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Lots of boat traffic in the Bermuda Triangle area explains the Bermuda Triangle. There are *lots* of auto accidents on the Capital Beltway around Washington D.C. Do you need to invole some mysterious source to explain those accidents? Perhaps toxic gas leaking out of the Capitol? (There certainly is a lot of hot air there!) Of course not. The Beltway is a heavily traveled, highly congested roadway. The Bermuda Triangle is much the same.

You missed a key reference, Ophiolite. M.W. McEhinny, S.R. Tayor, D.J. Stevenson (1978) Limits to the expansion of Earth, Moon, Mars and Mercury and to changes in the gravitational constant, Nature 271, 316-321. New estimates of the palaeoradius of the Earth for the past 400 Myr from palaeomagnetic data limit possible expansion to less than 0.8%, sufficient to exclude any current theory of Earth expansion. bombus: You need to refute this paper. Correction: Adams cherry picks data already in existence. He uses only data can be contorted in a way the bolsters his conjecture. Data that contradicts hist conjecture ((e.g. the Burgess shales, subduction) don't exist. Bzzzt, wrong. We do not like fallacies at this site. You are intentionally conflating fusion and fission here. 'Normal' geologists post nuclear fission, not fusion, in the inner core of the planet. EET has been investigated and has been falsified. It's proponents are mostly cranks, religious nuts, and comic book artists. There also exists a tiny, tiny handful of scientists who ascribe to this failed conjecture. Guess what? That is true of any breakthrough theory. It takes a long time to become proficient in a field of science. This can make scientists who invested their entire career in a falsified concept forget they are supposed to be scientists. This happens all the time. There is no mechanism for EET that doesn't break the laws of physics, there is tons of evidence against it, and there is no evidence for it that isn't explained by the prevailing theory. EET has had its day, and it failed. There is a difference between being open minded and being stupid. You are demanding that we be stupid.

Argghh! I am so stupid! The force that generates this constraint force must be in the same direction as the resistive force applied by the human. To see why, define coordinates as follows: [math]\hat{\boldsymbol x}[/math] is parallel to the plane on which the object is rolling and points in the direction in which the object is moving. [math]\hat{\boldsymbol y}[/math] is perpendicular to the surface on which the object rolling and points from the object / surface contact point to the object's center of mass. [math]\hat{\boldsymbol z}[/math] completes a right-hand system: [math]\hat{\boldsymbol z} = \hat{\boldsymbol x} \times \hat{\boldsymbol y}[/math]. The object's velocity is changing and the object is rolling without slipping. Some torque must exist on the object to keep to object rolling without slipping. The force applied by the human exerts zero torque on the object. From where does this torque arise? The only other possible source is friction at the contact point. A force [math]\vec F[/math] applied at a point [math]\vec r[math] away from the center of mass results in a torque [math]\vec{\tau} = \vec r \times \vec F[/math]. With the above reference system, the position of the contact point is [math]\vec r = -r \hat{\boldsymbol y}[/math]. The constraint force is of the form [math]\vec F_c = -F_c \hat{\boldsymbol x} + F_n \hat y[/math]. The normal force Fn does not contribute to the torque. Here Fc can be any number. I used a negative sign because doing so will make Fc be positive. The torque is [math]\vec{\tau} = \vec r \times \vec F_c = rF_c \hat{\boldsymbol y}\times \hat{\boldsymbol x} = -rF_c \hat{\boldsymbol z}[/math] To keep the object rolling without slipping the torque must be equal to [math]\vec{\tau} = I\dot{\vec \omega} = \frac I r \dot v \hat{\boldsymbol z}[/math]. (Note that since [math]\dot v < 0[/math] the angular acceleration points in the -z direction.) Equating the two [math]F_c = -\,\frac I {r^2} \dot v[/math] Once again, since [math]\dot v < 0[/math], Fc is positive. Continuing with the corrections to my previous post, [math]\aligned \vec F_r &= -F_r\hat x && \quad\text{Force applied by the human} \\ \vec F_c &= \frac I {r^2} \dot v \hat x && \quad\text{Constraint force} \\ \vec F_t &= \vec F_r + \vec F_c = -\left(F_r - \frac I {r^2} \dot v\right) \hat x &&\quad\text{Total force on the object} \endaligned[/math] The object's kinetic energy at any point in time is [math]T = \frac 1 2 Mv^2 + \frac 1 2 I \omega^2[/math] Since the object is rolling without slipping, [math]\omega = v/r[/math] and thus [math]T = \frac 1 2 \left(M + \frac I{r^2}\right) v^2[/math] The change in kinetic energy over a short period of time [math]\Delta t[/math] is [math]\Delta T \approx \left(M + \frac I{r^2}\right) v \Delta v[/math] The work done on the object is during this time period is [math]\Delta W \approx \vec F_t \cdot \vec v \Delta t = -\left(F_r - \frac I {r^2} \dot v\right) v \Delta t[/math] Applying the work-energy theorem, taking the limit [math]\Delta t \to 0[/math], and solving for [math]\dot v[/math] yields [math]\dot v = F_r/M[/math] In other words, the acceleration is independent of the moment of inertia. The stopping time and stopping distance are the same for both objects. Both objects have exactly the same linear momentum. The linear momentum transfered to the surface is the same in both cases. This is the only result that makes sense. A result that violates conservation of momentum means one of two things: (1) The system boundaries do not enclose a closed system, or (2) A mistake was made. There is a lesson to be learned here: It is easy to make mistakes, even on seemingly simple problems.

