stackexchange_physics_applied_physics.jsonl

{"unit_id": "stackexchange:physics.stackexchange:applied-physics:167077:0000", "text": "Question: Freefall into snow\n\nIn the movie Frozen, the following dialogue takes place:\n\n>Anna: \"It's a hundred-foot drop.\"\n>\n>Kristoff: \"It's two hundred.\"\n>\n>Anna: \"Okay, what if we fall?\"\n>\n>Kristoff: \"There's 20 feet of fresh powder down there. It will be like landing on a pillow... Hopefully.\n\nThen they fall all the way to the bottom and survive.\n\nMy question is this: would this be actually possible? My instinct tells me no, but I'm too awful at physics to back it.\n\nAccepted Answer:\n\nAs a very rude guess, <a href=\"http://www.dtic.mil/dtic/tr/fulltext/u2/a028622.pdf\">fresh snow</a> (see page vi) can have a density of $0.3 \\ \\mathrm{g/cm^3}$ and be compressed all the way to about the density of ice, $0.9\\ \\mathrm{ g/cm^3}$.\r\n\r\nUnder perfect conditions you could see a 13 feet uniform deceleration when landing in 20 feet of snow, or about 4 meters. \r\n\r\n![enter image description here][1]\r\n\r\n\r\nGoing from $30\\ \\mathrm{m/s}$ to $0\\ \\mathrm{m/s}$ (as @Sean suggested in comments), you'd have $(\\frac{4\\ \\mathrm m}{12.5\\ \\mathrm{m/s}})$ = 0.32 seconds to decelerate.\r\n\r\nThe acceleration is $\\frac{30\\ \\mathrm{m/s}}{0.32\\ \\mathrm{s}}$ = $93.75\\ \\mathrm{m/s^2}$. That's about:\r\n\r\n**9.5G's of acceleration**\r\n\r\n<a href=\"http://en.wikipedia.org/wiki/G-force\">Wikipedia</a> lists 25g's as the point where serious injury/death can occur, and 215g's as the maximum a human has ever survived.\r\n\r\nSo it seems plausible. \r\n\r\nBut it should be noted that since the snow at the bottom is under a lot of pressure from the weight of the snow above, it's likely the density would not be $0.3\\ \\mathrm{g/cm^3}$ throughout. It would help that the force lasts only a fraction of a second.\r\n\r\n**Edit** as pointed out in the comments, the force that the snow will exert could vary with its density. So initially, the force would be rather weak, and as you approach $0.9\\ \\mathrm{\\frac{g}{cm^3}}$ that force would increase, probably exponentially. So the above answer is really a \"best case scenario\" when it comes to snow compressibility\r\n\r\n\r\n  [1]: https://i.sstatic.net/EUMoj.png\n\nAnswer (score=28):\n\n@Señor O gives a very good answer, but he assumes an ideal deceleration.  Based on a viewing of the scene, Anna sinks a little under a meter, while Kristoff doesn't sink more than half a meter.\r\n\r\nSince they fell about 200 feet (about 60 m), my initial estimate for their impact velocity is (assuming no air resistance):\r\n\r\n$v = \\sqrt{2gh} = \\sqrt{2*60*9.8} \\approx 35 \\ \\mathrm{m/s}$\r\n\r\nHowever, using a handy chart found in the resource below, when we factor in air resistance, Anna and Kristoff's impact velocity is actually around $33 \\ \\mathrm{m/s}$\r\n\r\nIn Kristoff's case, \r\n\r\n$v^2 = v_o^2 + 2a\\Delta x$\r\n\r\n$1100 = 2(0.5)a$\r\n\r\n$1100\\ \\mathrm{ m/s^2} = a$\r\n\r\nwhich is about $110g$.  Possibly fatal, especially considering that the way he lands would cause severe stress on the spinal cord.\r\n\r\nIn Anna's case,\r\n\r\n$1100 = 2(1)a$\r\n\r\n$550\\ \\mathrm{m/s^2 }= a$\r\n\r\nwhich is about $55g$.  Probably survivable, (some car crashes experience higher gs), but would likely injure her.  She does land feet-first (probably the optimal way to land in this case), which would prevent some injury.  In short, the duo might survive, but they would not be able to just get up and continue on their merry way.\r\n\r\n[This](http://www.faa.gov/data_research/research/med_humanfacs/oamtechreports/1960s/media/am63-15.pdf) FAA paper is my primary source for my calculations.\n\nAnswer (score=21):\n\nThis is another chance to use one of my favorite approximations ever! I first offered it as [an answer](https://physics.stackexchange.com/questions/146010/platform-diving-how-deep-does-one-go-into-the-water/146013#146013) to a question about how deep a platform diver will go into the water. Now is the chance to use it again!\r\n\r\nIssac Newton developed an expression [for the ballistic impact depth](http://en.wikipedia.org/wiki/Impact_depth) of a body into a material. The original idea was expressed for materials of approximately equal densities when the ballistic body is moving fast enough for the target material to behave as a fluid (think cannon ball into dirt, meteorite into lunar regolith, etc). For a human body into snow, we can assume it will behave in a granular enough fashion. \r\n\r\nThe human body has a density of roughly $985 \\ \\mathrm{kg/m^3}$. Using the two limits for the density of snow provided in [another answer to this question](https://physics.stackexchange.com/a/167084/6634), snow has a density between $300$ and $900\\ \\mathrm{ kg/m^3}$. Let's assume the characters are 5 feet tall (you can easily change the number used, it's not a complicated formula). This gives us two limiting expressions:\r\n\r\n$$d = 5 \\times 985/300 = 16.4~\\text{feet}$$\r\n\r\nand \r\n\r\n$$d = 5 \\times 985/900 = 5.5~\\text{feet}$$\r\n\r\nSo it really would depend on the actual density of the snow, but if you assume that it starts out around $300 \\ \\mathrm{kg/m^3}$ and can reach a maximum of $900\\ \\mathrm{ kg/m^3}$, we can assume that the final depth will be close to the same as assuming the average value as $600\\ \\mathrm{ kg/m^3}$ which would give:\r\n\r\n$$d = 5 \\times 985/600 = 8~\\text{feet}$$\r\n\r\nThat will give you a pretty good idea of the penetration depths over that range of densities. These numbers are all pretty close to what is given assuming the ideal deceleration given [by this answer](https://physics.stackexchange.com/a/167084/6634).\r\n\r\nIf you want to do a much more complicated analysis of penetration depth, check out [the other, more detailed answer](https://physics.stackexchange.com/a/146016/6634) to the platform diver question. There it is actually shown that the penetration depth approaches this Newtonian approximation pretty well! It is also interesting to note that the penetration depth does not depend on the impact velocity/original height. Assuming one is going \"fast enough\" for the material to behave like a fluid, the expression seems to hold.\n\nAnswer (score=14):\n\nNice theoretical answers (I can certainly appreciate them, I'm a mathematician). But why delve into theory when experiment is available? In [this video][1] you can see a skier jump from more than 200 feet and get head first into the snow, without a helmet. \r\n\r\nThe video starts with the aftermath, if you want to see the jump right away  fast forward to about 1 minute into it. \r\n\r\n\r\n  [1]: https://www.youtube.com/watch?v=-RYkapHBVs8\n\nAnswer (score=1):\n\nAbout 50 years ago in Reader's Digest there was an article about a Soviet airplane pilot who bailed out at high altitude.  He fell into a snow-filled ravine and survived.  If the angle of the snow is high enough it is no big deal.  At Squaw Valley I have seen skiers do drops that might have been 100 feet.  If the landing is steep enough it is OK.  It is \"flat landings\" that will get you.\r\n\r\nRock climber Lynn Hill fell 100 feet onto a dirt slope.  She not only survived, she recovered completely.\r\n\r\nStunt men do quite high jumps onto airbags.  100 feet onto 20 feet of snow seems possible, but I wouldn't try it if I had any alternative.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 0, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "homework-and-exercises", "newtonian-mechanics", "free-fall", "estimation"], "page_start": null, "page_end": null, "quality_flags": ["mixed_license"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 167077, "title": "Freefall into snow", "url": "https://physics.stackexchange.com/questions/167077/freefall-into-snow", "share_url": "https://physics.stackexchange.com/q/167077", "content_license": null, "owner": {"display_name": "user3932000", "user_id": 74039, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/74039/user3932000"}}, "answers": [{"answer_id": 167084, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/167077/freefall-into-snow/167084#167084", "share_url": "https://physics.stackexchange.com/a/167084", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "Señor O", "user_id": 43294, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/43294/se%c3%b1or-o"}}, {"answer_id": 167089, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/167077/freefall-into-snow/167089#167089", "share_url": "https://physics.stackexchange.com/a/167089", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "Dave Coffman", "user_id": 49024, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/49024/dave-coffman"}}, {"answer_id": 167090, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/167077/freefall-into-snow/167090#167090", "share_url": "https://physics.stackexchange.com/a/167090", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "tpg2114", "user_id": 6634, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/6634/tpg2114"}}, {"answer_id": 167215, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/167077/freefall-into-snow/167215#167215", "share_url": "https://physics.stackexchange.com/a/167215", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Martin Argerami", "user_id": 42892, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/42892/martin-argerami"}}, {"answer_id": 167495, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/167077/freefall-into-snow/167495#167495", "share_url": "https://physics.stackexchange.com/a/167495", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "user11865", "user_id": 11865, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/11865/user11865"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:349115:0000", "text": "Question: Is frequent opening of the fridge really so significant for the power consumption?\n\nI've read several popular articles telling that frequent opening of the fridge *highly* increases the power consumption.\r\n\r\nIs it *really* so significant? Isn't the heat in the room-temperature food which is brought to the fridge *so much more* relevant that some air which goes into the fridge upon opening the door is nothing compared to that?\r\n\r\nTo make it more concrete: How many times do I have to open and close the fridge so the effect is comparable with putting there a 1 litre box of milk at the room temperature? Let's say the room has 22°C, the fridge 7°C.\n\nAccepted Answer:\n\nThat depends on whether the fridge monitors the temperature or not.\r\n\r\nWhere I work, the large walk-in fridge has a temperature monitor. It starts to cool only when the temperature rises above 4.7°C and stops when it sinks to 3.5°C.\r\n\r\nThe fridge is very well insulated, meaning the fridge very rarely has to turn on when the door is closed.\r\n\r\nI frequently retrieve items from the fridge. This normally means the door is open for less than 15 seconds, but in that time the fridge frequently rises to 5+°C, and you hear the cooler start up again.\r\n\r\nFor that fridge, energy consumption is close to 0 when not opened and reaches its maximum every time it is opened.\r\n\r\nHowever, you want to know the difference between opening the fridge and cooling 1l of milk.\r\n\r\n---\r\n\r\n[The Carnot coefficient of refrigeration][1]\r\n$$\\gamma = {T_c \\over T_h-T_c}$$\r\nis the ratio of the heat extracted to the work required to extract this heat.\r\n\r\n$T_c$ is the temperature in the fridge (I'll say 2°C = 275 K), and $T_h$ is room temperature (at 22°C = 295 K), So $\\gamma = 13.75$. This means to move one joule of heat energy from the milk to outside it takes 0.073 J from the mains.\r\n\r\nThe energy we want to remove from 1 litre of milk when cooling from $22°C$ to 2°C is ([a], [b])\r\n$$Q=mc\\Delta\\theta = 1\\text{kg} \\times 4181 {\\text{J} \\over \\text{kg} °C} \\times 20°C = 83620 \\text{J}$$\r\nremoved from the milk (assuming milk $\\approx$ water - [it's close, but not perfect][2]). This will take $83620 \\text{J} \\times 0.073 = 6104 \\text{J}$.\r\n\r\nMy fridge contains about 224l (10 mol) of air. Opening the door raises the temperature from 4°C to around 10°C (I just checked). The $\\gamma$ ratio for that is 46.17, so every Joule removed requires 0.02J.\r\n\r\nCooling 224l of air from 10°C to 4°C means moving $Q = 0.288 \\text{kg} \\times 1000 {J \\over kg °C} \\times 6°C = 1728 \\text{J}$. This will take $1728 \\times 0.02 = 34.56$.\n\nHowever, when I open my fridge, a 15W bulb is turned on. If I open the fridge for 10 seconds, the bulb has already used 4.3x more electricity than will be used cooling the air.\r\n\r\nThis means you can open the fridge over 175 times before you've reached the energy consumption of cooling your milk (although when including the light bulb, it’s closer to just 33 times). However, [at current electricity costs][3], it's around \\$0.00026 to cool that milk - so I doubt the power consumption will ever really *matter* to you.\n\nIf you drink the average amount of milk for a French citizen ([260 litres - Wikipedia has bizarre lists][4]) you’re spending just \\€0.067 per year on your milk.\n\n---\n\nInstead of worrying about the milk here’s a few quick suggestions:\n\n- turning lightbulbs off, and changing for energy saving ones - up to €180/yr\n- buy a TV which uses very little electricity in standby mode - up to €38/yr\n- don’t boil too much water - up to €58/yr\n\n  [a]: http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/heat.html\n  [b]: http://www.bbc.co.uk/schools/gcsebitesize/science/aqa/heatingandcooling/buildingsrev3.shtml\n  [1]: http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/heatpump.html\n  [2]: http://www.engineeringtoolbox.com/specific-heat-fluids-d_151.html\n  [3]: http://large.stanford.edu/publications/power/references/voltprice/\n  [4]: https://en.m.wikipedia.org/wiki/List_of_countries_by_milk_consumption_per_capita\n\nAnswer (score=10):\n\nIn order to cool 1 liter of room temperature water (why is your milk at room temperature?) from 22 C to 7 C, you need to remove $Q=(1 kg)(4186 \\frac{J}{kg ^\\circ C})(15^\\circ C)\\approx 63 kJ$ of energy.\r\n\r\nIn order to cool 250 liters of air (a reasonable estimate for the empty space in your refrigerator) by the same amount, you need to remove $Q\\approx 5 kJ$.  It seems that cooling the water requires somewhere around 13x as much energy.\r\n\r\nHowever, there are several issues here.  Most importantly, once the water is cooled, it stays cool; on the other hand, much of the cool air escapes *every time* you open your refrigerator.  How many times per day do you open and close your refrigerator? Ten? Twenty?  If you have a family with kids, it may be significantly higher than that.\r\n\r\nPut a temperature probe in your refrigerator and watch what happens when you open and close the door.  The temperature rises remarkably fast, because the cool air falls to the floor and is replaced by the ambient air in the room.  The effect is lessened as you go further back into the body of the refrigerator, which is why you should never store things that spoil (like milk) in the door.\r\n\r\nAlso, don't forget that the kitchen is typically warmer than the rest of the house - especially near the refrigerator, which pumps hot air out the back.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 1, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "thermodynamics", "energy", "everyday-life", "cooling"], "page_start": null, "page_end": null, "quality_flags": [], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 349115, "title": "Is frequent opening of the fridge really so significant for the power consumption?", "url": "https://physics.stackexchange.com/questions/349115/is-frequent-opening-of-the-fridge-really-so-significant-for-the-power-consumptio", "share_url": "https://physics.stackexchange.com/q/349115", "content_license": null, "owner": {"display_name": "Honza Zidek", "user_id": 72027, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/72027/honza-zidek"}}, "answers": [{"answer_id": 349129, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/349115/is-frequent-opening-of-the-fridge-really-so-significant-for-the-power-consumptio/349129#349129", "share_url": "https://physics.stackexchange.com/a/349129", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Tim", "user_id": 63383, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/63383/tim"}}, {"answer_id": 349116, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/349115/is-frequent-opening-of-the-fridge-really-so-significant-for-the-power-consumptio/349116#349116", "share_url": "https://physics.stackexchange.com/a/349116", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Albatross", "user_id": 156895, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/156895/albatross"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:142:0000", "text": "Question: What will happen if we add salt to boiling water?\n\nI would like to have a good understanding of what is happening when you add salt to boiling water.\r\n\r\nMy understanding is that the boiling point will be higher, thus lengthening the process (obtaining boiling water), but at the same time, the dissolved salt reduce the polarization effect of the water molecules on the heat capacity, thus shortening the process.\r\n\r\nIs this competition between these two effects real ? Is it something else ?\n\nAccepted Answer:\n\nI think the dominant effect might actually be the fact that the salt you add might not be at boiling temperature.  But this is just based on the fact that [the boiling-point elevation due to salt in water is actually quite low](http://en.wikipedia.org/wiki/Boiling-point_elevation#Uses) for typical amounts of salt used in cooking, say.  I'm not too familiar with the second effect you mention though.\n\nAnswer (score=7):\n\nOkay, first we have the phenomenon: Yes. adding salt increases the boiling point of water, which means that you have to input more energy to get the water to boil, but your egg or pasta will cook faster once you do, because the water will be hotter.\r\n\r\nThen there's the why.  The boiling point of a liquid is the temperature at which the vapor pressure of the liquid is the same as the atmospheric pressure above the liquid.  If we can artificially increase the vapor pressure of the liquid, we decrease the boiling temperature.  If we can artificially decrease the vapor pressure of the liquid, we increase the boiling temperature.  So the question has now become: why does the vapor pressure of water decrease when we add salt to it?\r\n\r\nSo imagine a pot of water.  At any given temperature there will be some water molecules in the gas phase above the pot (that's the origin of the vapor pressure), and some in the liquid phase in the pot.  The proportion in the two phases is determined by the interplay of lowering potential energy (by decreasing elevation in gravity, by forming hydrogen bonds, by lining up the polar ends of the molecules, etc.) and increasing the entropy (there's more accessible states in the gas phase, most liquids are incompressible, etc.).  The potential energy part favors the liquid phase, while the entropy part favors the gas phase.  The real requirement here is to minimize the free energy, F = U - TS, with F the free energy, U the potential, T the temperature, and S the entropy.  Since S is paired with the temperature, increasing the temperature increases the impact of the entropy part, which is why the vapor pressure increases as we increase the temperature.\r\n\r\nSo now we toss in some salt, while keeping the temperature fixed.  The volume fraction of the water decreases, and suddenly there are new accessible states for the water molecules in the liquid phase -- so the vapor pressure decreases.  We keep adding salt and the vapor pressure keeps decreasing.  If we keep going, eventually there's no vapor pressure.\r\n\r\nRaoult's law says that the vapor pressure of a solution is proportional to the vapor pressure of the pure solvent (basically that there is a straight line between the pure vapor pressure and zero, when we've buried it in salt).  That's taken as the definition of an ideal solution.  Real solutions have a curved functional form between the two boundary conditions, with the deviations from linearity coming from interactions between the solute (the salt) and the solvent (the water).  Those interactions might be things like breaking up the network of hydrogen bonds in the water, disrupting the polarization arrangement (both of which will favor gas phase), or bonding/pairing up with water molecules (which will favor liquid phase).  At relatively low concentrations of solute the interaction effects are pretty small, so the dependence of vapor pressure on solute concentration remains roughly linear.  The cool observation though is that at most temperatures and for most solvents, it doesn't matter what solute you use (as long as the solute itself doesn't have a vapor pressure), the vapor pressure of the solvent is still decreased by adding solute (which indicates that the entropic contribution is the most important part, and the interactions don't play a big role).\r\n\r\nNow to sum up: for a given concentration of salt dissolved in water, there are more states accessible to the water molecules in the liquid phase than there are in pure water.  So at every water temperature as we pour in energy to make it boil, there will be a lower vapor pressure than there would have been without the salt, and thus we won't get to the boiling point until the water has reached a higher temperature (until we've poured in more energy than we would have had to).  Salt does disrupt the network of hydrogen bonds in the water molecules, but the effect isn't very big at reasonable concentrations of salt, and it's never big enough to counteract the entropic effect.\n\nAnswer (score=6):\n\ngood theory\r\n\r\nhow about a test\r\n\r\nmy niece just did 3 trials each on 2 cups of water and varied the number of tablespoons of salt\r\n\r\n0 and 1 tablespoons boiled at about 10.5 minutes\r\n2 tablespoons boiled at about 9.3 minutes\r\n3 about 7.5 minutes\r\nand 4 boiled at about 6 minutes.\r\n\r\nand now she wants to know why she got those results\n\nAnswer (score=5):\n\nThe competition is real, and it's no contest. The reduction in specific heat from the polar effect swamps the miniscule elevation of the boiling point.\r\n\r\nWhen you dissolve salt in water, it makes ions in solution, and the ionic atoms trap a cage of water around them immobile. The net effect is that you reduce the number of degrees of freedom, and you reduce the specific heat. So a given amount of heat energy is more effective at heating salt water than ordinary water. The effect is large, see kwinb's answer for a qualitative experiment.\r\n\r\nThis means that when you add salt to boiling water, the act of dissolving the salt (which keeps the internal energy fixed, or releases internal energy), is more than enough to heat the water to the new boiling temperature. I have often added salt to boiling water, and I used to expect it to stop boiling momentarily, to catch up to the new boiling point. Instead, I consistently noticed hyper-boiling where I added the salt, and no time-lag. The reason is the heat released as the salt is dissolved.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 2, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-2.5", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "thermodynamics", "water", "physical-chemistry"], "page_start": null, "page_end": null, "quality_flags": ["mixed_license"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 142, "title": "What will happen if we add salt to boiling water?", "url": "https://physics.stackexchange.com/questions/142/what-will-happen-if-we-add-salt-to-boiling-water", "share_url": "https://physics.stackexchange.com/q/142", "content_license": null, "owner": {"display_name": "Cedric H.", "user_id": 82, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/82/cedric-h"}}, "answers": [{"answer_id": 152, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/142/what-will-happen-if-we-add-salt-to-boiling-water/152#152", "share_url": "https://physics.stackexchange.com/a/152", "content_license": "CC BY-SA 2.5", "owner": {"display_name": "j.c.", "user_id": 42, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/42/j-c"}}, {"answer_id": 2383, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/142/what-will-happen-if-we-add-salt-to-boiling-water/2383#2383", "share_url": "https://physics.stackexchange.com/a/2383", "content_license": "CC BY-SA 2.5", "owner": {"display_name": "Mark Betnel", "user_id": 1013, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/1013/mark-betnel"}}, {"answer_id": 18888, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/142/what-will-happen-if-we-add-salt-to-boiling-water/18888#18888", "share_url": "https://physics.stackexchange.com/a/18888", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "kwinb", "user_id": 6901, "user_type": "unregistered", "profile_url": "https://physics.stackexchange.com/users/6901/kwinb"}}, {"answer_id": 32077, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/142/what-will-happen-if-we-add-salt-to-boiling-water/32077#32077", "share_url": "https://physics.stackexchange.com/a/32077", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Ron Maimon", "user_id": 4864, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/4864/ron-maimon"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:790565:0000", "text": "Question: Calculating temperature when it is lower than your thermometers can read?\n\nWe have an old freezer.  I believe the thermostat is broken and think it may run all the time.  Food in it gets really cold (Ice cream like concrete).  I've tried measuring the temp with a freezer thermometer, but the needle is well below the lowest temperature (-20F or -30F).  The digital thermometer I have just shows \"Error\".\r\n\r\nAside from buying an expensive specialty thermometer (if they even exist), can anyone suggest the best straightforward way to calculate the approximate temp without any special equipment? \r\n \r\nI was thinking of something like putting a solid metal object (to avoid phase changes) in the freezer for a day or two and then placing it in a known quantity of liquid of a time and measuring the temp of the liquid (or the object) after a set time (measuring the mass of everything of course).  There may be an entirely better approach.\r\n\r\nI'm not shooting for super accuracy, so not looking to build a super insulated rig.  Just looking for a reasonably simple method to get a decent estimate (within 5 degrees?). \r\nEven specific suggestions on my proposed method appreciated.\n\nAccepted Answer:\n\nMass of polystyrene cup + lid (with hole for thermometer) = $m_{\\rm c}\\,\\rm g$ (assume thermal capacity is negligible)\r\nMass of polystyrene cup + lid + water = $m_{\\rm c+w}\\,\\rm g$  \r\nMass of water = $m_{\\rm w} = m_{\\rm c+w} -m_{\\rm c}\\,\\rm g$  \r\nInitial temperature of water = $\\theta_{\\rm i}\\,^\\circ \\rm C$  \r\nSpecific heat capacity of water, $c_{\\rm w} = 4.2\\,\\rm J\\,g^{-1}\\,^\\circ C^{-1}$ \r\n\r\nMass of metal object of known composition = $m_{\\rm m}\\,\\rm g$  \r\nMetal specific heat capacity, $c_{\\rm m}\\,\\rm J\\,g^{-1}\\,^\\circ \\rm C^{-1}$  \r\nKeep metal in freezer for a day  \r\n\r\nAdd to metal to polystyrene cup, close lid, shake without spillage until temperature constant, $\\theta_{\\rm f}\\,^\\circ \\rm C$\r\n\r\nFreezer temperature = $\\theta\\,^\\circ \\rm C$  \r\n$m_{\\rm m}\\,c_{\\rm m}(\\theta_{\\rm f}-\\theta) = m_{\\rm w}\\,c_{\\rm w}(\\theta_{\\rm f}-\\theta_{\\rm i})$  \r\n\r\nAn experiment that you might have done in your youth?  \r\n\r\n---  \r\n\r\nData from @PStallings  \r\n*This is the method I tried. I used a 1.5\" chrome steel ball bearing as the thermal mass and 150 g of water at 68F in a styrofoam cup.  \r\nFirst time water froze almost immediately. Retried with 80 proof vodka and more mixing. At 1 min vodka at 56F.  \r\nAt 2 min, at 55F. Same for next 3 min. Then slowly climbed for next half hour.  \r\nConverting to metric, vodka went from 20c to 13c. Change of 7c.  \r\nSpecific heat ~2.4 gives 150g*2.4*(7c) = 2520. \r\nMass of steel = 226g. Specific heat ~ 0.466.  \r\n2520/(226*0.466) = 24. Leaves us with 13c-Initial Steel=24.  \r\nGives -21c = -5.8F. Warmer than expected!* \r\n\r\nI checked the data assuming that the ball bearing was made of steel with a density of $7.85\\,\\rm g/cm^3$ which gives a mass for the ball bearing of $227\\,\\rm g$ which is in agreement with the OP.  \r\nHowever given that $80$ proof is equivalent to $40\\%$ ethanol [this table](https://detector-cooling.web.cern.ch/data/Table%208-3-2.htm) lists the specific heat capacity of the alcohol as $4\\,\\rm J/g\\,K$.  \r\nMaking the conversions to degree Celsius with $\\theta$ as the initial temperature of the ball bearing the energy balance equation is,  $150 \\times 4 \\times (20-12.8) = 227\\times 0.466\\times (12.8 - \\theta)\\Rightarrow \\theta = -28^\\circ \\rm C$.\n\nAnswer (score=29):\n\nThe freezing point of water ethylene glycol mixtures depends in the concentration of ethylene glycol. You can find data for this on the [Engineering Toolbox web site][1] (a valuable source of all sorts of info!). I did a quick graph to show the freezing point depression:\r\n\r\n[![FP depression][2]][2]\r\n\r\nSo all you have to do is fill a few jars with different concentrations of ethylene glycol, put then in the freezer and see which ones freeze. I'd suggest using a binary search i.e. start with 30% and 60%, then if only the 30% freezes try 45% and 60%, or if neither freeze try 15% and 30%. And keep going narrowing the range until you have the accuracy you want.\r\n\r\nEthylene glycol is just _anti-freeze_ as available at your local garage. Make sure you get neat ethylene glycol though and not the prediluted form.\r\n\r\nA brief note on the toxicity of ethylene glycol since a few people have mentioned it, ethylene glycol has roughly the same toxicity as ethanol so it's hardly a major poison. If it was we wouldn't use it in our cars. However unlike ethanol it has a sweet flavour so it's more tempting to drink, especially for children. If you're going to put it in your freezer make sure it's well labelled and keep children away.\r\n\r\n  [1]: https://www.engineeringtoolbox.com/ethylene-glycol-d_146.html\r\n  [2]: https://i.sstatic.net/26ZFl.png\n\nAnswer (score=2):\n\nBuy a small bottle of 100 mL vodka (white distilled spirits). This is an alcoholic beverage with 40% concentration of ethanol by volume, and it freezes at around -27 degrees Celsius. If it does not freeze, you can later dilute the vodka with a known volume of distilled water to obtain varying concentrations, and compare with lookup tables on the Internet. You will need a tool like the small plastic syringe from the pharmacy to perform the required volumetric measures.\r\n\r\nAlternatively, if the vodka somehow freezes, you can buy the stronger 95% rectified spirits and dilute it to obtain concentrations above 40%, but most home freezers aren't that cold.\r\n\r\nYou can also get an immediate, rough estimate by just making a saturated table salt solution and putting it in the freezer. The freezing point is around -21 degrees Celsius, so you will know if you are above that or below.\r\n\r\nDo not put a poison like ethylene glycol in a place where you store food, ever! This is beyond stupid and just asking for trouble.\n\nAnswer (score=1):\n\n**Adding a known amount of energy via a microwave oven**\r\n\r\nPour a known volume/mass of water into a lightweight plastic cup. Let's assume you pour 100 ml = 100 g.\r\n\r\nPlace the cup into the freezer and allow it to thermalize and freeze. Then place the cup into a microwave oven with and run it until the ice completely melts. Note the run time and measure the final temperature.\r\n\r\nLet's assume it took 2 minutes = 120 seconds and the end temperature is $65.0\\ ^\\circ \\mathrm{C}$.\r\n\r\nFind the IEC rated power of the microwave, which is the commonly advertised value. Let's assume 1200 W. This is critical: the [IEC wattage rating][1] is based upon the temperature change of a test cup of water, which is perfect for us. However, it has a 2x factor due to historical reasons<sup>1</sup>. Therefore, your \"1200 W\" microwave delivers 600 W to the water.\r\n\r\nIn our example, we delivered $E=120\\ \\mathrm{s} \\times 1200/2\\ \\mathrm{J/s} = 72 \\ \\mathrm{kJ}$ to the water.\r\n\r\nSince the ice melted, we subtract the heat of fusion, $334\\ \\mathrm{J/g}$ or $33.4\\ \\mathrm{kJ}$ for our 100 g of water.\r\n\r\nThat leaves us with $38.6\\ \\mathrm{kJ}$ of heating for our 100 g mass, or $386\\ \\mathrm{J/g}$.\r\n\r\nThe specific heat capacity of water we assume is constant at $4.19\\ \\mathrm{J/g\\ ^\\circ C}$, so our temperature change $\\Delta T = \\frac{386\\ \\mathrm{J/g}}{4.19\\ \\mathrm{J/g\\ ^\\circ C}}= 92.2\\ ^\\circ \\mathrm{C}$\r\n\r\nSince the final temperature was $65.0\\ ^\\circ \\mathrm{C}$, the initial temperature was $65.0-92.2=-27.2\\ ^\\circ\\mathrm{C}$\r\n\r\nThe major simplifications here are that the density and heat capacity of water are unaffected by temperature, the IEC wattage rating is accurate and applies to the cup of water, and the cup's thermal mass and heat transfer with the environment is negligible. \r\n\r\nWe could make the experiment more accurate by measuring the effective microwave oven wattage ourselves, by finding the $\\Delta T$ of an identical room-temperature test mass of water.\r\n\r\n---\r\n<sup>1</sup> Historically, magnetron tubes were rated by the DC input power, as this was easier to measure than high power RF, and they were roughly 50% efficient. The IEC measurement method keeps this factor for continuity in advertising.\r\n\r\n\r\n  [1]: http://www.celtek-electronics.com/microwave-leakage/microwave-oven-power-test\n\nAnswer (score=0):\n\nTake some liquid, put 10% of it in the freezer, wait a few hours. Measure the temperature of the liquid you left out, then pour in the liquid from the freezer, and measure again. The temperature of the freezer is ten times the second temperature, minus nine times the first temperature (using an absolute zero scale, of course). You can adjust the proportions; if you put percentage $p$ in and leave $1-p$ out, it will be $(T_f-(1-p)T_i)/p$.\r\n\r\nThis depends on the liquid not having a phase change. John Rennie suggests using ethylene glycol, but that is somewhat expensive and toxic; most jurisdictions have regulations regarding disposing of it. Sugar doesn't depress the freezing point quite as much, but it's much cheaper and less toxic. You can also try using salt. Many artificial sweeteners are more effective than sugar, but also are more expensive.\r\n\r\nAnother option is to see if you can find high precision resistance tester. A decrease of 5 degrees Fahrenheit will decrease the resistance of a copper wire by a bit over 1%.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 3, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-4.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "thermodynamics", "temperature", "measurements", "home-experiment"], "page_start": null, "page_end": null, "quality_flags": [], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 790565, "title": "Calculating temperature when it is lower than your thermometers can read?", "url": "https://physics.stackexchange.com/questions/790565/calculating-temperature-when-it-is-lower-than-your-thermometers-can-read", "share_url": "https://physics.stackexchange.com/q/790565", "content_license": null, "owner": {"display_name": "PStallings", "user_id": 385975, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/385975/pstallings"}}, "answers": [{"answer_id": 790576, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/790565/calculating-temperature-when-it-is-lower-than-your-thermometers-can-read/790576#790576", "share_url": "https://physics.stackexchange.com/a/790576", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "Farcher", "user_id": 104696, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/104696/farcher"}}, {"answer_id": 790612, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/790565/calculating-temperature-when-it-is-lower-than-your-thermometers-can-read/790612#790612", "share_url": "https://physics.stackexchange.com/a/790612", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "John Rennie", "user_id": 1325, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/1325/john-rennie"}}, {"answer_id": 790756, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/790565/calculating-temperature-when-it-is-lower-than-your-thermometers-can-read/790756#790756", "share_url": "https://physics.stackexchange.com/a/790756", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "user386095", "user_id": null, "user_type": "does_not_exist", "profile_url": null}}, {"answer_id": 790707, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/790565/calculating-temperature-when-it-is-lower-than-your-thermometers-can-read/790707#790707", "share_url": "https://physics.stackexchange.com/a/790707", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "user71659", "user_id": 172242, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/172242/user71659"}}, {"answer_id": 790743, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/790565/calculating-temperature-when-it-is-lower-than-your-thermometers-can-read/790743#790743", "share_url": "https://physics.stackexchange.com/a/790743", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "Acccumulation", "user_id": 167242, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/167242/acccumulation"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:2708:0000", "text": "Question: Practical applications for a Bose-Einstein condensate\n\nWhat are the main practical applications that a [Bose-Einstein condensate](http://en.wikipedia.org/wiki/Bose%E2%80%93Einstein_condensate) can have?\n\nAccepted Answer:\n\nI assume you mean the relatively recent phenomenon of Bose-Einstein Condensation in dilute atomic vapors (first produced in 1995 in Colorado). The overall phenomenon of Bose-Einstein Condensation is closely related to superconductivity (in a very loose sense, you can think of the superconducting transition in a metal as the formation of a BEC of pairs of electrons), and that application would trump everything else.\r\n\r\nThe primary application of atomic BEC systems is in basic research areas at the moment, and will probably remain so for the foreseeable future. You sometimes hear people talk about BEC as a tool for lithography, or things like that, but that's not likely to be a real commercial application any time soon, because the throughput is just too low. Nobody has a method for generating BEC at the sort of rate you would need to make interesting devices in a reasonable amount of time. As a result, most BEC applications will be confined to the laboratory.\r\n\r\nOne of the hottest areas in BEC at the moment is the use of Bose condensates (and the related phenomenon of degenerate Fermi gases) to simulate condensed matter systems. You can easily make an \"optical lattice\" from an interference pattern of multiple laser beams that looks to the atoms rather like a crystal lattic in a solid looks to electrons: a regular array of sites where the particles could be trapped, with all the sites interconnected by tunneling. The big advantage BEC/ optical lattice systems have over real condensed matter systems is that they are more easily tunable. You can easily vary the lattice spacing, the strength of the interaction between atoms, and the number density of atoms in the lattice, which allows you to explore a range of different parameters with essentially the same sample, which is very difficult to do with condensed matter systems where you need to grow all new samples for every new set of values you want to explore. As a result, there is a great deal of work in using BEC systems to explore condensed matter physics, essentially making cold atoms look like electrons. There's a good review article, a couple of years old now, by Immanuel Bloch, Jean Dalibard, and Wilhelm Zwerger ([RMP paper][1], [arxiv version][2]) that covers a lot of this work. And people continue to expand the range of experiments-- there's a lot of work ongoing looking at the effect of adding disorder to these systems, for example, and people have begun to explore lattice structures beyond the really easy to make square lattices of the earliest work.\r\n\r\nThere is also a good deal of interest in BEC for possible applications in precision measurement. At the moment, some of the most sensitive detectors ever made for things like rotation, acceleration, and gravity gradients come from atom interferometry, using the wavelike properties of atoms to do interference experiments that measure small shifts induced by these effects. BEC systems may provide an improvement beyond what you can do with thermal beams of atoms in these sorts of systems. There are a number of issues to be worked out in this relating to interatomic interactions, but it's a promising area. Full Disclosure: My post-doc research was in this general area, though what I did was more a proof-of-principle demonstration than a real precision measurement. My old boss, Mark Kasevich, now at Stanford, does a lot of work in this area.