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April 12

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Moment of Inertia of a Traingle

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Hi. So I'm having a little trouble trying to find the formula of the moment of inertia of a triangle. I have the base width of the triangle (4.6 meters), the height (8.6 meters), the area (19.78 m^2) and the surface density (.101 kg/m^m). Now I know the moment of inertia = but I'm not exactly sure where to plug in what i have into that. My guess is something like but I'm not exactly sure. Anyone's help to point me in the right direction would be appreciated.

--RedStateV (talk) 03:36, 12 April 2009 (UTC)[reply]

I have no clue where you got that formula - but it doesn't look right. There are a couple of easy-to-understand equations in List of area moments of inertia. SteveBaker (talk) 05:16, 12 April 2009 (UTC)[reply]
Also, there is more than one moment of inertia - you need to know about which axis you want the moment of inertia. Gandalf61 (talk) 09:06, 12 April 2009 (UTC)[reply]
If not otherwise specified, "moment of inertia" means the "area moment of inertia". StuRat (talk) 15:42, 12 April 2009 (UTC)[reply]

Steve, which formula are you unsure of? If it's the second one I know it's probably not right, that's why I was asking for some help. And I'm looking for mass moment of inertia not area moment of inertia.

RedStateV (talk) 16:22, 12 April 2009 (UTC)[reply]

But you still haven't told us what your axis is. Gandalf61 (talk) 16:32, 12 April 2009 (UTC)[reply]

Whoops, sorry. Through the center of mass which should be 2/3 up from the center of the base coming out of the page.

RedStateV (talk) 16:40, 12 April 2009 (UTC)[reply]

If you know that the centre of mass is above the centre of the base then I assume your triangle must be an isosceles triangle. The distance of the centre of mass from the base is actually 1/3 of the height, not 2/3. To find the moment of inertia about an axis through the centre of mass perpendicular to the plane of the triangle, first find moments of inertia about two perpendicular axes through the centre of mass and in the plane of the triangle - I suggest parallel and perpendicular to the base would be good choices. Then use the perpendicular axes theorem. Gandalf61 (talk) 17:28, 12 April 2009 (UTC)[reply]

Right, 1/3 my mistake. But the way I need to figure it out involves using that integral in some way. I do not know at all how to do the thing's you suggested. RedStateV (talk) 17:42, 12 April 2009 (UTC)[reply]

Okay. Let's start with an axis parallel to the base. dm is the mass of a thin strip of width dr at a (perpendicular) distance of r from the axis; r goes from -2h/3 at the apex to h/3 at the base. Can you find an expression for dm in terms of r and dr ? Gandalf61 (talk)

I think it's something like dm= Density*length of the strip dr RedStateV (talk) 01:08, 13 April 2009 (UTC)[reply]

Yes. And the length of the strip depends on r; it goes from 0 at the apex when r = -2h/3 to b at the base when r = h/3. So can you find an expression for the length of the strip in terms of r ? Gandalf61 (talk) 05:21, 13 April 2009 (UTC)[reply]

Area of a Heart

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Is it possible to find an area f a heart (The symbol, not the organ), because Ι tried to...

A = πr2+BhHb1/2

were the Bh is equal to the longest distance, the Hb is the hight to the Bh, and r is found by 1/4 *Bh.

I just want to see if this could be used? Buɡboy52.4 (talk) 05:00, 12 April 2009 (UTC)[reply]

