Bignose

What does that have to do with anything. The point is that different launch angles DO end up with different results. Are you going to try to argue that they don't?

you do get different results. The reason golfers carry 14 different clubs with 14 different lofts on the club heads on the end is so that they can hit the ball at different angles so that they get different results. If different angles didn't end up with different results, you'd only need 1 golf club. You know this -- if you throw a ball parallel to the ground and then throw a ball at 45* to the ground with the same force, the ball ends up in a different spot. Therefore, your idea that "things pull regardless of angle when gravity is applied" is wrong. Merged post follows: Consecutive posts mergedHave you played around with any of the simple gravity simulators on the web? Like http://www.arachnoid.com/gravitation/ This program it a pretty good simulation of the solar system, and yet doesn't have to include any new ideas to create a good simulation. Especially, please play around with the "Simple Orbit" simulation available on the drop down. You get to change the initial velocity of the green dot at it orbits the yellow dot. Note specifically what happens when you change the value higher or lower than the value needed for perfect orbits.

This statement is completely meaningless, because it can be 100% equally applied to anything you write as well. As in: "looking at gafferuk's idea is completely irrelevant as gafferuk is a man and his idea is manmade and could contain mistakes." Math is the universal language of physics. Whether you understand them or not, does not take away the fact that the mathematics of gravity and orbits have been verified an incredible amount of times.

What troubles are you having imagining a particle with a position, a velocity, and an acceleration at a certain time that requires 10 dimensions? If you need more dimensions, again, let's consider a special particle. Let's consider it to be a cell. Where we want to describe the cell by its size (volume as another dimension), by its age since it last split (age as another dimension), by the concentrations of 20 different chemicals in it (those 20 concentrations are another 20 dimensions), the location of the nucleus inside the cell may require another 3 space dimensions, etc. etc. etc. No matter how you try, you cannot describe the concentration of lysine in a cell using x,y,z. You need another dimension, concentration of the amino acid lysine. This is a real world example where you need more than 3 dimensions.

I can imagine many, many more than just 3 dimensions. You just have to know what you are looking for: Let me give you an example: Consider a single particle in space. It will use 3 dimensions just to describe its location, x, y, z. Now, consider further that that particle is moving. So it will will have velocities in the x,y,z directions as well, call them v_x, v_y, v_z. That velocity can really be considered a second set of dimensions. A new dimension is needed when the current dimensions cannot adequately describe different states that can exist. In this case, using only position, one cannot adequately discriminate between a particle at rest at 0,0,0 or a particle zipping along at half the speed of light that just happens to be at 0,0,0 at a single instance in time. So, to adequately describe the differences in these two particles, you have to introduce the velocity dimensions as well. This can be naturally extended again where the particle's accelerations could be another 3 dimensions. So, a single particle could need up to 9 dimensions to describe it. This is really only just about limited by your imagination. What if the size of the particle mattered? The particle volume could then be another dimension. What if it were made of different substances? A dimension capturing the concentration of the different materials in the particle could also be important. Now, let's further expand this idea of the single particle to a multi-particle system where position and velocity are the properties of the particles we want to study. Say we were studying a system with N particles. To describe that system, we would actually need 6N dimensions to describe the state of that system. A system of 500 particle would need 3000 dimensions! Let [math]P^{[N]}(\mathbf{x}_1,\mathbf{v}_1,\mathbf{x}_2,\mathbf{v}_2,...,\mathbf{x}_N,\mathbf{v}_N,t)[/math] denote the probability of finding the system in a state where particle 1 is within [math]d\mathbf{x}_1[/math] of position [math]\mathbf{x}_1[/math] with a velocity within [math]d\mathbf{v}_1[/math] of velocity [math]\mathbf{v}_1[/math], and so on for each of the N particles at time t. The equation that describes the system is known as the Liouville Equation: [math]\frac{\partial P}{\partial t} + \sum^{N}_{i=1}\mathbf{v}_i \cdot \frac{\partial P}{\partial \mathbf{x}_i} =0 [/math] And, again, P is a function with 6N+1 (+1 for time) dimensions. What "extra" dimensions come down to is the need to describe things that cannot be described by the "old" dimensions. They aren't necessarily some magical or unimaginable things. You just have to know what the math is saying they are, and know how to interpret them.

