Bignose

No. The mass (weight) doesn't matter. Assuming it remains constant (and there is no reason not to assume this in this problem) it drops out of the equation. Drop a bowling ball and a tennis ball from the same height and they will hit the ground pretty much simultaneously. One can only say "pretty much" because the different balls will experience different drags, but the results are quite close. Once you can remove the atmospheric drag, any two objects can be dropped at the same time and hit the ground at the same time. The Apollo astronauts proved that by dropping a feather and a hammer at the same time on the Moon and they hit the ground at the same time. Please see this link http://er.jsc.nasa.gov/seh/feather.html

It's an unfortunate happenstance that the common word and the scientific word have in many regards opposite meanings. But, that's the way it is. Unless we get all the scientists in the world together and say: ok, from now on we're not going to call theories 'theories' anymore, we're going to call them 'boogers' or 'peacocks' or 'super-theories' or 'dresses' or 'clocks' or 'schplitzes' or whatever. The word is going to stick, just like all the other unfortunate words stick. The best thing to do is to educate people as much as possible what the word means in a scientific sense.

Questions about why really kind of wander in to the realm of philosophy more than science. Science, physics in this case, isn't so much interested in the why as how to describe it mathematically so we can make predictions. Perhaps in the quest to describe it better, the why will come out, but that isn't a primary goal. The evidence for the description as given is very, very strong. They didn't just pick this description because it was their favorite story, this is the current model because this is what the evidence points to. The current model is testable and can make predictions that can be verified. It certainly isn't complete, but it is good within its known limitations. You can read about it in many physics books. Just because you can't understand it, doesn't mean that it is wrong. I don't understand all of the inner workings of my computer, but I know it does work. I don't understand all the inner workings of the physiology of people, but I know it works. I trust the words of the experts who have studied computers and chips and cell functions and organ functions. I think that you're going to find it very hard for someone to "do the math for you" because the evidence for the current model is strong. You have to provide the evidence that the current model is wrong, or that your idea does as good and better of a job than the current model. Like I said, they didn't pick it just because it was everyone's favorite -- the current model is the current model because it does the best job. Not to pile on you here, but perhaps had you stayed in school and learned about the current model, you would have learned just how good the evidence is for the current model and how it was obtained. You don't necessarily have to be in school to do this, however you do have to make the effort to go out and learn it yourself. But, without knowing about the current model, how can you fairly critique it?