I don't know that a typical 'heart shape' is sufficiently well-defined for there to be a definitive equation - there is scope for the angle at the two points to vary (which would obviously vary the area) - without changing Bh or Hb. The nearest shape I can think of is a Cardioid (which, literally, means "heart shaped") - although the mathematical cardioid curve doesn't have the point at the bottom. SteveBaker (talk) 05:12, 12 April 2009 (UTC)[reply]
A "heart symbol" isn't really a specifically-defined mathematical shape. Heck, when I draw it, the height is the longest distance...do you mean Bh as the maximum width? It sounds like your specific case is constructed with the top of each lobe as a perfect semicircle and the bottom as a triangle. In that case (but only in that case), you can indeed break it down into those two geometric figures and use a sum of your standard "area of a circle" (whose diameter is half the width and therefore your "r" is correct") and "area of a triangle" formulas to get the whole area. DMacks (talk) 05:14, 12 April 2009 (UTC)[reply]
well, my equestion is based of the idea that the heart is basically two circles and a triangle, were the circles overlap the triangle, so you have two semicircles. The equestion would work as long as the shape is symmetrical and only having two curves. Buɡboy52.4 (talk) 05:20, 12 April 2009 (UTC)[reply]
obviously not perfect
straight edges tangential to circles

so, what would be the area of a pentagram? Buɡboy52.4 (talk) 05:34, 12 April 2009 (UTC)[reply]

Try breaking it down into a collection of triangles. (Hint: The inner triangles will have half the height of the outer triangles.) -- Tcncv (talk) 05:58, 12 April 2009 (UTC)[reply]
I think that if the straight-edge parts of the heart approximation were tangential to the circles this would make a much better heart approximation. It would be less close to the heart with concave edges shown but not all heart symbols have this feature. A straight edged heart has an exact solution to its area. See also Heart (symbol)#Mathematical description and the Mathworld article linked from there which has some more mathematical heart shapes. SpinningSpark 13:53, 12 April 2009 (UTC)[reply]
You will also find the answer to your question on the area of a pentagram in an article on the Mathworld site. Desperately trying to fill up the huge blank space I have now stupidly created by adding a second diagram. SpinningSpark 14:00, 12 April 2009 (UTC)[reply]

Well, I was just thinking, it you could just find the area of the pentagon, and times it by two. Buɡboy52.4 (talk) 14:57, 12 April 2009 (UTC)[reply]

Clearly you can define a shape who's area you CAN calculate - and call that a "heart shape". But that doesn't help you in finding the areas of things that the rest of the world calls "heart shaped". Whether that matters to you or not depends on why you need to know. It's important to be clear about this kind of thing. SteveBaker (talk) 15:07, 12 April 2009 (UTC)[reply]
I think the OP is talking about his follow up question, the area of a pentagram. If you are suggesting a pentagram is double the area of the central pentagon, then no, that is not the right answer. Just follow the link to the Mathworld article I gave you above, it has the formula for the area of a pentagram. SpinningSpark 19:17, 12 April 2009 (UTC)[reply]

Perhaps the most straightforward-to-calculate and pretty-good approximation would be a square with semicircles attached to two adjacent sides. If it's a unit square (side = 1) then the radius of the added circle is 1/2 and the area of the "heart" is 1 + pi/4. --Scray (talk) 21:46, 12 April 2009 (UTC)[reply]

I'm shocked at how closely the OP's equation approximates the area of the heart in his diagram. I counted the pixels that make up the heart and found the actual area to be around 103 000 pixels. The equation gives 99 000 pixels, only 4% off the real answer! --Bowlhover (talk) 04:13, 13 April 2009 (UTC)[reply]

about baby

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how baby get develop and how is process get out of it? —Preceding unsigned comment added by 116.74.227.89 (talk) 05:08, 12 April 2009 (UTC)[reply]

Human embryogenesis may help. SteveBaker (talk) 05:13, 12 April 2009 (UTC)[reply]
Can you be more specific, are you asking about a specific organ, or organ system?? Maen. K. A. (talk) 12:59, 12 April 2009 (UTC)[reply]
I think this question is about prenatal development and childbirth. Axl ¤ [Talk] 20:30, 12 April 2009 (UTC)[reply]
This is close enough to a popular internet meme to make me wonder if the question is entirely serious... -- Captain Disdain (talk) 13:37, 13 April 2009 (UTC)[reply]
Hence the curt, strictly factual, here-is-a-boring-link-to-something-that's-not-porn, one-line answers. SteveBaker (talk) 14:12, 13 April 2009 (UTC)[reply]