I think that what you are asking here is imprecise. However, if you are asking how, if given a specified jerk, how would you find the position as a function of time? You would integrate the jerk with respect to time three times. You will need 3 initial/boundary conditions. velocity = [math] v = \frac{dx}{dt}[/math] acceleration = [math] a = \frac{dv}{dt} = \frac{d}{dt} \frac{dx}{dt}[/math] jerk = [math] j = \frac{da}{dt} = \frac{d}{dt} \frac{d}{dt} \frac{dx}{dt}[/math]

How conclusive was the evidence in Einstein's time of the expanding universe? How conclusive was the evidence for Hubble's idea over Doyle's in his day? If the evidence wasn't conclusive (as it is today with the better measuring methods), then it is perfectly reasonable to judge one idea wrong if the available evidence fits multiple theories. However, once the evidence was solidified, no actual scientist "scoffs" at it any more. There are plenty of open questions today where the evidence to date isn't decisive one way or the other. That doesn't mean that the people who support the side that will end up being wrong aren't scientists, or that they will end up being worthless. The argument stimulates the need to find the better, more conclusive, more objective, more significant evidence. So, maybe I didn't make my request clear. Can you cite any specific examples when there was clear, conclusive, significant evidence that once side was right, and that evidence was ignored or "scoffed" at by other scientists? Also, please don't insult me. I didn't insult you.

The whole rant is rather misguided, but this line is particular is way off. If there really was evidence, then the "mainstream" had no choice but to accept it. And refine their models and maybe even rethink. Almost every single working scientist would absolutely relish at that idea. That is the goal of almost every single scientist -- to be able to come up with something completely and totally new. Every working scientist is doing this right now -- there is no point in doing something old because it has already been done. What was "scoffed" at, was lack of evidence. Or poor evidence. But, if there was sound evidence, it was incorporated. And it will always be incorporated. The evidence has to be sound, and all evidence has to survive a trial by fire of inquiry, and possible counter-evidence and show to be statistically significant, etc. etc. But once there is actual evidence, then it will be accepted. Just saying it was scoffed at doesn't make it true. On the subject of evidence -- can you actually cite any examples where actual good evidence was "scoffed" at or deliberately ignored? Merged post follows: Consecutive posts merged No -- re-read this thread. The first mention of your model is post number 3 where you say "my model". Moo's response in post #2 is completely written about generalities. Neither post has the edited tag on them, so they haven't been changed. pywakit you are the first one to mention your model in this thread.

Given a f(x), you can find the inverse (if one exists, there certainly doesn't HAVE to be an inverse) by setting y=f(x) and then solving just for x. For example: let [math]f(x) = x^2 +1[/math] Set [math]y = x^2 +1 [/math] Then solve for x in terms of y: [math]y -1 = x^2 [/math] [math]\sqrt{y - 1} = x [/math] Then once you've isolated x, this is the inverse function: [math]x = f^{-1}(y) = \sqrt{y-1}[/math]

Is there a working model somewhere? I suspect that it loses energy somewhere, seeing as no one has ever created a truly perpetual motion machine ever. I'm not going to click on the link as I don't click on unknown links, but no matter what drawing is there, unless you have a working model that is open to study by any scientist, I shall remain skeptical.

Pressure is a force per unit area, but the important point is that it is a force. In a fluid, when two pressures are unequal, that means that the two forces are unequal. And, unless there is some other force like gravity to balance it all out, an unequal force would mean that movement occurs. You don't "have" to have a pressure difference to cause flow. However, because it is a fluid and rapidly deformable, any time there is a force imbalance, the pressure will adjust itself much as possible in an attempt to return to equilibrium. An example of a flow without a pressure difference would be flow between two infinite parallel plates and the top plate is moving. There will be a flow because of the moving plate, but there won't be any pressure drop.

The average velocity has to increase to maintain steady state -- if the velocity didn't increase, there would have to be a leak or accumulation in the system. And then, since the velocity increased -- the KE increases, and since the total energy remains constant, the energy that was in the pressure decreases.