\r\n\r\nThe other really hot area of BEC research is in looking for ways to use BEC systems for quantum information processing. If you want to build a quantum computer, you need a way to start with a bunch of qubits that are all in the same state, and a BEC could be a good way to get there, because it consists of a macroscopic number of atoms occupying the same quantum state. There are a bunch of groups working on ways to start with a BEC, and separate the atoms in some way, then manipulate them to do simple quantum computing operations.\r\n\r\nThere's a lot of overlap between these sub-sub-fields-- one of the best ways to separate the qubits for quantum information processing is to use an optical lattice, for example. But those are what I would call the biggest current applications of BEC research. None of these are likely to provide a commercial product in the immediate future, but they're all providing useful information about the behavior of matter on very small scales, which helps feed into other, more applied, lines of research.\r\n \r\nThis is not by any stretch a comprehensive list of things people are doing with BEC, just some of the more popular areas over the last couple of years.\r\n\r\n  [1]: http://rmp.aps.org/abstract/RMP/v80/i3/p885_1\r\n  [2]: http://arxiv.org/abs/0704.3011\n\nAnswer (score=3):\n\nBose condensation is interesting, because it is a quantum mechanical effect, that often results in macroscopic objects with unusual properies. \r\n\r\nFirst of all Bose condensation is believed to be responsible for such phenomena as [superfluidity][1] and [superconductivity][2]. I don't think that I should explain technological and, well, \"cognitive\" importance of those.\r\n\r\nBut I guess that you are mainly interested in [the Bose condensate][3] -- a cloud of atoms of ordinary (some gas) but very cold matter in come optical/magnetic trap. Physics of these is a rapidly developing area right now, so my information can be not the most up-to-date.   I know that people were thinking of making: \r\n \r\n - some time/frequency standards with it\r\n - some unusual chemical compounds/alloys with it (ultracold chemistry)\r\n - use those clouds as high-resolution alternative for [molecular beam epitaxy][4] \r\n  \r\nAnd, of course, the most bizarre application people consider is a quantum computing. I know that people managed to make those traps as small as 1cm. And that they made number of clouds in one trap, \"interacting\" with each other through spin entanglement: [see e.g. here][5].    \r\n\r\n [1]:http://en.wikipedia.org/wiki/Superfluid\r\n [2]:http://en.wikipedia.org/wiki/Superconductivity\r\n [3]:http://en.wikipedia.org/wiki/Bose%E2%80%93Einstein_condensate\r\n [4]:http://en.wikipedia.org/wiki/Molecular_beam_epitaxy\r\n [5]:http://www.itpro.co.uk/news/121086/trapped-atoms-could-advance-quantum-computing.html\n\nAnswer (score=1):\n\nMore recently, they have been [proposed][1] as an array of inexpensive gravity wave detectors.    \r\n\r\n\r\n  [1]: http://arstechnica.com/science/news/2011/01/pqe-2011-small-atoms-big-ideas-in-gravity-detection.ars\n\nAnswer (score=-2):\n\nit will be good for making very sensitive measurement instruments and maybe making tiny structures, like they use in computer chips.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 4, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-2.5", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "quantum-mechanics", "condensed-matter", "bose-einstein-condensate", "big-list"], "page_start": null, "page_end": null, "quality_flags": ["mixed_license"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 2708, "title": "Practical applications for a Bose-Einstein condensate", "url": "https://physics.stackexchange.com/questions/2708/practical-applications-for-a-bose-einstein-condensate", "share_url": "https://physics.stackexchange.com/q/2708", "content_license": null, "owner": {"display_name": "Andy Bale", "user_id": 592, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/592/andy-bale"}}, "answers": [{"answer_id": 2724, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/2708/practical-applications-for-a-bose-einstein-condensate/2724#2724", "share_url": "https://physics.stackexchange.com/a/2724", "content_license": "CC BY-SA 2.5", "owner": {"display_name": "Chad Orzel", "user_id": 166, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/166/chad-orzel"}}, {"answer_id": 2713, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/2708/practical-applications-for-a-bose-einstein-condensate/2713#2713", "share_url": "https://physics.stackexchange.com/a/2713", "content_license": "CC BY-SA 2.5", "owner": {"display_name": "Kostya", "user_id": 386, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/386/kostya"}}, {"answer_id": 2720, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/2708/practical-applications-for-a-bose-einstein-condensate/2720#2720", "share_url": "https://physics.stackexchange.com/a/2720", "content_license": "CC BY-SA 2.5", "owner": {"display_name": "rcollyer", "user_id": 770, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/770/rcollyer"}}, {"answer_id": 30396, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/2708/practical-applications-for-a-bose-einstein-condensate/30396#30396", "share_url": "https://physics.stackexchange.com/a/30396", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "isha shrivastava", "user_id": 9981, "user_type": "unregistered", "profile_url": "https://physics.stackexchange.com/users/9981/isha-shrivastava"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:659015:0000", "text": "Question: Minimum speed that a bike won't fall over\n\nI thought about this when riding the bike today:\r\n\r\nWhat is the minimum speed I have to go that my bike won't fall over with a given angle $\\alpha$ of tilt, diameter $d$ and weight $m$ of a tire (let's say the bike tilts 30 degrees at maximum when driving in a straight line and the diameter of a tire is 0.60&nbsp;m with a weight of 1&nbsp;kg per tire).\r\n\r\nI guess the angular momentum of the tires has to counter the torque of the gravitational force somehow.\r\nHow can I calculate this?\n\nAccepted Answer:\n\n> I guess the angular momentum of the tires has to counter the torque of the gravitational force somehow. Can someone help me calculate this?\r\n\r\nThat's the peculiar thing, the angular momentum of the tires doesn't actively provide torque to bring the bike back upright. Rather, it slows down the rate at which the bike can tilt, allowing a rider enough reaction time to make the proper adjustments to keep it upright.\r\n\r\n\r\nIf you get a bike up to high speed and then just \"let it go\", you'll notice it falls to the ground pretty quickly, almost as quickly as if you just let it go in your garage. \r\n\r\n**Edit**: There's a lot of discussion below about how a bike can be self correcting due to the ability to *turn* - lots of great physics in there but it's missing the point of the question, which is the correction when \r\n\r\n> moving in a straight line\r\n\r\nThe amount a bike can precess to stay upright will depend on a number of parameters about the bike. On one extreme you have a wheel by itself, which will continue to turn until it slows to a stop and then fall. On the other extreme, you can imagine an extremely long bike with locked handle bars - it will fall to the ground quite quickly. All that would be a great answer to a separate question.\r\n\r\nMoreover you'll notice I carefully worded my answer to say:\r\n\r\n> the angular momentum of the tires doesn't actively provide torque to bring the bike back upright\r\n\r\nAs I wanted to give a simple answer that doesn't overwhelm someone asking a simple question at their level (but I get that everyone loves to \"actually...\" on this site). This statement is correct that the angular momentum of the tires will slow the tilt toward the ground but never restore the bike toward its center. That was the point.\n\nAnswer (score=3):\n\nThe bike will not go straight if it is left alone and tipping. Secondly, it will tip slightly faster if not moving, but it will still tip over from any non-vertical angle whether moving or not. \r\n\r\n__________\r\n\r\nAll assumes no rider:\r\n\r\nThe right-had rule can tell you which way it’s path will curve as it tips, but your intuition will too: if leaning right the bike will gently turn right. And the handlebars/front-wheel as a unit has a lower moment of inertia around a vertical axis than the body of the bike, and hence they will turn faster. \r\n\r\nAlso, the gyroscopic “force” is just our way of trying to understand and communicate the dynamics of a spinning object when an external force is applied to its axis. The bike will tip over by itself any angle from vertical, however small, it may just take longer if moving. \r\n\r\nHere’s one rigorous way to see the situation: the wheels are spinning and have an axis of rotation which is the same as each wheel’s axis. The direction of the vector representing the angular velocity is pointed along the axis to the left, determined from the right-had rule with your fingers going the spinning wheel’s direction, and its length determined by how fast the wheel spins. \r\n\r\nIf the bike is tipped a little, let’s say to the right, then gravity is pushing downward, and **it is displaced slightly** from the center of the wheel’s axis (displaced horizontally). That creates a torque around the very center of the wheel. We know a torque angularly accelerates something by $T = I \\alpha , \\alpha = I / T$ and the direction of this angular acceleration vector is, by the right-hand rule, pointed in the direction of the bike’s travel. \r\n\r\nHow will this change the angular velocity vector of the wheel. Just add vectors. It will transform the angular velocity vector (which points left) by moving it forward, and this means the wheel is spinning about a new axis and will move perpendicular to that new axis, ie bend to the right. The front wheels can turn more easily as they only have to move the wheel/handle-bar assembly. \r\n\r\nIf not moving, the torque will go entirely into rotating the bike itself about the point where the tires touch the pavement and not have to slowly bend the existing axis of angular momentum. If moving, the torque modifies the current dynamic by moving axis of rotation. \r\n\r\n___________\r\n\r\n\r\nAs an aside, the right-hand rule is an arbitrary convention; there is nothing special about right vs left. In fact, handedness is a fundamental physical parameter, which **Immanuel Kant did not realize**. He thought a hand in space away from any object or orientation would be neither right- nor left-handed https://philosophy.stackexchange.com/a/84452/53366", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 5, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-4.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "homework-and-exercises", "newtonian-mechanics", "classical-mechanics", "everyday-life"], "page_start": null, "page_end": null, "quality_flags": [], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 659015, "title": "Minimum speed that a bike won't fall over", "url": "https://physics.stackexchange.com/questions/659015/minimum-speed-that-a-bike-wont-fall-over", "share_url": "https://physics.stackexchange.com/q/659015", "content_license": null, "owner": {"display_name": "juliangst", "user_id": 311224, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/311224/juliangst"}}, "answers": [{"answer_id": 659021, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/659015/minimum-speed-that-a-bike-wont-fall-over/659021#659021", "share_url": "https://physics.stackexchange.com/a/659021", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "Señor O", "user_id": 43294, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/43294/se%c3%b1or-o"}}, {"answer_id": 659023, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/659015/minimum-speed-that-a-bike-wont-fall-over/659023#659023", "share_url": "https://physics.stackexchange.com/a/659023", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "Al Brown", "user_id": 307354, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/307354/al-brown"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:67077:0000", "text": "Question: Do Microwave oven heating times grow linearly with Wattage? Calculating optimal heating time\n\nSo this is a completely random and trivial question that was prompted by looking at my microwave oven and the back of a TV dinner and my google searching failed to produce a meaningful answer so figured I'd ask here.\r\n\r\nOn my TV dinner box it has different cook times based on Microwave Oven Wattage:\r\n\r\n**1100 Watts** - Cook **2 minutes**, stir and cook for another **1.5 minutes**. (**3.5 minutes total**)\r\n\r\n**700 Watts** - Cook **3 minutes**, stir and cook for another **2.5 minutes**.  (**5.5 minutes total**) \r\n\r\nMy oven is **900 Watts**, which is right in the middle.\r\n\r\nAssuming those times listed on the box are the scientifically optimal cook time (which is doubtful, but just go with me), is it fair to assume I should use the linear average for **2.5 minutes**, stir and cook for another **2 minutes** (**4.5 minutes total**), or is there a different rate of growth between the **700 watt** and **1100 watt** ovens that would change the optimal cook time?\n\nAccepted Answer:\n\nThe rate at which a mass absorbs microwave radiation is characterized by the 'Specific Absorption Rate', which is proportional to the electromagnetic field intensity:\r\n\r\nWikipedia has a [dedicated article][1] to this phenomenon but in short it says \r\n\r\n$$\\text{SAR} = \\int_\\text{sample} \\frac{\\sigma(\\vec{r})|\\vec{E}(\\vec{r})|^2}{\\rho(\\vec{r})} d\\vec{r}$$\r\n\r\n**Because the absorption rate is proportional to the EM field intensity, $|\\vec{E}(\\vec{r})|^2$, which is in turn proportional to power, then the relationship will indeed be linear.**\r\n\r\nAssuming 100% energy efficiency (which is a wild overestimate: 20% might be more accurate but I do not know the answer to that question) your total 'energy' transferred to your dinner will be:\r\n\r\n$$ \\text{Energy} = \\text{Power} \\Delta t$$\r\n\r\ni.e. \r\n\r\n$$\\Delta t = \\frac{\\text{Energy}}{\\text{Power}} $$\r\n\r\nThe cook time will be inversely proportional to your oven power.\r\n\r\n1100 watts for 3.5 minutes computes to \r\n$$ \\text{Energy } = 1100 \\text{ Watts } \\times 210 \\text{ seconds } = 231,000 \\text{ Joules}$$\r\n\r\n700 Watts for 5.5 minutes computes to \r\n$$ \\text{Energy } = 700 \\text{ Watts } \\times 330 \\text{ seconds } = 231,000 \\text{ Joules}$$\r\n\r\nThus a 900 Watt oven would necessitate\r\n\r\n$$\\Delta t = \\frac{\\text{Energy}}{\\text{Power}} = 256.66 \\text{ seconds } = 4.278 \\text{ minutes }$$\r\n\r\n\r\n  [1]: http://en.wikipedia.org/wiki/Specific_absorption_rate\n\nAnswer (score=3):\n\nTo a first approximation, the product of power $P$ and time $t$ should be constant, since the energy put into heating the object is\r\n$$ E = Pt. $$\r\nThat is, to achieve the same effect, time should be *inversely proportional* to power. (Of course, if the power is *so* low that the process lasts for hours, one would need to consider the rate at which the food is cooling as well.)\r\n\r\nNote that\r\n$$ (1100\\ \\mathrm{W}) \\times (210\\ \\mathrm{s}) = 231\\ \\mathrm{kJ}, $$\r\nwhile\r\n$$ (700\\ \\mathrm{W}) \\times (330\\ \\mathrm{s}) = 231\\ \\mathrm{kJ}, $$\r\nso our assumption of constant energy seems to be what the manufacturer used. Then with a $900\\ \\mathrm{W}$ power source the required time is\r\n$$ t = \\frac{E}{P} = \\frac{231\\ \\mathrm{kJ}}{900\\ \\mathrm{W}} = 257\\ \\mathrm{s} $$\r\ntotal, to the nearest second. Note that this is *not quite* the mean of $210\\ \\mathrm{s}$ and $330\\ \\mathrm{s}$.\r\n\r\nBy analogy, think of this in terms of distances (rather than energies), speeds (rather than powers), and times. If a destination is $12$ miles away, you can walk at $1\\ \\mathrm{mph}$ for $12$ hours, $3\\ \\mathrm{mph}$ for $4$ hours, or $2\\ \\mathrm{mph}$ for $6$ (but *not* $(12+4)/2 = 8$) hours.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 6, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "thermodynamics", "microwaves"], "page_start": null, "page_end": null, "quality_flags": [], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 67077, "title": "Do Microwave oven heating times grow linearly with Wattage? Calculating optimal heating time", "url": "https://physics.stackexchange.com/questions/67077/do-microwave-oven-heating-times-grow-linearly-with-wattage-calculating-optimal", "share_url": "https://physics.stackexchange.com/q/67077", "content_license": null, "owner": {"display_name": "David Stinemetze", "user_id": 25415, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/25415/david-stinemetze"}}, "answers": [{"answer_id": 67081, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/67077/do-microwave-oven-heating-times-grow-linearly-with-wattage-calculating-optimal/67081#67081", "share_url": "https://physics.stackexchange.com/a/67081", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Joe", "user_id": 25331, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/25331/joe"}}, {"answer_id": 67080, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/67077/do-microwave-oven-heating-times-grow-linearly-with-wattage-calculating-optimal/67080#67080", "share_url": "https://physics.stackexchange.com/a/67080", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "user10851", "user_id": null, "user_type": "does_not_exist", "profile_url": null}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:572880:0000", "text": "Question: Physics of \"force spreading\" on impact on a surface\n\nConsider a plate $P$ of thickness $d$ (for example a plate of wood) laying on a hard surface $S$ (for example on concrete floor). Suppose you have a maximum value of pressure $p_{\\mathrm{max}}$ $S$ could tolerate before it fails in some way. Suppose further you know a pressure distribution acting on plate $P$ downwards (for example a given force $F$ acting on an area $A$ on $P$). \r\n\r\nThen I want to calculate the pressure distribution on $S$ to see if $p_{\\mathrm{max}}$ is respected everywhere. What would the idea to do so and what are the relevant formulas? What parameter of the material of $P$ determines of how the force acting on $P$ is spread out over a larger area resulting in lower maximal forces acting on $S$?\r\n\r\nThe original motivation for this question was to get a better understanding the physics of a olympic weightlifting platform and how to numerically model the difference between rubber and wood as a material for the platform in terms of reducing the impact force on the concrete floor and thus protecting the concrete. More specifically this quote was the starting point of this question to understand it deeper: \r\n\r\n> A good sheet of 3/4″ rubber is good in that it absorbs some of the\r\n> force, but it only spreads out the force a little bit. That’s where a\r\n> platform comes in. Wood is rigid and will spread the force out.\r\n\r\n(from https://www.tworepcave.com/4543/why-olympic-lifting-platform/)\r\n\r\nSo for example consider a barbell that falls from height $h$ directly on the concrete floor resulting in a pressure distribution $p_0$ on the concrete floor. \r\n\r\nThen lay a plate of rubber on the concrete floor and drop the barbell again on the rubber surface. Since the rubber deforms by a distance $s$, it enlarges the stopping distance and thus reduces the force on the concrete floor. Additionally it \"spreads\" the force a little bit over the area of the plate resulting in a pressure distribution (acting on the concrete floor) $p_{\\mathrm{rubber}} < p_{0}$. \r\n\r\nNow do the same with the wooden plate (same dimensions as the rubber plate). In this case it deforms much less, but \"spreads\" the force much better because it is stiffer than the rubber, the combined effect seems to be much better than in the rubber case (but I don't see to estimate the order of magnitude of difference between the materials), resulting in pressure distribution $p_{\\mathrm{wood}}$ with $p_{\\mathrm{wood}} \\ll p_{\\mathrm{rubber}} < p_0$.\r\n\r\nI didn't find anything in the web so far discussing this or a similar problem more in depth (either theoretically nor experimentally). So if you have further references, it would be great to include it in your answer. \r\n\r\n**Edit**\r\n\r\nFor the case of the barbell and the rubber tile, I would say that there for protection of the floor the rubber layer seems to have three main effects:\r\n\r\n- A \"Cushioning effect\": Since the barbell plate sinks a bit into the rubber tile, the contact area is increased (compared to the contact with the bare concrete), thus the force is spread over a specific area on the top of the rubber tile.\r\n- Increasing the \"breaking distance\": Since the rubber tile is softer than the concrete, it enlarges the breaking distance and thus reduces the total impact force significantly.\r\n- \"Spreading the force over an even larger area\" on the bottom of the rubber tile. This effect is usually utilized in weightlifting platforms where one uses relatively stiff wooden plates to \"spread the force over a large area\". Since the rubber is much less stiff than wood this effect will be much smaller than in the case of a wooden plate, but I guess that it also plays an important role when you use high density rubber tiles. However I am not able to quantify this effect.\r\n\r\nI am not sure of how large the three effects are compared to each other. Maybe one can show that one effect is negligible.\n\nAccepted Answer:\n\nThere is a huge amount of parameters to that problem that make it impossible to derive general formulae:\r\n\r\n - shape of the barbell (especially how sharp the edges are) and moments of inertia\r\n - impact angles of the barbell on the floor\r\n - dynamic (velocity dependent/viscous) stiffness/damping of the platform materials \r\n - nonlinearity of the platform materials (especially progression in the case of rubber, but also plasticity for other materials)\r\n - anisotropy of the materials (especially wood)\r\n - boundary conditions of the platform\r\n - random effects like grain size distribution of the aggregate (for concrete) or permanent stresses/fracture mechanics (think of a platform made out of glass as an illustrating extreme example)\r\n\r\nThe maximum stress (or even the stress distribution) during impact **very** sensitively depends on all of these parameters. \r\n\r\nFor calculating such events, one usually uses finite element software, namely explicit time-dependent solvers (crash simulation in the automotive industry, or bullet impact in defense). A commercial product dedicated to this is LS-Dyna (I am not paid for mentioning that, and I don't particularly like the product either, just had to work with it in the past). There may be other products, which anyone may feel free to mention in the comments.\r\n\r\nTrying to control the problem by deriving closed formulae is a waste of lifetime, because you will always have to focus on a specific view on the problem, and neglect others. For the special case of the static problem (which you should be cautious about substituting for the dynamic problem!), however, [Hertzian contact theory][1] might be of some insight with respect to general load distribution.\r\n\r\n\r\n  [1]: https://en.wikipedia.org/wiki/Contact_mechanics\n\nAnswer (score=2):\n\nWhen a barbell is slowly placed on the plate, both are elastic deformed according to the elastic constants of the materials, the barbell weight, and the geometry of the contact. \r\n\r\nBut when it falls, the impact is not transmitted at once to all volume of the bodies to generate the same deformed geometry. The small region of the contact on the plate is forced to accelerate downwards, and that movement is communicated to the surroundings in the form of an elastic wave with a finite speed. The mathematical description is outlined in [this][1] answer.  \r\n\r\nThe tensions are proportional to the deformations, as shown in https://physics.stackexchange.com/a/558821/195949, for the simplified case of uniaxial elastic waves. The wave speed is $v = \\sqrt{\\frac{E}{\\rho}}$ in this case, where $E$ is the modulus of elasticity, and $\\rho$ the density. \r\n\r\nThe 3D situation is more complex, but anyway the greater the stiffness of the plate, the greater is the wave speed. And the wave speed is a measure of how fast the impact is spread to the plate as a whole.\r\n\r\nAs the stiffness of rubber is much smaller than wood, much of the impact will be transmitted to the ground behind. Steel would be even stiffer, but I'm afraid that the barbell could be damaged by the impact. \r\n\r\nThe sound produced during the impact is a measure of the energy of the elastic waves. In the case of wood, part of the energy is also converted in heat, associated to a permanent deformation in the place of contact. \r\n\r\n\r\n  [1]: https://physics.stackexchange.com/a/555317/195949", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 7, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-4.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "newtonian-mechanics", "classical-mechanics", "contact-mechanics"], "page_start": null, "page_end": null, "quality_flags": [], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 572880, "title": "Physics of \"force spreading\" on impact on a surface", "url": "https://physics.stackexchange.com/questions/572880/physics-of-force-spreading-on-impact-on-a-surface", "share_url": "https://physics.stackexchange.com/q/572880", "content_license": null, "owner": {"display_name": "Sarah", "user_id": 30883, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/30883/sarah"}}, "answers": [{"answer_id": 648586, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/572880/physics-of-force-spreading-on-impact-on-a-surface/648586#648586", "share_url": "https://physics.stackexchange.com/a/648586", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "oliver", "user_id": 232973, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/232973/oliver"}}, {"answer_id": 603289, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/572880/physics-of-force-spreading-on-impact-on-a-surface/603289#603289", "share_url": "https://physics.stackexchange.com/a/603289", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "Claudio Saspinski", "user_id": 195949, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/195949/claudio-saspinski"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:3852:0000", "text": "Question: How does the Kinect device work?\n\nSome explanations of the device base it on a simple echo of light: \"The camera transmits invisible near-infrared light and measures its “time of flight” after it reflects off the objects. Time-of-flight works like sonar: If you know how long the light takes to return, you know how far away an object is.\" ([wired.com][1]). Is it so easy? On other hand, the developers, Primesense, speak about \"a sophisticated parallel computational algorithm to decipher the received light coding\". And they claim to avoid noise from ambiance light and to be able to obtain a resolution of 1cm at 2 meters.\r\n\r\nA motivation to ask this here in physics is that some other questions were asking for measurement of light speed with household devices.\r\n\r\n  [1]: http://www.wired.com/gadgetlab/2010/11/tonights-release-xbox-kinect-how-does-it-work/\n\nAccepted Answer:\n\nNo. It does not measure time of flight. Kinect is, deep down, a [structured light scanner][1], meaning that it projects an infrared pattern (so invisible for us). According to the underlying technology firm PrimeSense, [the structured light code is drawn with an infrared laser][2]. This pattern is then read by an infrared camera and the 3D information is reconstructed from the distortions of the pattern. This results in a depth channel which is made available through USB.\r\n\r\nIf you want to see the pattern, you may have some luck by turning off all the lights in the room, turn on the kinect, and try to use your cellphone camera. Generally, these camera sensors are sensitive to IR, which appears as green. You may verify if this is the case by trying the same with a TV remote and pressing the buttons. The LED should turn green.\r\n\r\n  [1]: http://en.wikipedia.org/wiki/Structured_Light_3D_Scanner\r\n  [2]: http://www.primesense.com/?p=535\n\nAnswer (score=2):\n\nHere is further confirmation that the Kinect uses structured light measurement.\r\n  \r\n[Presentation covering  time of flight and Kinect's structured light range imaging][1]\r\n\r\n\r\n  [1]: http://campar.in.tum.de/twiki/pub/Chair/TeachingSs11Kinect/2011-DSensors_LabCourse_Kinect.pdf", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 8, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-2.5", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "optics"], "page_start": null, "page_end": null, "quality_flags": ["mixed_license"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 3852, "title": "How does the Kinect device work?", "url": "https://physics.stackexchange.com/questions/3852/how-does-the-kinect-device-work", "share_url": "https://physics.stackexchange.com/q/3852", "content_license": null, "owner": {"display_name": "arivero", "user_id": 1335, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/1335/arivero"}}, "answers": [{"answer_id": 3885, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/3852/how-does-the-kinect-device-work/3885#3885", "share_url": "https://physics.stackexchange.com/a/3885", "content_license": "CC BY-SA 2.5", "owner": {"display_name": "Stefano Borini", "user_id": 217, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/217/stefano-borini"}}, {"answer_id": 17982, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/3852/how-does-the-kinect-device-work/17982#17982", "share_url": "https://physics.stackexchange.com/a/17982", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Joey", "user_id": 6539, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/6539/joey"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:49955:0000", "text": "Question: Can an induction coil heat two layers of metal?\n\nImagine we have an induction coil which is strong enough to heat a sheet of metal. We can put a sheet of ferromagnetic metal close to the coil at distance $h_1$, and it gets heated to temperature $t_1$, or at distance $h_2 > h_1$ so that the sheet gets heated to temperature $t_2 < t_1$. \r\n\r\nI want to know what happens if we have two identical sheets at once, one at distance $h_1$ and one at distance $h_2$, on the same side of the coil, with some insulator between the sheets (the insulator does not conduct electricity, is not ferromagnetic, and does not conduct heat well). Will the sheet farther away from the coil heat up at all, or will the closer sheet shield it from the electromagnetic field in some way? What will the temperatures $t_1'$ and $t_2'$ of the sheets in this experiment be, higher, lower or the same as $t_1$ and $t_2$? \r\n\r\nDoes the answer to the above change if we have a small conducting connection between the two sheets of metal, e.g. a wire which touches both the close and the far one, but most of their surface is still separated?\r\n\r\nThe application for this question: I am thinking of getting a cast iron waffle iron to use on my induction stove, and I am trying to imagine how this will function. By the way, I know that I will get some heat conducted through the waffle itself, and I will probably turn it anyway so both plates get hot, but please ignore these effects when answering the question and tell me the effects of induction only.\n\nAccepted Answer:\n\nThe answer is no. The penetration depth of the magnetic field in the first sheet is too small. Read [this][1] for example. The penetration depth $\\delta$ is typically given by a formula looking something like this:\r\n\r\n$$\r\n\\delta=\\sqrt{\\frac{\\rho}{\\pi\\mu f}}\\approx\\sqrt{\\frac{1\\cdot10^{-7}}{\\pi\\cdot8.8\\cdot10^{-4}\\cdot20\\cdot10^3}}\\approx4.3\\cdot10^{-5}\\mathrm{m}=0.043\\mathrm{mm}\r\n$$\r\n\r\nWhere $\\rho$ is the resistivity of the material (I've assumed steel), $\\mu$ is the magnetical permeability (I've assumed steel) and f is the freequency of the magnetic field (20 kHz is on the lower end of the range used in induction stoves. Higher frequencies would give even shorter penetration depths.) Assuming each side of the waffle iron is considerably thicker than 0.043 mm, your plan won't work.\r\n\r\n  [1]: http://en.wikipedia.org/wiki/Skin_effect", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 9, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "electromagnetism", "thermodynamics", "heat", "induction"], "page_start": null, "page_end": null, "quality_flags": ["single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 49955, "title": "Can an induction coil heat two layers of metal?", "url": "https://physics.stackexchange.com/questions/49955/can-an-induction-coil-heat-two-layers-of-metal", "share_url": "https://physics.stackexchange.com/q/49955", "content_license": null, "owner": {"display_name": "rumtscho", "user_id": 18752, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/18752/rumtscho"}}, "answers": [{"answer_id": 49958, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/49955/can-an-induction-coil-heat-two-layers-of-metal/49958#49958", "share_url": "https://physics.stackexchange.com/a/49958", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "jkej", "user_id": 18740, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/18740/jkej"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:22618:0000", "text": "Question: Are quantum mechanics calculations useful for engineering?\n\nI heard it's is pretty tough to get results for more than a few quantum particles. Are quantum mechanical calculations useful at all for any technology that is being sold?\r\nOr do they use quasi-classical results at most?\r\n\r\nIs there hope that advances in QM calculations would make any change to the technological world? I'm basically considering everything that could make a change to our life disregarding pure theoretical research results.\r\n\r\nWhich path of QM advances could potentially be the most yielding in terms of practical results?\r\n\r\nEDIT: From what I experienced, experiments are already producing results, when theorists are still trying to fit their theories to the data. So why do you need the theoretical calculations then? Do they have predictive power that would be found easier and more precise with experiments?\n\nAccepted Answer:\n\nThere are several different levels of advanced in quantum mechanics. I will try to answer using these levels of quantum mechanics:\r\n\r\n1. Basic: single particle or single particles interacting with a single atom/nucleus, or classical field picture--- anything Einstein would have been comfortable with.\r\n2. Advanced: highly entangled many-body quantum mechanics, involving many-body effects that cannot be understood from single-body or single-field picture.\r\n3. Inscrutable: quantum computing--- actual exponential computation as compared to classical behavior.\r\n\r\nI will give an off-the-cuff list of things that were predicted theoretically at each of the three levels, that was hard to understand from just seat-of-the-pants non-quantum intuition.\r\n\r\nAt level 1, there are essentially as many examples as you care to list:\r\n\r\n * Electron diffraction: The diffraction of electrons from crystals was one of the early predictions of quantum mechanics which was confirmed experimentally. Knowing that electrons diffract is important for the construction of electron microscopes, and you need to know the relation between wavelength and momentum.\r\n * lasers come from spontaneous emission theory, and Einstein's prediction that a coherent collection of bosons will make other bosons be created with the same momentum preferentially was very surprising. This is the basic idea behind lasers, and BEC's, and these were only found because the theoretical principles were known in advance.\r\n * Slow neutrons are dangerous: If you classically estimate the neutron scattering cross section off a nucleus, at low momenta, you are completely wrong, because of resonance effects. These effects can blow up the nucleus to look (to the neutron) as it it were the size of a barn, when it is normally the size of a kernel of corn. You can look up the unit \"barn\" for a more accurate etymology.\r\n * qualitative chemistry: If you use simple quantum mechanical orbitals, and the notion of superposition (which is called resonance in chemistry), you can get an idea of which molecules will make dyes, what shapes will be preferred, and so on. These types of things were worked out by Linus Pauling, and led to the discovery of the alpha-helix, and later, to the structure of DNA.\r\n\r\nThere are too many class-1 examples to list, so consider class 2. Here, one is looking for a theoretical insight in a many-body system, with a highly entangled wavefunction, which leads to practical predictions. The easiest example that comes to mind is BCS theory.\r\n\r\n * BCS theory: this predicts that any very cold Fermi system with the weakest of attractive interactions will produce a strange vacuum state, where it is like a Bose Einstein condensate of paired-fermions, _even when the force is too weak to bind two individual Fermions into actual pairs_. The presence of other Fermions in the sea is essential, it makes a condensate of particles which do not exist really.\r\n\r\nOne of the most striking prediction of BCS theory was the prediction that He3 should become superfluid at ultra-cold temperatures. There is no reason you would suspect this from experiments on superconductors, without the detailed theory of Cooper pairing. This was spectacularly confirmed by difficult experimental work of Lee, Osheroff, and Richardson, work which was awarded the 1996 Nobel prize.\r\n\r\nThe theory of renormalization is quantum, class 2--- many body. But it is equally applicable to statistical systems, where simple models allow one to predict all sorts of phenomena that were not suspected experimentally. Here is an example:\r\n\r\n* Anderson localization in 1d and 2d: Any sufficiently long wire is insulating. Any sufficiently large sheet of conductor is also insulating. You would never guess even the 1d business from experiment, but it is true, and needs to be considered when you make very thin wires. Anderson localization itself is in class 1, but the renormalization analysis which allows you to say things like this is class 2.\r\n\r\nQuantum field theory has made contact with experiment, most elegantly through 2d conformal field theory:\r\n\r\n* Rational 2d critical exponents: This was predicted from sophisticated quantum field theory considerations, relying on the conformal algebra from string theory, relying on the 2d conformal field theory of Belavin, Polyakov Zamolodchikov. That in itself was an extension of 1960s work on operator product expansion, by Zimmermann, Wilson, Kadanoff and Polyakov, which defined the correct algebra for renormalized fields. The rational critical exponents are confirmed experimentally using systems as divers as polymers, 2d fluids, but also using exact solutions, and conputer simulations. You would have a hard time guessing an exponent is rational from an experiment.\r\n\r\nBut by far the most spectacular type 2 quantum theoretical application is:\r\n\r\n* Semiconductor physics: The qualitative ideas of semiconductor physics, including the existence of \"P-type\" charge carriers, were understood theoretically in tandem with the experimental production of these materials. The theory of doping is not so sophisticated--- you need to know which are donors and which are acceptors, but the theory of p-type semiconductors relies crucially on many-body effects, so that you have particle hole symmetry. This is the central technological advance of the late 20th century, and made possible the computer revolution.\r\n\r\nIn class 3, there are several potential applications:\r\n\r\n* Simulating quantum systems: As Feynman noted, a quantum computer will be able to simulate other quantum systems efficiently. This is impossible on a classical computer.\r\n* Factoring: Given a quantum computer, Peter Shor showed how to factor numbers, which will make current cryptographic systems insecure.\r\n* Grover's database search: This allows you to search a database with N items in $\\sqrt{N}$ steps.\r\n* Guaranteed secure communications: You can make a channel in which you can ensure that you and your communication partner are not eavesdropped on.\r\n\r\nFor the other applications in this class, I defer to Nielsen and Chuang. The problem with class 3 applications (at least the full blown computational ones) is that we aren't going to be 100% sure they will work until we build them. The other option is that quantum mechanics will fail for these.\n\nAnswer (score=14):\n\nQM already made a big change to our lives:\r\n\r\nWithout QM no transistors. Without transistors, no modern computers. Without modern computers, you wouldn't have been able to ask your question here. \r\n\r\nBefore an integrated circuit (that encapsulates an array of transistors in a piece of computer equipment, say) is mass produced, one must do a huge number of simulation calculations that are all based on quantum mechanics proper. Simple semiclassical models only give the dominant behavior.