not really having any net change in location, the water will just be bashed around in place. Suction might be the answer to why we have cohesive clouds and not just hazes of water in the sky, but that also might have more complicated answers involving atomspheric science and heat transfer. If it's philosophy of science you're after, try Bruno Latour. He makes a solid argument for scientific ready-made widgets. Angular momentum isn't fundamental, but it's as close to true as one needs to get with physics. Physicists therefore take it as a tool and don't bother tinkering with it because it's been done for them already. Understanding mechanics through angular momentum and torque is no less valid even if it's difficult to tie it back into fundamental principles as long as it necessarily can be so tied. —Alorael, who thinks that lift is exactly like kites, except that aeronautical engineers have to make the most efficient kites possible. He'd go into more detail about the guts of super-kites if he were an aeronautical engineer, but he's no rocket scientist. Posts: 14579 | Registered: Saturday, December 1 2001 08:00 |
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Electric Sheep One
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written Wednesday, October 11 2006 10:53
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Was Latour by any chance a biologist by training? A lot of philosophers of science were trained as scientists at some point, but it's the blind men and the elephant. Anyway, I'm a theoretical physicist. A widget that's a black box isn't a tool, to me; it's a problem, no matter how well it works. Perhaps at some level everyone just accepts things; for instance, I use integrals all the time, but I have no idea what a Lebesgue measure is. At least I know Riemann's theory of integration, though. When I figured out how levers really work, in terms of stress and strain tensors in finitely rigid rods; or when I figured out that a Newton's cradle is always a sequence of two-body collisions, because of the finite speed of sound in steel; I had a very satisfying feeling of, Aha! So that's what's going on! Physics at least is pretty much entirely about reductionism. Finding a black box widget that reproduces what happens is only the very first step. -------------------- We're not doing cool. We're doing pretty. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
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Infiltrator
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written Wednesday, October 11 2006 11:03
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1) How do airplanes really fly? The answer must be in terms of molecules bouncing off the wings, and not in terms of hydrodynamics! Lots of people know some pat answer about Bernoulli's principle. That's not what I want. Do you want an answer in terms of equations or an explanation of principles? Also, part of the answer is explained with reference to fluid dynamics (pressure and velocity) and cannot be ignored - particles react to the wings shape and move in specific direction without coming into physical contact with the wing. Part of the answer relates to particles impacting on the lower surface and being redirected downward. -------------------- "Dikiyoba ... is demon ... drives people mad and ... do all sorts of strange things." "You Spiderwebbians are mad, mad, mad as March hares." Posts: 687 | Registered: Wednesday, January 19 2005 08:00 |
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Electric Sheep One
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written Wednesday, October 11 2006 11:14
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Gas temperature is just local average of molecular kinetic energy; for fixed temperature, pressure is just a surrogate for density of molecules; fluid velocity is just a local average of molecular velocities. In terms of equations, I guess I'm really not going to be happy with anything higher level than the Boltzmann equation. But if you can give a conceptual explanation in terms of molecules that's really clear and convincing, that would be great. EDIT: What do you mean by particles reacting to the wing's shape without ever touching the wing? There's a sense in which this true, but that's not exactly the way I would put it, because it also sounds like something crazy. [ Wednesday, October 11, 2006 11:18: Message edited by: Student of Trinity ] -------------------- We're not doing cool. We're doing pretty. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
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Infiltrator
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written Wednesday, October 11 2006 11:16
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2) What keeps clouds up? They're made of water droplets, not vapor, and water is heavier than air. So why don't clouds all fall? Actually, for a start I'd be happy for a hydrodynamic answer to this one. But ultimately I want a molecular story here, too. This relates to bouyancy forces and gravitational forces. Gravitational forces are a function of mass while bouyancy forces are a function of volume. As a particle decreases in size its mass decreases at a faster rate than its volume. At some point the two may reach equilibrium (small dust/moisture particles), at which point the particle becomes bouyant in air. -------------------- "Dikiyoba ... is demon ... drives people mad and ... do all sorts of strange things." "You Spiderwebbians are mad, mad, mad as March hares." Posts: 687 | Registered: Wednesday, January 19 2005 08:00 |
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Electric Sheep One
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written Wednesday, October 11 2006 11:22
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Water has a pretty nearly fixed density, and for fixed density, mass is directly proportional to volume. No matter how small a water drop may be, it will not be held up against gravity by its buoancy in air. [ Wednesday, October 11, 2006 11:23: Message edited by: Student of Trinity ] -------------------- We're not doing cool. We're doing pretty. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
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Infiltrator
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written Wednesday, October 11 2006 12:47