Transmition Of Aliment

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In the table at Basic reproduction number, it says that smallpox is transmitted by social contact. Does this mean that not only can it be transmitted via dermatological contact, but via air (but only when the vectors are close) as well?68.148.145.190 (talk) 10:37, 12 April 2009 (UTC)[reply]

See Smallpox#Transmission. The main mode of transmission is airborne droplets. But I don't think that is implied by the phrase "social contact", which can mean a variety of other means. SpinningSpark 13:09, 12 April 2009 (UTC)[reply]

Evolutionary advantage of oral sex, fellatio

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I don't know about cunnilingus but is there an evolutionary advantage in terms of natural selection in fellatio? If a pregnant woman performs this act on the man who got her pregnant it makes it less likely that he will go chasing after other women. Do you see what I mean.--I love onions (talk) 11:19, 12 April 2009 (UTC)[reply]

the book Sperm_Wars covers this topic --Digrpat (talk) 11:43, 12 April 2009 (UTC)[reply]
From the female point of view, any act which will tend to keep the man around longer will tend to allow her children to be at an advantage, increasing her ability to pass on her genes. From the male perspective, its a damn fun time... --Jayron32.talk.contribs 04:26, 13 April 2009 (UTC)[reply]
Well, optimally, it's also a damn fun time from the female perspective. -- Captain Disdain (talk) 13:35, 13 April 2009 (UTC)[reply]

Plant growth/death

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I have a houseplant which has what I would call a greenstick fracture on one of it's stalks. I would have expected one of the following results:

1) Plant fully recovers.

2) Plant dies.

3) That stalk dies.

4) Everything after the fracture on that stalk dies.

But, to my surprise, everything on that stalk before the fracture died (all the leaves shriveled up and fell off and the stalk itself turned from green to yellow), while everything after the fracture looks nice and healthy. What's going on here ? StuRat (talk) 15:32, 12 April 2009 (UTC)[reply]

My guess is that the phloem was damaged, leading to starvation of the roots and all the lower parts of the stem. Alternately, the damage triggered ethylene production (or some other stress-related hormone), which caused senescence in the lower part of the stem. Guettarda (talk) 20:33, 12 April 2009 (UTC)[reply]
Remember that plant stalks are two-way transport systems. Water and trace elements from the roots travels up to the leaves - but sugars and starches from photosynthesis in the leaves have to travel down to keep the root system going. I guess the lack of photosynthesis products heading down beat out the lack of water & trace elements going up. SteveBaker (talk) 20:46, 12 April 2009 (UTC)[reply]
The two-way transport is something I also thought of later. If the upward transport occurs in the undamaged core while the downward transport occurs in the ruptured outer layers, then I may have my answer. Does anyone know if that's how plants work ? StuRat (talk) 02:13, 13 April 2009 (UTC)[reply]
That happens to be exactly how plants work. The phloem, which mostly transports products of photosynthesis from the leaves down to the roots, forms the innermost layer of bark. The xylem, which carries water up from the roots, is part of the dead material inside the bark. See this diagram. --Bowlhover (talk) 04:09, 13 April 2009 (UTC)[reply]
Yes and what's being described here even has a name Girdling or ring barking Nil Einne (talk) 10:27, 13 April 2009 (UTC)[reply]
Thanks for the link. That article doesn't mention that initially the plant dies below the injury while the top thrives (except for the mention of using this method to develop larger fruit, which somewhat implies that). It also mentions that the plant eventually dies completely, which I was afraid might happen. Does the phloem ever regrow ? StuRat (talk) 14:39, 14 April 2009 (UTC)[reply]
If the roots are dead, there's not much hope of recovery. The best bet would be to cut the plant off above the damaged bit and try to root the cutting. The best way to do that depends on the species. I would recommend asking at WP:PLANT - with either the name of the plant, or a good picture. Guettarda (talk) 14:45, 14 April 2009 (UTC)[reply]
Well it does mention the roots die first although perhaps it's not clear enough "In this process, the xylem is left untouched, and the tree can usually still temporarily transport water and minerals from the roots to the leaves until the roots die. Death occurs when the roots can no longer produce ATP and transport nutrients upwards through the xylem." However it doesn't really say the top thrives first so definitely could be improved. As Guettarda mentioned, if the roots are dead, the chance of recovery is slim to none. Successful ring barking I believe usually removes not just the phloem but the vascular cambium too (if present) meaning the phloem can't really regrow although trees can sometimes do suprising things. [1] is of some interest here as is [2] & [3] I expect if you have access Nil Einne (talk) 22:40, 14 April 2009 (UTC)[reply]