\r\n\r\nOf course, once you have built a transistor you can use it as a classical device once you know the response curves. But to create a transistor with a desired behavior, you are very handicapped without a profound knowledge of quantum mechnaics.\r\n\r\nThe same holds for laser equipment. Using lasers is an essentially classical activity, but creating lasers with specific desirable properties requires detailed knowledge of quantum mechanical processes on the atomic or molecular level.\r\n\r\nIn many cases, (even long) quantum mechanical simulations are far cheaper than experimental studies. In many other cases, they complement each other. \r\n\r\nNote that experiments to improve parameters in theories usually address aspects of a theory on quite a different level from the part of the theory that is applied. \r\n\r\nThere is no need to tune QED to experiments, as all constants are already known to very high accuracy. Some physicists try to improve the accuracy further, but for applied work, far less accuracy is usually sufficient.\n\nAnswer (score=3):\n\nThis is only a response to your edit:\r\n> EDIT: From what I experienced, experiments are already producing results, when theorists are still trying to fit their theories to the data. So why do you need the theoretical calculations then? Do they have predictive power that would be found easier and more precise with experiments?\r\n\r\nWhat sort of predictive power can you get from experiments? Experiments only let you \"predict\" something by actually carrying it out. That's neither a prediction nor a retrodiction--you could call it 'diction', I guess ;).\r\n\r\nIf you carry out multiple experiments and use their results to predict stuff, you are _theorizing_ about the nature of physics. That means, you have a _theory_. if you want to make _predictions_ with experiments, then a theory is unavoidable. On the other hand, experiments can make _retrodictions_--basically verifying a theory with experimental results. \r\n\r\nThe issue is, while we try to make a general theory based on experimental results, more results keep coming in. Leads to a bit of an issue when the new results don't fit in. Of course, there's the flipside fanfare when they do fit in (Prediction of gallium, prediction of $\\Omega^-$, Gravitational lensing--and if the Higgs is found, we will have quite a bit of fanfare)\r\n\r\n\r\nHere's an extremely simple analogy(lifted from a math.SE post), which may explain the reason why theories never can keep up with experiments: In my experiment, I take natural numbers from $1,2,3,4...100$ and compare them with $10^6$. I discover the exotic property that all of them are less than $10^6$. From this, I theorize that all natural numbers are smaller than $10^6$. I feel happy in having creating a theory that checks out with experiments. The theory has use in the everyday world as well--we don't deal with such large numbers anyways. Now, someone decides to test this theory further. He tries larger numbers (no doubt using a Large Number Collider with floating-point arithmetic), and discovers that my theory no longer holds.\r\n\r\n Note that my theory is still pretty applicable, if someone asks me \"how much money is in your pocket?\", I can safely answer \"less than a million\" without having to count the money or know how much is there. But, if I did deal with that kind of money, my theory would no longer hold. Similar things happen in physics. Experiments rule out old theories, but they simultaneously set bounds for which they are valid. Theory comes from a half-baked perception of the world(imagine if I gave you a slice of a car and told you to figure out how it works), which is why it must keep up with experiments.\n\nAnswer (score=-2):\n\nOf course! Check for instance \"_Some chemical engineering applications of quantum chemical calculations_\" Advances in Chemical Engineering 28, 2001, 313–351 Stanley I. Sandler Amadeu K. Sum, Shiang-Tai Lin or this textbook [Quantum Mechanics for Scientists and Engineers](http://www.amazon.com/Mechanics-Scientists-Engineers-Classroom-Materials/dp/0521897831)", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 10, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "quantum-mechanics", "soft-question", "technology"], "page_start": null, "page_end": null, "quality_flags": [], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 22618, "title": "Are quantum mechanics calculations useful for engineering?", "url": "https://physics.stackexchange.com/questions/22618/are-quantum-mechanics-calculations-useful-for-engineering", "share_url": "https://physics.stackexchange.com/q/22618", "content_license": null, "owner": {"display_name": "Gere", "user_id": 5152, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/5152/gere"}}, "answers": [{"answer_id": 22651, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/22618/are-quantum-mechanics-calculations-useful-for-engineering/22651#22651", "share_url": "https://physics.stackexchange.com/a/22651", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Ron Maimon", "user_id": 4864, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/4864/ron-maimon"}}, {"answer_id": 22620, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/22618/are-quantum-mechanics-calculations-useful-for-engineering/22620#22620", "share_url": "https://physics.stackexchange.com/a/22620", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Arnold Neumaier", "user_id": 7924, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/7924/arnold-neumaier"}}, {"answer_id": 22654, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/22618/are-quantum-mechanics-calculations-useful-for-engineering/22654#22654", "share_url": "https://physics.stackexchange.com/a/22654", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Manishearth", "user_id": 7433, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/7433/manishearth"}}, {"answer_id": 41336, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/22618/are-quantum-mechanics-calculations-useful-for-engineering/41336#41336", "share_url": "https://physics.stackexchange.com/a/41336", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "juanrga", "user_id": 12998, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/12998/juanrga"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:6827:0000", "text": "Question: Cladding of optical fibers\n\nWhy do optical fibers usually have a cladding? Ok, if you put make a bundle of optical fibers this prevents that light leaks from one fiber to another fiber in contact. However, are there other reasons to use claddings? Are there applications of optical fibers without claddings?\r\n\r\n(I am mainly interested in optical fibres which can be described by geometrical optics, i.e. multimode fibers.)\n\nAccepted Answer:\n\nFor a fiber to guide light, even considering the situation using only geometrical optics, there must be total internal reflection (TIR) at the boundary of the fiber core. For TIR to occur, the angle of incidence of the light must be greater than the critical angle $\\theta_c$. If the material before the boundary has index of refraction $n_1$ and the material after the boundary has index $n_2$, then the critical angle is:\r\n\r\n$$ \\theta_c = \\arcsin(\\frac{n_2}{n_1})$$\r\n\r\nOf course, if $\\frac{n_2}{n_1} > 1$ then the critical angle is undefined -- TIR cannot occur. This is why TIR is only possible when light encounters an interface with a material of lower index. This should be familiar to you if you think about it: you can see the bottom of a pool from above the water, but the water surface looks silvery and reflective from underneath; the reflective face of a roof prism looks reflective when you try to look through it from the glass-to-air side, but if you look from the air side, you can see clearly.\r\n\r\nOn its own, this doesn't require a fiber to have cladding. Air has an index very near 1, so any other material will have a higher index, and therefore guide light without a cladding. However, this situation would be very unstable. Any material contacting the fiber could produce an area where TIR does not occur, and suddenly the fiber would begin leaking. Consider how easy it would be for this to happen! Any sort of dirt or oil on the fiber would either eliminate TIR completely, or raise the critical angle such that some of the light could escape. The same would be true of most materials you might use to mount the fiber, or even any type of coating you might apply as a mechanical barrier to dirt.\r\n\r\nThus, in practice, fibers have a cladding to ensure that the optical guiding characteristics continue to work in real world conditions. They also provide engineers with another way of adjusting the properties of the fiber, so its definitely not something we are unhappy about.\r\n\r\nDo keep in mind though, that there are examples of unclad \"fibers\" although they are usually just acrylic rods used in teaching demonstrations, so I wouldn't really call them a fiber in the common sense of the word.\n\nAnswer (score=7):\n\nDo you think a fiber that worked until is got some water on it would be acceptable? \r\n\r\nIn order for the fiber to have a reliable, known behavior (transmission speed, attenuation, wavelength acceptance) in all environments, it is necessary to the total internal reflection to happen against a well defined external material. \r\n\r\nThat's the cladding.\n\nAnswer (score=-1):\n\nan optical fibre without cladding exists but is hard to make profit of it:\r\n\r\nThe **contrail of jets** is an optical fiber under special circumstances:\r\nIce crystals in the form of hexagonal plates are created in wet and very cold temperatures at high altitudes, typically above 10 km, and form a tube, nearly cylindrical, that can extend for hundreds of kilometres.\r\nIf the atmosphere is quiet the ice crystals will descend slowly, parallel to the ground oscilating up to a maximum of 8 degrees from the vertical, and if It is lit by the Sun or the Moon, not visible at sea level, perpendicular to the cylindrical tube at the opposite site in relation to the observer he will see the light.\r\n\r\nThe light will bounce from crystal to crystal under total reflection conditions with very low absortion, and subjected to polarization.\r\n\r\n**The observational evidence:**\r\n\r\nThe perceived usual shapes are like 'discs, cigars, triangles' and correspond to some sort of intersection of a plane with a cylinder.\r\n\r\nA slight change of angle between the sun/moon, the contrail, and observers will make a significant change observed in the lights, which are a decomposition of white light.\r\nWhen observing a change in velocity inconsistent with the motion of any known object remember that the light moves at c speed ;-) and the Earth's rotation around its axis contributes to the changing angles.\r\nThe distribution of the observations of UFOs in space and time historically accompanies the evolution of aviation.\r\n\r\nIn colder areas like Alaska and northern Norway, with more candidates to observers and with polar commercial air routes means that there are more reports of observations. Besides the light reflected by the ice cap may also inject more light into the contrail.\r\nIn areas with little commercial air routes as the South Pacific there are hardly any observations of UFOs.\r\n\r\n**They are what we call UFOs by Night.**  \r\nThis is not the physics involved in the day light observations.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 11, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-2.5", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "geometric-optics", "fiber-optics"], "page_start": null, "page_end": null, "quality_flags": [], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 6827, "title": "Cladding of optical fibers", "url": "https://physics.stackexchange.com/questions/6827/cladding-of-optical-fibers", "share_url": "https://physics.stackexchange.com/q/6827", "content_license": null, "owner": {"display_name": "student", "user_id": 667, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/667/student"}}, "answers": [{"answer_id": 6852, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/6827/cladding-of-optical-fibers/6852#6852", "share_url": "https://physics.stackexchange.com/a/6852", "content_license": "CC BY-SA 2.5", "owner": {"display_name": "Colin K", "user_id": 869, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/869/colin-k"}}, {"answer_id": 6841, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/6827/cladding-of-optical-fibers/6841#6841", "share_url": "https://physics.stackexchange.com/a/6841", "content_license": "CC BY-SA 2.5", "owner": {"display_name": "dmckee --- ex-moderator kitten", "user_id": 520, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/520/dmckee-ex-moderator-kitten"}}, {"answer_id": 7046, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/6827/cladding-of-optical-fibers/7046#7046", "share_url": "https://physics.stackexchange.com/a/7046", "content_license": "CC BY-SA 2.5", "owner": {"display_name": "Helder Velez", "user_id": 1257, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/1257/helder-velez"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:6835:0000", "text": "Question: Why should optical fibers be thin?\n\nWhat are the reasons that optical fibers have to be thin (small radius of the fiber)? Is there a good picture which explains this in detail?\n\nAccepted Answer:\n\nThe answer comes from the use of optical fibers: information transfer for one. The thinner the more channels in a bundle. \r\n\r\nAlso the attenuation of the light is smaller in a thin fiber . There is [an article][1] explaining this.   \r\n\r\n\r\n  [1]: http://en.wikipedia.org/wiki/Fiber_optics\n\nAnswer (score=5):\n\nIf they are thicker then light can take many different paths, bouncing at slightly different angles and still being reflected - this means that the time taken for each photon a pulse to go down a fibre is slightly different which smears out the pulse and so reduces the bits/second that can be sent.\r\n\r\nThick plastic fibres are used for simply illuminating something because they are cheap, rugged and easy to make, thinner glass fibre is used for short distances and very thin very expensive single mode fibre is used for higher bandwidth long distance\n\nAnswer (score=2):\n\nJust to add a little more info, there are also <a href=\"http://en.wikipedia.org/wiki/Single-mode_optical_fiber\" title=\"example\">monomode optical fibers</a> that are even thinner (8 to 20 µm). These are useful to transport light pulses, and only allow one spatial mode within the fiber. That means that instead of the typical picture of light bouncing in the walls of the fiber, you get that light can only propagate forward with a certain intensity profile. Check [this link](http://www.answers.com/topic/optical-fiber) or just google for a comparison of the three main types of fibers: multimode, graded-index and monomode.\n\nAnswer (score=0):\n\nSize of optical fiber mean outer diameter of the fiber \r\nIn short for long transmission fiber should be thin to avoid the dispersion and power loss in optical fiber.\n\nAnswer (score=0):\n\nBy using a thinner core, the light reflects less and travels in a more direct line and travels faster. This reduces modal dispersion.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 12, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-2.5", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "optics", "geometric-optics", "fiber-optics"], "page_start": null, "page_end": null, "quality_flags": ["mixed_license"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 6835, "title": "Why should optical fibers be thin?", "url": "https://physics.stackexchange.com/questions/6835/why-should-optical-fibers-be-thin", "share_url": "https://physics.stackexchange.com/q/6835", "content_license": null, "owner": {"display_name": "student", "user_id": 667, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/667/student"}}, "answers": [{"answer_id": 6842, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/6835/why-should-optical-fibers-be-thin/6842#6842", "share_url": "https://physics.stackexchange.com/a/6842", "content_license": "CC BY-SA 2.5", "owner": {"display_name": "anna v", "user_id": 1492, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/1492/anna-v"}}, {"answer_id": 6847, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/6835/why-should-optical-fibers-be-thin/6847#6847", "share_url": "https://physics.stackexchange.com/a/6847", "content_license": "CC BY-SA 2.5", "owner": {"display_name": "Martin Beckett", "user_id": 2525, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/2525/martin-beckett"}}, {"answer_id": 7895, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/6835/why-should-optical-fibers-be-thin/7895#7895", "share_url": "https://physics.stackexchange.com/a/7895", "content_license": "CC BY-SA 2.5", "owner": {"display_name": "user2890", "user_id": null, "user_type": "does_not_exist", "profile_url": null}}, {"answer_id": 450433, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/6835/why-should-optical-fibers-be-thin/450433#450433", "share_url": "https://physics.stackexchange.com/a/450433", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "SABOOR Ratial", "user_id": 218087, "user_type": "unregistered", "profile_url": "https://physics.stackexchange.com/users/218087/saboor-ratial"}}, {"answer_id": 451197, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/6835/why-should-optical-fibers-be-thin/451197#451197", "share_url": "https://physics.stackexchange.com/a/451197", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "user218437", "user_id": 218437, "user_type": "unregistered", "profile_url": "https://physics.stackexchange.com/users/218437/user218437"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:507:0000", "text": "Question: Tire speed dependent friction\n\nI have an old, non power steered car.\r\n\r\nWhen the car is stationary, the steering wheel is really tough to move, but as soon as I gain very little (0.5 kph or so) speed, the resistance is dramaticly decreased.\r\n\r\nBut at higher speeds, if I wish to make a full steer, the steering wheel will be resisting again.\r\n\r\nWhat is going on with the wheel friction?\n\nAccepted Answer:\n\nIf the car is stationary, then you're rotating the tires about a vertical axis, so you're rotating the contact patch of the tire relative to the road, and there is a lot of friction coming from those two surfaces sliding across each other. (In the center of the contact patch, there's no friction because there's no relative motion, but on the edges of the contact patch, there's a lot of friction because the rotation of the tire moves those surfaces directly across each other.)\r\n\r\nIf the car is driving in a straight line, then there's no friction because there's no relative motion between the contact patch and the road (no slippage). The tire is rotating about a perfectly horizontal axis, so the part of the tire just in front of the contact patch is about to press down onto the road and the part just behind is lifting off, but no surfaces are sliding across each other. (There is still energy loss, but it comes from deformation of the tire and the road, not from friction between surfaces. See [Rolling resistance].[1]\r\n\r\nNow for the complicated part. If the car is moving forward at a moderate speed and the wheels are rolling as usual, but you're also turning the steering wheel so the car is following a curved path, then in order to think about the friction we have to think about the axis of the NET rotation of the tire. The forward motion of the car gives it a lot of rotation about a horizontal axis. If we use the right-hand rule then this angular velocity vector points to the left. But the steering motion is also rotating the tire, much more slowly, about a vertical axis. For example, if you're turning the car to the left, then this gives a small angular velocity vector pointing up. To find the NET angular velocity, we should add together those two angular velocity vectors, which gives a vector pointing mostly to the left, but slightly up. This is the axis of the NET rotation of the tire at an instant in time.\r\n\r\nSince this axis is much closer to horizontal than it is to vertical, the tire is mostly rolling forward and the difference in speed between the left and right sides of the contact patch (which causes the relative motion between surfaces, hence friction) is much less than it is when the car is stationary.\r\n\r\n\r\n  [1]: http://en.wikipedia.org/wiki/Rolling_resistance\n\nAnswer (score=0):\n\nOn high speed the wheels behave like a gyro. So you feel the resistance proportional to rotational speed and wheels mass.\n\nAnswer (score=0):\n\nwhen you stay still you have to win the friction caused by the contact between your tires and the street in order to turn your wheels. \r\nIf, for example, you try to inflate your wheels more (increasing the air pressure inside), you will reduce the contact surface, and the stearing wheel will be less hard! (but don't drive with your tires too inflated, please!!)\r\n\r\nOn the contrary, when your moving the contact surface (and hence the source of the friction) is dramatically reduced and that's the reason why the steering wheel becomes bearable when moving at slow speeds. \r\nWhen you keep increasing your velocity, the tires will rotate on their axis with higher velocity, thus incrementing their angular momentum that has the tendency to conservate itself! (that's also the reason the [spinning tops work][1]).\r\n\r\n\r\n  [1]: https://physics.stackexchange.com/questions/271/why-dont-spinning-tops-fall-over", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 13, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-2.5", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics"], "page_start": null, "page_end": null, "quality_flags": ["mixed_license"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 507, "title": "Tire speed dependent friction", "url": "https://physics.stackexchange.com/questions/507/tire-speed-dependent-friction", "share_url": "https://physics.stackexchange.com/q/507", "content_license": null, "owner": {"display_name": "Theodor", "user_id": 250, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/250/theodor"}}, "answers": [{"answer_id": 520, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/507/tire-speed-dependent-friction/520#520", "share_url": "https://physics.stackexchange.com/a/520", "content_license": "CC BY-SA 2.5", "owner": {"display_name": "Keenan Pepper", "user_id": 61, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/61/keenan-pepper"}}, {"answer_id": 546, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/507/tire-speed-dependent-friction/546#546", "share_url": "https://physics.stackexchange.com/a/546", "content_license": "CC BY-SA 2.5", "owner": {"display_name": "user299", "user_id": null, "user_type": "does_not_exist", "profile_url": null}}, {"answer_id": 568, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/507/tire-speed-dependent-friction/568#568", "share_url": "https://physics.stackexchange.com/a/568", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Steve", "user_id": 28, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/28/steve"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:145:0000", "text": "Question: Law for tap water temperature\n\nI was wondering if anyone put together a law to describe the rising temperature of the water coming out of a tap.\r\n\r\nThe setup is fairly simple: there's a water tank at temperature T, a metal tube of length L connected to it and a tap at the end where temperature is measured. The water flows at P l/s.\r\n\r\nGiven that the metal tube is at room temperature initially, what law describes the temperature of the water at any instant? What is the limit temperature of the water?\r\n\r\nThanks.\n\nAccepted Answer:\n\nWe can consider the following model: a tube of constant temperature $T_e$ of lenght L, radius $r$ where water is flowing uniformly at a speed $v$ (that you can obtain from your flow $P$).\r\n\r\nA \"slice\" of water travels an interval $dx$ in a duration $dt = \\frac{dx}{v}$.\r\n\r\nThe tube will contribute to the \"heating\" of the water by $\\frac{dQ}{dt} = (T-T_e) k 2 \\pi r dx$ where $k$ is the conductivity and where we use a very simple model (in particular for the radius, we do not distinguish external and internal radii).\r\n\r\nDuring this interval the temperature $T(x)$ of the water will vary by $dT = -\\frac{dQ}{c \\rho dV}$ where $C$ is the heat capacity at constant pressure of water, and where $dV = 2 \\pi r dx$.\r\n\r\nReplacing we have $\\frac{dT}{T-T_e}=-\\frac{k}{\\rho C v} dx$ whose solution, if the temperature in the tank (ie x = 0) is $T_t$ :\r\n\r\n$T(x) = (T_t - T_e) e^{(-\\alpha x)}+T_e$ where $\\alpha = \\frac{k}{\\rho C v}$.\r\n\r\nDepending on the lenght of the tube you have the temperature at the tap.\n\nAnswer (score=1):\n\nThe answer is going to depend on the heat transfer coefficient between the tube and the surrounding room (unless you specify that the tube is held at constant temperature), the heat transfer coefficient between the tube and water, the outside & inside diameter of the tube, and the length of the tube. This is a moderately involved heat transfer problem, unless additional constraints are provided to simplify it.   \r\n\r\nAn excellent resource for understanding the mathematics behind this sort of heat transfer problem can be found over [here][1]. It's very similar to the solution posted above by @Cedric, but may be a little easier for some to follow.\r\n\r\n\r\n  [1]: http://www.nzifst.org.nz/unitoperations/httrapps1.htm", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 14, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-2.5", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "thermodynamics"], "page_start": null, "page_end": null, "quality_flags": [], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 145, "title": "Law for tap water temperature", "url": "https://physics.stackexchange.com/questions/145/law-for-tap-water-temperature", "share_url": "https://physics.stackexchange.com/q/145", "content_license": null, "owner": {"display_name": "Sklivvz", "user_id": 66, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/66/sklivvz"}}, "answers": [{"answer_id": 151, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/145/law-for-tap-water-temperature/151#151", "share_url": "https://physics.stackexchange.com/a/151", "content_license": "CC BY-SA 2.5", "owner": {"display_name": "Cedric H.", "user_id": 82, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/82/cedric-h"}}, {"answer_id": 146, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/145/law-for-tap-water-temperature/146#146", "share_url": "https://physics.stackexchange.com/a/146", "content_license": "CC BY-SA 2.5", "owner": {"display_name": "Herb", "user_id": 36, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/36/herb"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:123813:0000", "text": "Question: Applications of physics beyond QFT\n\nAre there any applied results (inventions) based on physics beyond quantum field theory? By beyond QFT I mean any physical theory that is (maybe slightly) different from classical physics, relativity, quantum physics and quantum field theories.\r\nBy applied results I mean not-only-on-paper results.\n\nAccepted Answer:\n\nIf by results you mean only inventions, the answer is, to my knowledge, no, since how could we engineer something we don't know anything about? Unfortunately we are not anymore at the times where inventors could build things without really knowing the underlying physics. \r\n\r\n\r\nIf you accept Topological field theories as 'beyond',which are widely used in condensed matter, then yes. They are actually trying to build quantum processors using anyons, so you can consider this as an invention.\r\n\r\nA group of theoretical physicists at NASA is trying to build a warp engine using (almost)-beyond-GR. Not invented though! (yet?)", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 15, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics"], "page_start": null, "page_end": null, "quality_flags": ["single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 123813, "title": "Applications of physics beyond QFT", "url": "https://physics.stackexchange.com/questions/123813/applications-of-physics-beyond-qft", "share_url": "https://physics.stackexchange.com/q/123813", "content_license": null, "owner": {"display_name": "anonymous67", "user_id": 52718, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/52718/anonymous67"}}, "answers": [{"answer_id": 123871, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/123813/applications-of-physics-beyond-qft/123871#123871", "share_url": "https://physics.stackexchange.com/a/123871", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Semola", "user_id": 22866, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/22866/semola"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:380856:0000", "text": "Question: How does a metronome allow such a wide range of tempos in such a short distance?\n\nI've been working on a question for metronomes asking the following:\r\n>Suppose a metronome can be treated as a double-weighted pendulum. Let $m_1$ be the mass of the metronome's movable weight, $l_1$ the distance of $m_1$'s center of mass from the rotation point, $m_2$ the mass of the fixed counterweight, and $l_2$ the distance of $m_2$'s center of mass from the rotation point.  Derive an equation for the natural frequency of such a system in beats per minute.  Assume the mass of the rod is negligible and oscillations are small, and treat the two masses as point masses.     \r\n\r\n[![Idealized Metronome][1]][1]\r\n\r\n\r\n  [1]: https://i.sstatic.net/4VC0b.png\r\nI first set up the angular equation of motion as:   \r\n$$m_2g\\sin\\theta l_2-m_1g\\sin\\theta l_1=(m_1l_1^2+m_2l_2^2)\\frac{d^2\\theta}{dt^2}$$\r\nUsing that for small angles, $\\sin \\theta \\approx \\theta$ and rearranging, I get  \r\n$$\\frac{d^2\\theta}{dt^2}+\\frac{m_1l_1-m_2l_2}{m_1l_1^2+m_2l_2^2}g\\theta=0$$  \r\nfrom which I get the natural angular frequency\r\n$$\\omega_0=\\sqrt{\\frac{m_1l_1-m_2l_2}{m_1l_1^2+m_2l_2^2}g}$$  \r\nwhich I can convert to beats per minute by noting that a metronome beats twice per cycle, resulting in:\r\n$$bpm=\\frac{60}{\\pi}\\sqrt{\\frac{m_1l_1-m_2l_2}{m_1l_1^2+m_2l_2^2}g}$$  \r\n\r\nThe range of tempos for a metronome is typically 40-208 bpm, with 208 bpm being the closest marked tempo to the rotation point, and 40 bpm the farthest.  Since the counterweight is fixed, the bpm equation is essentially a function of $l_1$, and so if we fix particular values of $m_1$, $m_2$, and $l_2$, then we can find how long of a rod we need (i.e. the range of values for $l_1$ for tempos between 40 and 208 bpm).  If I set bpm=208 (and $m_1$=20 grams, $m_2$=22 grams, and $l_2$ around 20 mm, although these values are not particularly special) and solve for $l_1$, I get reasonable answers on the order of a few centimeters, but for bpm=40, I'm getting values on the order of meters, which is clearly much longer than an actual metronome rod.  So overall my questions are:  \r\n \r\n- Is my analysis correct based on the assumptions I've made?\r\n- If so, what is causing such a dramatic error in the length of the rod?\r\n\r\nMy guesses on potentially spurious assumptions I've made are:  \r\n\r\n-  assuming the rod has negligible mass, although this seems reasonable looking at a typical metronome.\r\n-  approximating the two masses as point masses, since the moment of inertia of the system is the denominator of the $\\omega_0$ term.\r\n-  Neglecting frictional losses/the type of frictional loss present.  Including a loss term proportional to the speed doesn't seem to help much, but I've seen that metronomes are typically modeled with a [Van der Pol](https://en.wikipedia.org/wiki/Van_der_Pol_oscillator) loss term, which could make a difference, but I don't know enough about the topic to say.  \r\n-  Neglecting the effect of the [escapement](https://en.wikipedia.org/wiki/Escapement), the gear-spring mechanism that regulates the amplitude of the metronome.  \r\n\r\nAny advice on this would be greatly appreciated, as well as any criticisms on formatting, as I am still learning.\n\nAccepted Answer:\n\nI suspect that your \"order of meters\" results are stemming from forgetting the sign in the  l.h.s. of your very first equation and subsequently jumping into the realm of purely imaginary frequencies.\r\n\r\nThe correct first equation is\r\n$$\r\n-m_2g\\, l_2 \\sin\\theta+m_1g\\,l_1\\sin\\theta =(m_1l_1^2+m_2l_2^2)\\frac{d^2\\theta}{dt^2}.\r\n$$\r\nTo check it, we can set lighter mass to zero and assume $\\theta \\ll 1$. We get $-  g \\theta =   l_2 \\ddot\\theta$, that is a normal equation for a pendulum.\r\n\r\nOne suggestion: your frequency $\\omega$ remains the same if you multiply both masses by  the same number. So in order to reduce the number of parameters you have to fit, eliminate one mass (say, $m_2$) from the equation by introducing ratio $x=\\frac{m_1 }{m_2 }$:\r\n$$\r\n\\omega_0=\\sqrt{\\frac{l_2 -x\\,l_1}{l_2^2+x\\,l_1^2}\\,g}.\r\n$$\r\nSigns were corrected w.r.t. your expression. \r\n\r\nSome analysis:\r\n\r\n 1. Since $m_1$ is the lighter mass we have $x<1$.\r\n 2. For the frequency to be real we have the maximum allowed value of $l_1$: $l_1 < x^{-1}\\,l_2$. The frequency would tend to zero in that case.\r\n 3. Maximum frequency achievable for a given $l_2$ is obtained by setting $l_1$ to zero: $\\omega_\\text{max}=\\sqrt{\\frac g {l_2}}$", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 16, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "newtonian-mechanics", "harmonic-oscillator", "oscillators"], "page_start": null, "page_end": null, "quality_flags": ["single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 380856, "title": "How does a metronome allow such a wide range of tempos in such a short distance?", "url": "https://physics.stackexchange.com/questions/380856/how-does-a-metronome-allow-such-a-wide-range-of-tempos-in-such-a-short-distance", "share_url": "https://physics.stackexchange.com/q/380856", "content_license": null, "owner": {"display_name": "Luke", "user_id": 182014, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/182014/luke"}}, "answers": [{"answer_id": 380869, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/380856/how-does-a-metronome-allow-such-a-wide-range-of-tempos-in-such-a-short-distance/380869#380869", "share_url": "https://physics.stackexchange.com/a/380869", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "A.V.S.", "user_id": 180269, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/180269/a-v-s"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:403485:0000", "text": "Question: Physical processes taking place inside Germanium detectors\n\nReading about differences between Silicon detectors and Germanium detectors, I decided to learn a bit more about the latter, since I've always used Silicon detectors in all the experiments I worked for. While reading about them, I found that Germanium detectors are usually calibrated using $^{60}$Co sources. These sources emit gammas in the ~MeV energy range, but I was wondering what is the process taking place in this measurement, is it photoelectric effect, Compton scattering or pair production? I ask this question because I do not have in mind the energy range of these processes and I know that, for example for gamma-ray satellites like Fermi, that uses a silicon tracker, the dominant effect is pair-production. On the other hand, I also know that gamma-ray satellites of lower energy like Comptel use the Compton effect. There are other gamma-ray satellites proposed as eAstrogam that use both effects. So I was wondering, at MeV energies, of those that I have mention, which one (or which ones) is negligible to measure the total energy of the $^{60}$Co emission?\n\nAccepted Answer:\n\nIt is not pair production. Although the energy of the Cobalt gamma rays is in principle greater than the 1.022 MeV needed for to create an electron and a positron, the cross section is negligible below ~4 MeV\r\n\r\nBoth photoelectric and Compton effect processes are important. In photoelectric absorption the electron gets all the energy of the photon, and as the electron energy is what's actually recorded these events appear as a sharp peak on the energy spectrum produced. For Compton processes the electron gets some of the energy (the recoil photon gets the rest) so these events appear as a continuum.\n\nAnswer (score=1):\n\nThe gamma photons produce highly energetic electron in Ge which by ionization generate a large number of electron-hole pairs proportional to the energy of the electron in the depletion or intrinsic  zone of the Ge pn-junction. This is similar to a ionization gas chamber detector. This charge generation leads to a corresponding current current pulse in the outer circuit for the detection of the radiation. All three named processes can produce energetic electrons in Ge. For gamma energy spectroscopy, the photoelectric effect is preferred because it generates electrons with the same energy as the absorbed photon.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 17, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-4.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "material-science", "particle-detectors", "sensor"], "page_start": null, "page_end": null, "quality_flags": [], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 403485, "title": "Physical processes taking place inside Germanium detectors", "url": "https://physics.stackexchange.com/questions/403485/physical-processes-taking-place-inside-germanium-detectors", "share_url": "https://physics.stackexchange.com/q/403485", "content_license": null, "owner": {"display_name": "Juanjo", "user_id": 194370, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/194370/juanjo"}}, "answers": [{"answer_id": 403499, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/403485/physical-processes-taking-place-inside-germanium-detectors/403499#403499", "share_url": "https://physics.stackexchange.com/a/403499", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "RogerJBarlow", "user_id": 194034, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/194034/rogerjbarlow"}}, {"answer_id": 403493, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/403485/physical-processes-taking-place-inside-germanium-detectors/403493#403493", "share_url": "https://physics.stackexchange.com/a/403493", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "freecharly", "user_id": 129209, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/129209/freecharly"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:65340:0000", "text": "Question: Does the slip-stick phenomenon have any application?\n\nThe [slip-stick phenomenon](http://en.wikipedia.org/wiki/Stick-slip_phenomenon) is present all around us, be it the noise of car breaks or in earthquakes. But does it have any real-life application?\n\nAccepted Answer:\n\nAnother application is the frictional force spectroscopy in the stick slip mode. There you use an AFM (atomic force microscope) and you move it laterally over the surface (Actually I think you move the sample, but it doesn't matter). You are performing this so slowly that the cantileaver sticks and slips. From these kinds of measurements you can determine the dissipated energy. See the wikipedia article for AFM for further informations or this article http://en.wikipedia.org/wiki/Chemical_force_microscopy#Frictional_force_mapping\n\nAnswer (score=3):\n\nYes, grasshoppers use it to create the sounds they use for attracting mates.\r\n\r\nActually I don't know of any applications other than generating sounds. As Calmarius mentions in the comment, stringed instruments played with a bow use stick-slip motion to make the string vibrate. In the old days teachers used it to make excruciating noises with chalk on the blackboard.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 18, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "newtonian-mechanics", "soft-question", "friction"], "page_start": null, "page_end": null, "quality_flags": [], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 65340, "title": "Does the slip-stick phenomenon have any application?", "url": "https://physics.stackexchange.com/questions/65340/does-the-slip-stick-phenomenon-have-any-application", "share_url": "https://physics.stackexchange.com/q/65340", "content_license": null, "owner": {"display_name": "Ron", "user_id": 24753, "user_type": "unregistered", "profile_url": "https://physics.stackexchange.com/users/24753/ron"}}, "answers": [{"answer_id": 65379, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/65340/does-the-slip-stick-phenomenon-have-any-application/65379#65379", "share_url": "https://physics.stackexchange.com/a/65379", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Noldig", "user_id": 20071, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/20071/noldig"}}, {"answer_id": 65347, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/65340/does-the-slip-stick-phenomenon-have-any-application/65347#65347", "share_url": "https://physics.stackexchange.com/a/65347", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "John Rennie", "user_id": 1325, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/1325/john-rennie"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:47160:0000", "text": "Question: If layers of insulation are continuously added to a heated object, will it continue to be better insulated?