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May 9

Force-Vector Diagrams (i.e. force calculations)

I asked a question on the Mathematics desk, but no one has responded yet, so maybe it's more physics than mathematics. It's available here: http://wiki.riteme.site/wiki/Wikipedia:Reference_desk/Mathematics#Force-Vector_Diagrams_.28i.e._force_calculations.29

And, this was my question: "-

I am designing a pedal box for a Formula Student vehicle. If I press the brake pedal with a force, it has to output that force into the piston of a master cylinder. I am trying to do a force-vector diagram, but it's impossible (for me). If it were a the pedal were straight, it would be easy, but it isn't, so it is difficult. I have attached a picture to show the problem, and hopefully you will be able help. I need to work out the three generic equations. Here are the problems:https://fbcdn-sphotos-d-a.akamaihd.net/hphotos-ak-prn2/t1.0-9/10320602_652593664832694_8003566249436072075_n.jpg

-" 81.110.73.68 (talk) 07:22, 9 May 2014 (UTC)[reply]

Unless you're interested in the forces within the metal of the pedal itself, it's irrelevant what shape it is. The only thing that matters is the distance & direction of the point where the force is applied (where your foot is) from the fulcrum. SteveBaker (talk) 13:14, 9 May 2014 (UTC)[reply]

Your sketches show forces that contribute to torque or turning moment around a pivot. Torque is the product of the force applied, the length of the lever arm connecting the axis to the point of force application, and the sine of the angle between the force vector and the lever arm. Balancing moments in your first sketch gives

F_x L₁ sine 90° = F_o L₂ sine θ

However before concluding that

F_o = (F_x L₁) / (L₂ sine θ)

I suggest you review these:

The foot pressure F_x is not actually normal (i.e. 90°) to the lever (tilting the pedal surface doesn't change where the point of application is) so the sketch doesn't quite match the mechanics
There must be a return spring whose torque must first be overcome by foot pressure before any force is transmitted to F_o.

Your plans 1 and 2 are classic examples of Levers Classes 1 and 2 respectively. I gave you the reference to Torque first because you will need it to analyze the more complicated third plan where I think you may have missed the need for a sliding joint (elongated hole?). 84.209.89.214 (talk) 13:35, 9 May 2014 (UTC)[reply]

84.209.89.214, you are so awesome!! Thank you so much!! 143.210.123.69 (talk) 13:56, 9 May 2014 (UTC)[reply]

How precisely can you measure a position on Earth without GPS?

Given time, date, a compass and some device to measure the position of the sun, how precisely can I know where I am? OsmanRF34 (talk) 15:41, 9 May 2014 (UTC)[reply]

Celestial navigation#Angular measurement has some commentary about precision. DMacks (talk) 17:01, 9 May 2014 (UTC)[reply]

According to this New York Times article, a sextant, chronometer, and referece materials can give a position that is within 3 miles of the true position.

This source indicates that observations with broken telescopes, such as the Wild T-4, could determine latitude and longitude accurtely enough to detect the diference between geodetic and astronomical latitude and longitude, which is related to deflection of the vertical. This could be as much as 5 arcseconds, which could correspond to as much as 150 meters on the ground. (Further research would be needed to find the actual accuracy; think of this as a rough upper bound). Jc3s5h (talk) 17:05, 9 May 2014 (UTC)[reply]

There's no such thing as "precisely where you are". A surveyor's instruments can get you to within a very small fraction of an inch relative to whatever you chose to set as your reference points. μηδείς (talk) 20:24, 9 May 2014 (UTC)[reply]

Aye. If there's an odd-shaped rock ten feet to the southeast, you are certainly ten feet northwest of the rock. Beyond that, we're lost in space. InedibleHulk (talk) 20:29, 9 May 2014 (UTC)[reply]

Isn't it obvious that I mean a position on Earth, measured on degrees? OsmanRF34 (talk) 20:34, 9 May 2014 (UTC)[reply]

Those are actually still measured relevant to Greenwich Observatory. It's not like there's a natural zero longitude. I'm not sure what the standard for GPS is now, last I remembered it was within a meter, but that was a while ago. Surveyors have had that beat for a long time. μηδείς (talk) 21:42, 9 May 2014 (UTC)[reply]

I remember centimeters, with long-term averaging. Was it 10 or 1? Sagittarian Milky Way (talk) 13:19, 10 May 2014 (UTC)[reply]

GPS is not necessarily very accurate. In the past couple hours I corrected two GPS locations of photos of houses of worship in Harlem. The Catholic church fix was half a city block too far north; the synagogue fix was two blocks west. Of course, diffent equipment differently used under different circumstances can do better, but on the whole the advantage of GPS is convenience, not precision. Jim.henderson (talk) 20:33, 9 May 2014 (UTC)[reply]

