mooeypoo

Helloo.. I have a function: (have no clue how to write a { 'group' for an equation in LaTeX.. did my best with what I could find..): [math] f(\theta) = sin^2(\theta ) \text{ when } 0 \le \theta \le \pi [/math] [math] f(\theta) = sin^2(\theta ) \text{ when } \pi < \theta \le 2\pi [/math] with values of the function given by periodicity for other domains of theta. Obtain the Fourier series expansion for f(\theta). Okay, so we've only done this once in class on the board, and it was with a completely different equation - one without 'conditions' for that matter, just periodicity (a saw-tooth function). I am having trouble doing this one. Okay, the periodicity on this function is 2pi. So here's what I started with: [math] a_{n} = \frac{2}{2\pi} \int_{0}^{2\pi} F(\theta ') cos(n\theta) d\theta ' [/math] [math] b_{n} = \frac{2}{2\pi} \int_{0}^{2\pi} F(\theta ') sin(n\theta) d\theta ' [/math] And so [math] a_{n} = 1/\pi \int_{0}^{2\pi} sin^2(\theta ) cos(n\theta) d\theta ' [/math] [math] b_{n} = 1/\pi \int_{0}^{2\pi} sin^2(\theta ) sin(n\theta) d\theta ' [/math] I am not sure how to go from here. I had an idea that I need to check what happens to my cos() and sin() - so, the sin will equal 0 every even n (n=2,4,6,8...) because that would make the theta in it in the domain of 2pi, but that doesn't happen to all values of theta, so that doesn't help me much. How do I expand this!? Anyone has any *useful* resources? I found some websites talking about Fourier Expansion but they don't quite explain, they give out a formula and state that this is the expansion - and my case the function is conditional... so.. I have no clue what to do. Help! Thanks ~moo

Hmm.. I'll have to try again when my head's clear, it's possible I am just overworking myself and missing an obvious. If you don't mind -- could you just verify that my *set up* is good? That's all I'm concerned with, since those are my problems. If I set it up well, for sure, then I think I understand and will be able to do it again. I just need to practice now, and I hope I am not perpetuating a mistake .. Thanks!!!!!! ~moo

I thought that the z vector notation came from my \rho definition, but I don't think that was right. In any case, I do know dirac delta (errr a bit.. we learned that in some depth a few lessons ago) but I 'simplified' it automatically (the book and the professor seem to do that all the time, I figured it's the way to do it) to apply to a line charge. If we were talking about a volume (like a charged sphere), then my \rho considerations would have been accross all space (I had a few questions like that with \rho function that isn't linear, hence we were supposed to integrate to get the Qenclosed and the Electrical field, etc). I must say I am now completely stuck in the integration... Is this integral even possible to solve? Or am I just letting the bunch of numbers in there confuse me..?

Thanks, I was looking for that.. Egh, yeah, I see .. I confused myself too much, and neglected the simple fact that first you add/subtract first to get the distance vector... okay.. i think I got that one now. I didn't think about that (that I do the minus in the integral), that's a good point.. okay. I agree. The book has the worst notation EVER, using variable squiggly forms of "r" and the professor is writing on the board with even WEIRDER notation, along with the fact he's insisting on using cursive (which I am having huuuuge difficulties with). So I am left with trying to figure this out on my own, hence my confusion. Please bear with me here, I'm sure that you're right - when I understand exactly what the integral means, I will have no more problems. I thought I did, though so.. I am not sure now. The book is using squigglies and bolded version of r to differentiate between r the vector, r the distance and |r-r0|. I'm desperately trying to make sense of those but they're REALLY confusing. As far as I understood, [math]V® = \left( \frac{1}{4\pi \epsilon } \right) \int \frac{\rho (r')}{r} d\tau ' [/math] (the notation r' is, in the book, bolded, and written exactly like that - with the 'prime' notation. so is the d\tau) r is the distance to the source (the magnitude of the vector \vec{r} to the source point). r' is the vector of the point or points of integration. d\tau is integration in all space. In my case, it's a line integral. So.. putting it this way, [math]r= \sqrt{a^2+b^2+(c-z)^2}[/math] [math]r'= z\hat{k}[/math] [math]\rho (r') = \lambda dz [/math] And so the integral should be: [math]\frac{1}{4\pi \epsilon} \int_{-L}^{0} \frac{\lambda}{\sqrt{a^2+b^2+(c-z)^2}} \hat{z} dz [/math] Does that seem better? I have a feeling I might've missed another z on the top, but I'm not sure, since it seems that my rho is set up correctly, but i"m ... not sure anymore.