\n\nIf you were to keep adding layers of insulation to something, like blankets to a person, would each blanket continue to improve the insulation?  Or do you reach some point at which the next blanket provides no marginal increase in insulation?\r\n\r\nLinks to explanations of heat or insulation for the layperson are more than welcome.\n\nAccepted Answer:\n\nThe answer is yes, but no, let me explain...\r\n\r\n[Heat flow][1] is proportional to the thermal conductivity of the insulating material, and to the temperature gradient, $q = -k \\nabla T$. If you have temperature $T_i$ inside and $T_o$ outside, and an insulating layer of thickness $h$ and conductivity $k$, the rate of heat loss in constant regime will be\r\n\r\n$$q = k\\frac{T_i-T_o}{h},$$\r\n\r\nwhich becomes ever smaller as you increase $h$, so extra insulation does have an effect.\r\n\r\nOn the other hand, if you already have a thickness of insulating material $h$, the effect that extra insulation will have on the heat loss rate is proportional to the derivative of $q$ with regards to $h$,\r\n\r\n$$\\frac{dq}{dh} = -k\\frac{T_i-T_o}{h^2},$$\r\n\r\nso the effect of extra insulation is ever smaller, and will eventually become negligible.\r\n\r\n\r\n  [1]: http://en.wikipedia.org/wiki/Heat_equation#The_physical_problem_and_the_equation", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 19, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "heat"], "page_start": null, "page_end": null, "quality_flags": ["single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 47160, "title": "If layers of insulation are continuously added to a heated object, will it continue to be better insulated?", "url": "https://physics.stackexchange.com/questions/47160/if-layers-of-insulation-are-continuously-added-to-a-heated-object-will-it-conti", "share_url": "https://physics.stackexchange.com/q/47160", "content_license": null, "owner": {"display_name": "DevinR", "user_id": 17024, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/17024/devinr"}}, "answers": [{"answer_id": 47164, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/47160/if-layers-of-insulation-are-continuously-added-to-a-heated-object-will-it-conti/47164#47164", "share_url": "https://physics.stackexchange.com/a/47164", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Jaime", "user_id": 995, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/995/jaime"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:18206:0000", "text": "Question: Do multiple permanent magnets aggregated together approach the same strength as a single magnet of the same size?\n\nHere's an applied physics question. ;) If I buy some cube or sphere magnets like [these][1], can I aggregate them together to create a stronger magnet (almost as strong as a single magnet)?\r\n\r\n  [1]: http://www.magnet4less.com/index.php?cPath=1_14\n\nAccepted Answer:\n\nAlthough the combined strength will be larger, it will not be exactly the same as the strength of single large magnet. This is because the magnets lower down in the stack are being shielded slightly by the magnets above and below them.\n\nAnswer (score=3):\n\nIf you stack the magnets the way they want to stack you will have no change in strength.  \r\nBut if you can push the magnets together like this \r\n-----→        》NS《》SN《》NS《        ←--------------\r\nThen you can increase the field and strength.\r\nbut the field extends  far in one direction only.\r\n\r\nMythbusters had a show about using magnets as breaks.\r\n\r\nThats where I learned about this.\r\n\r\nSo you need a\r\n                           NSSNNS or a SNNSSN alignment .\r\nhope this helps someone out with a project or two.\n\nAnswer (score=1):\n\nIt seems stacking smaller and smaller magnets on top of each other generates the affect you are looking for. Check out what [SuperMagnetMan did with \"pyramid\" magnets][1].\r\n\r\n\r\n  [1]: https://www.youtube.com/watch?v=tR_8f0DYK5s\n\nAnswer (score=0):\n\nTo expand on Omar's Answer: KJMagnetics has an FAQ that answers this question: http://www.kjmagnetics.com/FAQ.asp#stack.\r\nIf you wander round the KJMagnetics site, they give a lot of technical information (I bought some magnets off them 2-3 years ago).\r\n\r\nTheir FAQ answer describes the situation for stacking flat magnets vertically on top of each other. Note that if you place multiple magnets next to each other horizontally, instead of in a vertical stack, they will still act in the same way as a larger magnet having the same area. However, in the horizontal case, the magnets will repel each other because like poles are next to each other (N next to N, S next to S). So you would have to impose an equal and opposite force to keep them together. That's not easy when the magnets get large.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 20, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "electromagnetism", "magnetic-fields"], "page_start": null, "page_end": null, "quality_flags": [], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 18206, "title": "Do multiple permanent magnets aggregated together approach the same strength as a single magnet of the same size?", "url": "https://physics.stackexchange.com/questions/18206/do-multiple-permanent-magnets-aggregated-together-approach-the-same-strength-as", "share_url": "https://physics.stackexchange.com/q/18206", "content_license": null, "owner": {"display_name": "Matt Chambers", "user_id": 6630, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/6630/matt-chambers"}}, "answers": [{"answer_id": 18208, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/18206/do-multiple-permanent-magnets-aggregated-together-approach-the-same-strength-as/18208#18208", "share_url": "https://physics.stackexchange.com/a/18208", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Omar", "user_id": 6560, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/6560/omar"}}, {"answer_id": 110839, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/18206/do-multiple-permanent-magnets-aggregated-together-approach-the-same-strength-as/110839#110839", "share_url": "https://physics.stackexchange.com/a/110839", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "FrankyD", "user_id": 45671, "user_type": "unregistered", "profile_url": "https://physics.stackexchange.com/users/45671/frankyd"}}, {"answer_id": 286390, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/18206/do-multiple-permanent-magnets-aggregated-together-approach-the-same-strength-as/286390#286390", "share_url": "https://physics.stackexchange.com/a/286390", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Eric C.", "user_id": 133084, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/133084/eric-c"}}, {"answer_id": 18209, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/18206/do-multiple-permanent-magnets-aggregated-together-approach-the-same-strength-as/18209#18209", "share_url": "https://physics.stackexchange.com/a/18209", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Peter Morgan", "user_id": 1588, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/1588/peter-morgan"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:518321:0000", "text": "Question: What are real world applications of the Duistermaat–Heckman formula?\n\nIn the famous 1984 paper \"The Moment Map and Equivariant Cohomology\" by Atiyah and Bott, an equivariant de Rham theory was presented in relation to the [Duistermaat–Heckman formula](https://en.wikipedia.org/wiki/Duistermaat%E2%80%93Heckman_formula)\r\n$$ \\int_M e^{-itf} \\frac{\\omega^n}{n!} = \\sum_p \\frac{e^{-itf(p)}}{(it)^n \\text{e}(p)},$$\r\nwhere $(M,\\omega)$ is a symplectic manifold and $f: M \\to \\mathbb{R}$ is the moment map on $M$ coming from a circle action.\r\n\r\nThis sparked my curiosity in the physical applications of equivariant cohomology (i.e., equivariant de Rham theory), especially the above formula.\r\n\r\n**What are real world applications of the Duistermaat–Heckman formula?**\r\n\r\nBy real world applications, I mean physical applications in classical mechanics, statistical mechanics, quantum mechanics, or quantum field theory, but probably not string theory. I would appreciate if someone could provide real world applications of the Duistermaat–Heckman formula.\n\nAccepted Answer:\n\nHere are some applications that might qualify for your criterion of 'real world':\r\n\r\nYasui, Y., & Ogura, W. (1996). [Vortex filament in a three-manifold and the Duistermaat-Heckman formula][1]. Physics Letters A, 210(4-5), 258-266.\r\n\r\nKarki, T., & Niemi, A. J. (1994). [On the Duistermaat-Heckman Integration Formula and Integrable Models][2]. arXiv preprint hep-th/9402041.\r\n\r\nBismut, J. M. (2011). [Duistermaat–Heckman formulas and index theory][3]. In Geometric Aspects of Analysis and Mechanics (pp. 1-55). Birkhäuser Boston.\r\n\r\nZhang, L., Jiang, Y., & Wu, J. (2019). [Duistermaat–Heckman measure and the mixture of quantum states][4]. Journal of Physics A: Mathematical and Theoretical, 52(49), 495203.\r\n\r\n\r\n  [1]: https://arxiv.org/abs/hep-th/9508118\r\n  [2]: https://arxiv.org/abs/hep-th/9402041\r\n  [3]: https://www.math.u-psud.fr/~bismut/Bismut/2011e.pdf\r\n  [4]: https://arxiv.org/abs/1810.02630", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 21, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-4.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "quantum-mechanics", "hamiltonian-formalism", "mathematics", "semiclassical"], "page_start": null, "page_end": null, "quality_flags": ["single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 518321, "title": "What are real world applications of the Duistermaat–Heckman formula?", "url": "https://physics.stackexchange.com/questions/518321/what-are-real-world-applications-of-the-duistermaat-heckman-formula", "share_url": "https://physics.stackexchange.com/q/518321", "content_license": null, "owner": {"display_name": "Yuhang Chen", "user_id": 247425, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/247425/yuhang-chen"}}, "answers": [{"answer_id": 518448, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/518321/what-are-real-world-applications-of-the-duistermaat-heckman-formula/518448#518448", "share_url": "https://physics.stackexchange.com/a/518448", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "Arnold Neumaier", "user_id": 7924, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/7924/arnold-neumaier"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:115027:0000", "text": "Question: Why Shock wave propagation is faster\n\nFrom [The Blast Wave](http://www.atomicarchive.com/Effects/effects3.shtml)\r\n\r\n> _A fraction of a second after a nuclear explosion, the heat from the fireball causes a high-pressure wave to develop and move outward producing the blast effect. The front of the blast wave, i.e., the shock front, travels rapidly away from the fireball, a moving wall of highly compressed air._\r\n\r\nFrom [Wikipedia](http://en.wikipedia.org/wiki/Shock_wave)\r\n\r\n> _A shock wave is a type of propagating disturbance. Like an ordinary wave, it carries energy and can propagate through a medium (solid, liquid, gas or plasma) or in some cases in the absence of a material medium, through a field such as the electromagnetic field. Shock waves are characterized by an abrupt, nearly discontinuous change in the characteristics of the medium. Across a shock there is always an extremely rapid rise in pressure, temperature and density of the flow. A shock wave travels through most media at a higher speed than an ordinary wave._\r\n\r\nHow shock wave differs from ordinary wave, and how it can travel faster then ordinary wave in same medium. In first ex, In nuclear explosion why shock wave is traveling faster then fireball, when both are in same medium. Can someone please explain the phenomenon in detail.\n\nAccepted Answer:\n\nYou *can* push the air faster than the speed of sound. If you do that, you will get a shock wave. A shock wave in this sense is a \"wall\" of supersonic-moving particles. You can definitely achieve this if you push on the air hard enough. A nuclear explosion is definitely \"hard enough\" :)\r\n\r\nA shock wave will collide with \"normal\" stationary air, and give some of the energy to it. As the energy spreads to larger and larger volumes of air, the shock wave decays into a \"normal\" sound wave pulse. But before that, the wall of highly compressed air will travel at supersonic speed.\r\n\r\nA nuclear fireball is the region where the air and the debris from the explosion is so hot that it glows. In the first moments of the explosion, the shock wave compresses the air so hard, that it heats up and glows. As the shock wave loses energy, it will lose it's glow, first \"redshifting\" and then disappearing almost completely. This phenomenon can be seen in this video: https://www.youtube.com/watch?v=KQp1ox-SdRI\n\nAnswer (score=3):\n\nAs per my [answer here][1]. The air on the inside of the explosion is also moving \"faster then the speed of sound\" so relative to that air, the shock wave is traveling at subsonic speeds. Thus the shock wave travels at a weighted average of the velocity that sound would travel in the mediums on either side of it.\r\n\r\n\r\n  [1]: https://physics.stackexchange.com/questions/193246/how-can-shock-waves-travel-faster-than-sound/#193323", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 22, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "waves", "shock-waves"], "page_start": null, "page_end": null, "quality_flags": ["low_score"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 115027, "title": "Why Shock wave propagation is faster", "url": "https://physics.stackexchange.com/questions/115027/why-shock-wave-propagation-is-faster", "share_url": "https://physics.stackexchange.com/q/115027", "content_license": null, "owner": {"display_name": "a.m.", "user_id": 47563, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/47563/a-m"}}, "answers": [{"answer_id": 115072, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/115027/why-shock-wave-propagation-is-faster/115072#115072", "share_url": "https://physics.stackexchange.com/a/115072", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "netom", "user_id": 10710, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/10710/netom"}}, {"answer_id": 193402, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/115027/why-shock-wave-propagation-is-faster/193402#193402", "share_url": "https://physics.stackexchange.com/a/193402", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Eph", "user_id": 55225, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/55225/eph"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:39617:0000", "text": "Question: What are the applications of Gauss's law in technology?\n\nFreshmen physics textbooks use Gauss's law plus symmetry to calculate the electric field.\r\nI was wondering if this method of finding the electric field using a symmetry is used in real applications in life, science, research, or technology. For example do researchers use symmetry to find the electric field due to a charged virus that is spherically symmetric, or a charged DNA that has some kind of symmetry or charged symmetrical objects in nanotechnology. I am looking for such specific applications.\n\nAccepted Answer:\n\ndo researchers use symmetry to find the electric field due to a charged virus that is spherically symmetric?\r\n\r\nThe answer is **no**. Why they need to reinvent the wheel? They just use the *known* formula that exists for such situations that can be proved using Gauss Laws (though they all can be proved without using Gauss laws)\r\n\r\n\r\nSimilar answer can be given to your other question.\r\nThough note that since sizes are of atomic level, other forces can come into play.\r\n\r\n\r\n**Theoretically** we don't need Gauss law. Only law we need in electrostatics is Coulomb's law to find $\\vec E$ and $\\vec F = m\\vec E$. Gauss Laws and all other tools only help to simplify the calculations. So there is **no** application of Gauss Law *per se* but I think you must appreciate the power of Gauss Laws in simplification of many tough situations,many of which have profound practical applications. However theoretically all situations can be solved without using Gauss Laws or symmetry arguments.\r\n\r\nThough I recommend checking out http://en.wikipedia.org/wiki/Faraday_cage a really outstanding application of electrostatics and its working can be explained using Gauss' Laws along with properties of conductors.\n\nAnswer (score=2):\n\nGauss theorem is a law relating the **distribution of electric charge** to the **resulting electric field**. \r\n\r\nSo if scientist knows the distribution of charge on some DNA or the surfaces of some virus then they can calculate the electric field. \r\n\r\nIf you know that charge distribution is symmetrical, you can expect same result for electric field. \r\nFor example if the charge distribution has spherical symmetry then the field will depend only on the distance:\r\n\r\n$$E = k\\frac{q}{r^2} \\sim \\frac{1}{r^2}.$$\r\n\r\nMore examples of charge distributions you could find here:\r\n\r\nhttp://en.wikipedia.org/wiki/Gaussian_surface\r\n\r\nhttp://iweb.tntech.edu/murdock/books/v4chap2.pdf\r\n\r\n\r\nAnd this post may be useful:\r\n\r\nhttps://physics.stackexchange.com/questions/33930/in-which-cases-is-it-better-to-use-gauss-law?rq=1\n\nAnswer (score=1):\n\nThe freshman physics textbooks use the integral forms of Gauss's law, which (in the vacuum) look like this:\r\n\r\n$$ \\int \\mathbf{E} \\cdot d\\mathbf{A}=Q_{enc}/\\epsilon_0 $$\r\n$$ \\int \\mathbf{B} \\cdot d\\mathbf{A}=0 $$\r\n\r\nThese laws also have differential forms, which look like this:\r\n\r\n$$\\nabla \\cdot \\mathbf{E}=\\rho/\\epsilon_0 $$\r\n$$\\nabla \\cdot \\mathbf{B}=0 $$\r\n\r\nThese equations don't really require symmetry to be useful, and can be solved with standard partial differential equation techniques on a computer. For problems involving surfaces with variable charges (like cavities with conductive sides), these differential forms (and the PDEs for the scalar and vector potentials that they imply) are practically the only way to solve for the $\\mathbf{E}$ and $\\mathbf{B}$ fields everywhere.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 23, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "electrostatics", "symmetry", "gauss-law"], "page_start": null, "page_end": null, "quality_flags": ["low_score"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 39617, "title": "What are the applications of Gauss's law in technology?", "url": "https://physics.stackexchange.com/questions/39617/what-are-the-applications-of-gausss-law-in-technology", "share_url": "https://physics.stackexchange.com/q/39617", "content_license": null, "owner": {"display_name": "Revo", "user_id": 4521, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/4521/revo"}}, "answers": [{"answer_id": 39727, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/39617/what-are-the-applications-of-gausss-law-in-technology/39727#39727", "share_url": "https://physics.stackexchange.com/a/39727", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "TheJoker", "user_id": 12880, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/12880/thejoker"}}, {"answer_id": 39696, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/39617/what-are-the-applications-of-gausss-law-in-technology/39696#39696", "share_url": "https://physics.stackexchange.com/a/39696", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Nikita Matyukov", "user_id": 13008, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/13008/nikita-matyukov"}}, {"answer_id": 39620, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/39617/what-are-the-applications-of-gausss-law-in-technology/39620#39620", "share_url": "https://physics.stackexchange.com/a/39620", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Dan", "user_id": 3936, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/3936/dan"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:23160:0000", "text": "Question: Is chaos theory essential in practical applications yet?\n\nDo you know cases where chaos theory is actually applied to successfully predict essential results? Maybe some live identification of chaotic regimes, which causes new treatment of situations.\r\n\r\nI'd like to consider this from the engineers point of view. By this I mean results that are really essential and not just \"interesting\". For example one might say weather calculation effects are explained with chaos theory, but an \"engineer\" might say: \"So what? I could have told you without a fancy theory and it provides no added value since there is nothing I can change now.\"\n\nAccepted Answer:\n\nI think it depends on the meaning of \"application\". In the [wikipedia][1] entry there are a lot of applications of chaos theory listed:\n\n> Chaos theory is applied in many scientific disciplines, including: geology, mathematics, microbiology, biology, computer science, economics, engineering, finance, meteorology, philosophy, physics, politics, population dynamics, psychology, and robotics.\n\nFor example, in [engineering][2] there is the following in the abstract of a paper:\n\n> Control of chaos: Methods and applications in engineering ☆A survey of the emerging field termed “control of chaos” is given. \n>\n> Several major branches of research are discussed in detail: feedforward or “nonfeedback control” (based on periodic excitation of the system); “OGY method” (based on linearization of the Poincaré map), “Pyragas method” (based on a time-delay feedback), traditional control engineering methods including linear, nonlinear and adaptive control, neural networks and fuzzy control. Some unsolved problems concerning the justification of chaos control methods are presented. Other directions of active research such as chaotic mixing, chaotization, etc. are outlined. Applications in various fields of engineering are discussed.\n\nChaos theory is not chaotic in the everyday sense, there are those [strange attractors][3] and the behavior of collective solutions to dynamical equations, which is what chaos theory deals with, may very well give a handle to control complex systems.  It seems to still be at the exploration and research phase, but yes, there already seem to be possible applications.\n\n  [1]: http://en.wikipedia.org/wiki/Chaos_theory#Applications\n  [2]: http://www.sciencedirect.com/science/article/pii/S1367578805000040\n  [3]: http://en.wikipedia.org/wiki/Chaos_theory#Strange_attractors\n\nAnswer (score=1):\n\nI don't have a very detailed list of applications, but off the top of my head, I would say the Stability of Solar System is an essential prediction. Yes, I understand that it is not extensively essential, because I can't imagine what we would have done if, on paper, the System turned out to be unstable.\r\nAs far as the applications of Chaos Theory go, it is more about controlling the Chaos that make more sense. How much noise should you add to the system, how strongly should you couple two systems to make them predictable? These are some generically important question that Chaos Theory tries to answer.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 24, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "chaos-theory"], "page_start": null, "page_end": null, "quality_flags": ["low_score", "mixed_license"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 23160, "title": "Is chaos theory essential in practical applications yet?", "url": "https://physics.stackexchange.com/questions/23160/is-chaos-theory-essential-in-practical-applications-yet", "share_url": "https://physics.stackexchange.com/q/23160", "content_license": null, "owner": {"display_name": "Gere", "user_id": 5152, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/5152/gere"}}, "answers": [{"answer_id": 23228, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/23160/is-chaos-theory-essential-in-practical-applications-yet/23228#23228", "share_url": "https://physics.stackexchange.com/a/23228", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "anna v", "user_id": 1492, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/1492/anna-v"}}, {"answer_id": 127454, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/23160/is-chaos-theory-essential-in-practical-applications-yet/127454#127454", "share_url": "https://physics.stackexchange.com/a/127454", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Abinash Chakraborty", "user_id": 5787, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/5787/abinash-chakraborty"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:846894:0000", "text": "Question: Applications of systems exhibiting strange attractors\n\nI have always thought of [strange attractors](https://en.wikipedia.org/wiki/Attractor#Strange_attractor) as mathematically interesting and aesthetically pleasing phenomena. In investigating a system for my PhD research, I have surprisingly stumbled across the fact that they can sometimes exhibit strange attractors. \r\n\r\nMy question is: are strange attractors just cool? Or are there any applications?\n\nAccepted Answer:\n\nIf you're interested in characterizing your system's dynamics, then showing it has a strange attractor is in itself worthwhile. Producing some basins of attraction in case there's also multistability and investigating its parameter space would then be natural next steps.\r\n\r\nIf the system in question has applications, then an interesting question is what are the consequences of it behaving chaotically. And also whether it's chaotic for realistic parameter ranges.\r\n\r\nAs for applications in general, cryptography might be one. [Wikipedia](https://en.wikipedia.org/wiki/Chaos_theory#Applications) gives examples in a number of areas, e.g.:\r\n- Cryptography\r\n- Robotics\r\n- Biology\r\n- Economics\r\n- Weather and climate\r\n- Chemistry\r\n- Space travel", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 25, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-4.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "non-linear-systems", "chaos-theory", "complex-systems", "fractals"], "page_start": null, "page_end": null, "quality_flags": ["low_score", "single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 846894, "title": "Applications of systems exhibiting strange attractors", "url": "https://physics.stackexchange.com/questions/846894/applications-of-systems-exhibiting-strange-attractors", "share_url": "https://physics.stackexchange.com/q/846894", "content_license": null, "owner": {"display_name": "Paddy", "user_id": 114907, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/114907/paddy"}}, "answers": [{"answer_id": 846966, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/846894/applications-of-systems-exhibiting-strange-attractors/846966#846966", "share_url": "https://physics.stackexchange.com/a/846966", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "stafusa", "user_id": 75633, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/75633/stafusa"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:324248:0000", "text": "Question: Refractive Index Base Wavelength\n\nThe refractive index of a medium is usually stated as a single \"number\" rather than something depending on wavelength. However, it does in fact depend on wavelength. This lead to a question I haven't been able to find the answer to:\r\n\r\nThe refractive index of Borosilicate glass is always stated to be $1.517$. However, is this with respect to some sort of standardised \"white light\" with known quantities of different wavelengths? Or is it with respect to one specific wavelength of light in the middle of the visible spectrum, around green or yellow?\n\nAccepted Answer:\n\n\"Standard refractive index measurements are taken at the \"yellow doublet\" sodium D line, with a wavelength of $589$ nanometers\"\r\n\r\nTurns out another 15 minutes of googling was what it took to find an answer!", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 26, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "optics", "visible-light", "refraction"], "page_start": null, "page_end": null, "quality_flags": ["low_score", "single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 324248, "title": "Refractive Index Base Wavelength", "url": "https://physics.stackexchange.com/questions/324248/refractive-index-base-wavelength", "share_url": "https://physics.stackexchange.com/q/324248", "content_license": null, "owner": {"display_name": "Harambe", "user_id": 151320, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/151320/harambe"}}, "answers": [{"answer_id": 324250, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/324248/refractive-index-base-wavelength/324250#324250", "share_url": "https://physics.stackexchange.com/a/324250", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Harambe", "user_id": 151320, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/151320/harambe"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:298366:0000", "text": "Question: How does a humidifier save on heating?\n\nI have heard that using a humidifier in the winter can help you save money in heating costs. If this is true, I was curious about the physics behind why this is.\n\nMy thoughts were that since water has a very high specific heat, adding more water into the air would actually require you to use more energy to raise the temperature of the air the same amount.\n\nIs it that if you use a humidifier, the perceived temperature is higher?(so maybe 67 degrees F with a humidifier would feel like 70 without, thus saving because you can keep the thermostat down?) If so, then how does humidity affect perceived temperature? \n\nOr is it that this claim is wrong?\n\nMy background: I am a graduate student in combinatorics, a branch of math not very related to physics. I have seen undergraduate physics 1 & 2 in a formal setting, and enjoy learning about physics.\n\nAccepted Answer:\n\nI don't think it results in any savings. Given some interior temperature and outside temperature, heat flows from inside to outside by conduction through walls. Even if humidity were to change conductivity of air, heat transfer in most cases (say from your body to air) is by turbulent convection, and so change in conductivity of air matters little. Having said that, I am not from a cold country, so it is possible that I have overlooked something subtle.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 27, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "thermodynamics", "soft-question", "humidity"], "page_start": null, "page_end": null, "quality_flags": ["low_score", "single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 298366, "title": "How does a humidifier save on heating?", "url": "https://physics.stackexchange.com/questions/298366/how-does-a-humidifier-save-on-heating", "share_url": "https://physics.stackexchange.com/q/298366", "content_license": null, "owner": {"display_name": "Sean English", "user_id": 139069, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/139069/sean-english"}}, "answers": [{"answer_id": 298411, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/298366/how-does-a-humidifier-save-on-heating/298411#298411", "share_url": "https://physics.stackexchange.com/a/298411", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Deep", "user_id": 122958, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/122958/deep"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:361470:0000", "text": "Question: Modes in a subwavelength-diameter optical fiber\n\nI would love to know about propagation modes in a subwavelength-diameter optical fiber. For example: There is an optical fiber (core diameter = 0.7 μm), the refractive index of the core (n1 = 2.1), the cladding is air (refractive index n2 = 1). What happens if light (λ = 1.5 μm) is transmitted in this fiber ? How many propagation modes ? Is optical energy lost between the output and the input of this fiber ? \r\nThank you very much!\n\nAccepted Answer:\n\nThe answer is given as part of my answer to your other similar question [here](https://physics.stackexchange.com/q/356562/26076). \r\n\r\n**In a dielectric waveguide**, nothing special happens: the field spreads out so that it is significantly different from zero over a diameter that is much greater than the core diameter. There is still no loss for a straight fiber even if the core is arbitrarily small. However, the mode becomes more and more weakly guided: theoretically lossless for a straight fiber but more and more subject to loss, through coupling into the radiation field, when the fiber is bent. For a very small core, even the mildest bend curvatures lead to significant loss. \r\n\r\nChapter 23 of Snyder and Love, \"Optical Waveguide Theory\" describes this phenomenon in detail. The propagation constant for a bend step index fiber has a real (attenuating) part with a term  given by (See Eq. 23-12 in Snyder and Love):\r\n\r\n$$\\exp\\left(-\\frac{4\\,R_c\\,\\Delta\\,W^3}{3\\,\\rho\\,V^2}\\right)$$\r\n\r\nwhere $\\rho$ is the core radius, $R_c$ the bend radius, $\\Delta$ and $V$ are the waveguide parameters and $W$ the cladding eigenvalue for the fundamental mode. This quantity increases swiftly with decreasing bend radius, and the ratio $\\Delta\\,W^3/V^2$ measures the guiding strength: for small cores, this is large which means even mild bends lead to high loss. For large cores and large core-cladding index differences, this ratio is small, and it takes a very tight bend to beget significant loss. \r\n\r\n**In a metal clad waveguide**, as in my other answer, the field vectors for the fundamental mode vary with radial position $r$ and axial position $z$ within the fiber like $J_0(k_\\perp\\,r)\\,\\exp\\left(i\\,\\sqrt{k^2\\,n^2-k_\\perp^2}\\,z\\right)$ and we must have $k_\\perp\\,r_0 = \\omega_{0\\,1}\\approx 2.405$, where $\\omega_{0\\,1}$ is the first zero of the Bessel function and $r_0$ the core radius, to fulfill the field continuity boundary conditions. This sets a minimum core radius $r_0$ that one can have for a propagating field; this minimum radius is $r_{min}\\approx 2.405\\,\\lambda/(2\\,\\pi\\,n)$. For $1.5{\\rm \\mu m}$ wavelength (in freespace) light and a core refractive index of 1.5, the minimum possible mode field diameter is about 770nm. If the core is any smaller, then $\\sqrt{k^2\\,n^2-k_\\perp^2}$ is imaginary, *all* modes of the metal clad waveguide are cut off and propagation becomes evanescent, *i.e.* non power transporting. This is the mechanism that stops EM waves getting through subwavelength holes in conductive materials of any significant thickness: this is how the mesh on a microwave oven door stops leakage even though we can see through the mesh.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 28, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "optics", "geometric-optics", "fiber-optics"], "page_start": null, "page_end": null, "quality_flags": ["low_score", "single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 361470, "title": "Modes in a subwavelength-diameter optical fiber", "url": "https://physics.stackexchange.com/questions/361470/modes-in-a-subwavelength-diameter-optical-fiber", "share_url": "https://physics.stackexchange.com/q/361470", "content_license": null, "owner": {"display_name": "Nguyen Duc Viet", "user_id": 168787, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/168787/nguyen-duc-viet"}}, "answers": [{"answer_id": 361474, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/361470/modes-in-a-subwavelength-diameter-optical-fiber/361474#361474", "share_url": "https://physics.stackexchange.com/a/361474", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Selena Ballerina", "user_id": 26076, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/26076/selena-ballerina"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:668133:0000", "text": "Question: Does pressure affect heat transfer between two mediums?\n\nI'm a self-taught Coca-Cola connoisseur and try to use science to be able to have the best taste possible in every glass. I usually try to get the bottles as cool as possible before opening them. I've noticed that when I open a bottle too soon (not cool enough yet), and then put it again to cool down, it does so faster than a bottle that has been in the refrigerator without interruption. This, however, is just empirical and I've not taken exact measures or data.\r\n\r\nTo make it more explicit, take two bottles of Coca-Cola that start off at room temperature. Let $t=0$ be the time they are put inside to cool down and let's say the wanted temperature is $0$°C:\r\n\r\n - Bottle 1 is put in the refrigerator and cools down from room temperature to $0$°C in $t_1$ seconds.\r\n - Bottle 2 starts the same but is opened before it reaches $0$°C, a glass is poured and then the bottle is closed again and put back inside. It then reaches $0$°C at, seemingly, $t_2 < t_1$ seconds.\r\n\r\nIt would be safe to assume the initial pressure inside the bottles is always greater than $1$ atm. When opened, Bottle 2's internal pressure goes down and it also loses around $200$ml of liquid. Does the difference of pressure between the inside of the bottle and the refrigerator affect the heat transfer and the time the bottle takes to cool down? Could it be another physical phenomenon that explains this (such as the loss of liquid)? (Am I making this up?)\n\nAccepted Answer:\n\nYes, gas pressure affects the rate of heat transfer to or from a gas, but that's not what you're measuring. \r\n\r\n**What's probably going on:**\r\n\r\nIf you've poured $200mL$ out of the bottle, the remaining liquid will cool faster, because the rate of heat transfer is roughly proportional to the surface area, while heat capacity is proportional to the volume. Surface area varies as the $2/3$ root of volume, so if you multiply the volume by a factor of $0.8$, you multiply the volume by $0.8^{2/3}$, and so the cooling time is multiplied by $0.8/0.8^{2/3} \\approx 0.93$. \r\n\r\n---\r\n\r\n**A pressure-related effect that is happening, but may be too small to measure:**\r\n\r\nWhen you open the soda, releasing the pressure, the dissolved carbon dioxide molecules boil out of the liquid. This is an endothermic process, so the liquid is cooled: heat flows from the liquid into the gas to pay for the phase change. I have no idea how much gas is released, but suppose it's somewhere on the order of 1 L from a 1L bottle being opened for a few seconds for the first time, which seems about right for how much they can froth over. Then that's about 2 g of CO2 , which has a latent heat of vaporization of about 700J, or about 1/5 of a degree worth of heat from your liter of water. \r\n\r\n\r\n---\r\n\r\n\r\n**A pressure related effect that isn't happening:**\r\n\r\nAs I said at the beginning - yes, gas pressure affects heat transfer to the gas. If you isothermally pressurized your freezer, the rate of cooling would increase because density increases the conductivity of air. This isn't what's happening here, of course, but it's a direct answer to your question so I didn't think I should leave it out. The effect on cooling rate for the kinds of pressures that wouldn't be life-threatening would be negligible. \r\n\r\n---\r\n\r\nIf you actually want to cool the beverage quickly, just immerse it in a bucket of ice water. It'll cool rapidly to 0 and won't freeze. \r\n\r\n---\r\n\r\n*EDIT - oops! I wrote exothermic when I meant endothermic. Fixed.*", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 29, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-4.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "thermodynamics", "energy"], "page_start": null, "page_end": null, "quality_flags": ["low_score", "single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 668133, "title": "Does pressure affect heat transfer between two mediums?", "url": "https://physics.stackexchange.com/questions/668133/does-pressure-affect-heat-transfer-between-two-mediums", "share_url": "https://physics.stackexchange.com/q/668133", "content_license": null, "owner": {"display_name": "condosz", "user_id": 199563, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/199563/condosz"}}, "answers": [{"answer_id": 668141, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/668133/does-pressure-affect-heat-transfer-between-two-mediums/668141#668141", "share_url": "https://physics.stackexchange.com/a/668141", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "g s", "user_id": 285671, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/285671/g-s"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:556945:0000", "text": "Question: Radiation and windows for building of a great project in a low Earth orbit: reference request or exercise as a ficticious need to build it\n\nI know about the existence of certain windows for which it is more suitable to launch a probe for the exploration of a cellestial body in our Solar System (see the Wikipedia [*Launch window*](https://en.wikipedia.org/wiki/Launch_window)). I wondered about a different problem.\r\n\r\nIn the past, if I refer well there was in the literature projects to build certain structures (you can to illustrate your answer with a generic example or with a specific one) in low orbits around of our planet Earth: for example a (great) spacecraft, telescope (we evoke a very big telescope) or a space elevator. \r\n\r\n>**Question.