Update: The portion of the plant above the fracture has now started to die, too, beginning with the fracture and moving slowly upwards. StuRat (talk) 15:32, 15 April 2009 (UTC)[reply]

What bird is this?

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Does someone know what kind of bird this might be? (Picasaweb) I don't have the slightest idea, it doesn't really look like some parrot. It is very likely that it recently escaped from someone. Thanks, --Dendre (talk) 17:13, 12 April 2009 (UTC)[reply]

Nevermind... most probably it is Green Rosella. Took me some time, though. Thanks anyway --Dendre (talk) 18:16, 12 April 2009 (UTC)[reply]

What is the name of this bird?

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Does anyone know the name of this bird, photographed in Southern Germany? It is likely to be a very common bird. But I am not an expert at all in this area... Thanks. --Edcolins (talk) 18:48, 12 April 2009 (UTC)[reply]

With the low resolution silhouette, we can't be sure. It looks like a passerine. A senior consultant once taught me "Sparrows are more common than canaries." So I guess it's probably a sparrow. Axl ¤ [Talk] 20:18, 12 April 2009 (UTC)[reply]
You might also wish to check through List of birds of Germany. From your picture it's really hard to tell. 76.97.245.5 (talk) 21:30, 12 April 2009 (UTC)[reply]

Stability of 3 particles

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Two identical positively-charged particles are held stationary, while a third positive particle is placed in the exact middle and given a small force F at an angle "b" from the horizontal. What angle(s) can "b" be if the particle does not escape?

My math (and my textbook) give me b < 54.7 degrees, while intuition and Working Model say b must be 0. Please help! --99.237.234.104 (talk) 21:26, 12 April 2009 (UTC)[reply]

Something must be missing in your statement of the problem. Looie496 (talk) 23:08, 12 April 2009 (UTC)[reply]
Unfortunately, the original problem is in Chinese, so I cannot copy it here exactly as written. I am quite sure, however, that nothing is missing. Why do you think additional information is needed? --99.237.234.104 (talk) 23:45, 12 April 2009 (UTC)[reply]
Quantum physics may yield a different solution, but in classical physics, this arrangement (as stated) appears to be an unstable equilibrium. Both of the first two particles are exerting equal but opposite forces on the third, so the net force is zero. As soon as any outside force is applied from any angle other than the axis of the three particles, the third particle will leave its equilibrium position and will accelerate away. A force applied exactly along the axis of the three particles is a special case, and will not destabilize the system. -- Tcncv (talk) 23:19, 12 April 2009 (UTC)[reply]
No quantum mechanics necessary, because I've yet to learn it. You analyzed the problem the same way I did, but the textbook choose an arbitrary position P very close to the unrestrained particle's initial position, O. It then expressed the component of the electrostatic force acting in the direction PO as a function of "b" and noted that this component only acts toward O if b < 54.7 deg. Did the textbook make a mistake, and if so, where? --99.237.234.104 (talk) 23:45, 12 April 2009 (UTC)[reply]
As presently stated, the situation described is indeed an unstable equilibrium. But if you add the extra requirement that the particle is restrained to move along only one direction, like a bead in a wire, a short calculation shows that the critical angle , where the transition from stable equilibrium to unstable equilibrium happens, is given by which gives . Dauto (talk) 04:24, 13 April 2009 (UTC)[reply]
Thanks, but can you explain how you got that angle? Also, why is the reasoning below not valid: if the particle's velocity has any vertical component, no matter how small, the particle would be displaced vertically from the axis. A vertical displacement causes the two stationary particles to exert a force pushing the particle away from its initial position. Therefore, the system is only stable if theta = 0 degrees. --99.237.234.104 (talk) 05:11, 13 April 2009 (UTC)[reply]
Your reasoning is fine for the unrestrained case which really is unstable. For the restrained case (bead on a wire) the wire also exerts a force on the bead that cancels the components of the other forces that are perpendicular to the wire. That helps stabilize the system. I'll see if post a more detailed explanation later. Dauto (talk) 06:01, 13 April 2009 (UTC)[reply]
OK, just to avoid confusion: the particle is not literally restrained by a string. Instead, we can pretend that the only force which can disturb the particle acts at an angle "b" from the horizontal. For this case, are you saying that the system is unstable if "b" isn't 0? --99.237.234.104 (talk) 06:52, 13 April 2009 (UTC)[reply]