Edgar, While I am completely unfamiliar with anything by Saxon, I would like to just say a few words about repetition. In a lot of things, knowing how to do something and owning how to do something are very different. Case in point from my own life, I know how Albert Pujols hits a baseball, but I cannot copy it, time after time. Once in a while I can hit a baseball hard and far, but nowhere like Pujols can. I know how Tiger Woods hits a golf ball long and hard -- I know what actions he makes in what order he makes, and while I have hit a golf ball a far way once in a while, again, nowhere nearly as consistently as Woods can. Now, I cannot deny that each of them have a significant amount of natural born talent -- but, a primary reason I am nowhere near either of them is also lack of practice. Through practice, you don't just know how to do something -- you own how to do it. Maybe a few more examples are in place. I have taken apart and put back together a carburetor -- but I still take my car to a mechanic when it breaks down. I know I could do a lot of the things needed to fix it, given the correct tools and parts, but the mechanic can do it in probably a tenth of the time, because he is an expert. I know I can cut down a tree, but I still called a tree service to cut down four silver maples in my yard -- because they can do it probably one hundredth the time I can, and they are insured -- if they drop it on my roof, they'll have to pay to get it fixed. If I did it, it's on me. Again, they are experts. It is very similar in mathematics. To become really good at it, to really own mathematics, you need to practice. Sure, you knew how to multiply the very first time you were taught how to do it. But the practice resulted in you owning it. You'd be surprised how many people who are in pretty advanced programs do not own mathematics. As an example, in a senior level engineering class I was TA'ing, several people who were working together on a homework assignment at one point has to multiply a three digit number and a two digit number -- and gave me answers with six digits in it. This was 10 or 15 people who all took the answer of the person who punched it into thier calculator at face value. Not a single one said/thought "hey! a number in the 100s times a number in 10s cannot multiply together to get a number in the hundred thousands -- we better check that again" They didn't own their mathematical knowledge. Being seniors in an engineering program, I don't have any doubt that they know how to multiply, but they didn't have an internal check to think about what their answer was and think to re-check the computed answer. Quite literally an example of garbage in, garbage out. Another example from a junior level fluid mechanics class I TA'ed a different semester. The students where asked to calculate how large of a pump would be needed to pump water from a reservoir to the top of a water tower. Several of them came up with answers that were negative -- in other words, they told me in their homework that they would get energy OUT of a system by pumping water to the top of a tower (whose elevation was well above the reservoir's). Again, they just "plugged 'n' chugged" in that they just threw what they thought we the right numbers into the calculator and got an answer and said "done!" They didn't stop to think about what their answer actually said and meant. This is NOT the goal of any education program. Not to put too fine of a point on it, but anyone can read about how to do something and have at least some knowledge of that topic. But, not many people own a topic, and have a strong intuition about it. The repetition ensures that you own it and have a very strong intuition about the subject. In general, I don't think that enough students do anywhere near enough repetition of mathematics problems. There is way too much reliance on computers and calculators. Again, like above, garbage in equals garbage out. And, when you get to calculus, it's going to be the same way. Perhaps in calculus, the repetition may be even more crucial. You will have to develop a good intuition on how derivative and integrals are done, and that can only be accomplished by repetition unless you are some kind of savant. When I TA'ed those classes, again, the students were supposed to have had 3 semesters of calculus and one semester of differential equations, yet I had to review some of the most basic concepts. Edgar, you won't know it yet, but anyone else who read this through will understand how dumbfounded I was was I had to review what the derivative of [math]e^{2x}[/math] was. Or that I had to review separable differential equations. Again, these were seniors and juniors in an engineering program. They had not had anywhere near enough repetitions because otherwise they would have owned these fairly simple problems. So, I hope that you won't turn away from the program simply because of the repetition. It is really the only way you will own the concepts in the program. You said it yourself that it delivers in terms of the tests. That's in no small way because you own the concepts by the time test time comes and a test is no big deal anymore. Once you own a concept, being tested on it is no longer the stressful event most people take tests as. If you don't understand what is being taught, then seek out other sources. There are many, many calculus texts out there. But, again, I sincerely hope that you won't give up on it just because of the repetition. If it way easy, everyone would do it.

even with the missing info (which really is missing CS!), I think that 1-0.9032 is not 0.9068

Just some small points here... that definitely needs to read b^2 in the LaTeX: [math]x = {\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}}[/math] And secondly unless you define what a, b, and c are, this isn't much help. a, b, and c come from the equation [math] a x^2 + b x + c = 0 [/math] whose solutions are given by the equation above.

Every 15 degrees has a "special" representation [math]\sin(\frac{\pi}{12} = 15\deg) = \frac{\sqrt{2}}{4} (\sqrt{3}-1) = \frac{\sqrt{6}-\sqrt{2}}{4}[/math] [math]\sin(\frac{\pi}{6} = 30\deg) = \frac{{1}}{2}[/math] [math]\sin(\frac{\pi}{4} = 45\deg) = \frac{\sqrt{2}}{2}[/math] [math]\sin(\frac{\pi}{3} = 60\deg) = \frac{\sqrt{3}}{2}[/math] [math]\sin(\frac{5\pi}{12} = 75\deg) = \frac{\sqrt{2}}{4} (\sqrt{3}+1) = \frac{\sqrt{6}+\sqrt{2}}{4}[/math] [math]\sin(\frac{\pi}{2} = 90\deg) = 1[/math]

Well, I think that a small correction first. 'Eliminate' is the wrong word, but 'solve for' is right. Eliminate would be get rid of or ignore or remove, but what you want to do is find the value of k and the integration constant, not get rid of them. Ok, well, there are two completely equivalent ways to solve this. Again, I won't do it for you, but I will give you hints. Method 1) You have a differential equation with the differential alone on the left hand side and a polynomial on the right hand side. You can always divide both sides by that polynomial. Then, if you look at your integral tables, you should find some inspiration. Method 2) You can implement a change of variables. Let Z = 100-kR. Then write an expression for dZ in terms of dR. Then, rearrange so that you only have Z terms on one side -- that expression should be directly integrable. Be sure to remember to put the definition of Z back into the final expression when you're done to solve it in the original variables. You should try both methods to confirm that they are in fact equivalent. Both methods are useful, sometimes it helps to look at a table of integrals to inspire you to see what forms may be available with the problem at hand. And, change of variables can be very powerful to simplify very messy situations. Sometimes you need both methods -- a change of variables makes the messy expression into a form that is covered by an integral table. So, both methods are powerful and should be practiced. If you need further help, just ask.