As discussed earlier in many posts, threads and IRC chats late at night with you, traveler, as much as you want to fight against this, General Mechanics (force/power/velocity, F=ma, for that matter, and your power definitions) do not explain everything. As we've discussed on IRC before, the subatomic is not consistent with "F=ma" (which is, btw, by itself, very simplistic, as the actual formula is F=m dv/dx ). Neither do variable stars, for that matter. Quazars are a good example. Good luck explaining those with only F=ma in your arsenal. you seem to be ignoring everything outside of General Mechanics. Then, things make no sense to you (as they should, since they don't work with that theory, like behaviour of subatomic particles), then instead of doing the scientifically-correct thing and reexamining your methodology, you force your theory on the problem and insist that existing phenomena do not happen. Ignoring reality does not make reality different than what it is.

all hail overcomplicating myself. Help, seriously, I'm sure I'm stressing out over nothing and hence doing things wrong for just confusion, but.. I'm trying.. [math]\overrightarrow{x} = a\hat{x}+b\hat{y}+c\hat{z}[/math] and [math]\overrightarrow{r} = -z\hat{z}[/math] So.. uhm.. [math] |r-x|=\sqrt{a^2+b^2+c^2-z^2} [/math] Which would make my integral: [math] V® = \left( \frac{1}{4\pi \epsilon } \right) \int \frac{\rho ®}{r} d\tau = \left( \frac{1}{4\pi \epsilon } \right) \int_{-L}^{0}\frac{\lambda dz}{\sqrt{a^2+b^2+c^2-z^2}} [/math] Is that right??

Hey guys, I have a hw question I'm completely stuck with.. I know which formula I am supposed to use, and I know how, in theory, this should be solved, but I'm having trouble seeting up my vectors. This is a problem I'm constantly having.. I know how to generally solve questions like these, as long as the vectors are 'easy' (on the origin, or stuff like that). The moment the vectors are a bit more complicated, I confuse myself to oblivion. So.. help me out, please, and if you can, explain *how* you do this, so I can finally get rid of my uberconfusion over these type of questions... So, I know that the electrostatic potential can be found by: [math]V® = \left( \frac{1}{4\pi \epsilon } \right) \int \frac{\rho ®}{r} d\tau [/math] And I know that: [math] \rho ® = \lambda dx [/math] But.. but... my r. meh. I'm getting confused setting up the vector r (distance from the arbitrary point to the line charge). Help me... don't solve the equation, please, just help me see how to set up the r vector, so I can continue on my own. Thanks! ~moo

I love Erik Von Danniken, I think his stories are imaginative and interesting, and the move "Stargate" (as well as the show, even more) is one of my favourites. But to go from that to stating it's realistic.... not so much. There are a few problems with Von Danniken's theories, the least of which is that he has no proof. If you research what he is writing online, you will see that some of what he wrote is not only baseless but misleading (that means that the 'evidence' he saw weren't.. really.. there...), or with high possibility to be fake. Regardless, he never offered any of the more tangible evidence (little statues, artifacts, etc) for outside examination which is another suspicious point as to their validity. Another point is that everything he describes -- from the structures that have huge stones that "fit perfectly to one another" to huge temples at the edge of cliffs that seemingly "couldn't have been built there without transporting the stones by flying" (or something of this sort) can be - and are, usually - completely explainable through a simpler, more realistic theories. Also, he seems to slightly ignore facts that don't suit him. For example, he claims that the huge drawings on the ground, made by the Maya I think, in Peru and other places, could not have been made by people on the ground - there must be someone watching from above to make sure the drawing comes out right, because it's so big. But that's *proven* to be false -- there was a group of researchers that created such a drawing on the ground without "looking" from above, within a few days, and succeeded greatly, and they've used only equipment that was available 2000 years ago... The stories are very interesting and they do offer an imaginative explanation to the way things look in the world -- but so does "Buffy, Vampire Slayer", and so do "Charmed" and so does "Firefly". That's the point of good stories -- that they SOUND realistic. They sound as if they actually explain everything. That's the beauty of a good author. But if we want to actually see if they're realistic, we need to critically examine the proofs and see if they fit reality and can explain things. And frankly, they don't. ~moo

Go learn physics, seriously, and stop trolling. Your physics claims are hideous. I'm calling the cavalry.

There is a spring mattress in the middle of the desert. A ball is, theoretically, bouncing up and down on top of it continously. The ball has velocity. It is moving. It will also never reach the center of the Earth. You are ignoring our questions and again jumping from subject to subject in hopes we will forget. We didn't. You're disobeying the rules. Troll. Reported. I suggest you read the rules again.