When you 'pretend' that only disturbances along the direction b are to be taken in consideration, you are effectively restricting the motion of your test particle, preventing if from moving along any directions perpendicular to the one you stipulated. That is equivalent to the bead on a wire prescription I used. May be your text book didn't make that clear enough and that's the source of your confusion.

To make things as simple as possible I will assume that all three particles have unit charges . I place the first two charges on the x-axis one unit-length away from the origin in oposit directions and the third at a small distance from the origin along a direction that makes an angle with the x-axis (I don't like using roman letters for angles). is small enough that any quadratic terms (or higher) will be considered negligible and will be dropped.

The total electric force acting on the third particle is the sum of the forces due to each of the first particles.

Each one of the forces is given by Coulomb's law

where is the unit vector in the direction.

So we have

where, as stated before, quadratic terms on have been dropped.

Where I performed a Taylor's expansion. Now we calculate the forces

Adding the two forces above, we get

Since we are only interested on the stability along the direction of the displacement, we take the scalar product of the force above with the position vector , and check for its sign

If the product above is negative, we have stable equilibrium. If it's positive, the equilibrium is unstable. The critical angle is given by

degrees

Dauto (talk) 18:24, 13 April 2009 (UTC)[reply]

Begining of time

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I saw this in an episode of Justice League. I was browsing through the programs, stumbled upon it, wikied it but couldn't find what was in the episode. It was about a guy who invented a time machine and used it to such a state that the space-time fabric began to rupture. So he decided to jump to the begining of time to reset everything. Then somebody said that it's a universal law : nobody can see the begining of time. Is there such a law? Or legend? Or mith? I think it's very interesting. All I could wiki on the subject was the Plank era —Preceding unsigned comment added by 95.76.242.3 (talk) 21:29, 12 April 2009 (UTC)[reply]

If you believe the Big Bang theory, then at the beginning of time, the entire universe occupied less space than a single atomic particle. So where could he have jumped back to? Looie496 (talk) 23:05, 12 April 2009 (UTC)[reply]
Time travel is fictional, so the writers can make up whatever "laws" they like for it. But: to restart time, wouldn't you have to get to before the beginning? —Tamfang (talk) 23:08, 12 April 2009 (UTC)[reply]


Sure, that makes sense. But I think the authors were refering to some kind of legend or something. The guy was in this tunnel when he "jumped" and at the end of it there was a hand with a spiral of a somewhat blue color on it that was flowing so I guess this is what I read about on wikipedia namely that time flows. As he got closer, the hand started to close its grasp on the spiral. Managed to get a picture of it, courtesy of wikia.com. [4] I hope there's more to this than just some sleepover idea. It would be interesting. Thanks for your answers, guys! —Preceding unsigned comment added by 95.76.242.3 (talk) 07:46, 13 April 2009 (UTC)[reply]