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SoT, you are correect. Should proofread more often than just fire off an answer. The two opposing forces are gravitational force, a function of mass, and aerodynamic drag, a function of surface area. As volume increases mass increases at a faster rate than surface area, so the ratio of mass to surface area gets larger. At some point this ratio reaches a critical point and the particle is large enough for it to overcome drag (also know as air resistance). Edit: fired off in haste, contains spelling areas. Quicker to fix errors but less thinking to add comment. Edit 2: In order to have drag a particle must be in motion, in otherwords it is settling. But if the particle is small enough it settles at an extremely slow rate (can be <<10 cm/hr). And this is in an absolutely still environment in which the only two factors at work on the particle is drag and gravity. For instance, this ignores the effect of a particle passing through a rising stream of warm air, where small gas particles are impacting the water molecule and transfering kinetic energy to the particle. [ Wednesday, October 11, 2006 12:58: Message edited by: 2bit ] -------------------- "Dikiyoba ... is demon ... drives people mad and ... do all sorts of strange things." "You Spiderwebbians are mad, mad, mad as March hares." Posts: 687 | Registered: Wednesday, January 19 2005 08:00 |
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Law Bringer
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written Wednesday, October 11 2006 12:52
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[Edit: That's an interesting idea. What's the coefficient of static friction between water and air? I don't think that there's no mass-volume ratio that allows water to levitate, but it's actually quite possible.] I'd be surprised if Latour has any real scientific background. I also bastardized his point, but you didn't disagree with it. Enjoying the exercise of understanding doesn't make understanding scientifically necessary. Either way, that's not what Latour talks about. He's more concerned with sociology of science, really. In a bad nutshell, building a new theory out of old theories is perfectly acceptable and necessary, because the it's harder for people to dismantle your theory if they have to dismantle the universally accepted theories to do it. Or, more charitably, building new knowledge out of old knowledge is more scientifically reliable than inventing it whole cloth, which tends to be a mark of junk science and crackpots. Latour picks some good examples, among them the structure of DNA. There's really no need to worry about the structure of DNA anymore. It's so proven that trying to re-evaluate makes everyone think you're a lunatic. Working with that as a solid building block gives your own research a very solid foundation and makes your work harder to undermine. —Alorael, who just got into unfortunate construction metaphors/puns and still didn't explain it very well. He doesn't agree completely with Latour, particularly in some of his wilder conclusions (politicians are not scientists!), but his explanation of scientific literature seems spot-on and highly amusing. Making science deliberately full of jargon to keep the rubes out is only the beginning. [ Wednesday, October 11, 2006 12:54: Message edited by: Victim Rich Environment ] Posts: 14579 | Registered: Saturday, December 1 2001 08:00 |
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Electric Sheep One
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written Wednesday, October 11 2006 13:08
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Well, who wants rubes? I've sometimes wondered whether wikis would be a good way to do research, but there are so many crackpots out there, that I figure I'd have to put in some sort of mini-exam as a password. Kind of 'let no-one ignorant of geometry enter here', and we really mean it. About drag balancing gravity: this is what defines terminal velocity, which as I said above, is very slow for tiny drops. It would take me too much thought for tonight to calculate it, but I've watched sprayed mist fall. It's slow. So yes, I think this is why clouds don't fall. They do, but very slowly, and they fall relative to the air in which they are spread, which may well be rising. I still give the prize to 'Suction!'. It's an answer that will do nicely to keep out the rubes. -------------------- We're not doing cool. We're doing pretty. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
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Infiltrator
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written Wednesday, October 11 2006 13:15
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quote:The upper surface of an airplane wing has a greater radius of curvature than the lower surface. So, air flowing over (or molecules) follow a more curved path than those flowing under. this is what I was referring to. The particle "reacts" to the different curvatures of the wing's surfaces by taking different shaped paths when flowing past the two surfaces. This creates a lower pressure region on the top surface of the wing. Particles accelerate into this lower pressure region, and that faster airforce generates the net upward force on the wing. This relation of pressure and fluid speed (and elevation) is explored by Bernoulli, which you asked us to stay away from. The other apect of lift was briefly explained by my statement of particles striking the lower surface of the wing and directed downwards, generating an upward force. -------------------- "Dikiyoba ... is demon ... drives people mad and ... do all sorts of strange things." "You Spiderwebbians are mad, mad, mad as March hares." Posts: 687 | Registered: Wednesday, January 19 2005 08:00 |
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Infiltrator
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written Wednesday, October 11 2006 13:22
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SoT, for a 8.0 micrometer particle with density of 1 gram per cubic centimeter, the terminal velocity is approximately 0.2 cm/sec, for a particle a tenth of the size it is 0.002 cm/sec. Also, I note that while suction has nothing to do with terminal velocity or the fact that molecules of air stay suspended in air it has lots to do with airplanes staying up. I suspect that military man didn't know the answer and was avoiding a toughie. [ Wednesday, October 11, 2006 15:13: Message edited by: 2bit ] -------------------- "Dikiyoba ... is demon ... drives people mad and ... do all sorts of strange things." "You Spiderwebbians are mad, mad, mad as March hares." Posts: 687 | Registered: Wednesday, January 19 2005 08:00 |
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Off With Their Heads
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written Wednesday, October 11 2006 20:50