Troll. Reported. Read the rules.

You are either trolling on purpose or your memory is shorter than an ant's. Here's a summary of the thread: Post #1: in post #2 insane_alien points out that the sun is PLASMA, and not liquid and gas. Raises another question of why wouldn't more planets be formed the same way. In post #4 big314mp points out the Sun doesn't have the proper elemental composition to "spit out" planets. Post #3: Post #5: Klaynos raises the point that trillion years is longer than the universe (hence irrelevant), and that we know how old the sun is. Post #6: Post #7: Klaynos states that traveler's theory lack the percision that current theories do have, therefore they have more to offer over traveler's theory, they are more accurate, and therefore there's no reason to see traveler's theory as better. Post #8 traveler distinctly ignores Klaynos remark about the reason the other theories are more valid and states: Post #9: Klaynos points out there are no references to traveler's claims. Post #10: Repeating the point of #8 while ignoring, it seems, both of Klaynos' explanations. Lastly; Rephrasing (and hereby changing completely the meaning of) "Ice Giants" to "Outer Planets" (that are, by no means, Ice Giants). Post #11: Klaynos is repeating posts #9 and #7, and asking again for references. Post #12: traveler is repeating his insistence on ignoring Klaynos now 3rd time answering his question about the validity of his theory, again ignoring request for substantiation. Post #13 and #15: Klaynos explains the meaning of science and the importance of the scientific method. Finally, explaining why physical theories must be validated by mathematics as well. big314mp adds to Klaynos' points with the same spirit. Post #14: Contain some version of red herring and anecdotal references, no actual references, no substantiations, on the part of traveler. Post #16: traveler's version of what gravity is; no substantiation, no references, blatant jumps from subject to subject - and ends up with an unsubstantiated version of planet formation: Posts #17, #18, big314mp and yourdadonapogos try to point out what current planet formation theories state, and add observations. Post #19: traveler regresses to arguing about validity of theories regardless of evidence. Finally, claims that No substantiation, no reference, and absolutely no physics. Post #20, #21, #22: big314mp, Klaynos and Edtharan point out there are no proofs and substantiation to any of traveler's claims. Edtharan seems to do a good job (as usual) explaining (again in this thread) the point of the scientific method and the necessity for reference and proof. Again, claims that the other theories do have proof and traveler's theory has no proof whatsoever is raised. Traveler is asked to provide substantiation. Post #21 BabyAstronaut points out this is a moot discussion, since the arguments supplied by traveler are unsupported by reality or by any sort of proof. Post #22: traveler tries to argue no one knows better than him, and attempts to convince everyone that his theory is correct despite evidence to the contrary by supplying absolutely no evidence. Post #25, #27: Kyrish joins the parade and - AGAIN - states traveler is speaking with no substantiation about theories that are proven OTHERWISE. big314mp raises more points that are posing a serious problem to traveler's theory. Finally the thread moves to Speculation. Post #28: traveler tries to convince everyone that he has supplied evidence. Then, that others haven't. Posts #29,#30, #31, 33 - Klaynos, Sayonara, Edtharan and elas explain again that the current theories are more valid than traveler's theory, and that traveler must supply evidence and math to support his claims. Post #32: traveler claims he has no theory, but rather an idea. Post #33: Sayonara points out the inconsistencies in traveler's claims. and on and on everyone try to point out the same. Post #38: traveler asks a seemingly unrelated question: Many replies are confused as to how this is related to anything on the thread. On the next posts, traveler tries to claim it is, with no substantiation, no proof, no connection. When it is pointed out that the two subjects are unrelated, he claims they are, again with no proof or substantiation. And on. And on. And on. To sum this up, traveler: You have raised an idea/hypothesis/theory that is inconsistent with current observations and factual data. Your idea/hypothesis/theory does not support ITSELF. Your idea/hypothesis/theory does not have any validation or substantiation, no referencing whatsoever. Any attempts to get you to bring anything forward resulted in you totally ignoring it. Not once in this thread have you posted any mathematical equations or mathematical computations that shall attempt to validate your theory. You have been consistently ignoring our requests for references and substnatiations and any question you dislike you answer back with an emotional retort of the spirit of "you claim I'm hallucinating??"; a red herring at best, an attempt at personal attack at worst. You are not doing science, it seems you don't understand basic physics, but the worst of all is that you seem to think no one knows better than you. Your theory is unsupported in reality, has no math, cannot predict anything and is based on flawed physics. You have just failed peer review. Welcome to the club. ~moo