That is a very key point. Extrapolation is always a dangerous thing to do in science, even when there is a strong theoretical basis. Case in point: Newtonian mechanics. 19th century physicists had a quarter of millennium of accumulated evidence of the validity of Newtonian mechanics. Yet they started seeing big problems when they extrapolated what they thought they knew to be true to the realms of the very small, the very large, and the very fast. They had anything but a sample size of one on which to base these extrapolations, they had a very strong theoretical basis for thinking the extrapolations were correct, and yet the extrapolations didn't agree with observations. Extrapolating from a sample size of one is just ludicrous. Extrapolating from a sample size of one for which we do not have a theoretical basis (we do not yet have a cogent theory that describes how life arose) is beyond ludicrous. Doing so might, for example, lead one to believe that space is chock full of blast furnaces. Or life. The bottom line is, we do not know yet.

You are failing to look at the whole picture, ABV. Let's look at the whole picture. The object is slowing down because of the external force applied by the human. However, the object rolls without slipping. Its angular velocity is also decreasing. There must be a torque acting on the object as well. This torque comes from the contact with the ground. This force is directed opposite to the force applied by the human (but is lesser in magnitude). Denoting direction in which the object is moving as the positive x axis, then [math]\aligned \vec v &= v\hat x && \quad\text{Object center of mass velocity} \\ \vec F_r &= -F_r\hat x && \quad\text{Force applied by the human} \\ \vec F_c &= -\,\frac I r \dot \omega \hat x = -\,\frac I {r^2} \dot v \hat x && \quad\text{Constraint force} \\ \vec F_t &= \vec F_r + \vec F_c = -\left(F_r + \frac I {r^2} \dot v\right) \hat x &&\quad\text{Total force on the object} \endaligned[/math] After a bit of work, the object has a constant acceleration equal to [math] \dot v = -\,\frac {F_r} {M+2I/r^2} [/math] The stopping time and distance given this constant (negative) acceleration are [math]\aligned t_{stop} &= -\,\frac {v_0}{\dot v} = \frac {v_0\left(M+2I/r^2\right)} {F_r} \\ d_{stop} &= -\,\frac 1 2\, \frac {v{_0}^2}{\dot v} = \frac 1 2 \,\frac {v{_0}^2\left(M+2I/r^2\right)} {F_r} \endaligned[/math]

You are mixing and matching Newtonian and relativistic mechanics here. This is not a good idea in general and is a very bad idea in this case. Gravitational force is a fictional force in general relativity. There is no such thing as gravitational potential energy in general relativity. The mass-energy an infalling object adds to a black hole is the object's energy-at-infinity. That the object follows a geodesic into the black hole doesn't change that.