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quote:Let me give it a shot. "U=0" is very compact, but it cannot actually be measured or tested without a very elaborate definition of U. Something like (torque) = (moment of inertia) * (angular acceleration) is slightly less compact, but the definitions of the relevant variables involve many fewer and much shorter statements than U. quote:Why should they be able to? They can just look up the derivation. Being able to solve such problems is only useful insofar as it correlates with being able to solve new, as yet unsolved, problems, which professional physicists ideally should be able to do. Still, the extent to which solving this old problem would be anything like solving new problems is related to the field in which the physicist works; I suspect that many physicists don't work a lot with complex Newtonian mechanics these days, so this would hardly be similar to the new problems that would come up. SoT, I realized that I've been wondering this for a while now and have always forgotten to ask: what research do you do? -------------------- Arancaytar: Every time you ask people to compare TM and Kel, you endanger the poor, fluffy kittens. Smoo: Get ready to face the walls! Ephesos: In conclusion, yarr. Kelandon's Pink and Pretty Page!!: the authorized location for all things by me The Archive of all released BoE scenarios ever Posts: 7968 | Registered: Saturday, February 28 2004 08:00 |
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Law Bringer
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written Wednesday, October 11 2006 21:12
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Regarding #1 airplane lift from just Brownian motion. This isn't a complete explanation, but the shape of the wing causes random collisions to impart their motion into the wing. If you breakdown the momentum transfer into horizontal and vertical components then those collisions on the underside mostly transfer their momentum in the vertical direction providing lift. The collisions on the upper surface because of the shape only transfer part of their momentum in the vertical direction and the bulk is in the horizontal. The difference in curvature between the front and rear parts of the top surface can partailly account for drag. Note this explanation breaks down for supersonic plane wings which have a significantly different shape. The difference in air pressure between the upper and lower surfaces will effect the number of collisions. Posts: 4643 | Registered: Friday, February 10 2006 08:00 |
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Electric Sheep One
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written Wednesday, October 11 2006 22:13
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quote:This is sort of right, I think, but it has a big problem. (Apart from the radius of curvature typo. The lower surface is indeed flatter, which means it has the larger radius of curvature.) Molecules do not feel pressure, any more than shopkeepers feel GNP. Pressure is a concept that only makes sense for large numbers of particles treated collectively. Individual molecules do not follow the streamlines of hydrodynamics, and do not simply 'flow past' the wing surfaces. What molecules feel is other molecules. In a dilute gas like air, molecules are essentially never actually touching each other; but they very briefly collide and bounce away from each other, exchanging momentum and kinetic energy. At normal atmospheric pressure and room temperature, the typical molecule hits another one after travelling about a micron. And at a typical speed of 300 meters per second (the speed of sound, not coincidentally) this happens every few nanoseconds. From these facts one can derive hydrodynamics as an accurate description of the collective behavior of the molecules on length scales much greater than a micron, and time scales much longer than a nanosecond. But what I want is to undo this derivation enough to understand just how and why molecules end up hitting the underside of the wing harder than the upperside. In a sense this is random thermal motion doing all the lift; but not exactly. (Brownian motion is technically the motion of small but visible objects being hit by molecules, not the motion of the molecules themselves.) An airplane that is not moving forward does not float in midair; and airplane with an upside down wing would be in trouble, too. The combination of the wing shape and forward motion induces a general tendency for the randomly moving molecules to hit the lower surface of the wing more and/or harder. This is what I want to have explained. Why is this stuff worth knowing? In one way, it is directly related to major unsolved problems. Ever since Boltzmann, the ideal gas has been a sort of paradigm system for the so-called arrow of time. It's not that dilute gases are responsible for my inability to remember tomorrow, but that they seem like the simplest system in which we might try to understand the emergence of time asymmetry in complex systems. Unfortunately we're not very close yet. The Boltzmann equation simply puts in this asymmetry by hand, and we have yet to truly explain it even in ideal gases. Otherwise, physics is all about the buck stopping here. We're supposed to be able to explain everything from first principles; we're not a bunch of engineers who turn out working products without necessarily understanding our own tools. And the impulse that makes a physicist go, "Hey! Why can't I explain that precessing top?" is precisely the same emotion that makes them try to explain things that no-one can yet explain. It's kind of like how you can get a real athlete keenly interested in practically any game of physical skill, even if it's a professional basketball player playing shuffleboard. It's not a matter of the specific tasks they need for their job; it's a matter of the general mentality they need for their job. My own research can be described as the middle ground between quantum information theory, condensed matter theory, and quantum optics. 10 years ago this would have been practically an empty set, but these days it is one of the hottest fields in physics, thanks to the development of techniques for trapping small samples of gas and cooling them to insanely low temperatures. It turns out that this gives us, in effect, designer matter. So you can take a whole slew of profound questions, and realistically contemplate putting them into the laboratory with all the confusing and irrelevant junk that usually clouds the issues stripped away. The field is usually called 'cold atoms', or 'ultracold atoms', even though strictly speaking it is not the coldness of the individual atoms, but of the gases they make up, that is important and new. We should call it either 'cold gases' or 'slow atoms'. Anyway, I do theoretical calculations about this stuff, then try and talk experimentalists into doing hard experiments. Or I look at their data and try to figure out what is going on. -------------------- We're not doing cool. We're doing pretty. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
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