** I would like to know what is the more suitable period in terms of the expossition of radiation that is allowed for our workers, I mean an approximation of the date(s) of the more suitable periods, with a deadline for our project in next $30$ years (or few decades from your discussion) in which I evoke the fictious situation that we want/need (and we can in this thought experiment) to build a great construction project in a low orbit similar than the orbit of the International Space Station or other low orbit more suitable (see below again the requirement in the context of our ficticious project, since we want to minimize the radiation for our workers). **Many thanks.**\r\n\r\nThus you add an answer as a draft of computations or estimations for our generic project, you can to add all those variables that you need in your computations for our great project in order to get a more precise answer (if possible).\r\n\r\n\r\n**Important goal/assumption.** While our workers have the possibility to save their bodies of radiation (this radiation in a wider meaning of ther word, but that I mean are the more probable conditions, I emphasize radiation exposure, that scientists should to expect in next few decades) eventually in shelters or those conventional protection means for the astronauts, we want to minimize this impact of radiation in their bodies and to know an approximation of when will be a suitable period/date for do a work of building of a great project in next few decades (for this thought experiment we evoke that the starting of activities for this ficticious project is at this year $2020$).\r\n\r\nIf my question is in the literature (or you know remarkable articles in this context), then please refer the literature answering my question as a **reference request** and I try to search and read the answer for my question from the literature.\n\nAccepted Answer:\n\nThere's *always* dangerous radiation in space near Earth, but there are regions which are more dangerous, in particular, the [Van Allen radiation belts](https://en.wikipedia.org/wiki/Van_Allen_radiation_belt). And there are events like solar flares and [coronal mass ejections](https://en.wikipedia.org/wiki/Coronal_mass_ejection) which increase the radiation temporarily. The Wikipedia article on [space weather](https://en.wikipedia.org/wiki/Space_weather) gives some details about this topic.\r\n\r\nIt's hard to make long-term predictions of space weather, but there are some long-term regularities due to the 11 year [sunspot cycle](https://en.wikipedia.org/wiki/Solar_cycle). Also, the Sun rotates on its axis with a period of about 1 month (25 days at its equator, 34.4 days at its poles), so we can predict when a given group of sunspots will be facing the Earth.\r\n\r\nIt takes on average 3.5 days for the particles of a coronal mass ejection to reach Earth (although in extreme cases the particles can get here in less than a day). So for these events, astronauts have time to take shelter in radiation-hardened shelters, or to return to Earth.\r\n\r\nSo, unlike the launch window, which is easy to calculate using orbital mechanics, there is no simple \"building window\" which can be calculated, apart from the [solar minimum](https://en.wikipedia.org/wiki/Solar_minimum) that is caused by the sunspot cycle. And as Wikipedia says, \"Their non-linear character makes predictions of solar activity very difficult\". Long term prediction of space weather is difficult, like long term prediction of the weather on Earth.\r\n\r\n---\r\n\r\nhoneste_vivere mentions in the comments that solar flares and CMEs can accelerate particles to relativistic speeds, which can reach Earth in under half an hour. These are called [solar energetic particles](https://en.wikipedia.org/wiki/Solar_energetic_particles) or SEPs. These particles are especially dangerous because they have high energy, and because we don't get much warning time. Fortunately, only about about 1% of CMEs produce strong SEP events. \r\n\r\nFrom [Solar particle event](https://en.wikipedia.org/wiki/Solar_particle_event):\r\n\r\n> Significant proton radiation exposure can be experienced by astronauts who are outside of the protective shield of the Earth's [magnetosphere](https://en.wikipedia.org/wiki/Magnetosphere), such as an astronaut in-transit to, or located on the Moon. However, the effects can be minimized if astronauts are in a low-Earth orbit and remain confined to the most heavily shielded regions of their spacecraft. Proton radiation levels in low earth orbit increase with orbital inclination. Therefore, the closer a spacecraft approaches the polar regions, the greater the exposure to energetic proton radiation will be.\r\n\r\nhoneste_vivere also mentions the [Forbush decrease](https://en.wikipedia.org/wiki/Forbush_decrease), whereby the effects of CMEs actually *protect* us from energetic particles that originate outside the solar system:\r\n\r\n> A Forbush decrease is a rapid decrease in the observed galactic cosmic ray intensity following a coronal mass ejection (CME). It occurs due to the magnetic field of the plasma solar wind sweeping some of the galactic cosmic rays away from Earth.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 30, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-4.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "magnetic-fields", "radiation", "cosmic-rays", "solar-wind"], "page_start": null, "page_end": null, "quality_flags": ["low_score", "single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 556945, "title": "Radiation and windows for building of a great project in a low Earth orbit: reference request or exercise as a ficticious need to build it", "url": "https://physics.stackexchange.com/questions/556945/radiation-and-windows-for-building-of-a-great-project-in-a-low-earth-orbit-refe", "share_url": "https://physics.stackexchange.com/q/556945", "content_license": null, "owner": {"display_name": "user250478", "user_id": 250478, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/250478/user250478"}}, "answers": [{"answer_id": 556971, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/556945/radiation-and-windows-for-building-of-a-great-project-in-a-low-earth-orbit-refe/556971#556971", "share_url": "https://physics.stackexchange.com/a/556971", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "PM 2Ring", "user_id": 123208, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/123208/pm-2ring"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:500095:0000", "text": "Question: Pressure done by a bar/beam inserted in a continuous medium (wall)\n\nRelated to a DIY project, I'm facing the following question: \r\n\r\n[![enter image description here][1]][1]\r\n\r\nAssume a metal bar (beam) of square section,  $a \\times a$, is inserted partially in a continuous medium (lets say, a wall) in a way that $h$ of the beam is inside the medium and $l$ is outside of the wall, and a force $F=200 N$ is done in the other extreme of the bar, perpendicular to it. The question is: how the pressure ( the force per unit area, $N/mm^2$ ) is distributed **in the contact surfaces between the cantilever beam and the wall** ?\r\n\r\nNote: we could say that the beam has no weight, no friction forces and the system is stable, no displacements. An infinite wall in width, height and thickness. If easier, we can consider a beam of circular section instead of square.\r\n\r\nInside the wall the beam has 5 surfaces: right, left, top, bottom and back. In the ideal case of no friction, I think forces in right and left surfaces will be null. No idea if forces in back and top are also null. Force in bottom must allow to keep fixed all system, with an unknown distribution of pressure on it ( uniform? maximum at $h$ deep? ). \r\n\r\nI've no knowledge to solve it as a continuous problem. A strong simplification that came to my mind is consider the system as equivalent to a lever with lengths $h$ and $l$, being the support axe the red line in the draw. That means to the force in the other extreme of the beam (green line in the draw) will be $F' = F \\frac {l}{h}$. By example if h=5cm and l=50 cm, then $F'=200*50/5=2000N$. \r\n\r\nBackground: if we stand a TV of 20 kg using a $l=50 cm$ beam, how to estimate the forces over the wall ?\r\n\r\n \r\n\r\n\r\n  [1]: https://i.sstatic.net/x4EHh.jpg\n\nAccepted Answer:\n\nThis shows a combination of a steel rod and a concrete wall in 3D. The rod is embedded in the wall 1/6 of the length. Section of a rod 1x1. We take the effective force divided by the cross-sectional area as 1. The middle picture is the distribution of the vertical component of the deformations in the wall; in the right-hand picture, this is the distribution of the $\\sigma_{zz}$ stress component. It can be seen that in such a situation, a stress increase of 30 times can be obtained. The calculations are performed using FEM and Mathematica 12.\r\n[![Figure 1][1]][1]\r\n\r\n\r\n  [1]: https://i.sstatic.net/h3xH8.png\n\nAnswer (score=2):\n\nI'm not sure what you mean by distribution of the \"pressure\", but this is a static problem involving a cantilever beam. The beam inside the wall is ignored. First from a static equilibrium perspective, there has to be an upward reaction force exerted by the wall of 200 N for vertical equilibrium to counter the downward 200 N force. There also has to be a counter-clock wise moment reaction at the wall of 200N x 50 cm = 10000 N.cm to counteract the clockwise moment (the \"rotational effect\") of 10000 N.cm due to the 200 N load.\r\n\r\nThe beam is subjected to an internal bending moment as well as a vertical shear force throughout the exposed portion.  The vertical shear force divided by the beam cross section is the shear stress. Stress has units of force per unit area, just like pressure. So maybe that is what you are thinking of. The bending moment creates tensile and compressive stresses at the extremes (top and bottom bottom of the beam, respectively).\r\n\r\nBending moment is a maximum at the wall and zero at the free end. Shear force is constant throughout and equals 200 N. If you look at the shear and moment diagrams for the cantilever with a force at the end, you will see the shear is constant and the moment linearly increasing progressing from the free end to the wall.   \r\n\r\nThis is the best I can give you without more detail, and without being sure what you mean by pressure. You really need to take a statics and mechanics of materials course to progress.\r\n\r\nHope this helps.\n\nAnswer (score=1):\n\nIt is a good pratice in structural engineering to check that both the beam material and  the material supporting the beam can withstand the loads. The admissible pressure for the wall of course  depends on the type of material and could vary from say few tens of bars for bricks to over 100 bars for concrete. Solving exactly your problem might not be so easy.  A possible simple approach is to model the wall material as a distribution of very stiff springs reacting at the bottom and on the top of the beam to the moment and shear stress imposed by the load. I would suggest to use the reacting stress on the beam as shown in  diagram a). The resulting reactions on the beam are shown in b). The 2 equations of equilibrium (moment and resultant) make it possible to solve for $R_{top}$ and $R_{bot}$. Since $R_{bot}=R_{top}+ P$, the max stress will be at the bottom and worth $\\sigma_{max}=2R_{bot}/ha$, $ha$ being the surface of the beam resting on the wall material.![enter image description here](https://i.sstatic.net/iRaKM.jpg)", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 31, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-4.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "continuum-mechanics"], "page_start": null, "page_end": null, "quality_flags": ["low_score"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 500095, "title": "Pressure done by a bar/beam inserted in a continuous medium (wall)", "url": "https://physics.stackexchange.com/questions/500095/pressure-done-by-a-bar-beam-inserted-in-a-continuous-medium-wall", "share_url": "https://physics.stackexchange.com/q/500095", "content_license": null, "owner": {"display_name": "pasaba por aqui", "user_id": 164884, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/164884/pasaba-por-aqui"}}, "answers": [{"answer_id": 500299, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/500095/pressure-done-by-a-bar-beam-inserted-in-a-continuous-medium-wall/500299#500299", "share_url": "https://physics.stackexchange.com/a/500299", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "Alex Trounev", "user_id": 208245, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/208245/alex-trounev"}}, {"answer_id": 500100, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/500095/pressure-done-by-a-bar-beam-inserted-in-a-continuous-medium-wall/500100#500100", "share_url": "https://physics.stackexchange.com/a/500100", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "Bob D", "user_id": 199893, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/199893/bob-d"}}, {"answer_id": 500256, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/500095/pressure-done-by-a-bar-beam-inserted-in-a-continuous-medium-wall/500256#500256", "share_url": "https://physics.stackexchange.com/a/500256", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "user8736288", "user_id": 239727, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/239727/user8736288"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:601708:0000", "text": "Question: Please Give a Few Examples of the Schrodinger Equation in Use\n\nI know the schrodinger equation has valuable uses in the creation of computers, lasers etc, but how exactly in the construction of these devices is the equation used? Under what circustances does the physicist/engineer say, \" I can't construct this until I use schrodinger equation to tell me something.\" I know the equation gives the probability of finding an quantum particle at a certain loction. How is that used in practice? A few examples would be great. Please be specific. This question is in no why challenging its use. I know it is used and is valuble. My question is how specifically it is used in the creation of a device.\n\nAccepted Answer:\n\nThis is a fairly broad question, and I'm sure others will add other things, but I think by far the most direct answer is: Density-functional theory.\r\n\r\nThis is a way to approximately solve the many-body Schrödinger equation, which is used in materials design processes as a standard in pretty much every industry which manufactures or researches materials. It is used to predict elastic moduli of steel, various properties of finely tuned nanomaterials, and basically anything else in the realm of material science you can think of.\r\n\r\nThere's actually a matter modelling S.E. which is devoted almost exclusively to density-functional theory.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 32, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-4.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "quantum-mechanics", "schroedinger-equation"], "page_start": null, "page_end": null, "quality_flags": ["low_score", "single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 601708, "title": "Please Give a Few Examples of the Schrodinger Equation in Use", "url": "https://physics.stackexchange.com/questions/601708/please-give-a-few-examples-of-the-schrodinger-equation-in-use", "share_url": "https://physics.stackexchange.com/q/601708", "content_license": null, "owner": {"display_name": "Lambda", "user_id": 129433, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/129433/lambda"}}, "answers": [{"answer_id": 601709, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/601708/please-give-a-few-examples-of-the-schrodinger-equation-in-use/601709#601709", "share_url": "https://physics.stackexchange.com/a/601709", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "G.Lang", "user_id": 149208, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/149208/g-lang"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:216039:0000", "text": "Question: How can the transfer function of an infinite ladder network be used to solve real world problems?\n\nIn his lectures on Physics, Feynman illustrates a mathematical 'trick' in formulating the impedance of an infinite ladder, LC network. It basically counts on the assumption that adding one more 'rung' in an infinite ladder is just a drop in the bucket - you still have the same infinite ladder. I researched this question in our Physics Stack Exchange, and came upon these two questions that basically deal with the same trick:\r\n\r\nhttps://physics.stackexchange.com/q/189897/45613\r\n\r\nhttps://physics.stackexchange.com/q/189903/45613\r\n\r\nBut to the point of my question given the expression for the infinite ladder how can you apply it to a real physical system? (Feynman does not elaborate further). \r\n\r\nFor example, what physical values might one use for $L$, and $C$ in the infinite  ladder given they are modeling infinitesimal elements? We first say the ladder is of infinite length, but in the practical world its length is finite, and the best you might have available are specs like Ohms/meter, Henries/meter, etc.\n\nAccepted Answer:\n\nUsing the \"drop-in-a-bucket\" trick, we find that an $LC$ laddar has impedance\r\n\r\n\\begin{align}\r\nZ\r\n&= Z_L + Z_C||Z \\\\\r\n&= Z_L + \\frac{Z_C Z}{Z + Z_C} \\\\\r\nZ^2  - Z Z_L - Z_L Z_C &= 0 \\\\\r\nZ &=\\frac{1}{2} \\left( Z_L \\pm \\sqrt{Z_L^2 + 4 Z_L Z_C} \\right) \\, .\r\n\\end{align}\r\n\r\nThe impedance of an inductance $L$ is $Z_L = i \\omega L$ and the impedance of a capacitor $C$ is $Z_C = 1 / i \\omega C$.\r\nPlugging that in we get\r\n$$Z = \\frac{1}{2} \\left( i \\omega L \\pm \\sqrt{-\\omega^2 L^2 + 4 \\frac{L}{C}} \\right) \\, .$$\r\n\r\nNow suppose that each rung on the ladder has an inductance per length of $\\mathcal{L}$ and a capacitance per length of $\\mathcal{C}$.\r\nSuppose that each section of transmission line has length $\\delta x$.\r\nThen we have $L = \\mathcal{L}\\delta x$ and $C = \\mathcal{C} \\delta x$, so\r\n\r\n$$Z = \\frac{1}{2} \\left( i \\omega \\mathcal{L}\\delta x \\pm \\sqrt{-(\\omega \\mathcal{L}\\delta x)^2 + 4 \\frac{\\mathcal{L}}{\\mathcal{C}}} \\right) \\, .$$\r\n\r\nNow at this point you might hear people tell you to consider some sort of continuum limit by sending $\\delta x$ to zero.\r\nWhile that does recover the usual result that $Z = \\sqrt{\\mathcal{L}/\\mathcal{C}}$, it is totally bogus.\r\nYou should *never* consider a limit as a quantity with physical dimensions goes to zero.\r\nInstead, we must identify a dimensionless quantity, i.e. a *ratio* of physical parameters, which tends to zero.\r\nOnly then will we understand the physical limit in which the approximation applies.\r\n\r\nConsider the limit in which the second term under the square root is much larger than the first:\r\n\r\n\\begin{align}\r\n\\frac{\\mathcal{L}}{\\mathcal{C}} &\\gg (\\omega \\mathcal{L} \\, \\delta x)^2 \\\\\r\n1 &\\gg \\omega^2 \\mathcal{LC} \\, \\delta x^2 \\\\\r\n1 &\\gg \\left( \\frac{\\omega \\, \\delta x}{v} \\right)^2\r\n\\end{align}\r\n\r\nwhere $v \\equiv 1 / \\mathcal{LC}$ is a characteristic wave speed for the ladder.\r\nThe usual relation between frequency $\\omega$, wave speed $v$, and wave length $\\lambda$,\r\n\r\n$$v = \\frac{\\lambda \\omega}{2 \\pi}$$\r\n\r\nbrings us to\r\n\r\n$$ 1 \\gg \\frac{\\delta x}{\\lambda} \\, .$$\r\n\r\nThis equation says that the continuum approximation works when the wave length of the electrical signals put onto the ladder is much larger than the size of each rung.\r\n\r\nThis is precisely the case in real life.\r\nLadder transmission line structures have a cutoff frequency above which their wavelength is on the same size scale as the ladder rungs.\r\nAbove this frequency, the ladder doesn't act like a transmission line (they tend to become either open or short circuits).\r\n\r\nThis answer explains a few of the questions in the original post:\r\n\r\n> what physical values might one use for L, and C in the infinite ladder given they are modeling infitesimal elements?\r\n\r\nYou use the actual inductance and capacitance *per length* of the physical ladder.\r\nIf each rung has length $l$ and inductance $L$ then $\\mathcal{L} = L/l$.\r\n\r\n> We first say the ladder is of infinite length, but in the practical world its length is finite, and the best you might have available are specs like Ohms/meter, Henries/meter, etc.\r\n\r\nYou can certainly build a ladder out of discrete parts, and then figure out the inductance and capacitance per length form the physical extent of those parts.\r\nAgain, this only yields the usual continuum limit expression if the wavelength is large enough (frequency is low enough).", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 33, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "electric-circuits", "electrical-resistance", "network"], "page_start": null, "page_end": null, "quality_flags": ["low_score", "single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 216039, "title": "How can the transfer function of an infinite ladder network be used to solve real world problems?", "url": "https://physics.stackexchange.com/questions/216039/how-can-the-transfer-function-of-an-infinite-ladder-network-be-used-to-solve-rea", "share_url": "https://physics.stackexchange.com/q/216039", "content_license": null, "owner": {"display_name": "docscience", "user_id": 45613, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/45613/docscience"}}, "answers": [{"answer_id": 216110, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/216039/how-can-the-transfer-function-of-an-infinite-ladder-network-be-used-to-solve-rea/216110#216110", "share_url": "https://physics.stackexchange.com/a/216110", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "DanielSank", "user_id": 31790, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/31790/danielsank"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:556841:0000", "text": "Question: Radio wave speed in air\n\nCouldn't Google credible answer.\r\n\r\nWhat is accepted constant in applied physics to estimate radio wave speed in earth atmosphere near water surface? \r\n\r\nTaking on account humidity inside few meters off water surface. \r\n\r\nDisregarding ionisation clouds and all other high altitude effects\n\nAccepted Answer:\n\nThe figure I was looking for is about 0.9997c\r\n\r\n* according to https://www.tau.ac.il/~tsirel/dump/Static/knowino.org/wiki/Electromagnetic_wave.html *\n\nAnswer (score=2):\n\nThere is no simple answer because it will depend on the humidity of the air *and* the frequency. From the humidity you get the fractional water vapor content and *average permittivity*; having the RF frequency and the dispersion relationship for water $\\varepsilon_w=\\varepsilon_w(\\omega)$ weighted by the relative vapor content will give you $\\langle\\varepsilon\\rangle$ and the refractive index $n(\\omega)=\\sqrt{\\langle\\varepsilon\\rangle}$ and finally the speed $v=c/n$", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 34, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-4.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "electromagnetic-radiation"], "page_start": null, "page_end": null, "quality_flags": ["low_score"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 556841, "title": "Radio wave speed in air", "url": "https://physics.stackexchange.com/questions/556841/radio-wave-speed-in-air", "share_url": "https://physics.stackexchange.com/q/556841", "content_license": null, "owner": {"display_name": "Boppity Bop", "user_id": 266423, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/266423/boppity-bop"}}, "answers": [{"answer_id": 557167, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/556841/radio-wave-speed-in-air/557167#557167", "share_url": "https://physics.stackexchange.com/a/557167", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "Boppity Bop", "user_id": 266423, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/266423/boppity-bop"}}, {"answer_id": 556879, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/556841/radio-wave-speed-in-air/556879#556879", "share_url": "https://physics.stackexchange.com/a/556879", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "hyportnex", "user_id": 31748, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/31748/hyportnex"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:263623:0000", "text": "Question: Examples of Riccati equations in physics\n\nI am looking for a Riccati equation \r\n\r\n$$y'(x)=a(x)+b(x)y(x)+c(x)y^2(x),$$\r\n\r\nwhere $a(x),b(x)$ and $c(x)\\neq 0$ in **physics that is solvable** (by easy methods). It would be great if at least one coefficient function would be non-constant so that it is not separable. \r\n\r\n**EDIT:** Maybe my question was not clear enough. Are there any real problems in physics which lead to a Riccati equation? Or are Riccati equations only of theoretical interest in physics?\n\nAccepted Answer:\n\nThe first this that comes to my mind is the time dependent logistic equation with production:\r\n\r\n$$\\frac{dN}{dt}=r(t)N(t)\\bigg(1-\\frac{N(t)}{K(t)}\\bigg) + A(t)$$\r\n\r\nwhich arises in population dynamics describing the time evolution of a population (animals, cells, etc). The coefficient $r(t)$ represents the growth rate, while $K(t)$ is the carrying capacity, i.e. the maximum number of individuals the population can attain. In addition there is a source term $A(t)$ accounting for migration, for example. Notice that I wrote all the coefficients explicitly time-dependent, as you want to do it with non-constant coefficients. This equation can be written as:\r\n\r\n$$\\frac{dN}{dt}=A(t) + r(t)N - \\frac{r(t)}{K(t)}N^2$$\r\n\r\nwhich is a Riccati equation. The coefficients could be for example periodic, accounting for seasonal oscillations in breeding, etc.\r\n\r\nFor physics related examples, look up to this paper:\r\n\r\nhttps://arxiv.org/pdf/physics/0110066.pdf", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 35, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "differential-equations"], "page_start": null, "page_end": null, "quality_flags": ["low_score", "single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 263623, "title": "Examples of Riccati equations in physics", "url": "https://physics.stackexchange.com/questions/263623/examples-of-riccati-equations-in-physics", "share_url": "https://physics.stackexchange.com/q/263623", "content_license": null, "owner": {"display_name": "MrYouMath", "user_id": 97523, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/97523/mryoumath"}}, "answers": [{"answer_id": 263730, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/263623/examples-of-riccati-equations-in-physics/263730#263730", "share_url": "https://physics.stackexchange.com/a/263730", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "josepmercadal", "user_id": 118951, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/118951/josepmercadal"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:482878:0000", "text": "Question: Irradiated Film Negatives from Chernobyl\n\nThe images attached are taken during the cleanup at Chernobyl. The white \"streaks\" at the bottom of each picture are said to be from intense radiation striking the film negatives, which makes sense (that's how they were discovered after all). \r\n\r\n**Question**: My main question is about the structure of those white streaks? Why are they perfectly vertical? \r\n\r\n**Guess**: My guess is that they are due to the geometry of the camera's shutter, but I just don't know enough about cameras to assert this with confidence. \r\n\r\n[![][1]][1]\r\n[![][2]][2]\r\n[![][3]][3]\r\n\r\n\r\n  [1]: https://i.sstatic.net/LmPWK.jpg\r\n  [2]: https://i.sstatic.net/g5q45.jpg\r\n  [3]: https://i.sstatic.net/QvYBZ.jpg\n\nAccepted Answer:\n\nThe spacing is very similar to what would be expected from the sprocket holes on 35mm film.\r\n\r\n[![enter image description here][1]][1]\r\n\r\nCC image by Voxphoto.\r\n\r\nThis is consistent with the film being stored rolled-up in a cartridge, with other layers of film protecting most of the emulsion from radiation.  But the removal of material for the holes reduced the absorption from that direction, leaving the extra exposure visible as streaks.\r\n\r\nThe film I'm familiar with has sprocket holes on both sides.  I don't see anything similar on the top of the images, so it's possible this reflects a difference in how the film was stored.  Perhaps the top of the image was stored downward and received less radiation in that direction, while the bottom of the image was stored upward.  Other scenarios are possible.  \r\n\r\n  [1]: https://i.sstatic.net/PE66A.png\n\nAnswer (score=0):\n\nLooks more like bromide drag, which is a result of developing with insufficient agitation. (If I understand it correctly.)\r\n\r\nI am not an expert, but I recall reading that old film which was exposed many years before the film expired is often developed in a very dilute solution and for a long development time. This requires little agitation and is prone to this effect.\r\n\r\nI do have a better understanding of gamma radiation and beta decay. These would not yield such a nice uniform pattern as the gamma radiation will mostly pass through the material or scatter depending on the energy. What you would see under heavy radiation is a fogging of the entire film.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 36, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-4.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "radiation"], "page_start": null, "page_end": null, "quality_flags": ["low_score"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 482878, "title": "Irradiated Film Negatives from Chernobyl", "url": "https://physics.stackexchange.com/questions/482878/irradiated-film-negatives-from-chernobyl", "share_url": "https://physics.stackexchange.com/q/482878", "content_license": null, "owner": {"display_name": "InertialObserver", "user_id": 56599, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/56599/inertialobserver"}}, "answers": [{"answer_id": 483022, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/482878/irradiated-film-negatives-from-chernobyl/483022#483022", "share_url": "https://physics.stackexchange.com/a/483022", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "BowlOfRed", "user_id": 55662, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/55662/bowlofred"}}, {"answer_id": 593902, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/482878/irradiated-film-negatives-from-chernobyl/593902#593902", "share_url": "https://physics.stackexchange.com/a/593902", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "Kevin", "user_id": 279805, "user_type": "unregistered", "profile_url": "https://physics.stackexchange.com/users/279805/kevin"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:426471:0000", "text": "Question: Different types of mechanic jacks\n\nI need help. **I would like to know:** **what the differences between the jacks illustrated below are and with which jack a car can be lifted easiest (according to the answer sheet it is jack **B**).**\r\n\r\n**My preliminary-knowledge on the topic:** I know how a car jack works in a general sense, I know about the principle of trading Force for distance.\r\n\r\n**My perception:** It seems to me that **A** shouldn't be able to work at all as it looks like the two rods aren't connected to each other. Or do I get it wrongly? I can't see the difference between **B** and **C**.\r\n\r\nI have tried to find out schematics of the jack illustrations below on the web by typing in different word-combies, but, unfortunately, I haven't managed to find yet. If one does know a source, that's also always welcome!\r\n\r\n**Note:** I received the questions exactly as I present them here from the organization I got them from. Therefore, I suffer from not being able to provide more context and specifications. I am only being able to provide my assumptions based on my preliminary knowledge.\r\n\r\nThanks a lot in advance for your assistance!\r\n\r\n[![enter image description here][1]][1]\r\n\r\n\r\n  [1]: https://i.sstatic.net/qRvax.png\n\nAccepted Answer:\n\nAssuming that all the threads involved have the same pitch, we can say that one turn of the crank in case A (two nuts), will move the jack up twice as much as in case B (one nut). In case C, the jack would not do any lifting (thanks to @tfb for pointing that out).\r\n\r\nThis, of course, means that, for any given state (height) of the jack, the applied force (required to move the load up) in case A has to be twice bigger than in case B.\r\n\r\nSo, it is just another example the force-distance trade-off.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 37, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-4.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "homework-and-exercises", "forces", "pressure", "work"], "page_start": null, "page_end": null, "quality_flags": ["low_score", "single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 426471, "title": "Different types of mechanic jacks", "url": "https://physics.stackexchange.com/questions/426471/different-types-of-mechanic-jacks", "share_url": "https://physics.stackexchange.com/q/426471", "content_license": null, "owner": {"display_name": "Englishterian", "user_id": 205429, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/205429/englishterian"}}, "answers": [{"answer_id": 426491, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/426471/different-types-of-mechanic-jacks/426491#426491", "share_url": "https://physics.stackexchange.com/a/426491", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "V.F.", "user_id": 189477, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/189477/v-f"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:391571:0000", "text": "Question: How to determine the force of a spring-damper in 3D\n\n**This is not homework. I just often have to calculate forces between objects and I am interested in a systematic procedure for determining the forces.**\r\n\r\nImagine two point masses with mass $m_1$ and $m_2$ which are connected by a linear spring (relaxed if the distance between both masses is $r_0$; spring constant $c$) and a linear viscous damper (damping constant $d$). The positions of both masses are given by the position vectors $\\boldsymbol{r}_1$ and $\\boldsymbol{r}_2$. The forces $\\boldsymbol{F}_1$ and $\\boldsymbol{F}_2=-\\boldsymbol{F}_1$ are the internal forces that result from creating the free body diagram. My question is how can I write down an expression for the force $\\boldsymbol{F}_1$ as a function of $\\boldsymbol{r}_1,\\boldsymbol{r}_2, \\dot{\\boldsymbol{r}}_1,\\dot{\\boldsymbol{r}}_2,r_0$ as well as the parameters $c$ and $d$?\r\n\r\nI know that the total internal force $\\boldsymbol{F}_1$ is the result of the addition of the spring force $\\boldsymbol{F}_{\\text{spring}}$ and the damper force $\\boldsymbol{F}_{\\text{damper}}$. Hence,\r\n\r\n$$\\boldsymbol{F}_1 = \\boldsymbol{F}_\\text{spring}+\\boldsymbol{F}_\\text{damper}.$$\r\n\r\n\r\n> Credit to @ja72: The damping force $\\boldsymbol{F}_\\text{damper}$ is given by\r\n> \r\n> $$\\boldsymbol{F}_\\text{damper}=-d\\left[\\dfrac{{\\boldsymbol{r}}^T_2-{\\boldsymbol{r}}^T_1}{|{\\boldsymbol{r}}_2-{\\boldsymbol{r}}_1|}(\\dot{\\boldsymbol{r}}_2-\\dot{\\boldsymbol{r}}_1)\\right]\\dfrac{{\\boldsymbol{r}}_2-{\\boldsymbol{r}}_1}{|{\\boldsymbol{r}}_2-{\\boldsymbol{r}}_1|}.$$\r\n> \r\n\r\nAnd how can I set up the force $\\boldsymbol{F}_\\text{spring}$? If the general case with the distance $r_0$ is too complicated I would also accept an answer in which $r_0=0$.\r\n\r\nEDIT: After the answer of @ja72. I thought that maybe it is possible to express the spring force as:\r\n\r\n$$F_\\text{spring}=-c\\left[|\\boldsymbol{r}_2-\\boldsymbol{r}_1|-r_0\\right]\\dfrac{\\boldsymbol{r}_2-\\boldsymbol{r}_1}{|\\boldsymbol{r}_2-\\boldsymbol{r}_1|}.$$\r\n\r\nIs that correct?\r\n\r\n[![enter image description here][1]][1]\r\n\r\n\r\n  [1]: https://i.sstatic.net/urShf.png\n\nAccepted Answer:\n\nCreate a vector with the direction of the force\r\n\r\n$$ \\boldsymbol{e} = \\frac{ \\boldsymbol{r}_2 - \\boldsymbol{r}_1 }{\\|  \\boldsymbol{r}_2 - \\boldsymbol{r}_1 \\|} $$\r\n\r\nNow the relative velocity is\r\n\r\n$$ v = \\boldsymbol{e}^\\top (\\dot{\\boldsymbol{r}}_2 - \\dot{\\boldsymbol{r}}_1 ) $$\r\n\r\nand the damping force\r\n\r\n$$ \\boldsymbol{F}_{\\rm damping} = -(d v) \\boldsymbol{e} = -d\\,\\left( \\boldsymbol{e}^\\top (\\dot{\\boldsymbol{r}}_2 - \\dot{\\boldsymbol{r}}_1 ) \\right)\\boldsymbol{e} $$\r\n\r\nSimilarly for the spring force\r\n\r\n$$ \\boldsymbol{F}_{\\rm spring} = -(c x) \\boldsymbol{e} = -c\\,\\left( \\boldsymbol{e}^\\top (\\boldsymbol{r}_2 - \\boldsymbol{r}_1 ) -\\ell \\right)\\boldsymbol{e} $$\r\n\r\n<sub>Where $\\ell$ is the free length of the spring.</sub>\r\n\r\nThere is a simplification that can happen with the spring force\r\n\r\n$$ \\boldsymbol{F}_{\\rm spring} = -c\\,\\left(  \\|  \\boldsymbol{r}_2 - \\boldsymbol{r}_1 \\| -\\ell \\right) \\frac{ \\boldsymbol{r}_2 - \\boldsymbol{r}_1 }{\\|  \\boldsymbol{r}_2 - \\boldsymbol{r}_1 \\|}  = $$\r\n\r\n$$ \\boldsymbol{F}_{\\rm spring} = -c\\,\\left( (\\boldsymbol{r_2}-\\boldsymbol{r_1}) - \\ell\\, \\frac{( \\boldsymbol{r}_2 - \\boldsymbol{r}_1 )}{\\|  \\boldsymbol{r}_2 - \\boldsymbol{r}_1 \\|} \\right)\r\n$$", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 38, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "newtonian-mechanics", "forces"], "page_start": null, "page_end": null, "quality_flags": ["low_score", "single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 391571, "title": "How to determine the force of a spring-damper in 3D", "url": "https://physics.stackexchange.com/questions/391571/how-to-determine-the-force-of-a-spring-damper-in-3d", "share_url": "https://physics.stackexchange.com/q/391571", "content_license": null, "owner": {"display_name": "MrYouMath", "user_id": 97523, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/97523/mryoumath"}}, "answers": [{"answer_id": 391580, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/391571/how-to-determine-the-force-of-a-spring-damper-in-3d/391580#391580", "share_url": "https://physics.stackexchange.com/a/391580", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "John Alexiou", "user_id": 392, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/392/john-alexiou"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:276515:0000", "text": "Question: Spinning cricket balls and weight distribution\n\n[An article on ESPN Cricinfo][1] discusses the possibility of the internal weight distribution of cricket balls having an impact on the ability of a bowler to achieve 'spin'.\r\n\r\nIn cricket, a spin bowler imparts rotations on the ball at the point of release and thereby seeks to deceive their opponent (the batter) through either (i) the trajectory of the ball through the air; or (ii) the ball's behaviour once it comes into contact with the playing surface. [The ball will, as a general rule, be delivered at an initial velocity of 80-90kph and will travel c. 15 metres after it is delivered prior to bouncing, and a further 3 metres before reaching the position in which the batter is initially situated]\r\n\r\nIn the article, a cricket ball manufacturer states:\r\n\r\n>You can change the construction of the core so that it is more conducive to spin bowling, by weighting the core more heavily in the middle. It has an effect like an ice skater on the rink: when she spins with her arms wide, she spins slowly, and as she brings her arms in, she accelerates. All she has done is bring her weight in, which has enabled her to spin faster. \r\n\r\nIs this claim accurate?\r\n\r\n\r\n  [1]: http://www.espncricinfo.com/duleep-trophy-2016-17/content/story/1048403.html\n\nAccepted Answer:\n\nYes, different weight distributions in cricket balls affect how conducive they are to being spun. \r\n\r\nThe quote seems self-explanatory. You must have encountered this phenomenon in school physics.  A solid cylinder rolls down an incline more quickly than a hollow cylinder of the same mass and radius. After rolling the same distance they lose the same PE and gain this same amount as KE. However, the solid cylinder has greater translational KE while the hollow cylinder has greater rotational KE. \r\n\r\nHow this distribution of mass is achieved can be seen in the following photo from [your link](http://www.espncricinfo.com/duleep-trophy-2016-17/content/story/1048403.html). This core is made up of cork and rubber particles which have been heated and compressed. Surrounding it are alternate layers of cork bound by woollen yarn. The outer coating of the ball is made of smooth leather, but a heavy thread is used around the seam (just visible at the rim) to give the bowler enough grip to spin the ball. \r\n\r\n[![enter image description here][1]][1]\r\n\r\nHow difficult a ball is to spin - its rotational inertia - is measured by its moment of inertia (MI). For a ball of mass $M$ and radius $R$ the MI about an axis through the centre can be written as $\\frac25 kMR^2$ where $k$ is a fraction depending on the distribution of mass. If the mass of the ball is distributed uniformly then $k=1$ whereas if all the mass were concentrated in a shell at the rim then $k=\\frac53$. If the mass were concentrated at the centre then $k=0$. \r\n\r\nThe Laws of Cricket require the mass of the ball to be within the range 156-163g and to have a circumference of 224-229mm, but there are no restrictions on internal construction or distribution of mass. National standards (eg British Standards Institute, BSI) cover seam height, hardness and wear.