Just a real quick glance here, but this popped out as being wrong The last line has a sign error: when you have a - on the outside of a parentheses with both a positive and a negative sign inside them, both terms cannot achieve the same sign on the inside by multiplying on the outside. Also (λ - (1+λ))/(1+λ) becomes λ/(1+λ) - 1, NOT (1+λ). You have a division error, too. I haven't checked any of the rest of the math, but to be frank, with these basic of errors, the rest of the math has to be considered suspect until it is verified. You also may want to consider using the LaTeX capabilities of this forum, to improve the ease of reading. x' = vtλ( (λ - (1+λ))/(1+λ) ) becomes [math]x' = vt\lambda \left( \frac{\left( \lambda - (1+\lambda) \right)}{(1+\lambda)} \right) [/math] is significantly easier to read (I hope that I got all the ()'s correct, because when it is all in one line, it is very hard to read.)

Cap'n, you are a moderator here, and how you want to run the forum is up to you and the other mods. But, I think that it is very important to use the words correctly, especially on a science forum. As per other threads, we don't let people misuse the words force and energy and momentum and the like. We don't let people misrepresent what that the theory or evolution says, or what the theory or gravity says. Allowing one to misuse the word theory is inconsistent with almost everything else this forum does. In general, can the explanation of the proper use of the word be better? It sure can. Have sometimes the post that points out the incorrect usage of the word sometimes been rude? It sure has. (For the record, I think that BA here definitely wasn't rude, but could have done a better job explaining why the word hypothesis is more scientifically correct than the word theory.) But, I think that it is still very important to instill the correct use of the word in any place where science is to be discussed. And that includes the Speculations section.

How does the latent heat definition explain how a glacier can act like a fluid over a time scale of years? How does the latent heat definition explain how glass can flow again over a large number of years? The latent heat definition has its flaws, too.

I still think that you can think of it as a continuum of time scale behavior. Some very solid solids, like rocks or wood, probably would need time scales longer than the life of the universe to act "fluid-like", but there is still a theoretical time scale. The molecules of a rock are very, very, very slowly moving about and in a time scale of billions, trillions, quadrillions of years, will eventually rearrange themselves into the absolute lowest minimum of energy. Just because such behavior is essentially unobservable (by the tools we have today) doesn't mean that it isn't happening. Just happening very slowly. And, the flip side is that there are going to be materials that act fluid-like in all but the quickest timescales. Most gases are going to be fluid-like in all but the shortest time-scales. A better description of how a material acts is what is the cause of the stress in the material. In a solid, it is displacement, in a fluid is the rate of shear. And, in polymers that have both liquid and solid-like properties, it is some combination of both.

You may be interested in doing a little reading about the Deborah number used in rheology of polymers: http://en.wikipedia.org/wiki/Deborah_number In short, it is a number that quantifies how "solid" a fluid can act like. Every liquid can act "solid-like" depending on the time scale, and I think that it is equally fair to say that every solid can act "liquid-like" again depending on the scale. I good example from Mythbusters that they did a while back was to see how well bullets penetrate water and remain deadly. They found that the slower-velocity bullets, like from hand guns, penetrated the water well and could easily harm or kill someone several meters underwater. But, the high-velocity guns, like a sniper rifle, the bullet would actually fracture and fall apart very quickly after hitting the water. In this case, the bullet was moving so fast that the water was "solid-like" from the perspective of the bullet. The bullets disintegrated because they were in effect hitting a solid. In the time scales of the high-velocity bullet, the water didn't have enough time to be pushed out of the way like with the slower bullets. A glacier is another good example. It is seemingly very solid. But, the experiment has been done where they placed beacons in the ice on a glacier that was between two mountains. They came back several years later, and the beacons had shifted in the flow direction into a perfect parabolic profile, just like the Navier-Stokes equations predict. On the time scale of years, the glacier acts like a fluid.

"Nano" is soooooo 2007. I would personally go with femto-crystals.

http://www.publicservice.co.uk/news_story.asp?id=11434 You know, I don't have any problem with someone being a skeptic, but (as is typical) this guy seems to go a little too far. From the article: He [Professor Fred Singer] suggested people should be suspicious of any science where there was a consensus -- this just blows my mind away. How can anybody consider themselves a professor in any kind of science if the eventual goal isn't consensus?!? I guess he's probably pretty skeptical of gravity, and light as a wave and particle, and of fluid mechanics, and of any other part of science where there is significant consensus. Math probably just kills him. "1+1=2" "I'm suspicous of that consensus!" Maybe the article makes it seem worse than he really is, but it is truly a terrible quote/idea.