Do buildings screw with GPS in uncorrectable ways, at least for cheap/non professional units? Also, number of visible satellites affects accuracy. It won't even work with <4. Were you in a street canyon? Sagittarian Milky Way (talk) 13:19, 10 May 2014 (UTC)[reply]

This topic is one of my main interests, but in this forum I'm afraid it constitutes clutter and ought to be moved to a quieter venue, such as my talk page or yours or Wikipedia talk:WikiProject Geographical coordinates. Jim.henderson (talk) 13:27, 10 May 2014 (UTC)[reply]

Yep. Hard to get a talented surveyor out to your unknown location without a cell phone. And by the time he got there, you'll have probably moved. InedibleHulk (talk) 02:19, 10 May 2014 (UTC)[reply]

Relative to the national grid in the UK a typical classical surveyor should be able to fix his position to a 50% probability within a circle approximately 300 mm across. This is of course aided by the network of triangulation pillars on top of many hills. Using the sun, only, and accurate clocks and compasses, and many many observations, I would /guess/ 10-100 times more error. Greglocock (talk) 01:40, 10 May 2014 (UTC)[reply]

Indeed. In the 1790s Pierre Méchain measured the latitude of Mont-Juoy fort in Barcelona to an accuracy of within forty feet (see The Measure of All Things by Ken Adler). He spent months taking many observations, as he was interned there while Spain was at war with France. And he used observations of stars rather than the sun. Gandalf61 (talk) 09:55, 10 May 2014 (UTC)[reply]

Presumably he needed a telescope at least 1 foot in diameter to even see .4 arcseconds, even in vacuum? How'd he get a telescope that big in a fort in the 1790s? A scope his size was probably overkill for military purposes. The star would look like a boiling, mottled, slightly moving blob at best a hundred feet of ground accuracy wide. Not bad. I don't know what it the seeing conditions are like from a fort. Probably worse. Sagittarian Milky Way (talk) 13:17, 10 May 2014 (UTC)[reply]

First: you don't actually have to be inside the fort, harbour or any other installation to measure its position. You can just be outside and measure the offset. Modern low-lever bombers often use offset when the intended target does not return a good radar image (such as a military runway). Second: As he was determining latitude, it suggest to me, that he used a transit telescope. They don't have a large foot-print and so it could have gone inside said fort. Third: He was an intern. So plenty of time on his hands to configure a mirror of amply size (and thus keep the favour of his captives). Fourthly: The academic base from which to archive accurate navigation is vitally important to the military– as then so it is today. So it was far from and overkill, anymore the the US and Russia spending billions on Transit, SatNav and Glonass. Filthy: he was French and they have a habit of muttering pas de problème then shouting Voilà !. --Aspro (talk) 17:34, 11 May 2014 (UTC)[reply]

What happens when our bodies get colder?

Why do we need to keep our body temperature to survive? Why do we die by temperatures marginally lower than 37.0 °C (98.6 °F)? What chemical process needs exactly this temperature and not 5 °C for a couple of hours? OsmanRF34 (talk) 15:49, 9 May 2014 (UTC)[reply]

There's some stuff at hypothermia and at human body temperature, but the description at therapeutic hypothermia actually seems to have the most detail. Matt Deres (talk) 16:28, 9 May 2014 (UTC)[reply]

Advocates of Cryonics assure us that a person preserved at low temperature and considered medically dead may not necessarily be dead according to an information-theoretic definition of death, and may be resuscitated in the future. Some 270 people have undergone cryopreservation procedures, where a Cryoprotectant is used to protect tissue from freezing damage, since cryonics was proposed in 1962. 84.209.89.214 (talk) 19:00, 9 May 2014 (UTC)[reply]

In other words, "You're not dead until you're warm and dead". 24.5.122.13 (talk) 19:32, 9 May 2014 (UTC)[reply]

Dr. Peter Cox of the The Hospital for Sick Children said the same thing of a totsicle he thawed in 2001. InedibleHulk (talk) 19:38, 9 May 2014 (UTC)[reply]

He somewhat explains the science behind it here. Better to freeze fast than slow, and babies are lucky, in that sense. Also good for organic food. InedibleHulk (talk) 19:43, 9 May 2014 (UTC)[reply]

Not exactly, it's more like, "You're not dead until your brain can't function." The teen who stowed away in the wheel well from a California to Hawaii flight recently was flirting with death. The story said that most folks do not survive such attempts, but some do, evidently by slipping into kind of cryogenic coma (my words, not necessarily theirs). ←Baseball Bugs ^{What's up, Doc?} carrots→ 19:45, 9 May 2014 (UTC)[reply]

I'd go with "Not dead until your brain can't regain function". That baby's brain couldn't function, for a while. And she's still here. InedibleHulk (talk) 19:54, 9 May 2014 (UTC)[reply]