\r\n\r\nAlthough all balls are traditionally made of cork and rubber inside a leather cover, there is [considerable variety in construction](http://onlinelibrary.wiley.com/doi/10.1002/jst.8/pdf) even at international level. There is usually a core surrounded by 5-6 layers of cladding which alternate cork with wool or cotton yarn. Cores vary from solid cork to solid rubber, or a mixture of the two - or none at all - which may or may not be compressed. Cladding varies between winding the woollen yarn under tension when wet (which increases the tension when it has dried) or relatively loosely (as in the image above). With these options. the mass of the ball could be concentrated in the core (easy to spin) or in the cladding (more difficult to spin). Another variation is an irregularly-shaped core - which gives the ball a preferred axis of spin.\r\n\r\nAssuming that core and cladding densities are in the ratio $d+1$, and the radii of the core and the ball are in the ratio of $r$, and ignoring any difference between cladding and leather cover, the MI of the ball is characterised by  \r\n$k=(dr^5+1)/(dr^3+1)$.  \r\n\r\nCork and rubber have densities of about 14-16 and 69-74 lb/cu.ft respectively. Assuming these are the extreme densities possible for the core and cladding - giving $d \\approx 4$ or $d \\approx -\\frac45$ - and assuming $r \\approx \\frac12$, then by switching cork and rubber between core and cladding we can achieve the extreme values $k \\approx \\frac34$ and $k \\approx \\frac{13}{12}$. \r\n\r\nSo the moment of inertia of a cricket ball could be varied in the ratio of about $13:9$ by shifting mass from the cladding to the core. \r\n\r\n  [1]: https://i.sstatic.net/qyF42.jpg", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 39, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "classical-mechanics", "rotational-dynamics", "drag", "everyday-life"], "page_start": null, "page_end": null, "quality_flags": ["low_score", "single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 276515, "title": "Spinning cricket balls and weight distribution", "url": "https://physics.stackexchange.com/questions/276515/spinning-cricket-balls-and-weight-distribution", "share_url": "https://physics.stackexchange.com/q/276515", "content_license": null, "owner": {"display_name": "Paul", "user_id": 128347, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/128347/paul"}}, "answers": [{"answer_id": 276709, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/276515/spinning-cricket-balls-and-weight-distribution/276709#276709", "share_url": "https://physics.stackexchange.com/a/276709", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "sammy gerbil", "user_id": 114696, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/114696/sammy-gerbil"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:110554:0000", "text": "Question: Magnetic field resistance material: are there any?\n\nI was wondering with a question for a quite long time, thought to ask here.\r\n\r\nI need to know is there any material or element which can block magnetic field? I mean I am searching for such material or element that cannot allow magnetic field though itself?\r\n\r\nThe practical scenario is, there are two permanent magnets and those are positioned within each other's magnetic field. I want to put something so that both the magnets become free of interference withing themselves.\r\n\r\nHope I could clarify my question.\r\n\r\nCan anyone help me of give me some suggestion on this aspect please?\n\nAccepted Answer:\n\nThe *only* materials that can block a magnetic field are those that strongly interact, such as a ferromagnetic material (iron, steel, etc), or a superconductor. Since we don't live in a sea of liquid nitrogen, for weaker fields mu-metal is best, but for stronger magnets mu metal loses it's advantage and any iron-based metal is just as good.\r\n\r\nAn unobtanium that blocks magnets but is not affect by them can't exist. If it did, you could make a perpetual motion machine by letting the magnets attract (which relases energy), inserting a plate of said material between them (you would leave a small gap in between the magnets), and pulling the magnets back apart with negligible energy expenditure.\r\n\r\nIron won't let you do this. The magnets release energy when you let them attract, and the plate releases additional energy when you insert it. However, the presence of an attracting metal plate means it will take more energy to remove the magnets with the plate in between than without, and you end up having to put all the energy back in you got out in the first place (Nature is an accurate banker).\n\nAnswer (score=0):\n\nA material with such resistance is a material with high [magnetic permeability](http://en.wikipedia.org/wiki/Permeability_(electromagnetism)).\r\n\r\nA much used example is [Mu-metal](http://en.wikipedia.org/wiki/Mu-Metal).", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 40, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "electromagnetism", "magnetic-fields"], "page_start": null, "page_end": null, "quality_flags": ["low_score"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 110554, "title": "Magnetic field resistance material: are there any?", "url": "https://physics.stackexchange.com/questions/110554/magnetic-field-resistance-material-are-there-any", "share_url": "https://physics.stackexchange.com/q/110554", "content_license": null, "owner": {"display_name": "Razib Ali", "user_id": 45531, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/45531/razib-ali"}}, "answers": [{"answer_id": 110556, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/110554/magnetic-field-resistance-material-are-there-any/110556#110556", "share_url": "https://physics.stackexchange.com/a/110556", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Kevin Kostlan", "user_id": 15559, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/15559/kevin-kostlan"}}, {"answer_id": 110555, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/110554/magnetic-field-resistance-material-are-there-any/110555#110555", "share_url": "https://physics.stackexchange.com/a/110555", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Nathaniel Bubis", "user_id": 7650, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/7650/nathaniel-bubis"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:280529:0000", "text": "Question: Is there a way to estimate fan capacity at altitude?\n\nProvided you know the capacity of a fan (flow rate) at constant speed and at sea level, is there an analytical way to predict what the flow rate would be at altitude? Or is this specific to the fan's design?\n\nAccepted Answer:\n\nFor a fixed speed, a fan, blower or any turbo-machine in general will deliver the same *volumetric* flow regardless of the ambient pressure since the machine essentially *scoops* out a volume of air as each blade of the machine passes the machine's inlet.\r\n$$Q_{SL}=Q_{alt}$$ \r\nwhere $SL$ designates 'Sea Level' as reference and $alt$ as some higher altitude\r\n\r\nBut at higher altitudes there are fewer molecules per unit volume (lower gas density) and so the *mass* flow rate is lower with increasing altitude and barometric pressure.\r\n$$\\dot{m}_{alt} < \\dot{m}_{SL}$$\r\nSo since the volumetric flow rates are the same then\r\n$${\\dot{m}_{alt}\\over{\\rho}_{alt}} = {\\dot{m}_{SL}\\over{\\rho}_{SL}}$$\r\nand\r\n$$\\dot{m}_{alt}={{\\rho}_{alt}\\over {\\rho}_{SL}}\\dot{m}_{SL}$$\r\nBut if we were to measure these mass flows as volumetric flows relative to sea level then\r\n$${{\\dot{m}_{alt}}\\over {{\\rho}_{SL}}}={{{\\rho}_{alt}}\\over {{\\rho}_{SL}}}{{\\dot{m}_{SL}}\\over {{\\rho}_{SL}}}$$\r\nwhich becomes\r\n$$Q_{Malt}={{{\\rho}_{alt}}\\over {{\\rho}_{SL}}}Q_{MSL}$$\r\nAnd the $Q_M$'s are the measured volumetric flows at altitude and sea level respectively.\r\nThis result shows the the measured volumetric flow is reduced as altitude increases by the ratio of air density as it decreases. And this is consistent with zero volumetric flow as one moves out of the atmosphere and no more scooping is possible.\n\nAnswer (score=0):\n\nFollowing answer is speculative.\r\n\r\nFlow rate of air ($Q$) is determined once fan's geometry, its angular speed ($\\omega$), and thermodynamic state of air (in particular its $\\rho,\\mu$) is specified. Since geometry of fan is not being changed, let us take any linear dimension associated with it (say, length of fan blade) as a length scale, $d$. Flow rate $Q$ is determined by these variables means that there exists a functional relationship:\r\n\r\n$f(Q,\\rho,\\mu,d,\\omega)=$constant\r\n\r\nwhich results in dimensionless groups:\r\n\r\n$g(\\frac{Q}{\\omega d^3},\\frac{\\omega d^2}{\\nu})=$constant\r\n\r\nor\r\n\r\n$\\frac{Q}{\\omega d^3}=h(\\frac{\\omega d^2}{\\nu})$\r\n\r\nwhere $f,g,h$ are functions. Now since flow Reynolds number is high (and therefore flow is turbulent), viscosity plays little role in determining the flow (hypothesis). In that case, \r\n\r\n$\\frac{Q}{\\omega d^3}\\approx $constant.\r\n\r\nSince angular speed of the fan isn't varying either I would guess that flow rate of the fan shall remain constant (to a good approximation).\r\n\r\nOne may object that density of air hasn't appeared in the final conclusion, so if one were to take the fan to such a height where there is practically no air, the equation still predicts the same flow rate, which is wrong. However in this case continuum approximation breaks down, and the entire analysis would become inapplicable.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 41, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "fluid-dynamics", "pressure", "flow"], "page_start": null, "page_end": null, "quality_flags": ["low_score"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 280529, "title": "Is there a way to estimate fan capacity at altitude?", "url": "https://physics.stackexchange.com/questions/280529/is-there-a-way-to-estimate-fan-capacity-at-altitude", "share_url": "https://physics.stackexchange.com/q/280529", "content_license": null, "owner": {"display_name": "docscience", "user_id": 45613, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/45613/docscience"}}, "answers": [{"answer_id": 280973, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/280529/is-there-a-way-to-estimate-fan-capacity-at-altitude/280973#280973", "share_url": "https://physics.stackexchange.com/a/280973", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "docscience", "user_id": 45613, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/45613/docscience"}}, {"answer_id": 280642, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/280529/is-there-a-way-to-estimate-fan-capacity-at-altitude/280642#280642", "share_url": "https://physics.stackexchange.com/a/280642", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Deep", "user_id": 122958, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/122958/deep"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:314793:0000", "text": "Question: Air pressure in a car tyre increases during driving\n\nPlease tell me the reason in reference of thermodynamics that why pressure in a car tyre increases during driving.\n\nAccepted Answer:\n\nwhen we drive , the frictional force between the tires and the road increases the temperature of the air inside the tire.\r\n\r\nAccording to Gay-Lussac's Law,\r\n\r\np ∝ T ; [When volume is constant]\r\n\r\nso the increase in temperature also increases tire pressure.\n\nAnswer (score=2):\n\nThe tyre does heat up, **but not because of friction:** the tyre does not slide along the road and the friction between tyre and road therefore does no work.\r\n\r\nWhat does happen is that the tyre is not perfectly circular. It is squashed by the weight of the vehicle. As the vehicle moves, the part of the tyre that was squashed moves towards the back of the vehicle, up away from the road, and recovers its shape; and the part of the tyre that was towards the front rolls down to the road surface and is squashed in its turn.\r\n\r\nThis constant flexing of the rubber is what makes it hot. (In racing cars the tyres are often designed to be slippery and useless when cold, becoming stickier as they get hot). \r\n\r\nThe hot rubber warms the air inside the tyre. As other answers have said, given a constant volume, this results in an increase in pressure.\r\n\r\nIf you had steel wheels instead of rubber ones, they would flex much, much less and get much, much less hot.\r\n\r\nYou can try the \"flexing = heat\" experiment yourself by taking a nice thick piece of copper wire and bending it back and forth until it breaks. If you immediately touch one of the broken ends you will burn yourself quite nicely.\n\nAnswer (score=1):\n\nWhen we drive our vehicle, the tyre pressure gets increased by the road. Inside the tyre, the air gets heated up and thus causes expanding of the tyre, due to the high pressure force created by the friction.\n\nAnswer (score=1):\n\nDuring the motion of wheel friction force acts between tyre and wheel which cause the loss energy in form of heat and this heat increases the temperature and kinetic energy of gas molecules increases hence the pressure increase\n\nAnswer (score=0):\n\nThe more you run, the more heated the tire would be. Seen a pressure cooker haven't you? the gas molecules expand (start to move in a larger area). Thus needing a larger are, the pressure increases. This often leads to loss of air because the pressure is high and some amount of air has to escape or else the tire will burst. That is exactly why it is also said, fill lesser air in the tire during summers.\n\nAnswer (score=0):\n\nWhen we drive the frictional force between the tyre and the road increase the temperature then, r.m.s. speed increases the gas molecules. The pressure exerted by gas is due to collision so, when a car is driven some distance, the air pressure in the tyre increases. \r\nAs according to the law of pressure, \r\nP is directly proportional to T.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 42, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "thermodynamics"], "page_start": null, "page_end": null, "quality_flags": ["low_score", "mixed_license"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 314793, "title": "Air pressure in a car tyre increases during driving", "url": "https://physics.stackexchange.com/questions/314793/air-pressure-in-a-car-tyre-increases-during-driving", "share_url": "https://physics.stackexchange.com/q/314793", "content_license": null, "owner": {"display_name": "user41522", "user_id": 146729, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/146729/user41522"}}, "answers": [{"answer_id": 314796, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/314793/air-pressure-in-a-car-tyre-increases-during-driving/314796#314796", "share_url": "https://physics.stackexchange.com/a/314796", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "gUUBI", "user_id": 146730, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/146730/guubi"}}, {"answer_id": 484797, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/314793/air-pressure-in-a-car-tyre-increases-during-driving/484797#484797", "share_url": "https://physics.stackexchange.com/a/484797", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "Martin Kochanski", "user_id": 97235, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/97235/martin-kochanski"}}, {"answer_id": 484753, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/314793/air-pressure-in-a-car-tyre-increases-during-driving/484753#484753", "share_url": "https://physics.stackexchange.com/a/484753", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "Yui", "user_id": 233990, "user_type": "unregistered", "profile_url": "https://physics.stackexchange.com/users/233990/yui"}}, {"answer_id": 484802, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/314793/air-pressure-in-a-car-tyre-increases-during-driving/484802#484802", "share_url": "https://physics.stackexchange.com/a/484802", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "आर्यभट्ट", "user_id": 233551, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/233551/%e0%a4%86%e0%a4%b0%e0%a5%8d%e0%a4%af%e0%a4%ad%e0%a4%9f%e0%a5%8d%e0%a4%9f"}}, {"answer_id": 462513, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/314793/air-pressure-in-a-car-tyre-increases-during-driving/462513#462513", "share_url": "https://physics.stackexchange.com/a/462513", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "Bryan Greene", "user_id": 223642, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/223642/bryan-greene"}}, {"answer_id": 614261, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/314793/air-pressure-in-a-car-tyre-increases-during-driving/614261#614261", "share_url": "https://physics.stackexchange.com/a/614261", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "Mariyam Khan", "user_id": 288898, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/288898/mariyam-khan"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:23468:0000", "text": "Question: Magnetic flying engine\n\nI invented a flying engine moving entirely by magnetic forces (such as the force related with magnetic field of the Earth).\r\n\r\nSee http://porton.wordpress.com/2011/12/23/magnetic-vehicle/\r\n\r\nThe question is, can we build an engine of this type which is enough powerful to actually fly?\r\n\r\nThe question is both about the mechanical engine described in the post above and about a hypothetical (not developed by me in details) purely electronic version.\r\n\r\nMy question is: Describe operating characteristics of these kinds of engines.\n\nAccepted Answer:\n\nNo such engine can exist--unless you custom-tailor your magnetic field.\r\n\r\nAny such engine you build will need a current loop--since current requires a closed circuit to flow. \r\n\r\nA current loop never has any force on it in a uniform magnetic field{*}. It can have a torque, so at max you can create a device that spins.\r\n\r\nIf you want something to levitate, you need to generate a nonuniform magnetic field. A large magnet on the ground is one way to do this, but it leads to instability. And you'd have to keep the magnet with you wherever you went, so you effectively have to drag a large magnet along the ground to make a teensy thing fly.\r\n\r\nOf course, you can lay out the magnet like a track. Which has already been done in [maglev][1] trains.\r\n\r\n![enter link description here][2]\r\n\r\nIn a maglev train, there are magnets in the track, and electromagnets at the bottom of the train (or is it the other way around? Doesn't really matter here) The electromagnets rapidly switch polarity.\r\n\r\nIn the diagram above, you can see that the train will be pushed towards the left. If you think a bit, you way also notice that, due t the symmetry of the situation, once the train is left, it will be pushed towards the right. But, in the time it takes for the train to be pushed left, the polarity of the electromagnets switches, and the train gets pushed further left.\r\n\r\nHere, the magnets serve two purpses: they make the train go, and the levitate it (reduces friction). Maglev trains are one of the fastest type of trains and have been in use in many major cities for quite some time now.\r\n\r\n\r\n<sup>*The Earth's field is nonuniform, but locally uniform as long as you don't have any electrical devices nearby. I really don't think that any nonuniformity in this magnetic field could be harnessed to make a flying machine. Then again, I may be wrong about this.</sup>\r\n\r\n\r\n  [1]: http://en.wikipedia.org/wiki/Maglev\r\n  [2]: https://upload.wikimedia.org/wikipedia/commons/c/c2/Maglev_Propulsion.svg\n\nAnswer (score=3):\n\n@leftaroundabout is correct; the net force (to lowest order) would be zero, regardless of the amount of current.  The only net-force would come from higher order terms (i.e. from the divergence in the earth's magnetic field) ... and thus amounts to a very small effect.  Additionally, producing high-power magnetic fields in very difficult and takes a-lot of a very heavy machinery (which is thus, not inclined to fly).\r\n\r\nIf you're interested in designing a flying machine, you should consider studying aeronautics.  If you're interested in electrodynamics, you should consider studying that.  In either case, its appropriate to establish a background of basics before you try to make your own creations.\n\nAnswer (score=0):\n\n1- in order to levitate an object you need a force or G+1, were G is the gravitational force of a device against the earth,\r\n\r\n2- using the Frisbee configuration , you can create a force to be close or cancel the G force,\r\n\r\n3-the use of solar power panels on such device will give the sustain energy for the device to maintain the movement,\r\n\r\n4- the use of vent principle on the construction with the remote control system(6 channels) you can control the openings and directional movement of device.(also the stabilization of the center console),\r\n\r\n5-think to have it as a toy of 3 feet wide and go by face1,2,3, and 4.\n\nAnswer (score=-1):\n\nI think it is entirely possible!!! you just need to use momentum of the magnets to keep the other one going using centrifficle foce as well.There is no law of motion that disaproves this very easily plausible science project.\n\nAnswer (score=-3):\n\nI'm no professional. With that said...      Using a wireless energy supply from the earths current (Tesla), you could provide quite a load to an electromagnet, used to push one way with displacement on the vehicle (or whatever)  while pulling on everything else with mass, from the opposite. Flying saucers I'll bet are shaped that way so the center bubble can swivel as the vehicle turns instantly as all atoms are magnets, and being acted on by the vehicle magnet in the shape of a donut, would all respond instantly, like in a gravitational field. Tune into the scalar waves and away you go.....    I'm sure computers can handle the math. Magnets with wireless energy supply.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 43, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "electromagnetism", "electricity"], "page_start": null, "page_end": null, "quality_flags": ["low_score"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 23468, "title": "Magnetic flying engine", "url": "https://physics.stackexchange.com/questions/23468/magnetic-flying-engine", "share_url": "https://physics.stackexchange.com/q/23468", "content_license": null, "owner": {"display_name": "porton", "user_id": 8569, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/8569/porton"}}, "answers": [{"answer_id": 23482, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/23468/magnetic-flying-engine/23482#23482", "share_url": "https://physics.stackexchange.com/a/23482", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Manishearth", "user_id": 7433, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/7433/manishearth"}}, {"answer_id": 23478, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/23468/magnetic-flying-engine/23478#23478", "share_url": "https://physics.stackexchange.com/a/23478", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "DilithiumMatrix", "user_id": 8521, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/8521/dilithiummatrix"}}, {"answer_id": 116365, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/23468/magnetic-flying-engine/116365#116365", "share_url": "https://physics.stackexchange.com/a/116365", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Gustavo", "user_id": 48686, "user_type": "unregistered", "profile_url": "https://physics.stackexchange.com/users/48686/gustavo"}}, {"answer_id": 80984, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/23468/magnetic-flying-engine/80984#80984", "share_url": "https://physics.stackexchange.com/a/80984", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "user31141", "user_id": 31141, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/31141/user31141"}}, {"answer_id": 56714, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/23468/magnetic-flying-engine/56714#56714", "share_url": "https://physics.stackexchange.com/a/56714", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "cameron downie", "user_id": 21918, "user_type": "unregistered", "profile_url": "https://physics.stackexchange.com/users/21918/cameron-downie"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:784475:0000", "text": "Question: Where special and general relativity must be used in engineering?\n\nAs I know Newton physics is used for most engineering, aerospace, mechanical, naval etc.\r\n\r\nWhere we must use Theory of Special Relativity and Theory of General Relativity to get correct results, only for astronomy, big distances/objects etc?\n\nAccepted Answer:\n\nEinstein was so prolific, that by \"Einstein Physics\" you may be referring to three different things:\r\n1. Einstein's Theory of Special Relativity.\r\n2. Einstein's Theory of General Relativity.\r\n3. Einstein's discoveries about the photoelectric effects that led to the development of Quantum Mechanics.\r\n\r\n**Quantum Mechanics** - which was only started by Einstein but then fully developed by others (Planck, Bohr, Schrodinger, Dirac, Fermi, and many many others), is super-important in many areas of practical engineering, including the invention of the transistor in the 1940s which allowed modern computers, LED lighting, LASER (light amplification by stimulated emission of radiation), superconducting magnets, and a lot lot more.\r\n\r\nThe theory of **special relativity** effects calculation of extremely fast-moving objects, and isn't used for most \"normal\" engineering (e.g., isn't relevant when calculating trajectories of bullets or airplanes), but was very important for the development of the GPS (global positioning satellites) system. In the GPS system, we need to calculate the movement of satellites and electromagnetic beams coming from them very very accurately, to achieve good accuracy of the position on the ground. It turns out that without including special relativity (because these satellites are moving quickly around the earth), the calculations are not accurate enough.\r\n\r\nIt turns out that the GPS system also needs **general relativity**: Among other things, general relativity predicts that time slows down near a massive object. Because of general relativity, the time flows a bit more slowly on Earth than it does on the GPS satellites, and if this is not taken into account - the GPS calculations would not turn out to be accurate. Note that this is a separate effect than the velocity-related time dilation I mentioned above (due to special relativity), and both were needed to achieve good accuracy with GPS.\n\nAnswer (score=3):\n\nI'm going to add:\r\n\r\n1) Space craft attitude control (star trackers). They account for stellar aberrations which are a form of the relativistic Doppler shift.\r\n\r\n2) Radiation oncology uses the relativistic form of the Bethe-Bloch eq (1932): https://en.wikipedia.org/wiki/Bethe_formula\r\n\r\n3) PET scans, since they involve annihilating your body's electrons with positrons it's inherently relativistic and quantum.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 44, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-4.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "general-relativity", "special-relativity", "gps", "big-list"], "page_start": null, "page_end": null, "quality_flags": ["low_score"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 784475, "title": "Where special and general relativity must be used in engineering?", "url": "https://physics.stackexchange.com/questions/784475/where-special-and-general-relativity-must-be-used-in-engineering", "share_url": "https://physics.stackexchange.com/q/784475", "content_license": null, "owner": {"display_name": "Elizabeth", "user_id": 315125, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/315125/elizabeth"}}, "answers": [{"answer_id": 784478, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/784475/where-special-and-general-relativity-must-be-used-in-engineering/784478#784478", "share_url": "https://physics.stackexchange.com/a/784478", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "Nadav Har'El", "user_id": 219989, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/219989/nadav-harel"}}, {"answer_id": 784501, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/784475/where-special-and-general-relativity-must-be-used-in-engineering/784501#784501", "share_url": "https://physics.stackexchange.com/a/784501", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "JEB", "user_id": 82339, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/82339/jeb"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:839612:0000", "text": "Question: Modelling the spring \"constant\" for a rubber band\n\nI am doing a practical in class which requires me to calculate the spring constant of a single rubber band.\n\nAccepted Answer:\n\nYou have been given a difficult assignment as the force vs extension graph of a rubber band might look like this.  \r\n\r\n[![enter image description here][1]][1].  \r\n\r\nAs it the relationship between force and extension is non-linear you have a problem defining a spring constant particularly as the graphs for loading and unloading differ from one another.  \r\n\r\nRubber is an elastic material which exhibits [hysteresis][2] with more work being done stretching the rubber than is returned when the rubber contracts back to its original size.  \r\nThe area $X$ represents the amount of heat which is generated when the rubber contracts back to its original length.  \r\n\r\nSo you could define the spring constant as $\\dfrac{\\rm force}{\\rm area}$ and plot it as a function of force noting that the loading and unlaoding values will be different.  \r\nAnother way is to find the gradient of the graph at a given load and call this the incremental (small change in force) spring constant.  \r\n\r\n[Richard Feynman Rubber Bands][3]\r\n\r\n\r\n  [1]: https://i.sstatic.net/51ys0WvH.jpg\r\n  [2]: https://en.wikipedia.org/wiki/Hysteresis#In_mechanics\r\n  [3]: https://www.youtube.com/watch?v=baXv_5z7HVY", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 45, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-4.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "homework-and-exercises", "material-science", "spring", "elasticity"], "page_start": null, "page_end": null, "quality_flags": ["low_score", "single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 839612, "title": "Modelling the spring \"constant\" for a rubber band", "url": "https://physics.stackexchange.com/questions/839612/modelling-the-spring-constant-for-a-rubber-band", "share_url": "https://physics.stackexchange.com/q/839612", "content_license": null, "owner": {"display_name": "lmg", "user_id": 336771, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/336771/lmg"}}, "answers": [{"answer_id": 839620, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/839612/modelling-the-spring-constant-for-a-rubber-band/839620#839620", "share_url": "https://physics.stackexchange.com/a/839620", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "Farcher", "user_id": 104696, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/104696/farcher"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:496910:0000", "text": "Question: Is it possible to have a situation in which velocity of the particle is never 0 but its average velocity in an interval is 0?\n\nMy book states that-\" It is not possible to have a situation in which speed of the particle is never 0 but the average speed in an interval is 0\"\nI would like to know if the same holds true for velocity?\n\nAccepted Answer:\n\nSpeed is the magnitude of velocity and hence must always be a positive quantity.  \r\nThis means that the distance travelled, $\\displaystyle \\int_{t_{\\rm initial}} ^{t_{\\rm final}} v\\,dt$ must always be positive and so the time average $\\displaystyle \\dfrac {\\displaystyle \\int_{t_{\\rm initial}} ^{t_{\\rm final}} v\\,dt}{\\displaystyle \\int_{t_{\\rm initial}} ^{t_{\\rm final}} \\,dt}$ must always be positive.  \r\n\r\nIf the motion is such that the total displacement, $\\displaystyle \\int_{t_{\\rm initial}} ^{t_{\\rm final}} \\vec v\\,dt$, is zero, with the speed never being zero, then the average velocity is also zero.  \r\nUniform circular motion is an example where the velocity is never zero but after a period the total displacement is zero and hence so is the average velocity.\n\nAnswer (score=1):\n\nIf you end up where you started, your average velocity will be zero over that time frame:\r\n\r\n    v = dx/dt \r\n\r\nFor the average speed, you would want the path length over time. If you've left your original position, even to return, your path length is now non-zero, so you've got an average speed of greater than zero in that case.\n\nAnswer (score=0):\n\nPresumably, if the (1D) velocity changed continuously, then along the way of the velocity changing from positive to negative or vice versa it must have a velocity of 0 at some point due to the intermediate value theorem. \r\n\r\n(If you were to look at 2D or 3D velocity, it can be broken up into 1D components, but the 2D or 3D velocity wouldn't necessarily have a resultant velocity of 0. In this case you could have an average velocity = 0 without instantaneous velocity = 0.)\r\n\r\nIf the (1D) velocity could change instantaneously, say from -2 m/s to 2 m/s, then you could have an average velocity of 0 m/s. It's never possible for speed to have an average of 0 (given that it can't equal 0) even if it could change instantaneously, because speed can never be negative.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 46, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-4.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "kinematics"], "page_start": null, "page_end": null, "quality_flags": ["low_score"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 496910, "title": "Is it possible to have a situation in which velocity of the particle is never 0 but its average velocity in an interval is 0?", "url": "https://physics.stackexchange.com/questions/496910/is-it-possible-to-have-a-situation-in-which-velocity-of-the-particle-is-never-0", "share_url": "https://physics.stackexchange.com/q/496910", "content_license": null, "owner": {"display_name": "Happy Unicorn", "user_id": 203504, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/203504/happy-unicorn"}}, "answers": [{"answer_id": 496919, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/496910/is-it-possible-to-have-a-situation-in-which-velocity-of-the-particle-is-never-0/496919#496919", "share_url": "https://physics.stackexchange.com/a/496919", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "Farcher", "user_id": 104696, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/104696/farcher"}}, {"answer_id": 496914, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/496910/is-it-possible-to-have-a-situation-in-which-velocity-of-the-particle-is-never-0/496914#496914", "share_url": "https://physics.stackexchange.com/a/496914", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "user234140", "user_id": null, "user_type": "does_not_exist", "profile_url": null}}, {"answer_id": 496912, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/496910/is-it-possible-to-have-a-situation-in-which-velocity-of-the-particle-is-never-0/496912#496912", "share_url": "https://physics.stackexchange.com/a/496912", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "highm", "user_id": 239116, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/239116/highm"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:478394:0000", "text": "Question: Scope of $E=mc^2$\n\nAs far as I can see, Einstein's $E=mc^2$ is most often mentioned in the context of nuclear physics, even though it is more generally applicable. I understand that this is due to the large nuclear binding energies that are involved.\r\n\r\nIn what other situations (outside of nuclear physics) is this mass-energy equivalence\r\n\r\n 1. relevant?\r\n 2. measurable?\n\nAccepted Answer:\n\nI'll take measurability first. Particle physics and nuclear physics you already mention. In other areas:\r\nmodern mass measurements are precise enough to detect the impact of electron binding energies in atoms and molecules. Tests of the equivalence principle are sensitive to many different contributions to the total mass-energy of whatever objects are used. Precision spectroscopy in atoms can detect tiny contributions to the energy levels; many of these are, as we say, 'relativistic corrections', which amounts to saying they are closely related to $E=mc^2$.\r\n\r\nNow on relevance. The relationship is relevant whenever speeds reach a significant fraction of the speed of light, or whenever high precision is available and needed. The former includes very hot plasmas in astrophysics and laser physics, as well as nuclear and subatomic particle physics. The latter includes precision measurements in atoms, including the determination of the fine structure constant and the gyromagnetic ratio of the electron. These present precision tests of fundamental physics. \r\n\r\nBut one could argue that the relation has a wider relevance because it is a central part of the ability of physics to be logically and mathematically consistent.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 47, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-4.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "special-relativity", "nuclear-physics", "mass-energy", "binding-energy"], "page_start": null, "page_end": null, "quality_flags": ["low_score", "single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 478394, "title": "Scope of $E=mc^2$", "url": "https://physics.stackexchange.com/questions/478394/scope-of-e-mc2", "share_url": "https://physics.stackexchange.com/q/478394", "content_license": null, "owner": {"display_name": "user1583209", "user_id": 135334, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/135334/user1583209"}}, "answers": [{"answer_id": 478410, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/478394/scope-of-e-mc2/478410#478410", "share_url": "https://physics.stackexchange.com/a/478410", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "Andrew Steane", "user_id": 207910, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/207910/andrew-steane"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:827490:0000", "text": "Question: Leaning on a bike while turning: how can moments be balanced?\n\nConsider a cyclist turning a corner. The cyclist will lean, so that the sum of friction $F$, normal reaction $N$ and weight $W$ will equal the centripetal force.\r\n\r\nHowever, I cannot understand how the cyclist does not rotate to the ground. For the bike not to rotate to the ground, the sum of torques about the point of contact between the bike and the ground (point $P$) must be zero. However, it is not zero. The normal reaction force $N$ and the friction $F$ produce a zero torque, as they are applied exactly at the point of contact. The weight $W$ instead does provide torque, because it is applied at the center of mass, which is at a non-zero distance to the point of contact $P$. So there is a net torque and the bike should rotate.\r\n\r\nFor clarity, consider the image below:[![Diagram of cyclist and forces][1]][1]\r\n\r\n\r\n  [1]: https://i.sstatic.net/AA4zZu8J.png\n\nAccepted Answer:\n\n> For the bike not to rotate to the ground, the sum of torques about the point of contact between the bike and the ground (point 𝑃) must be zero. \r\n\r\nThis is only necessarily true for a non-accelerating body in an inertial frame. \r\n\r\n- Bike Frame\r\n\r\nIn the non-inertial frame where the bike is at rest, a centrifugal force appears.   When added to your FBD above, it zeroes the total torque.\r\n\r\n- Ground Frame\r\n\r\n\"non-zero torque implies rotation\" is a simplification that is true for non-accelerating objects.  A more general statement is that \"non-zero torque implies change in angular momentum\".\r\n\r\nFor an accelerating object, that change in angular momentum can be solely from it's changing translational velocity and no rotation is required.   That's happening for the bicycle.   If you calculate the angular momentum as it moves away from $P$, you'll find it exactly matches the unbalanced torque.\n\nAnswer (score=0):\n\n> However, I cannot understand how the cyclist does not rotate to the\r\n> ground.\r\n\r\nTo show why the cyclist does not rotate, it’s not necessary to analyze this in the non inertial (accelerating) frame of the cyclist requiring introducing the fictitious centrifugal force. \r\n\r\nIn the inertial ground frame we can relocate the friction force $F$ parallel to its line of action to act on the center of gravity (COG) of the bike (the point where $W$ acts) as long as we add a clockwise couple (pure moment) about point $P$ to cancel the torque created about $P$ due to relocating $F$. See the Figures below. The net effect is we now have a clockwise moment about $P$ that balances the counter clockwise moment of $W$ about $P$ so that the cyclist does not fall.\r\n\r\nHope this helps.\r\n\r\n[![enter image description here][1]][1]\r\n\r\n\r\n  [1]: https://i.sstatic.net/XoYFRgcg.jpg", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 48, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-4.