Are you trying to just write an equation or are you trying to solve said equation? Because, it seems to me that you've already written an equation. The only thing you are missing at the moment is an initial or boundary condition. You need at least as many boundary/initial conditions as the order of the differential equation, so far you've written down a 1st order DE, so you need at least one boundary or initial condition. If that's all you are looking for, then you are done. If you need help solving it too, just say so in the thread here, and I can help with that too (though I won't do it for you -- doing homework for you is explicitly against the forum's rules and the spirit of the forums -- I'll give you as many hints as I can).

Small, but significant typo there Dave. The second term in the numerator should be g'h not gh' [math]f(x) = \frac{g(x)}{h(x)} \Rightarrow f'(x) = \frac{h'(x)g(x) - g'(x)h(x)}{(h(x))^2}[/math]

shade, idealizations occur all the time... and incredibly accurately, too. Where should we draw the line? Do we model a golf ball flying through the air, or should we model each layer in the construction of the ball, or should we model every molecule of the golf ball and their interaction with every molecule of air? Heck, that's still an idealization, because really we should be modeling each atom in each molecule, and each proton, neutron and electron in each atom, and each quark in each neutron and proton and each lepton in each electron, right? Shoot, even those may be idealizations of strings, so, once we figure string theory out we won't have to use idealizations at all any more, unless there are substrings or something like that. What the heck is the problem with some idealizations? That is where a lot of the true experience in physics comes in -- when it is okay to make an idealization/assumption and when it isn't and when to go back and double check that your assumptions are valid. It really all comes down to what level of exactness do we need. Do we need to know within one yard of where the golf ball came down? Then we better have a good model of the drag and lift and good initial data on its spin rate and initial velocity. Do we only need within 10 yards? Then maybe treating it as a smooth (non-dimpled) sphere might be okay. Or, do we need to know approximately where Mars is so we can locate it with our telescopes tonight? -- use Kepler's laws of planetary motion. Or, do we need to know where it exactly is like if we wanted to land a probe at a specific place on Mars? -- then more exacting calculations will be needed. It really all comes down to how exacting do you need to be, or how exacting your measuring instruments can be. There are always idealizations in every single problem, where do you draw the line? Even in the unbelievably accurateness of landing a probe on Mars, there are still idealizations -- The gravitational influence of the far away planets are included in the calculations, but they are treated as a point source, not as a full sphere. That idealization turns out to be very, very accurate in certain cases. Is it really that bad to treat it as such? How about an ideal gas like Helium at higher temperatures and pressure? If you treat the molecules as points and derive their properties from that idealization, you get very, very accurate results. Idealization in this case, as well, is perfectly fine. There is nothing wrong with idealizations, when the assumptions behind the idealizations are valid. Why do you think that they are so bad? Why should we insist on dramatically increasing the difficulty of problems when there isn't any significant increase in accuracy? Where does the need or reward or even the desire for that come from? If the easier, simpler problems give the same answers, then they are just as good.

Shade You might want to use the \sin and \cos terms in LaTeX in your equations there, without them, all the text runs together and is very hard to read e.g. [math] \sin^2{\alpha} + \cos^2{\alpha} = 1[/math] or [math] \cot{\alpha} = \frac{\cos{\alpha}}{\sin{\alpha}}[/math] the trig functions are written in a more upright script and there is a space between "sin" and "alpha" that is much easier to read. It gets really hard to read the angle sum and difference equations, for example. [math] \sin{(\alpha \pm \beta)} = \sin{\alpha}\cos{\beta} \pm \sin{\beta}\cos{\alpha} [/math]