But, that is beside the point. The point is that when a planet is in a stable orbit, there is plenty of motion and plenty of forces acting on the planet, yet no energy transfer. walkntune keeps trying to equate the two. Mr. Skeptic gave a good example of a situation where there are plenty of very strong forces, and yet no energy transfer. walkntune's idea is therefore incorrect and needs revision.

Insisting that force and energy are the same is wrong. Why is because they are defined to be two different things. Einstein's quote is one where he is speaking artistically, not scientifically. Einstein did not equate force and energy, he knew the difference between them, which is more than clear enough if you actually study his scientific works. Because he was a famous scientist, he was often sought out for quotes and his thoughts on things, and the like; Einstein was not above giving out a good PR quote or quip that makes good reading. "Energy is the basic force in creation." is the same thing. Einstein is also quoted as saying "Put your hand on a hot stove for a minute, and it seems like an hour. Sit with a pretty girl for an hour, and it seems like a minute. THAT'S relativity". Again, a nice quip, but you cannot start reading any scientific knowledge into it.

This is nowhere near right. At that high of a level of oxygen, humans would all be suffering from oxygen toxicity. We are adapted to the actual oxygen concentration of the Earth's atmosphere. Besides several websites that will give you the correct numbers, you should be able to find it in many texts as well. Felder & Rousseau's Elementary Principles of Chemical Processes has a listing of the 1st 9 components of air, for example. Merged post follows: Consecutive posts merged this is much better, though you need to get in the habit of citing where you got these numbers from rather than just using the numbers. Unless you want to imply that you measured this yourself, where then you should state how you measured them yourself. You may want to consider expanding on what kind of % you are using, too. Is that mass % (meaning that if you take 1 kg of air, that 0.21 kg of that will be oxygen), or is it a mole% (if you take 1 mole (6.022*10^23 molecules) of air, then 0.21 moles of that is oxygen). It is important because very rarely are mass and mole percents the same. There are other percentages as well, but those two are the most common.

Read it more closely, John, he actually is assuming the opposite of FLT. This is a classic technique of proof, a proof by contradiction. Specifically, you assume the opposite of what you want to prove is true -- then discover what logical consequences that assumption leads to. The consequences of allowing the assumption to be true usually end up breaking one of the other assumptions/axioms/initial conditions/etc. and therefore, the assumption must be false.

Most of the time when hyperbolic trig functions have not been introduced yet, the intention of the book is to make you think of good substitutions to use. In this case, I suspect that you were supposed to let [math]u=e^x[/math]. Then you get a quadratic in u, which you can solve, and then as the final step re-translate the u back into x.

For a constant volumetric flow rate, it is indeed true that as you make the pipe smaller, the average velocity of the output would have to increase. This is necessary to maintain the constant rate of volume. However, most real-life situations are not going to be constant volume. I real-life, if you introduce constrictions downstream, the pump isn't going to be able to output the exact same volume as before. Bernoulli's equation, usually written as: [math]0.5 \rho v^2 + \rho g z + p = constant[/math] where [math]\rho[/math] is the fluid density v is the fluid velocity g is acceleration due to gravity z is horizontal distance and p is pressure A lot of times you will see this written as: [math]0.5 \rho (v_2^2-v_1^2) + \rho g (z_2-z_1) + (p_2-p_1) = 0[/math] where the subscripts indicate different locations along the same line. The above equation is derived from an integration of Euler's equations. One huge thing is missing in Euler's equations: viscosity. Euler's equations assume a perfectly inviscid fluid. There is an "engineering" Bernoulli's equation that tries to remedy some of these short comings. Typically it may look like: [math]0.5 \rho (v_2^2-v_1^2) + \rho g (z_2-z_1) + (p_2-p_1) + \Sigma F + W= 0[/math] where [math]\Sigma F[/math] stands for the sum of all the frictional energy loss and W stands for any work done by or added to the fluid. There are good correlations out there to estimate F based on the type of pipe material and average fluid velocity. But, I think you can see now that as you constrict the flow, you will increase the F term, and thereby causing the output velocity to decrease. Consult a good undergraduate-level engineering fluid mechanics text for a lot more information. This is an equation that is used quite a lot still because it is usually good enough (with the right correlations).