Well the big blue hand is nothing to do with science but the concept of not being able to get back to the beginning of time being a law may be vaguely taken from the Planck time. It is the shortest meaningful period of time (and it is very short). At a time closer to the big bang than the Planck time all our known laws of nature can no longer be applied, and consequently science is not able to provide any information on what may have happened in that time, it does not even make sense to say something happened there. SpinningSpark 14:03, 13 April 2009 (UTC)[reply]
This is fiction - it bears no resemblance whatsoever to reality. As far as we can tell, time-travel is completely impossible - or at least so insanely impractical as to be effectively impossible. So this is a non-question. What would happen if something impossible happened? It's impossible to say. Feel free to make up any answer that makes you happy! SteveBaker (talk) 14:09, 13 April 2009 (UTC)[reply]
At the very least I believe our current understanding of physics says that, even if we can overcome the various problems with creating a time machine (eg. we find some matter with negative mass), we still wouldn't be able to travel back to before the time machine was created so travelling to the beginning of the universe would certainly be impossible. --Tango (talk) 12:39, 18 April 2009 (UTC)[reply]

Pharmacology question - IC50s

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I'm writing up a lab report for college and have a problem. I've got some 'logIC50' values for my antagonists but if I take the antilog of these, what are the values that I'm left with. I read in the IC50 article that they may be the 'pIC50' but wasn't sure if that's right. Is there a way I can make the data I've got more understandable - to me at least? Please help. Out of my depth. Thanks. 94.193.240.88 (talk) 21:43, 12 April 2009 (UTC)[reply]

Our IC50 article defines the term as "half maximal inhibitory concentration", i.e. the inhibitor concentration at which the reference activity is reduced to half-maximum. Does that help? --Scray (talk) 21:50, 12 April 2009 (UTC)[reply]
Not really. It's more a problem of working with the logs and what different values mean in terms of how potent the drug is. Like, if my logIC50 values getting bigger, does this mean it's more or less potent...thanks, anyway —Preceding unsigned comment added by 94.193.240.88 (talk) 21:52, 12 April 2009 (UTC)[reply]
Sorry - did not realize that's where the problem was. Say that you have two substances A and B; A has an IC50 of x for this enzyme, and B has an IC50 of 10x for the same enzyme. A is more potent than B, because at the same concentration (x), A inhibits enzyme activity by 50% while B at that concentration will inhibit less than 50%. Log transformation affects the magnitude, but not the direction, of these relationships. --Scray (talk) 01:13, 13 April 2009 (UTC)[reply]

Exact burn temperature of skin

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It's all in the title. If you think this is medical advice, I'll walk away with no argument, but I don't think it is. If "exact" isn't possible, then the nearest thing is fine. Thanks Vimescarrot (talk) 22:26, 12 April 2009 (UTC)[reply]

There is no exact burn temperature, and not really even a "nearest thing". Skin surface temperatures up to about 120F can be tolerated for a long time. Above that level, the higher the temperature, the quicker a burn will appear. A temp of 150F will produce a burn in a few seconds. See this web page. Looie496 (talk) 23:02, 12 April 2009 (UTC)[reply]
In hot water, yes. But values are different for hot air (and probably different for different humidities). --Polysylabic Pseudonym (talk) 08:27, 13 April 2009 (UTC)[reply]
And I'll add, do you mean:
  • Hottest oven you could put your arm in for a few seconds
  • Hottest day you could survive
  • Hottest water in which you could bathe
  • Hottest sauna in which you could spend half an hour
  • Or (obviously) what your title asks - at what temperature will skin char or ignite.
--Polysylabic Pseudonym (talk) 08:46, 13 April 2009 (UTC)[reply]
Let's go for...coolest water in which you could bathe and still get burned. Vimescarrot (talk) 14:15, 13 April 2009 (UTC)[reply]
On the other hand, that chart in the link up ther seems to answer my question nicely. 49 degrees C? Cooler than I thought... Vimescarrot (talk) 14:16, 13 April 2009 (UTC)[reply]
That would take 10 minutes to burn you - there would have to be something stopping you from getting out in that time. Either that, or you have amazing pain tolerance. --Tango (talk) 12:41, 18 April 2009 (UTC)[reply]