dark, do you learn to solve differential equations before you learn to take a derivative? For that matter once you learned the number system, did you jump right to multiplication, division, fractions, decimals? When you take a new job, are you expected to work at 100% maximum immediately or are you given some training first? When you leaned how to read, did you then immediately pick up War and Peace? Of course not to all off that -- you work your way up, dealing with simpler problems and build up a repertoire of knowledge. No one jumps right to the hardest problems first. So, you do idealized problems with no drag, no friction, to start with the simpler problems. Simpler problems also you to check yourself to make sure that you have the basic concepts down before you move on to to harder problems. Many, many of the problem threads on this forum and others could be resolved if the authors/OPs knew the basics before trying the complicated. There are others, but here: ( http://www.scienceforums.net/forum/showthread.php?t=25275 ) is the one I specifically remember. The author there had really had a poor grasp of the basics before he was trying to do more complex things. Using idealized situations allow one to learn to walk before they learn to run. Sure, real life has many, many additional complications. But, you don't throw all those in at the beginning -- you learn the basics and then learn how to include those additional complications later.

If you did this in your lab, what do you think was flawed with the lab, then? Shouldn't you believe your own experiments? and their results? Intuition is a valuable thing mankind developed. The more intuitive members of our species learned to trust their intuition, and not go into the deep grasses when intuition said that there was a tiger in there. But, just because our intuition says that there is a tiger there, doesn't mean that there actually is a tiger -- intuition can be wrong. Intuition is not fact, and that's why experiments are performed... to test whether your intuition is correct or not. And, if your intuition doesn't agree with the experiment, there are really only two choices: the experiment was flawed in some way, or your intuition is wrong and needs to be righted. Don't feel too bad. Not many people are born with a true physics intuition. Many, many people will argue how the heavier object should fall faster than the lighter one... until the experiment is done. To be a good physicist, however, you will have to abandon those first instincts and learn to accept the physics ones. It's not easy, but worthwhile because your intuition will be more in tune with how nature really acts.

Why are you integrating over z? The P you are looking for is written in terms of x and y, right? I don't think that you need to do that in z variables. Though, even then, if you still did it in z, the limits of x and y can be used to find what the limit of z is. x is always positive and y is always positive, so you should be able to figure out how z is limited. Look at the definition of z again. Think about how x and y are allowed to vary, and what that does to z according to its definition.

Also if there is a bug for just two points, surely you can just write a special case for that --- since the closest point will be in the line between the two points at half the distance. Good use of IF statements should catch that pretty easily. I was actually even thinking a genetic algorithm could be a neat way to solve this... http://en.wikipedia.org/wiki/Genetic_algorithm Should only take a few generations, and again, probably less than second.

alex, as this is sure looks homework-ish, it is against the forum rules to tell you directly the answer. But, I will do my best to help. Firstly, what is the definition of independent variables? What about that property can you use to determine if your two variables are independent? Can you re-write the distribution in terms of x & z? For the second question, what does it mean to find the probability of all cases x>0 and y>0? What procedure do you have that performs such a task? Do you remember how to do it with one variable? It is a natural extension to 2.

swansont, I was just trying to deal with his own personal numbers. I too would like him to explain why he thinks it is a problem.

You didn't really change your question! Explain what? Firstly, the two links to Mathworld have a wealth of information, and I am sure that wikipedia and many other websites have a lot, too. Secondly, any good textbook in probability should cover them. But, just saying "explain" doesn't mean anything. Ask a very specific question. Explain what precisely? Give me an example of what you are trying to do. Vague questions don't help, specific questions can help a lot.