Yes. ←Baseball Bugs ^{What's up, Doc?} carrots→ 20:36, 9 May 2014 (UTC)[reply]

Isn't the central issue here that a lower body temperature lowers the rate of breathing and pulse, starving the brain of oxygen unless the brain itself is swiftly coole, lowering it's demand of more than 1/5 of the body's resting rate consumption? I think diving reflex might address this. μηδείς (talk) 20:22, 9 May 2014 (UTC)[reply]

Well, the answers and links above still don't explain why we die by a lower temperature. They even point in the other direction, being kept at a lower temperature can save us. But why would we die just because every process in our body gets slower: we can produce less energy, but we also would need less. So, why don't we just get sluggish if we reduce our body temperature some degrees? What metabolic process can't 'run' at 27 °C, and need 37 °C? It's clear that freezing temperature will destroy cells, but what gets destructed/stopped/screwed by lower temperature? OsmanRF34 (talk) 20:29, 9 May 2014 (UTC)[reply]

Not being a chemist, I'd still guess it boils down to certain reactions just not possibly happening outside of certain temperature ranges, for insanely complicated (but basic) reasons. Since that's a terrible answer, here's a medical source about hypothermia impairing renal function. InedibleHulk (talk) 20:50, 9 May 2014 (UTC)[reply]

One dies much more quickly of oxygen depravation than renal failure. μηδείς (talk) 20:51, 9 May 2014 (UTC)[reply]

What's oxygen depravation? OsmanRF34 (talk) 16:13, 10 May 2014 (UTC)[reply]

A lack of oxygen moving through the blood. Cells love the stuff. When your brain cells don't get any, they go on strike and let cerebral hypoxia take over. When your brain stops sending out chemical signals that tell your body it's alive, apoptosis starts, then the bacteria inside decide to eat it, rather than go down with the ship. InedibleHulk (talk) 01:06, 11 May 2014 (UTC)[reply]

That's deprIvation, not depravation. There is no such a thing as oxygen depravation, unless oxygen is queer. OsmanRF34 (talk) 11:21, 11 May 2014 (UTC)[reply]

Oh. Yeah, it's spelled wrong. Took it you were still asking an honest question, not sarcastic. Being invisible, it's hard to say which way oxygen leans, but it's supported the ~~homophagous~~ heterotrophic lifestyle for eons. InedibleHulk (talk) 22:18, 11 May 2014 (UTC)[reply]

Looking at the depraved Google results for that word, I think I should clarify that I meant life which eats life. Thought it was a common enough word, but apparently not. InedibleHulk (talk) 22:43, 11 May 2014 (UTC) [reply]

Absolutely. Didn't mean to imply otherwise. Just saying a lot goes wrong, even after initial recovery. It's why God invented sweaters.^{[citation needed]} Letting Google Autosuggest for "Effects of hypothermia on" should be useful. InedibleHulk (talk) 20:54, 9 May 2014 (UTC)[reply]

That's a ^{[dubious – discuss]}, not a cn, Hulk. God created the sheep; all else is the work of man. - ¡Ouch! (^{hurt me} / _{more pain}) 06:45, 13 May 2014 (UTC)[reply]

Here is an interesting (humanly readable) overview of the pathophysiology of it. InedibleHulk (talk) 21:04, 9 May 2014 (UTC)[reply]

Philosophically, to paraphrase an eternal musing on the Others, do we even die when we get cold, or do we just get cold when we die? InedibleHulk (talk) 21:13, 9 May 2014 (UTC) [reply]

Human body temperature says death usually occurs due to irregular heart beat or respiratory arrest. When body temperature drops you start shivering, vasoconstriction and diuresis occurs, enzyme activity drops, blood viscosity rises, heart rate drops. At too low temperature your heart malfunctions, the blood flow stops, no more oxygen to the cells and they die. 37° is the optimum temperature for most human enzymes, so our body works best at that T°; having a constant core T° has been an evolutionary advantage for us, that's why our hypothalamus keeps it at that "setting", even when a lower temperature would be advantageous (like hibernation). But there have been cases with lower body temperature, sometimes in people with MS, see this paper, in one case a woman whose temperature was between 33° and 35.2°C during nine months observation, another who stayed at 35°C. So if our hypothalamus turns down the thermostat, we can live at 33°, if it doesn't our body will spend all the energy reserves it has to get up to 37°, instead of settling at a lower metabolic rate at 33°C. Ssscienccce (talk) 22:04, 9 May 2014 (UTC)[reply]

This answer explains the effect of the chemical imbalance, but not why or which metabolic processes can work at 10 degrees lower. OsmanRF34 (talk) 16:13, 10 May 2014 (UTC)[reply]