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "forces", "classical-mechanics", "rotational-dynamics", "torque"], "page_start": null, "page_end": null, "quality_flags": ["low_score"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 827490, "title": "Leaning on a bike while turning: how can moments be balanced?", "url": "https://physics.stackexchange.com/questions/827490/leaning-on-a-bike-while-turning-how-can-moments-be-balanced", "share_url": "https://physics.stackexchange.com/q/827490", "content_license": null, "owner": {"display_name": "Pol", "user_id": 124697, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/124697/pol"}}, "answers": [{"answer_id": 827505, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/827490/leaning-on-a-bike-while-turning-how-can-moments-be-balanced/827505#827505", "share_url": "https://physics.stackexchange.com/a/827505", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "BowlOfRed", "user_id": 55662, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/55662/bowlofred"}}, {"answer_id": 827511, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/827490/leaning-on-a-bike-while-turning-how-can-moments-be-balanced/827511#827511", "share_url": "https://physics.stackexchange.com/a/827511", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "Bob D", "user_id": 199893, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/199893/bob-d"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:738518:0000", "text": "Question: How is it possible to receive 2 pulses from only 1 sent pulse?\n\nIf we have a sample of a certain material to characterize it The sample is a cube with side length (L=1m). You used an ultrasonic (US) transducer to send an US pulse of frequency (f=5MHz) at normal incidence, and receive it at the other end of the sample. Assuming that the incident wave is composed of both shear and lateral waves.\r\n\r\nWhy would I receive here 2 pulses at the receiver at the other end of the sample although the transducer sent only one pulse?\n\nAccepted Answer:\n\nIn solids sound can propagate as a longitudinal wave or as a shear wave and these two waves have different velocities. [The speed of a longitudinal wave is][1]:\r\n\r\n$$ v_p = \\sqrt{\\frac{K + \\tfrac{4}{3}G}{\\rho}} $$\r\n\r\nand the speed of a shear wave is:\r\n\r\n$$ v_s = \\sqrt{\\frac{G}{\\rho}} $$\r\n\r\nwhere $K$ is the bulk modulus and $G$ is the shear modulus. The longitudinal wave travels faster than the shear wave so from the original pulse you receive the longitudinal wave first then your receive the shear wave later. That's why you receive two pulses.\r\n\r\n\r\n  [1]: https://en.wikipedia.org/wiki/Speed_of_sound#Speed_of_sound_in_solids\n\nAnswer (score=0):\n\n@JohnRennie 's answer is interesting, but OP says that the ultrasound pulse is sent at \"normal incidence\". This implies that the ultrasound first travels in air and, therefore, is initially a longitudinal wave. My understanding is [there is no conversion of longitudinal wave to transverse wave at normal incidence][1]. I am not sure though this is true for anisotropic media as well.\r\n\r\nAnother possible explanation can be that the second pulse is produced after two reflections inside the cube (initially from the \"rear\" wall and then from the \"front\" wall).\r\n\r\n\r\n  [1]: https://www.nde-ed.org/Physics/Waves/modeconversion.xhtml", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 49, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-4.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "quantum-mechanics", "waves"], "page_start": null, "page_end": null, "quality_flags": ["low_score"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 738518, "title": "How is it possible to receive 2 pulses from only 1 sent pulse?", "url": "https://physics.stackexchange.com/questions/738518/how-is-it-possible-to-receive-2-pulses-from-only-1-sent-pulse", "share_url": "https://physics.stackexchange.com/q/738518", "content_license": null, "owner": {"display_name": "Youssef Mohamed", "user_id": 323276, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/323276/youssef-mohamed"}}, "answers": [{"answer_id": 738523, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/738518/how-is-it-possible-to-receive-2-pulses-from-only-1-sent-pulse/738523#738523", "share_url": "https://physics.stackexchange.com/a/738523", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "John Rennie", "user_id": 1325, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/1325/john-rennie"}}, {"answer_id": 738530, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/738518/how-is-it-possible-to-receive-2-pulses-from-only-1-sent-pulse/738530#738530", "share_url": "https://physics.stackexchange.com/a/738530", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "akhmeteli", "user_id": 6974, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/6974/akhmeteli"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:737685:0000", "text": "Question: How do we deal with doppler effect in $3D$ space?\n\nIn $2D$ it's easy to deal with doppler effect given the velocity of the source and the velocity of the observer like in fig (1) where we have the observer at A static and the source in direction of $\\vec{u}$ emitting waves with velocity $v$ and frequency $f$ and moving with velocity $v_s$ we will say that \r\n\r\n$$f'=\\frac{v}{v-v_s\\cos(\\theta)}*f$$ \r\nWhere theta is the angle between the $x$-axis and the $\\vec{u}$.\r\n\r\n\r\nNow if we have have a vector in space with the same frequency and velocity and a static point in space how do we represent the actual frequency $f'$ that the observer receives? \r\n\r\n\r\n\r\n\r\nfig (1)\r\n[![enter image description here][1]][1]\r\n\r\n\r\nfig (2)\r\n[![fig1][2]][2]\r\n\r\n\r\n  [1]: https://i.sstatic.net/CfGsH.png\r\n  [2]: https://i.sstatic.net/2H8TA.png\n\nAccepted Answer:\n\n[![enter image description here][1]][1]\r\n\r\n **2D case**    \r\n$$\\vec R=\\begin{bmatrix}\r\n a-u\\,t \\\\\r\n b \\\\\r\n\\end{bmatrix}$$\r\nand $~\\vec R~$ with polar coordinate\r\n\r\n$$\\vec R_p=r\\,\\begin{bmatrix}\r\n \\cos(\\phi) \\\\\r\n \\sin(\\phi) \\\\\r\n\\end{bmatrix}$$\r\n\r\nwith \r\n\r\n$$\\vec R=\\vec R_p\\quad \\Rightarrow\\\\\r\nr=\\sqrt{b^2+(a-\\,t)^2}\\quad,\r\n\\tan(\\phi)=\\frac{b}{a-u\\,t}\\\\\r\nv=\\dot r=-\\frac{u\\,(a-u\\,t)}{\\sqrt{b^2+(a-u\\,t)^2}}$$\r\n\r\nsubstitute $~(a-u\\,t)=\\frac b{\\tan(\\phi)}~$ in $~v~$ you obtain\r\n$~v=-u\\,\\cos(\\phi)$\r\n\r\n$$\r\nf' = \\frac{c}{c -u\\,\\cos(\\phi)  } f\r\n$$\r\n\r\n\r\n\r\n**3D case** \r\n\r\n$$\\vec R=\\begin{bmatrix}\r\n  a-u\\,t \\\\\r\n b \\\\\r\n  c\\\\\r\n\\end{bmatrix}\\quad,\r\n\\vec R_p=  r\\left[ \\begin {array}{c} \\cos \\left( \\phi \\right) \\sin \\left( \\theta\r\n \\right) \\\\  \\sin \\left( \\phi \\right) \\sin \\left( \r\n\\theta \\right) \\\\  \\cos \\left( \\theta \\right) \r\n\\end {array} \\right] $$\r\n\r\n$\\vec R=\\vec R_p\\quad\\Rightarrow$\r\n\r\n$$r=\\sqrt{b^2+(a-u\\,t)^2+c^2}\\\\\r\n\\tan(\\phi)=\\frac{b}{a-u\\,t}\\\\\r\n\\tan(\\theta)=\\frac{\\sqrt{b^2+(a-u\\,t)^2}}{c}\\\\\r\nv=\\dot r=-\\frac{u\\,(a-u\\,t)}{\\sqrt{b^2+(a-u\\,t)^2+c^2}}=-u\\,\\cos(\\phi)\\,\\sin(\\theta)\r\n$$\r\n\r\n$$\r\nf' = \\frac{c}{c -u\\,\\cos(\\phi)\\,\\sin(\\theta)  } f\r\n$$\r\n \r\n\r\n\r\n  [1]: https://i.sstatic.net/D4gWf.png\n\nAnswer (score=1):\n\nIf $\\hat{r}$ is a unit vector pointing from the source to the receiver, then   $v_s \\cos \\theta = \\hat{r} \\cdot \\vec{v}_s$, where $\\vec{v}_s$ is the velocity vector of the source.  So the natural generalization is\r\n$$\r\nf' = \\frac{c}{c - \\hat{r} \\cdot \\vec{v}_s} f\r\n$$\r\nwhich is perfectly well-defined in 3D.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 50, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-4.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "waves", "doppler-effect"], "page_start": null, "page_end": null, "quality_flags": ["low_score"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 737685, "title": "How do we deal with doppler effect in $3D$ space?", "url": "https://physics.stackexchange.com/questions/737685/how-do-we-deal-with-doppler-effect-in-3d-space", "share_url": "https://physics.stackexchange.com/q/737685", "content_license": null, "owner": {"display_name": "Youssef Mohamed", "user_id": 323276, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/323276/youssef-mohamed"}}, "answers": [{"answer_id": 737733, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/737685/how-do-we-deal-with-doppler-effect-in-3d-space/737733#737733", "share_url": "https://physics.stackexchange.com/a/737733", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "Eli", "user_id": 196140, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/196140/eli"}}, {"answer_id": 737735, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/737685/how-do-we-deal-with-doppler-effect-in-3d-space/737735#737735", "share_url": "https://physics.stackexchange.com/a/737735", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "Michael Seifert", "user_id": 81133, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/81133/michael-seifert"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:737497:0000", "text": "Question: Questions about overdamping, critical damping and underdamping\n\nI am a math lecturer and in my teaching of second-order linear differential equations I present, as an application, the classical mass-spring-dashpot system (and its RLC analogue). According to my understanding, if the overdamping case modelled an automobile suspension system, the ride would be uncomfortable. Furthermore, critical damping represents the minimum damping that can be applied to the physical system without causing oscillation.\r\n\r\nOne textbook I use (Ordinary Differential Equations and Applications by Weighfer and Lindsay) says:\r\n*(Critical damping) is often the desired configuration for practical aplications since it represents the weakest damping before oscillatory becomes possible.*\r\n\r\nNevertheless, another textbook I use (Differential Equations for Engineers by Xie) states that: \r\n*Most engineering structures fall in this category (i.e. underdamping\r\ncase) with (the dimensionless) damping coeffient $\\zeta$ usually less\r\nthan $10\\%$.*\r\n[$\\zeta=\\frac{\\gamma}{2\\sqrt{mk}}$ for the mechanical system; $\\zeta=\\frac{2}{R}\\sqrt{\\frac{C}{L}}$ for the electrical analogue].\r\n\r\nQuestion 1: Which author is right?\r\n\r\nQuestion 2: In general What are some practical applications where each case (heavy, critical and light damping) is desirable or not desirable?\r\n\r\nThank you very much.\n\nAccepted Answer:\n\nIf damping factor is a design driver, you'll usually choose damping close to critical. It is often true that given the parameters you can control, less damping leads to a faster response of the system to disturbance, so you may choose damping a bit less than critical.\r\n\r\nOn the other hand, it may be perfectly acceptable for the system to ring, and adding friction may be undesirable. Or, the design of a high inertia system may naturally lead to overdamping.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 51, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-4.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "oscillators", "differential-equations"], "page_start": null, "page_end": null, "quality_flags": ["low_score", "single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 737497, "title": "Questions about overdamping, critical damping and underdamping", "url": "https://physics.stackexchange.com/questions/737497/questions-about-overdamping-critical-damping-and-underdamping", "share_url": "https://physics.stackexchange.com/q/737497", "content_license": null, "owner": {"display_name": "Dimitris", "user_id": 181947, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/181947/dimitris"}}, "answers": [{"answer_id": 737509, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/737497/questions-about-overdamping-critical-damping-and-underdamping/737509#737509", "share_url": "https://physics.stackexchange.com/a/737509", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "John Doty", "user_id": 264639, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/264639/john-doty"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:673995:0000", "text": "Question: Running electrolysis on inside surface of a tube\n\nI use electrolysis for rust removal and electroplating. I notice that when one of the electrodes is a closed tube or has other topological holes with a sufficiently large height:diameter ratio, the inside surface does not react.\r\n\r\nMy hypothesis is that current is not flowing through these surfaces because I didn't pay attention in the electromagnetism part of Physics 1 in high school, and karma has finally caught up with me 25 years later.\r\n\r\nMy questions are:\r\n\r\n- What is going on here? I vaguely remember something about Michael Faraday. Am I on the right track?\r\n\r\n- More importantly, how can I induce a reaction on the inside surface? Will running the opposite electrode through the hole work?\r\n\r\nHere is a video of the effect: https://youtu.be/H6TrLn8TkS8\r\n\r\n|![enter image description here](https://i.sstatic.net/Phrmf.jpg)|![enter image description here](https://i.sstatic.net/7fqYA.jpg)|\r\n|-|-|\r\n|Reaction visible on outer surface|Calm, quiet inner surface|\r\n\r\n\r\n---\r\n\r\nI don't think the setup details are that important, since the context here is physics not chemistry. However, for completeness, an example setup:\r\n\r\n- electrolyte is sodium bicarbonate and distilled water\r\n- both electrodes are mild carbon steel\r\n- cathode is a square tube\r\n- width of electrodes and distance between them is pretty much the same order of magnitude as the diameter of the tube, lengths of electrodes are one higher order\r\n- typically running 5-10A at 12-20V\r\n- electrolyte temperature held around 100-130F\n\nAccepted Answer:\n\nExactly.  It's much easier for the current to flow to the outside of the piece than the inside.  So almost no reactions take place there.\r\n\r\nIt can be tricky to plate the inside of something like that.  You'll probably need to run auxiliary anodes inside the tube.  \r\n\r\nThe other problem that can happen is the volume inside the pipe can be small and the solution inside can be stagnant.  If so, you can deplete the solution of your plating material.  You may need a pump or similar to force flow through the pipe and exchange with the rest of the tank.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 52, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-4.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "electricity", "electric-current", "conductors", "topology"], "page_start": null, "page_end": null, "quality_flags": ["low_score", "single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 673995, "title": "Running electrolysis on inside surface of a tube", "url": "https://physics.stackexchange.com/questions/673995/running-electrolysis-on-inside-surface-of-a-tube", "share_url": "https://physics.stackexchange.com/q/673995", "content_license": null, "owner": {"display_name": "Jason C", "user_id": 41010, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/41010/jason-c"}}, "answers": [{"answer_id": 674006, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/673995/running-electrolysis-on-inside-surface-of-a-tube/674006#674006", "share_url": "https://physics.stackexchange.com/a/674006", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "BowlOfRed", "user_id": 55662, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/55662/bowlofred"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:445662:0000", "text": "Question: How does a gas spring work?\n\nI read [Wikipedia](https://en.wikipedia.org/wiki/Gas_spring) and do not understand the following.\r\n\r\nIf you create pressure on the gas (or any spring) it gives pressure against.\r\nWhy is the gas spring holding mass when pulled out, and while umounted does not extend to max length forced by the pressurized gas inside?\r\n\r\nTypically, you see pictures with these springs being in \"slide-in\" state. Same I can see at home. The spring does not slide out itself.\r\n\r\n[![enter image description here][1]][1]\r\n\r\nOr maybe they are *already* in the slide out state?\r\n\r\n  [1]: https://i.sstatic.net/DnObW.jpg\n\nAccepted Answer:\n\nthe gas spring exerts force even when the rod is fully extended because the pressure inside the cylinder is greater than atmospheric. I do not understand what you mean by \"whole umounted\".\n\nAnswer (score=1):\n\nI have replaced such gas springs in my cupboard, and I can assure you that they do extend to their maximum, so that you need to compress them to fit between the mount points. If you have one such spring, and it doesn't extend, then it's broken (or past its end of life).\n\nAnswer (score=0):\n\nYou have to consider the pressure of the ambient atmosphere too. If you expand the gas in the cylinder so much, that its pressure drops below the ambient pressure, the net effect is a force trying to suck the piston in.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 53, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-4.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "thermodynamics", "pressure", "spring", "ideal-gas"], "page_start": null, "page_end": null, "quality_flags": ["low_score"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 445662, "title": "How does a gas spring work?", "url": "https://physics.stackexchange.com/questions/445662/how-does-a-gas-spring-work", "share_url": "https://physics.stackexchange.com/q/445662", "content_license": null, "owner": {"display_name": "J. Doe", "user_id": 158881, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/158881/j-doe"}}, "answers": [{"answer_id": 445675, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/445662/how-does-a-gas-spring-work/445675#445675", "share_url": "https://physics.stackexchange.com/a/445675", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "niels nielsen", "user_id": 40292, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/40292/niels-nielsen"}}, {"answer_id": 445775, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/445662/how-does-a-gas-spring-work/445775#445775", "share_url": "https://physics.stackexchange.com/a/445775", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "Ruslan", "user_id": 21441, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/21441/ruslan"}}, {"answer_id": 445674, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/445662/how-does-a-gas-spring-work/445674#445674", "share_url": "https://physics.stackexchange.com/a/445674", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "b.Lorenz", "user_id": 141674, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/141674/b-lorenz"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:361838:0000", "text": "Question: A single-mode optical fiber with a large core\n\nI know that the core of a single-mode optical fiber is small (approximately 8 μm), because the core diameter is small, the light is propagated in one mode. \r\nAnd I accidentally read this article which mentions a single-mode optical fiber with a large core: https://www.rp-photonics.com/large_core_fibers.html  \r\nI do not understand why a single-mode optical fiber has a large core ? What is the purpose of this fiber, transfer communication or energy ? With a large core, is light propagated in one mode ?\r\n\r\nI would love to know the answer. Please help me. Thank you !\n\nAccepted Answer:\n\nOne can make a large core fiber single moded by adjusting the core-cladding index difference so that the waveguide parameter:\r\n\r\n$$V = \\frac{2\\,\\pi\\,\\rho}{\\lambda}\\sqrt{n_{co}^2-n_{cl}^2}$$\r\n\r\nis less than the first zero $\\omega_{01}\\approx 2.405$ of the zeroth order first kind Bessel function.\r\n\r\nThis is often done when high optical powers must be borne by the single mode to:\r\n\r\n1. Reduce nonlinear effects;\r\n2. Reduce solarization and other damage wrought by high intensity fields\r\n\r\nbecause the intensity is inversely proportional to the mode field diameter squared.\n\nAnswer (score=0):\n\nthere is modal dispersion during the signal spreading. And transmission distance is greatly influenced by the dispersion. Luckily, single mode fiber have the ability to transmitting data for miles without losing too much data. Thus it can carry information for a longer distance than the multimode fiber.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 54, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "optics", "geometric-optics", "fiber-optics", "non-linear-optics"], "page_start": null, "page_end": null, "quality_flags": ["low_score", "mixed_license"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 361838, "title": "A single-mode optical fiber with a large core", "url": "https://physics.stackexchange.com/questions/361838/a-single-mode-optical-fiber-with-a-large-core", "share_url": "https://physics.stackexchange.com/q/361838", "content_license": null, "owner": {"display_name": "Nguyen Duc Viet", "user_id": 168787, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/168787/nguyen-duc-viet"}}, "answers": [{"answer_id": 361854, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/361838/a-single-mode-optical-fiber-with-a-large-core/361854#361854", "share_url": "https://physics.stackexchange.com/a/361854", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Selena Ballerina", "user_id": 26076, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/26076/selena-ballerina"}}, {"answer_id": 406176, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/361838/a-single-mode-optical-fiber-with-a-large-core/406176#406176", "share_url": "https://physics.stackexchange.com/a/406176", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "Klose", "user_id": 195774, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/195774/klose"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:348491:0000", "text": "Question: A bee inside a car - An application of Newton's laws\n\nThis is a situation based question and I don't know whether is it directly connected to physics or not. Sorry, if not, I thought that it would be best to ask it here, of it has some interesting application.\r\n\r\nAnyways, I recently started to learn Newtonian mechanics as a high school student and recently learnt about laws of motion.\r\n\r\nNow consider this situation which I have encountered many times. The situation is that I'm inside car and car is moving, window are open and suddenly a fly enters the car and it is pretty comfortable inside (making us disturbed). Now I wonder how the bee is managing inside the car. What I mean here is that we are having a velocity because we are in contact with car(as we are seated on the seat and not flying) whereas the bee is apparently, not in contact with car and hence should not possess the velocity of car ( I deliberately said that windows are open, because may be closing of windows affect the motion of bee, which I neither know nor experienced), but the bee is flying here and there annd this according to road frame must have a velocity greater than car, which is of course not the case ( I searched speed of a bee on browser and found it to be around 10-15 miles per hour, which is way less than speed of car, I am in.\r\n\r\nSo what's the reason for this result. May be it's biological, which I don't think and I considered this situation from physics's viewpoint, with conditions idealized. So according to me the bee should be thrown back to the end of car, because there is no considerable friction and as per the law of inertia. Other thing which I considered was pressure, which I came to conclusion can surely not change as windows are open. I'm not able to go beyond.\r\n\r\nMay be the question seems stupid, but the real aim of physics is understanding real situations and not completely idealized ones. So, I would appreciate any help on how to analyse this situation and to know what is going on from a physicist point of view.\r\n\r\nEDIT\r\nIn the other question, the conditions are different from mine. There windows are closed and here open, which may make a difference, I suppose. Also I didn't found a satisfactory answer there, so I posted it on the basis of my common experience.\r\n\r\nThanks a lot.\n\nAccepted Answer:\n\nThe bee flies in air. \r\n\r\nOutside, the air is often still, which means it has the same speed as the ground. The bee flies at 10 - 15 mph through the air, which means 10 - 15 mph with respect to the ground. \r\n\r\nThe car contains air and carries that air with it. The air has the speed of the car. The bee flies at 10 - 15 mph through the air, which means 10 - 15 mph with respect to the car. If the bee flies forward, it moves over the ground faster than the car. If it flies backward, it moves over the ground slower than the car. \r\n\r\nSuppose a wind is blowing and the car drives just as fast as the wind. The bee could do the same thing outside the car as inside.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 55, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "newtonian-mechanics", "reference-frames"], "page_start": null, "page_end": null, "quality_flags": ["low_score", "single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 348491, "title": "A bee inside a car - An application of Newton's laws", "url": "https://physics.stackexchange.com/questions/348491/a-bee-inside-a-car-an-application-of-newtons-laws", "share_url": "https://physics.stackexchange.com/q/348491", "content_license": null, "owner": {"display_name": "Abhinav Dhawan", "user_id": 120609, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/120609/abhinav-dhawan"}}, "answers": [{"answer_id": 348494, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/348491/a-bee-inside-a-car-an-application-of-newtons-laws/348494#348494", "share_url": "https://physics.stackexchange.com/a/348494", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "mmesser314", "user_id": 37364, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/37364/mmesser314"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:46784:0000", "text": "Question: Wavelength comparison of two waves\n\nIs there any non-digital (naturally existing) mechanism to compare two or more waves in such a way:\r\n\r\n    Input 1           Input 2          ....            Output\r\n    -------           --------         ....          ------------\r\n    Lower             Higher           ....          Lower/Higher\r\n    Wavelength        Wavelength       ....          Wavelength\r\n\r\n... some kind of selectively permeable membrane which allows one wave to pass-through?\r\n\r\nPardon my poor physics knowledge. I don't have a clue; would it be related to wave theory, applied physics or applied optics?\n\nAccepted Answer:\n\nYou may want to look [resonance][1] up. There are all manners of physical systems that have a natural oscillation frequency, be this mechanical, optical, or whatever. When excited by a multi-frequency signal, they will amplify their natural frequency more than any other. So in a way you can think of them as blocking all other frequencies.\r\n\r\n**EDIT**\r\n\r\nOK, look at this image taken from the wikipedia article... Lets say you have a system with a resonant frequency of 100 Hz. Any real system also has some amount of attenuation due to friction, which is indicated by the $\\delta$ parameter. Lets say that our system follows the curve $\\delta = 0.2\\omega_0$.\r\n\r\n![enter image description here][2]\r\n\r\nSo lets now excite this system with a combination of three frequencies: 50, 100 and 200 Hz. The 50Hz excitation will be amplified to about 133% of the input, the 100 Hz excitation to about 240%, and the 200 Hz to only 33% of the input.\r\n\r\nAs the graph shows, you can actually use any resonant system with strong dampening to filter out the higher frequencies, and adjust the cut frequency with the natural frequency of your system.\r\n\r\n  [1]: http://en.wikipedia.org/wiki/Resonance\r\n  [2]: https://i.sstatic.net/zDXKm.png\n\nAnswer (score=1):\n\nI'm not sure if it's exactly what you're asking, and arguably it's just a special case of Jaime's answer, but a [heterodyne][1] sort of does this.\r\n\r\n\r\n  [1]: http://en.wikipedia.org/wiki/Heterodyne", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 56, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "optics", "wavelength"], "page_start": null, "page_end": null, "quality_flags": ["low_score"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 46784, "title": "Wavelength comparison of two waves", "url": "https://physics.stackexchange.com/questions/46784/wavelength-comparison-of-two-waves", "share_url": "https://physics.stackexchange.com/q/46784", "content_license": null, "owner": {"display_name": "vulcan raven", "user_id": 16877, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/16877/vulcan-raven"}}, "answers": [{"answer_id": 46787, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/46784/wavelength-comparison-of-two-waves/46787#46787", "share_url": "https://physics.stackexchange.com/a/46787", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Jaime", "user_id": 995, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/995/jaime"}}, {"answer_id": 46829, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/46784/wavelength-comparison-of-two-waves/46829#46829", "share_url": "https://physics.stackexchange.com/a/46829", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "John Rennie", "user_id": 1325, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/1325/john-rennie"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:483657:0000", "text": "Question: Elastic potential energy per unit volume,stress-strain and strain-stress curve\n\nFrom what I understand, when we calculate elastic potential energy per unit volume of a material which extends linearly, we calculate the area under the graph of stress- strain OR strain- stress graph, they both will give the same value. Likewise, if I want to calculate the elastic potential energy of a linear extension, I could get the value from the area under the graph of force-extension/ extension- force graph. However, I am unable to understand why we can’t do the same for a non linear extension. For example in a non linear extension, the areas obtained from stress-strain and strain-stress curve are not the same. I only know that this has something to do with integration, but I still can’t seem to wrap my head around it. \nSo to conclude, my question is\n1) why we can’t obtain elastic potential energy per unit volume under a curve of a strain stress graph\n\nAccepted Answer:\n\nIf $F=kx$, in which $k$ is a constant,\r\n$$\\int_{x=0}^X Fdx=\\int_{x=0}^X kxdx=\\left[\\tfrac12\\ kx^2\\right]^X_0=\\tfrac12F_XX$$\r\nin which $F_X=kX$.\r\nBut\r\n$$\\int_{F=0}^{F_X} x dF=\\int_{x=0}^X x d(kx)=\\int_{x=0}^X k x dx=\\tfrac12F_XX$$\r\nThis equality of the two integrals is wholly dependent on our initial assumption: $F=kx.$ The same argument applies for the stress vs. strain graph.\r\n\r\nLess precisely, if the graph of $F$ against $x$ started as $F=kx$ but curved upwards for higher values of $x$, this would make the area between the graph and the x-axis (up to a given value, $X$) higher, but would make the area between the graph and the $F$ axis (up to $F_X$) lower!", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 57, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-4.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "quantum-mechanics", "material-science", "elasticity", "solid-mechanics"], "page_start": null, "page_end": null, "quality_flags": ["low_score", "single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 483657, "title": "Elastic potential energy per unit volume,stress-strain and strain-stress curve", "url": "https://physics.stackexchange.com/questions/483657/elastic-potential-energy-per-unit-volume-stress-strain-and-strain-stress-curve", "share_url": "https://physics.stackexchange.com/q/483657", "content_license": null, "owner": {"display_name": "imaginarybuddy", "user_id": 228850, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/228850/imaginarybuddy"}}, "answers": [{"answer_id": 483667, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/483657/elastic-potential-energy-per-unit-volume-stress-strain-and-strain-stress-curve/483667#483667", "share_url": "https://physics.stackexchange.com/a/483667", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "Philip Wood", "user_id": 149533, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/149533/philip-wood"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:443013:0000", "text": "Question: Microwave cooking\n\nThis is just a little curiosity I've had, and I wonder what y'all think:\r\n\r\nI am poaching a chicken egg in a small (about 4 in. diameter) glass dish in my microwave. Let's assume the microwave is set on a medium level of heat intensity that is held constant throughout heating (I'm not sure if that's a reasonable assumption). \r\n\r\nHere's the quandary: suppose I run two separate experiments. In the first experiment, I poach a single egg in the microwave for some time, $t$. In the second experiment, I simultaneously poach two eggs (each in its own dish) for the same amount of time, $t$. The glass dishes are essentially identical.\r\n\r\nWill the eggs in the two experiments reach the same temperature?\r\n\r\nIn practice, it seems that when there are two eggs (each in its own dish) being microwaved they each obtain a lower temperature than the single egg alone in the microwave. Is that an expected result?\n\nAccepted Answer:\n\nYes, that is what you'd expect.  Think of the magnetron pumping out photons at a set rate.  Imagine that the walls of the box are perfectly reflective. Each photon bounces around inside the box until it gets absorbed by the food.  With a small amount of food, it takes more bounces on average for a given photon to be absorbed, but in steady state, one photon must be absorbed for every photon emitted: all the energy coming out of the magnetron goes into the food.  Double the food, and the temperature would be expected to increase half as quickly.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 58, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-4.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "thermodynamics", "electromagnetic-radiation", "everyday-life", "microwaves"], "page_start": null, "page_end": null, "quality_flags": ["low_score", "single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 443013, "title": "Microwave cooking", "url": "https://physics.stackexchange.com/questions/443013/microwave-cooking", "share_url": "https://physics.stackexchange.com/q/443013", "content_license": null, "owner": {"display_name": "Not Sure", "user_id": 201856, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/201856/not-sure"}}, "answers": [{"answer_id": 443018, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/443013/microwave-cooking/443018#443018", "share_url": "https://physics.stackexchange.com/a/443018", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "Ben51", "user_id": 180385, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/180385/ben51"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:426376:0000", "text": "Question: Stability of differently shaped gyroscopes\n\n**1) Would it be correct to state the following:** \"The longer the radial distance (the distance from the center of the gyro disc) and the lower the height from ground to disc, the greater the angular momentum, and, thus, the more stable the gyro.\"\r\nIt seems to me that torque must, somehow, be related to the matter, but not sure if I am on the right track by taking the radial distance as starting point.\r\n\r\n**2) Are there other differences in the properties of the gyroscope illustrations shown below?**\r\n\r\n**Note:** I received the questions exactly as I present them here from the organization I got them from. Therefore, I suffer from not being able to provide more context and specifications. I am only being able to provide my assumptions based on my preliminary knowledge.\r\n\r\nPlease note that I am a beginner (maybe intermediate) at physics.\r\n\r\n[![enter image description here][1]][1]\r\n\r\n\r\n  [1]: https://i.sstatic.net/iGJoW.jpg\n\nAccepted Answer:\n\n1. A spinning gyroscope has an angular momentum vector $\\vec L$ pointing along its axis, given by the right-hand rule. Gravity exerts a torque on the gyroscope, [trying to rotate it around an axis perpendicular to its current axis][1], changing its angular momentum by $d\\vec L$ in a time $dt$. Since the axes are perpendicular, $\\vec L$ and $d\\vec L$ are perpendicular. Thus, the magnitude of the angular momentum does not change, only its direction is changing, causing it to precess. Torque is the rate of change of angular momentum: $$\\vec{\\tau} = \\vec r \\times \\vec F = \\frac{d \\vec L}{dt}$$ The ground exerts a normal force, equal to the weight in magnitude, upwards on the point of contact with the ground, while the weight pulls it down at the disk, forming a torque couple given by $\\vec r \\times \\vec F = rF \\sin \\theta$ above, where $\\vec r$ is the vector from the point of contact to the disk and $\\theta$ is the angle of the axis from the vertical. The height of the disc above the point of contact with the ground, which is proportional to $r$, affects the lever arm of gravity, causing a larger torque when the gyroscope is \"taller\" and smaller torque when the gyroscope is \"shorter\". We are assuming that the point of contact with the ground does not slip/move, and hence using it as our origin.\r\n\r\n2. The size of the disc affects its [moment of inertia][2]. Torque is the rate of change of angular momentum with respect to time. The larger and heavier the disc, the greater its moment of inertia and angular momentum and the more resistant it is to changes in its angular momentum and will thus precess more slowly. This is also why the gyroscope precesses faster and faster as it slows down due to friction.\r\n\r\n\r\n  [1]: http://hyperphysics.phy-astr.gsu.edu/hbase/top.html\r\n  [2]: https://en.m.wikipedia.org/wiki/Moment_of_inertia", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 59, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-4.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "homework-and-exercises", "forces", "torque", "gyroscopes"], "page_start": null, "page_end": null, "quality_flags": ["low_score", "single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 426376, "title": "Stability of differently shaped gyroscopes", "url": "https://physics.stackexchange.com/questions/426376/stability-of-differently-shaped-gyroscopes", "share_url": "https://physics.stackexchange.com/q/426376", "content_license": null, "owner": {"display_name": "Englishterian", "user_id": 205429, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/205429/englishterian"}}, "answers": [{"answer_id": 426398, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/426376/stability-of-differently-shaped-gyroscopes/426398#426398", "share_url": "https://physics.stackexchange.com/a/426398", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "Vincent Thacker", "user_id": 174766, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/174766/vincent-thacker"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:333787:0000", "text": "Question: Concept of Projectile in electrostatics\n\n[![enter image description here][1]][1]\nHow do I solve the 3rd question?\nMy attempt at the solution:\n[![enter image description here][2]][2]\nI got the answer to be zero. But since an electric field already exists, the particle should have been deflected in the direction of electric field. So I think the range shouldn't be zero.\nI've got no idea on how to proceed from now. The key says the correct option is (a). please guide me from here.\n\n  [1]: https://i.sstatic.net/UA15v.jpg\n  [2]: https://i.sstatic.net/BwXOh.jpg\n\nAccepted Answer:\n\nHINT: You need to consider the force acting on the particle F =  qE\nThe vertical and horizontal motions are independent of each other. So time of flight is 2u/g. I think this hint is enough.\n\nAnswer (score=0):\n\nThere is no need to calculate $a_{net}$ and if you do so, then to find the range you will have to use the vertical component of the $a_{net}$, which will be $'g '$.\r\n\r\nTo find range you need the time of flight and to find time of flight you only need the vertical velocity and vertical acceleration. Their respective horizontal components have no influence over the time of flight.\r\n\r\n **Time of flight will be independent of acceleration due to electric field.**\r\n\r\n**The time of flight :**\r\n\r\nIn the presence or absence of electric field one thing that you can be certain of is the time of flight of the projectile, i.e, the time it takes for the projectile to reach maximum height and the reach to the *same initial vertical displacement*.\r\n\r\n\r\n\r\n$\\vec{s}=\\vec{u}t+\\frac{1}{2}\\vec{a}t^2$, $\\tag1$\r\n\r\nWhen the projectile moves for time equal to its time of flight (say, T), its vertical displacement $(\\vec{s})$ is $0$.  Therefore,\r\n \r\n$T=\\frac{2\\nu}{g}$, \r\n\r\n\r\n**The Range :**\r\n\r\n*Lets talk about the range now,*\r\n\r\nYou know that range (due to gravity only) is given by,\r\n\r\n$R=\\frac{v^2\\sin{2\\theta}}{g}$, \r\n\r\nBut when $\\theta$ is $90^{\\circ}$,\r\n\r\n$R=\\frac{v^2\\sin{180^{\\circ}}}{g}=0$, \r\n \r\n\r\nWhatever will the range be, it will only be due to the acceleration that the projectile experiences due to electric field. \r\n\r\nAll you need to do is find the the time of flight and use equation $(1)$ to find the displacement of the projectile with time of flight equal to $T$.