It's all the same why? bcause you say so?? It's NOT all the same, and if you claim otherwise you need to do much more than just CLAIM it's all the same. This is a SCIENCE forums, not a fantasy writers forum. The fact you're in love with your own theory does not make it REALISTIC. Math, factual data and scientific substantiation, MIGHT. ~moo

Okay the above "equation" is meaningless without units.. what are you subtracting.. forces? Please mark your numbers with proper units so I understand what you're doing. If you ARE subtracting forces, then "100" and "75" are forces applied on your system in different direction, and "25" is the net force. Since I have no idea what you're talking about in terms of physical system - is this a simple mechanical system like 2 people pushing from opposite directions? is this a system of charged particles moving one towards the other? what is it? - I can't answer as to what they are. I can't know. I'm also still waiting to see how this fits into gas pressure.

Generally speaking, Force is whatever can cause an object with mass to accelerate. You can see that definition through the famous F=ma equation. It is, of course, a bit more complicated than that when you go into details or other subjects. There was a need to redefine force in electrodynamics, for example, since it is not QUITE the same definition as force above. An electrostatic force is defined as existing intrinsically between two charges. In other words, unlike the general definition of force, an electrostatic force will not cause any mass to accelerate, but rather masses with a certain charge. Those are definitions taht were invented by human beings to describe physical phenomena. The fact those two definitions use the same word - "FORCE" - does not mean that the phenomena is equal. That's a very broad answer, since I'm trying to understand what it is you're trying to get at here.

Read the resource I put up, it actually answers your question with those nice images.

http://www.grc.nasa.gov/WWW/K-12/airplane/pressure.html And about the sun: source: http://www.astronomynotes.com/starsun/s7.htm Equilibrium (or not, but that's a different subject altogether) between forces; between pressure and gravity:

That's not the only way. At least 4 people explained to you what the other = REALISTIC, PHYSICAL = ways are. At least 3 people explained, about 3 times already, what pressure is. You are ignoring them, and you keep repeating the same questions that were ALREADY ANSWERED. Troll. Reported.

... Okay, now prove it. Uhm, also I don't quite think the pair of words "NET FORCE" applies as a "unified theory".

Your comparison is wrong, and your attempt to explain what you mean by mixing different subjects of physics is not helping and is confusing. Go back to the topic at hand and stop jumping all over the place; you were talking about pressures, and people answered you, but you obviously didn't like their answers, because you kept claiming no one made a decent reply -- so how about you just, as straight forwardly as possible, without unneeded comparisons or opposing questions or anything that makes things more complicated than they are, just ASK your question. What do you want to know? What, exactly, in gas pressures doesn't work for you? what is it you disagree with you wonders about? Just ask to the point, my goodness, and stop jumping around in physical concepts that have nothing to do with one another.

Are you claiming that in order to see what goes on with pressurized gasses we need to look at torque? You need to go back to 9th grade physics, my friend, seriously now, I don't even know where to START explaining how wrong this entire discussion is. You are completely oversimplifying physics, is what you are. It's as if I will claim that an apple will keep bouncing endlessly after falling from a 7 story building because of Newton's laws of 'every action has a similar and opposite reaction'.

Yeah, dude, you're all over the place. What does torque has to do with gas pressures?!

I can't help it.... it's the physics... it's screaming for my help!!!!

okay wow, things are going too fast for me to answer. give me a second here. Human being is NOT a good example because the human body doesn't apply constant force; it has varying other conditions that can slow you down or not slow you down. It's a BAD EXAMPLE, because it's NOT THE SAME *physically*. Different processes with the same apparent (note: APPARENT, not complete) result are *NOT* the same, and they should not be equated. I still don't get how this is related to the expansion of gases if you surround the sun, or anything else about PRESSURE.

This is a bad analogy, since the human body gets tired (unlike a force.. or an atom...); the answer is non indicative, then. The mere proposition that "you give it everything you have" is showing you that it is a wrong analogy. I still don't see what you're trying to say and how this has anything to do with relative anything, or with pressure... the proper way to make a comparison or to understand the process that goes on under pressures is to represent it mathematically. That would be much better than trying to use non-equivalent systems like the human body and atoms. Maybe so (again, read what I wrote about the human body -- you have more consideration there, therefore it's NOT a good analogy) but even so, the term "work" is MUCH different in everyday life and in physics. For that matter, if I am preventing a -q charge - as strong as it may be - from getting closer to a +q charge, I can be almost-dying from stress, and using the help of a truck to prevent the charge from moving, and yet my BODY might be "working" but in physical term the system has no work. Because the -q charge is NOT moving.