The central problem that underlies all this is that metabolism involves vast numbers of protein interactions that are strongly temperature sensitive (i.e. a few degrees of temperature change can double or halve the reaction rate), but each is sensitive in its own way. So if you reduce the temperature very much, the reactions don't just slow down, they slow down by different amounts and get out of balance. Once the system gets too far out of homeostasis, it can't recover. Looie496 (talk) 02:52, 10 May 2014 (UTC)[reply]

We don't necessarily die when our body temp is " marginally lower than 37.0 °C (98.6 °F)? " Mine is normally around 97.1 and my wife's is 97.4 as measured in medical checkups or at home. If it measures 98.6 we have a fever. Edison (talk) 12:54, 10 May 2014 (UTC)[reply]

3 °C below your normal temperature will surely kill you. OsmanRF34 (talk) 16:13, 10 May 2014 (UTC)[reply]

More like 5 to 6, according to Human body temperature. ←Baseball Bugs ^{What's up, Doc?} carrots→ 20:46, 10 May 2014 (UTC)[reply]

Have scientists determined the optimal number of hours since you've woken up to do important things?

It depends on the person of course (introversion, neuroticism, laziness/(un)procrastinater..), what kind of event (taking the bar, watching your team's World Cup final, losing your virginity..) and whether the event is enjoyable or bad but maybe people have discovered some things. I would guess that the Army's thought of this and found it important enough to find the answer for when the type of person is a soldier important thing is combat. Probably they are enough one-chance life-altering tests in the world that studies have been done to try to find any edge? In my experience hour 16 or very early is bad - especially if you have an hour or two of rapid fire prep to do like test cramming/the homework equivalent, 75 minute commutes, and running in the subway (if you've ever seen Gladiator it reminds me of how the final fight starts, or a hero being awoken by fists followed by 10 minutes of kung fu). Maybe some people just have a back-loaded, atypically skewed circadian curve, even if they sleep as late as desired? Sagittarian Milky Way (talk) 22:07, 9 May 2014 (UTC)[reply]

All I know is that if I have meetings or presentations before 9am, I am useless - cloudy headed, tending to jumble words, etc. I need a good 1.5 hours to ease into my days and get the gears spinning. Justin15w (talk) 22:37, 9 May 2014 (UTC)[reply]

What happens if you get up 1.5 hours earlier than usual? HiLo48 (talk) 23:00, 9 May 2014 (UTC)[reply]

Do you happen to have a caffeine addiction ? It might take that long for your morning coffee/tea/cola to kick in. Nicotine addiction is less likely, since it's a lot quicker, and presumably a nicotine addict lights up as soon as they awake (although maybe one trying not to smoke at home would be an exception). And there's always alcohol addiction, but hopefully that's not your issue. In any case, this sort of thing could make people with a longer drive to work more successful, if they are at 100% by the time they arrive at work. StuRat (talk) 03:14, 10 May 2014 (UTC)[reply]

Here's a newspaper article discussing just this topic a couple of years ago. [1] The ebb in energy around 2pm isn't too surprising, it is siesta time in civilized countries after all... Mental acuity supposedly peaks in the late morning. There are studies out there that pinpoint the best times of day for physical exercise too. OttawaAC (talk) 00:56, 10 May 2014 (UTC)[reply]

It varies as a function of genetics, habits, and age. When I was in my 20s I was nonfunctional before 8 AM and did my best work late at night, but now that I am in my 50s I am nonfunctional late at night and do my best work around 7 AM. Wikipedia doesn't have very good coverage of this topic, but our Morningness-eveningness questionnaire article gives a little bit of relevant information and a few useful references. Looie496 (talk) 02:44, 10 May 2014 (UTC)[reply]

Just saw this story on the BBC 'Tired teenagers' at Surrey school to start lessons later, about a VIth Form in Surrey which is to commence lessons at 13:30. DuncanHill (talk) 13:55, 10 May 2014 (UTC)[reply]

Several books written to advise the budding author advise setting a requirement of some unit of work (2000 words, say) "first thing in the morning." In one book this was taken as "before you even have your morning cup of coffee or breakfast," while kinder authors suggested "right after breakfast, before you read your email or check the news." It may have been an issue of "mental energy" (avoiding procrastination) rather than "intellectual acuity." I would be surprised if the US armed forces had never studied this, since they have a large stock of experimental subjects, and it would be useful to know what hour of the day some student, analyst or planner would be most effective. Edison (talk) 00:30, 11 May 2014 (UTC)[reply]

I can barely remember my name, let alone write, until I've had a couple of cups of tea and a fag or three. DuncanHill (talk) 00:35, 11 May 2014 (UTC)[reply]

When a Brit writes this sentence it means he hates mornings. When an American.. Sagittarian Milky Way (talk) 13:41, 12 May 2014 (UTC) [reply]