\r\n\r\n\r\nThe direction of displacement will be same as the direction of electric field.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 60, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "homework-and-exercises", "electrostatics"], "page_start": null, "page_end": null, "quality_flags": ["low_score"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 333787, "title": "Concept of Projectile in electrostatics", "url": "https://physics.stackexchange.com/questions/333787/concept-of-projectile-in-electrostatics", "share_url": "https://physics.stackexchange.com/q/333787", "content_license": null, "owner": {"display_name": "Aditya DS", "user_id": 127834, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/127834/aditya-ds"}}, "answers": [{"answer_id": 333793, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/333787/concept-of-projectile-in-electrostatics/333793#333793", "share_url": "https://physics.stackexchange.com/a/333793", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Jay N", "user_id": 153235, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/153235/jay-n"}}, {"answer_id": 333803, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/333787/concept-of-projectile-in-electrostatics/333803#333803", "share_url": "https://physics.stackexchange.com/a/333803", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Mitchell", "user_id": 138746, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/138746/mitchell"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:293067:0000", "text": "Question: Applications of gravitational waves\n\n**What are the technological/engineering applications currently being explored that make use of gravitational waves?** I realize this can be broad and opinionated, so I want to emphasize narrowing the question down to *current, tangible explorations* or at least *substantial speculations with solid basis*, and *not* purely fanciful speculations as interesting as sci.fi. may be.\r\n\r\nI ask this as a scientist but one with no expertise in physics aside from a popular science interest in it, and considering how the growth in our familiarity with the fundamental force of electromagnetism led to very significant technological advances. I'm not sure how analogous our technological advancements with electromagnetism are however, as gravitational waves are a fundamentally different force (pun intended) and appear so far to be very, very minuscule compared to the events which generate them. \r\n\r\n\r\n----------\r\nThis question is related to https://physics.stackexchange.com/questions/229243/what-are-the-benefits-of-gravitational-wave-studies?rq=1 but I'm asking more specifically what, if any, applications are currently being explored. I recognize actual gravitational wave interactions are relatively new to us, so we may be blind to future implications as @AccidentalFourierTransform on that question mentioned was the case with EM progress:\r\n\r\n> Why did scientists spend time and money on studying EM waves right after Maxwell theory? Just to test the theory? Or with some economical/practical benefit in mind? Well, I like to think they did because of scientific curiosity and love for the natural philosophy. They might have had practical intentions, but they could never expect that some day, every aspect of our life would depend on EM waves. How can we know what will be the applications of G waves?\r\n\r\nThis is also a similar question to https://physics.stackexchange.com/questions/123813/applications-of-physics-beyond-qft?rq=1 but I am specifically interested in gravitational waves in general, not quantum physics theory.\n\nAccepted Answer:\n\nThere are no foreseeable applications of gravitational waves.\r\n\r\nThe gravitational waves that were detected last year... granted, they were produced quite a distance away, but their production required two roughly 30 solar mass black holes to coalesce, converting roughly 3 solar masses worth of mass into gravitational wave energy, producing gravitational waves at a power level that, at its peak, briefly outshone *all the electromagnetic radiation from the entire visible universe*.\r\n\r\nAnd that, we were able to detect, just barely, with two gigantic detectors that were situated half a continent apart.\r\n\r\nElectromagnetic waves were used widely long before Maxwell's theory, e.g., in the form of visible light (even if it was not recognized before Maxwell that these are, in fact, electromagnetic waves). But the specific predictions of Maxwell's theory, which allowed electromagnetic waves to be produced directly using electric and/or magnetic equipment, were indeed tested initially just to validate the theory. Here is a quote from Heinrich Hertz, who conducted the first such experiment, a quarter century after Maxwell's prediction: \"*It's of no use whatsoever* [...] *this is just an experiment that proves Maestro Maxwell was right—we just have these mysterious electromagnetic waves that we cannot see with the naked eye. But they are there.*\"", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 61, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "gravitational-waves"], "page_start": null, "page_end": null, "quality_flags": ["low_score", "single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 293067, "title": "Applications of gravitational waves", "url": "https://physics.stackexchange.com/questions/293067/applications-of-gravitational-waves", "share_url": "https://physics.stackexchange.com/q/293067", "content_license": null, "owner": {"display_name": "cr0", "user_id": 116396, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/116396/cr0"}}, "answers": [{"answer_id": 293099, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/293067/applications-of-gravitational-waves/293099#293099", "share_url": "https://physics.stackexchange.com/a/293099", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Viktor Toth", "user_id": 58602, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/58602/viktor-toth"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:261191:0000", "text": "Question: On parabolic concave mirror in car flashlights\n\nSorry for the seemingly silly question but what's the advantage of having a concave mirror in car flashlight? I understand how the physics works but I just don't get what the advantage of having this over just a light flashing out is.\n\nAccepted Answer:\n\nLight from the focus, when reflected to a parabolic mirror, will all be reflected in parallel rays.\r\n[![enter image description here][1]][1]\r\n\r\n\r\n  [1]: https://i.sstatic.net/SvTDB.gif", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 62, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "optics", "visible-light", "reflection"], "page_start": null, "page_end": null, "quality_flags": ["low_score", "single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 261191, "title": "On parabolic concave mirror in car flashlights", "url": "https://physics.stackexchange.com/questions/261191/on-parabolic-concave-mirror-in-car-flashlights", "share_url": "https://physics.stackexchange.com/q/261191", "content_license": null, "owner": {"display_name": "MystMan", "user_id": 120424, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/120424/mystman"}}, "answers": [{"answer_id": 261195, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/261191/on-parabolic-concave-mirror-in-car-flashlights/261195#261195", "share_url": "https://physics.stackexchange.com/a/261195", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "philip_0008", "user_id": 118480, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/118480/philip-0008"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:253756:0000", "text": "Question: Bungee balls vs. extension springs\n\nThis is a mix between a DIY question and an applied physics question, but I figure the folks here are more interested in these details.\r\n\r\nMy application is attaching a projection screen to a frame with tension to stretch the screen flat. One of the recommended products to do this is [bungee balls][1]. In my case, I am considering replacing the bungee balls with extension springs because I can affix them with a twist-tie on one side and it will be easier to attach/detach the screen on the other side. The specifications for extension springs are well detailed (e.g. [spring rate measured in lbs/in][2], but I can't find any equivalent information on bungee balls. How can I find this information (my Google-fu failed)? Or is there a simple test I can do with a bungee ball to measure the spring rate?\r\n\r\n\r\n  [1]: http://www.amazon.com/King-Canopy-Ball-Bungees-Black/dp/B004G7PTB8\r\n  [2]: https://www.grainger.com/product/GRAINGER-APPROVED-Ext-Spring-1MZX5\n\nAccepted Answer:\n\nIt is difficult to give a definitive answer.  The spring constant refers to an ideal spring which obeys Hooke's Law (extension proportional to load).  Real springs and especially elastic materials such as bungee cord do not necessarily follow this law.  Usually they do initially for 'smallish' loads, but they depart from it gradually at large loads.  What counts as 'large' differs between materials and structures (springs are structures rather than materials) and is very difficult to predict.  \r\n\r\nThe bungee cord is more likely than the springs to deviate from ideal behaviour.  Since you have these already, you will be familiar with the way they extend.  \r\n\r\nSo as a tentative answer, as long at the load isn't 'too large' the test value of the spring constant should give a reliable comparison.  Ultimately I think you can only be sure by getting hold of the springs and comparing performance in situ.  Even if they are equally springy, you may discover some other reason to prefer one over the other.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 63, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "spring"], "page_start": null, "page_end": null, "quality_flags": ["low_score", "single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 253756, "title": "Bungee balls vs. extension springs", "url": "https://physics.stackexchange.com/questions/253756/bungee-balls-vs-extension-springs", "share_url": "https://physics.stackexchange.com/q/253756", "content_license": null, "owner": {"display_name": "Matt Chambers", "user_id": 6630, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/6630/matt-chambers"}}, "answers": [{"answer_id": 253946, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/253756/bungee-balls-vs-extension-springs/253946#253946", "share_url": "https://physics.stackexchange.com/a/253946", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "sammy gerbil", "user_id": 114696, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/114696/sammy-gerbil"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:21415:0000", "text": "Question: Eliminating IR light reflection perceived by a steep viewing angle\n\nI am having a problem with reflection on an acrylic surface, in the IR part of the spectrum. This reflection is interfering with an algorithm that looks at objects, as it makes two show up when only one exists.\r\n\r\n**Some background:**\r\n\r\nAn IR sensitive (and IR filtered) camera must view an IR backlit stage below at a steep angle, the walls of which are perpendicular to the IR light source, the cameras are at about 30 degrees tilted back with respect to the walls of the stage. \r\n\r\nBecause the walls of the stage must be translucent to visible light, they are made of acrylic  (just about the same optical properties as glass). \r\n\r\nA problem arises when an object comes close to the surface of the glass, as a reflection of that object appears from the acrylic. This confuses the software that uses the camera into thinking there are two objects. To get rid of this problem, a matte finish is applied to the inner surface of the wall to blur the reflection enough, and this works. However it doesn't work perfectly, and the inner surface of the wall would ideally be perfectly smooth.\r\n\r\n**The first question is:\r\nHow can I eliminate the reflection due to the internal reflection, in the IR part of the spectrum, of my object?**\r\n\r\n\r\n**Specifications:**\r\n\r\n- A wall of acrylic is reflecting an object at a steep angle in the IR spectrum\r\n\r\n- The inner wall must be kept smooth (although could have some filter added, and then a smoothing film added over top, perhaps, if it would still elimiate the reflection)\r\n\r\n- The viewing angle is steep and cannot be changed\r\n\r\n- Visible light must be able to pass from the outside of the wall to the inside.\r\n\r\n\r\n**Proposed solution is now:** \r\n\r\nUsing an IR filter applied to the outside wall to prevent the reflection from coming in and up to the camera as strongly, this leaves the inside smooth. Or applying a matte to the outside of the wall to blur the reflection, which also leaves the inside able to be perfectly smooth.\r\n\r\n**A second question is: will the proposed solution work?**\n\nAccepted Answer:\n\nIf you have the budget for special purpose stuff, I would go for an [anti-reflective coating][1]. Since the angle of incidence is fixed and well defined and since you are filtering the IR illumination ideally what would happen is you use a very narrow pass IR filter and an anti-reflective coating that is specifically 'tuned' for the frequency and angle of illumination. You should be able to eliminate most of the reflection.\r\n\r\n\r\n  [1]: https://en.wikipedia.org/wiki/Anti-reflective_coating\n\nAnswer (score=0):\n\nwhat about using a reflective lense on the camera or anti glare? or even adjusting the IR with some type of filter?", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 64, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "optics", "reflection"], "page_start": null, "page_end": null, "quality_flags": ["low_score"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 21415, "title": "Eliminating IR light reflection perceived by a steep viewing angle", "url": "https://physics.stackexchange.com/questions/21415/eliminating-ir-light-reflection-perceived-by-a-steep-viewing-angle", "share_url": "https://physics.stackexchange.com/q/21415", "content_license": null, "owner": {"display_name": "St-Ste-Ste-Stephen", "user_id": 7826, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/7826/st-ste-ste-stephen"}}, "answers": [{"answer_id": 21443, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/21415/eliminating-ir-light-reflection-perceived-by-a-steep-viewing-angle/21443#21443", "share_url": "https://physics.stackexchange.com/a/21443", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Snowhare", "user_id": 4262, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/4262/snowhare"}}, {"answer_id": 48453, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/21415/eliminating-ir-light-reflection-perceived-by-a-steep-viewing-angle/48453#48453", "share_url": "https://physics.stackexchange.com/a/48453", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "DUMBASS", "user_id": 17533, "user_type": "unregistered", "profile_url": "https://physics.stackexchange.com/users/17533/dumbass"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:610103:0000", "text": "Question: Is there any way to focus the mechanical vibration or stress of an object?\n\nI am looking for a way to focus the vibration of a metal sheet at a specific point on that sheet so that other points vibrate less. Just like light and lens. Is there any way to focus the mechanical vibration or stress of an object?\n\nAccepted Answer:\n\nYes, there is. I furnish two cases here. \r\n\r\nFirst we take the case where the vibration wavelength is of order ~the physical dimensions of the part. For small parts, this implies ultrasonic waves. These can be focused and concentrated by artfully tapering the part towards the zone where you want the vibrations concentrated and by adding chunks of mass upstream of the tapered zone to  place a displacement maximum at the end of the tapered zone. This principle is used in the design of what are called *ultrasonic welders* that are used to friction-weld plastic parts together. The piece of metal used to carry the ultrasonic waves from the generator to the part to be welded is called the *horn* and adjusting its mass distribution is called *tuning the horn*.\r\n\r\nThe second case is where the vibrating part is flexible enough that its resonances come about through macroscopic flexure, as in the case of a thin vibrating membrane like for example a drum head. In the acoustics field this sort of vibration is called *oil-canning* and if you are designing a noise-blocking enclosure for a loud piece of machinery, you must avoid this because the enclosure becomes acoustically transparent if the enclosure walls are resonant like this at the noise frequency. \r\n\r\nOil-canning can be reduced by \"clamping\" the enclosure walls either with internal struts that prohibit movement of the wall or by adding mass to the center of the wall panels to move their resonances away from the noise spectrum of the source. The opposite can be done by deliberately tuning the acoustic compliance of the air inside the enclosure coupled to the mass of the vibrating wall so the fundamental excitation frequency of the system (air + wall) is a close match to one of the dominant frequencies in the noise spectrum of the source. In this case, the noise control enclosure makes the noise source a more efficient noise radiator and the noise problem becomes *worse*.\r\n\r\nThis effect is used in musical instruments like a marimba, in which the wooden bars are backed up with tuned lengths of tube which are resonant at the bar frequencies.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 65, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-4.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics"], "page_start": null, "page_end": null, "quality_flags": ["low_score", "single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 610103, "title": "Is there any way to focus the mechanical vibration or stress of an object?", "url": "https://physics.stackexchange.com/questions/610103/is-there-any-way-to-focus-the-mechanical-vibration-or-stress-of-an-object", "share_url": "https://physics.stackexchange.com/q/610103", "content_license": null, "owner": {"display_name": "zeynab ", "user_id": 286944, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/286944/zeynab"}}, "answers": [{"answer_id": 610123, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/610103/is-there-any-way-to-focus-the-mechanical-vibration-or-stress-of-an-object/610123#610123", "share_url": "https://physics.stackexchange.com/a/610123", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "niels nielsen", "user_id": 40292, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/40292/niels-nielsen"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:557429:0000", "text": "Question: Can I build a cuvette for 400-700 nm using simple microscope slides?\n\nI want to measure the absorbance spectrum of some solutions, in the 400-700 nm range. I've always used regular \"optical glass\" cuvettes for this. But I've been wondering, is this really necessary?\r\n\r\nIf the glass looks transparent to the eye, then its absorbance in the 400-700 nm range is negligible. And if the surface looks smooth and clear, then it shouldn't disperse the incident light. So any thin sheet of smooth transparent glass should work, right?\r\n\r\nFor example, I could try to build my own cuvette simply by getting a few microscope slides and tops, (which are thin, flat and smooth panels of glass) and gluing them together with a suitable adhesive.ç\r\n\r\n**Edit: What I mean is, creating a hollow 3D shape with 4 rectangular panels and a smaller square bottom panel, by gluing thin pieces of flat smooth glass (microscope slides for example). This would be a \"home-made\" cuvette. (I'm not proposing to simply sandwich a droplet between to slides!)**\r\n\r\nHas anyone tried this? \r\nIs there a reason why it wouldn't work?\n\nAccepted Answer:\n\nYes you can do that. The only thing to watch out for is that microscope glass is usually borosilicate glass but cuvettes are typically made of quartz. You can always take a calibration measurement to account for this difference anyways.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 66, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-4.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "visible-light", "spectroscopy", "glass"], "page_start": null, "page_end": null, "quality_flags": ["low_score", "single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 557429, "title": "Can I build a cuvette for 400-700 nm using simple microscope slides?", "url": "https://physics.stackexchange.com/questions/557429/can-i-build-a-cuvette-for-400-700-nm-using-simple-microscope-slides", "share_url": "https://physics.stackexchange.com/q/557429", "content_license": null, "owner": {"display_name": "Juan Perez", "user_id": 123183, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/123183/juan-perez"}}, "answers": [{"answer_id": 557530, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/557429/can-i-build-a-cuvette-for-400-700-nm-using-simple-microscope-slides/557530#557530", "share_url": "https://physics.stackexchange.com/a/557530", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "KF Gauss", "user_id": 16713, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/16713/kf-gauss"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:389003:0000", "text": "Question: How does frictional force work?\n\nI have read that frictional force is equal and opposite to the force that is applied on a body to move it from rest. Meaning \r\n\r\nFrictional force = -(m*a)\r\n\r\nSo if there are 2 objects each of mass 100 kg but one is a cube shaped and the other one is wheel shaped then why do we require less force to move the wheel shaped object while we require more force to move the cube shaped object?  And I have also read that when the object is wheel shaped then the surface of the object doesn't get enough time to attach to the irregularities in the surface of the ground. But how is this possible even if both the objects have same mass?\n\nAccepted Answer:\n\nYour equation means that nothing can ever be accelerated because the frictional force always opposes the acceleration exactly--but a body in constant motion on a not-frictionless surface will always remain in motion--it can nether accelerate because of friction, nor can it decelerate because friction will work to keep it going.\r\n\r\nClearly something is wrong.\r\n\r\nBefore working on wheels, consider a block (mass $m$) on a surface:\r\n\r\nHere one has to consider the coefficient of static friction, $\\mu_s$. Here it requires a force greater than $mg\\mu_s$ (the weight of the object times the friction coefficient) to get the motion started. As you ramp your force up from zero, the frictional force matches it and keeps the block motionless. When you pass the threshold, it starts to move.\r\n\r\nOnce that happens, you consider the coefficient of kinetic friction, $\\mu_k$, which is generally less that $\\mu_k$. If you apply a horizontal force $F$ to accelerate the object, some portion goes to overcoming friction:\r\n\r\n$$ F - mg\\mu_k = ma $$.\r\n\r\nWhen considering wheels, the instantaneous point of contact is static--so you use the coefficient of static friction. Under braking circumstances, this is higher than the coefficient of kinetic friction, and this is why we have anti-lock brakes. If the wheels lock up, you're now using $\\mu_k$, which provided less stoping power, thereby increasing your stopping distance.\r\n\r\nLikewise when accelerating: funny cars than spin their tires lose the race.\r\n\r\nNote the frictional force involves a total downward force term $mg$--this is why F1 cars (for example) have wings. The wings are mounted upside down (relative to an airplane), so the lift actually pushes the car down.\r\nThis is called \"downforce\", and is added to the weight of the car to increase the frictional force. Hence, F1 cars can pull 5+ g's in a turn--with the odd effect (for recreational drivers like us) that the faster you go, the more g's you can pull.\n\nAnswer (score=0):\n\nThe friction with which the motion of a block is opposed is kinetic friction while rolling doesn't require the large value of kinetic friction it can do with static friction. Take a look at this image:\r\n\r\n![kinetic static friction](https://qph.ec.quoracdn.net/main-qimg-1777eca07e89468f4e4c3533aa0583eb.webp)\r\n\r\nIn rolling the (static) friction is somewhere on the straight line and generally lower than kinetic friction.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 67, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "experimental-physics", "mathematical-physics", "friction"], "page_start": null, "page_end": null, "quality_flags": ["low_score"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 389003, "title": "How does frictional force work?", "url": "https://physics.stackexchange.com/questions/389003/how-does-frictional-force-work", "share_url": "https://physics.stackexchange.com/q/389003", "content_license": null, "owner": {"display_name": "user179174", "user_id": null, "user_type": "does_not_exist", "profile_url": null}}, "answers": [{"answer_id": 389006, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/389003/how-does-frictional-force-work/389006#389006", "share_url": "https://physics.stackexchange.com/a/389006", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "JEB", "user_id": 82339, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/82339/jeb"}}, {"answer_id": 389011, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/389003/how-does-frictional-force-work/389011#389011", "share_url": "https://physics.stackexchange.com/a/389011", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "SmarthBansal", "user_id": 183700, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/183700/smarthbansal"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:805246:0000", "text": "Question: Okay, I know the risks. ( Amateur Rocket.)\n\nI am currently attending a school for electrical science. A small group of students and our instructor are attempting group project to build a liquid fuel rocket. (I know it is a bit out of the scope of our field of study.)\r\n We have encountered a few issues when attempting to calculate the thrust of the rocket. (None of us have ANY prior experience with fluid/thermo dynamics.) The formula we found is \r\n$$T=\\dot m V_e+(p_e−p_a)A_e. $$\r\n\r\nAs I understand the formula, this reads \"thrust = the amount of mass flowing multiplied by the speed of the exhaust, plus the difference in pressures multiplied by the area of the exhaust.\"\r\n\r\nThere are multiple questions. The first one is: how does one solve for the $V_e$ in this formula? The second is, does the simple mass flow equation $\\dot m =rVA$ work? And if so, once again, how does one solve for velocity?\r\n\r\n\r\nIf it has not been made abundantly clear, this type of calculation is far beyond my current level of comfort. But I find it all quite fascinating.\n\nAccepted Answer:\n\n$V_e$ is a property of the chosen propellant. In particular its   [specific impulse][1]. For example the liquid-hydrogen liquid oxygen combination has a specific impulse of 450 seconds.  This means that  a thrust of 450 pounds weight is produced  when the fuel is being burned at a rate of one pound mass per second. \r\n\r\nIncidently I think  your thrust equation should be be \r\n$$\r\nT= \\dot m  v_{e} \\approx  A(p_{chamber}- p_{outside})\r\n$$ \r\ni.e there is an approximately-equal sign and not a \r\n sum of the two terms.  \r\n\r\n\r\n[1]:https://en.wikipedia.org/wiki/Specific_impulse", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 68, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-4.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "thermodynamics", "fluid-dynamics", "rocket-science", "home-experiment"], "page_start": null, "page_end": null, "quality_flags": ["low_score", "single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 805246, "title": "Okay, I know the risks. ( Amateur Rocket.)", "url": "https://physics.stackexchange.com/questions/805246/okay-i-know-the-risks-amateur-rocket", "share_url": "https://physics.stackexchange.com/q/805246", "content_license": null, "owner": {"display_name": "TylerTheSparky", "user_id": 390201, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/390201/tylerthesparky"}}, "answers": [{"answer_id": 805255, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/805246/okay-i-know-the-risks-amateur-rocket/805255#805255", "share_url": "https://physics.stackexchange.com/a/805255", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "mike stone", "user_id": 80687, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/80687/mike-stone"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:237406:0000", "text": "Question: Applications of laws of Physics\n\nThe problem i always suffered was that all the texts books of Physics although states the laws of physics but they never tell about the applications of these laws in daily life. Many students like me spend their time in memorizing the laws of Physics stated in the text books but they hardly come to know that what is the usefulness of these laws, how we can use them, for what purpose they are stated. May be many people here have different and better academic experience. Can anyone one tell me about any book that concentrates more on the applications of the laws of physics so that a high school or a college reader may understand physics better?\n\nAccepted Answer:\n\nI think every textbooks describe a little on the application of a law or theory. Because most theories of physics were developed to explain some physical phenomena or understanding our surrounding better. Generally, a textbook can't go deep to any theory because of its limited size. But you can use some general physics textbooks which describe a lots of physical consequences regarding the theory or its application. In fact, some textbooks like \"Fundamentals of Physics\" or \"University Physics\" make us curious by asking a question at the very beginning and then only introduce us the theories to solve that question. I think these books will be extremely helpful to you. You have \"The Feynman Lectures of Physics\" also which provide a deep insight to the theories and Feynman's own viewpoint of understanding.\n\nAnswer (score=1):\n\nAs an applied physicist, a field which is the bridge between physics and engineering, my work is to apply physical concepts to practical problems.  Sometimes it is in the context of setting up experiments for fundamental physics; other times it is finding solutions to problems.\r\n\r\nThough there may be a \"magic text book\" which answers your specific needs, the usual way to learn is to actually apply the physics taught in the class room to practical problems in a laboratory; the teaching lab is the first place to start, though you can also do basic things at home, or anywhere: inertia, friction, moment arms, static electricity, potential energy, optical diffraction and refraction, reflection and scattering, and the same for acoustics.\r\n\r\nThe possibilities are literally endless.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 69, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "resource-recommendations"], "page_start": null, "page_end": null, "quality_flags": ["low_score"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 237406, "title": "Applications of laws of Physics", "url": "https://physics.stackexchange.com/questions/237406/applications-of-laws-of-physics", "share_url": "https://physics.stackexchange.com/q/237406", "content_license": null, "owner": {"display_name": "hur chu chu", "user_id": 108402, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/108402/hur-chu-chu"}}, "answers": [{"answer_id": 237467, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/237406/applications-of-laws-of-physics/237467#237467", "share_url": "https://physics.stackexchange.com/a/237467", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Priyankush Deka", "user_id": 106702, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/106702/priyankush-deka"}}, {"answer_id": 237451, "is_accepted": false, "url": "https://physics.stackexchange.com/questions/237406/applications-of-laws-of-physics/237451#237451", "share_url": "https://physics.stackexchange.com/a/237451", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Peter Diehr", "user_id": 106192, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/106192/peter-diehr"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:516589:0000", "text": "Question: Applications of analytical mechanics in real life\n\nI'm currently taking a course of analytical mechanics, I'd like to read more about it. I'm interested in reading about what kind of appliances are there for analytical mechanics in computer science or electrical engineering? I would be really happy to read some articles or research about it. I tried searching online but couldn't find much information.\n\nAccepted Answer:\n\nFor just one example in each:\r\n\r\n- Coupled oscillators are usually quite important in electrical engineering, and the related concept of normal modes is one that is best dealt with using analytical mechanics.\r\n\r\n- Methods of numerically solving ODEs like the Runge-Kutta method tend not to conserve energy over long periods of time (i.e. over many timesteps). A class of ODE solvers based on the Hamiltonian formalism allows for energy conservation for those differential equations that are amenable to being cast in such a formalism. More generally, the kind of geometry induced by the behavior of a Hamiltonian dynamical system (symplectic geometry) inspires the many kinds of _symplectic integrators_ used for a similar purpose.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 70, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-4.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "lagrangian-formalism"], "page_start": null, "page_end": null, "quality_flags": ["low_score", "single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 516589, "title": "Applications of analytical mechanics in real life", "url": "https://physics.stackexchange.com/questions/516589/applications-of-analytical-mechanics-in-real-life", "share_url": "https://physics.stackexchange.com/q/516589", "content_license": null, "owner": {"display_name": "E. Ginzburg", "user_id": 228703, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/228703/e-ginzburg"}}, "answers": [{"answer_id": 516592, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/516589/applications-of-analytical-mechanics-in-real-life/516592#516592", "share_url": "https://physics.stackexchange.com/a/516592", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "probably_someone", "user_id": 139781, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/139781/probably-someone"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:394383:0000", "text": "Question: The relationship between mass and incline on an object's speed\n\nI took my daughter and son for a ride in there Red Rider Wagon on the weekend. We went down a small incline on one block in our neighborhood. My daughter, who is 5 years old, asked me in her own way, what effect does the mass of the kids in the wagon and the incline of the hill have on their speed?\n\nAccepted Answer:\n\nIf the incline is frictionless then the mass and therefore the weight has nothing to with the speed. But a steeper incline will mean in the vertical direction there will be greater acceleration. If the incline is not frictionless then ultimately the terminal velocity (maximum speed reached) will be higher with a greater weight.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 71, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-3.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "newtonian-mechanics"], "page_start": null, "page_end": null, "quality_flags": ["low_score", "single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 394383, "title": "The relationship between mass and incline on an object's speed", "url": "https://physics.stackexchange.com/questions/394383/the-relationship-between-mass-and-incline-on-an-objects-speed", "share_url": "https://physics.stackexchange.com/q/394383", "content_license": null, "owner": {"display_name": "user384754", "user_id": 189621, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/189621/user384754"}}, "answers": [{"answer_id": 394387, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/394383/the-relationship-between-mass-and-incline-on-an-objects-speed/394387#394387", "share_url": "https://physics.stackexchange.com/a/394387", "content_license": "CC BY-SA 3.0", "owner": {"display_name": "Amara", "user_id": 76619, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/76619/amara"}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:485128:0000", "text": "Question: Railroad train on tracks\n\nWhat keeps the railroad trains on the tracks?\r\n\r\n\r\nP.S: It is not the flanges, as already remarked by Dr. Richard Feynman.\r\n\r\nI want a detailed explanation of this question, if possible.\r\n\r\nThanks.\n\nAccepted Answer:\n\nThe surface of the track is slightly curved and the wheels are tapered or conical so that they centre themselves between the tracks.\r\n\r\nThe larger diameter of the cone is on the inside.\r\n\r\nSee [this on wikipedia for more info][1]\r\n\r\n\r\n  [1]: https://en.wikipedia.org/wiki/Train_wheel", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 72, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-4.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "newtonian-mechanics", "rotational-kinematics", "stability"], "page_start": null, "page_end": null, "quality_flags": ["low_score", "single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 485128, "title": "Railroad train on tracks", "url": "https://physics.stackexchange.com/questions/485128/railroad-train-on-tracks", "share_url": "https://physics.stackexchange.com/q/485128", "content_license": null, "owner": {"display_name": "Shishir Maharana", "user_id": 234064, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/234064/shishir-maharana"}}, "answers": [{"answer_id": 485134, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/485128/railroad-train-on-tracks/485134#485134", "share_url": "https://physics.stackexchange.com/a/485134", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "user207455", "user_id": null, "user_type": "does_not_exist", "profile_url": null}}]}}}
{"unit_id": "stackexchange:physics.stackexchange:applied-physics:832504:0000", "text": "Question: Rating this old physics manual for engineering\n\nI found this old physics manual for engineering it's no doubt outdated, but I like the overall formatting and short nature of the book. Is there anything in it outdated and now found inaccurate?\n\nAccepted Answer:\n\nYou omitted the link, but here are some general observations on this topic. \r\n\r\nThe great advances in physics that have occurred in the last ~50 years have happened in fields involving neutrinos, quarks, electroweak unification, supernovas, the Hubble constant/cosmology, black hole thermodynamics, gravitational waves and high-temperature superconduction. Within this list, only high-temperature superconductivity impinges on any everyday engineering field. \r\n\r\nThis means that a short book on physics for engineers, even if 50 years old, would still be worth reading and understanding.", "source": "stackexchange", "source_doc_id": "physics.stackexchange", "source_title": "Physics Stack Exchange", "domain": "physics", "subdomain": "qa_community", "level": "mixed", "order_index": 73, "metadata": {"module_id": "applied-physics", "source_format": "stackexchange_api_v2.3", "extraction_method": "stackexchange_api_v2_3_extractor_v1", "license": "CC-BY-SA-4.0", "language": "en", "hierarchy_path": ["Physics Stack Exchange", "applied-physics", "resource-recommendations", "education"], "page_start": null, "page_end": null, "quality_flags": ["low_score", "single_answer"], "ocr_confidence": null, "layout_confidence": null, "math_confidence": null, "stackexchange_attribution": {"network": "Stack Exchange", "site_name": "Physics Stack Exchange", "site_url": "https://physics.stackexchange.com", "api_site": "physics", "api_terms_url": "https://stackoverflow.com/legal/api-terms-of-use", "license_help_url": "https://physics.stackexchange.com/help/licensing", "question": {"question_id": 832504, "title": "Rating this old physics manual for engineering", "url": "https://physics.stackexchange.com/questions/832504/rating-this-old-physics-manual-for-engineering", "share_url": "https://physics.stackexchange.com/q/832504", "content_license": null, "owner": {"display_name": "Haridasa", "user_id": 409160, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/409160/haridasa"}}, "answers": [{"answer_id": 832511, "is_accepted": true, "url": "https://physics.stackexchange.com/questions/832504/rating-this-old-physics-manual-for-engineering/832511#832511", "share_url": "https://physics.stackexchange.com/a/832511", "content_license": "CC BY-SA 4.0", "owner": {"display_name": "niels nielsen", "user_id": 40292, "user_type": "registered", "profile_url": "https://physics.stackexchange.com/users/40292/niels-nielsen"}}]}}}