At some point here, jeff, the only way you won't be able to understand these simple discussions is if you are being intentionally obtuse. Here is, yet again, another example. Let's consider two snails. Snails move slowly, so we can deal with small distances. Let's further say that a snail can move 13.7 m per hour, and let's call 13.7m a "snail-hour" because that is the distance that a snail moves in one hour. Now, start two snails at the same starting point, but start them in straight opposite directions. Since for a long time now, races start with a pistol going off, let's call the beginning of the race "The Loud Bang". Both snails move at their top speed the entire hour, and on the same straight line they started on. So, after one hour, both snails are 13.7m from the starting line -- one snail-hour's distance. They are 27.4 m apart from each other however. They are 2 snail-hours apart from one another even though is has only been one hour since "The Loud Bang". Now... that is some 3rd grade math. Now, if you really are still going to be intentionally obtuse about understanding this, replace "snail" with "galaxy", replace "hour" with "year", replace "snail-hour" with "light-year", replace "Loud Bang" with "Big Bang", and my little story there shows how two galaxies that are 13.7 billion years old can be as much as 27.4 billion light years apart by now -- not to mention a mere 24 billion light years. Does this clear that up? Do I need to explain it better? Do you need more examples? If this is unclear, please explain how. My hope is that this completely 100% fixes that issue, so you can get back to actually defending your idea instead of trying to locate holes where there aren't any.

"Means" in what way? How they are related to one another? What their properties are? Your question is exceptionally vague. I will suggest finding a decent university-level book on probability and reading through that -- that will explain what the two functions and how they are used. Whether that give you want they "mean", I am not sure. Mathworld has entries on both, too, but again, I'm not sure if they will satisfy your curiosity about what they "mean" http://mathworld.wolfram.com/ProbabilityFunction.html http://mathworld.wolfram.com/DistributionFunction.html Part of the issue is that "what they mean" is context related. If we are talking about coin flipping, then you use the density function to tell you how likely it is that you are going to get 5 heads when you flip the coin 10 times, for example. And you use the distribution function to tell you how many times you would get 5 or less head when flipping it 10 times. Or, as another example, if you are using the math to describe the velocity distribution of particles, you use the functions to know how many particles are in a certain velocity range. The "meaning" is always context related to the problem at hand. Again, if you study a good university-level textbook and do the practice problems, you'll get a really good understanding of how to use both functions. The practice problems will give you lots of practices deciphering what each function "means" in specific cases.

Here in Iowa they use a combination of both salt and sugar on the roads. They use calcium chlroide as the salt, and a sugar beet juice. It goes by the commercial name Geomelt. http://www.hawkeyereadymix.com/product_geomelt_55.html I think that the nice thing about spraying a juice and not just a solid is that the liquid sticks to where you squirt it. So, instead of the salt bouncing everywhere as it falls out of the truck, the salt & sugar is going to stay right on the road and do its job instead of bouncing away. There are many different approaches to this problem. When I was an undergraduate, the school would scatter ashes from the power plant on the sidewalks and roads on campus. It had some ice-melting properties, but I think its primary function was to increase traction.

jeff has apparently moved on: http://www.bautforum.com/against-mainstream/68918-galaxy-spin.html This should make for a good read in a day or two. If he thought SFN was unreceptive, he's in for a huge surprise at BAUT.

jeff, Cap'n is right. The Bohr model is actually a very, very poor representation of what is actually happening. This goes back to many previous posters' point. That you still think that Bohr's model is good representation of what is going on indicates that you are unfamiliar with a lot of modern theory. And, if you don't know something -- at least enough to be able to talk about the current model -- it's awfully hard for you to tear it down. Look, no one is going to be foolish enough to say that the current model is perfect. There are holes in it, there are errors in it. But, you have to know it reasonably well in order to critique it. You also should probably know how successful it has been. Also, again, do you have a mathematical description of your idea? Can you make any kind of predictions at all? Until you can, you really aren't doing science. You are writing stories.

jeff mitchel, Here is a completely unvenomous sincere question: Can you demonstrate/cite/provide any evidence that supports your idea? Can you provide a mathematical model of what you are saying, and show how that model makes predictions -- and then even better that those predictions are at least as good or better than the theory that is accepted today? Science is the search for the true nature of things, but this search does not include looking down every wayward path unless there is good reason to believe that the path will get us closer to the goal. Please post some good reasons to show that your path heads in the right direction, because at the moment the main road we're on seems to be doing an excellent job. Show us that your road is indeed a shortcut. If you can do these things, I guarantee that people will change their mind. But, at the moment, all you've provided is an idea and words and nothing of any substance at all. If you can provide that much needed substance, you'll get people to support you. Give us some evidence that things like "whirlies" exist, and you'll get supporters. Otherwise all it is is fiction writing. You have the new ideas, it is up to you to bring the evidence that shows your ideas are better than what's out there right now.