The two objects have different energy. Work is energy. The human has to do more work to bring the object with more kinetic energy to a stop. So, what happens to the linear and angular momentum that was initially stored in the object and the human? Simple: It was transfered to whatever the object was rolling on / the human was sliding on. What about energy? It's conserved also. Humans can't conjure up force out of the clear blue sky. (Superman doesn't count. He's not human and he doesn't do Lagrange multipliers...for him there are no constraints). That force presumable arises from the human sliding on the surface. Friction converts kinetic energy to thermal energy. Energy is still conserved, just not in a useful way. Note: The frictional force of the human's feet with the ground is greater than the force the human applies to the rolling object. The human is coming to a stop as well.

Then you should learn some real ones. You have not discovered "an antigravity, a time machine and open door to a deep space". You have discovered nonsense.

What do you mean by "no slippery at all"? Thread moved to pseudoscience.

You are once again drawing your boundaries incorrectly, you are not looking at the whole picture, and you are being very unclear. I realize there is a language problem here, but your problems transcend language boundaries. What do you mean by "Would human gains different momentums to the surface?" If you mean the change in the human's momentum, they are the same in both cases. If you mean the momentum transfered to the surface, of course these are different. Which do you mean?

The "yes" answer was to the question "Would these rolling bodies have different [stopping] distance and time?" This is obvious. They two objects have different initial kinetic energy, so different amounts of work are needed to stop the two objects. Work in this case is simply force * stopping distance. The "no" answer was to the question "Would human gains different momentums to the surface?". In both cases the human start with the same initial velocity and end with the same final velocity. The change in the human's momentum is the same in both cases. Once again, this is obvious.

Yes. No.

Stop spamming, please. You are posting multiple threads on the same topic. Thread merged with your other nonsense. Merged post follows: Consecutive posts mergedWell, dang. I don't have the authority to merge a thread with another thread in the pseudoscience sub forum.

This barely qualifies as pseudoscience, let alone real science. Thread moved. Merged post follows: Consecutive posts merged A big part of your problem, ABV, is that you are not specifying the problem clearly. This includes properly drawing system boundaries, which is the chief source of your problems to date. Here you have not fully the specified initial conditions and the initial conditions are contradict your equations of motion. Is the body initially rolling or sliding? You didn't say. Is the object rolling without slipping? I guess that is what "no rolling resistance" means. Is the object rolling rolling up or down an incline or rolling on a flat surface? You didn't say. If the object is initially slipping, the dynamic frictional forces will do two things: It will reduce the object's kinetic energy and it will make the object start rolling. If the object is rolling without slipping, it will keep on rolling forever. Why? The velocity at the contact point is zero. The friction needed to keep the body rolling does zero work. Zero work = zero change in energy.

First off, you are being too strict here. Scientific theories are not proven to be true and in general cannot be proved. We cannot (yet) send a probe down to the center of the Earth to tell us exactly what is going on down there. The best we can do is infer what is going on. This includes seismograph readings, high pressure / high temperature experiments, and dynamic models of the Earth. The pressure inside the Earth rises with depth. It eventually starts flattening, but this flattening occurs inside the inner core. The pressure at the inner core / outer core boundary is still rising with increased depth. The temperature is rising also, but not as sharply as the pressure. Finally, the melting curve for iron is anything but a flat line. At the kinds of pressure experienced deep within the Earth the melting curve has a marked slope. If you increase the pressure on a blob of molten iron enough it will solidify. By way of analogy, think of a disposable lighter. You can see the contents as liquid because the contents are under pressure. At ordinary pressure, that liquid would be a gas.

That assumes the Earth has a uniform density: A nice, simple freshman physics problem. Unfortunately, that is all this assumption is good for. It does not reflect reality. Inside the real world, Earth's gravitational force initially increases with depth. This increase continues down to the mantle/outer core boundary; only then does it start dropping. Think of it this way: The Earth's core represents about 9.4% of the total volume of the Earth but represents about 32% of the total mass of the Earth.

http://en.wikipedia.org/wiki/APL_(programming_language)#Examples Scroll down to the final example. APL has been derisively called a "write-only language". The problem with any powerful language is it invites the author to write completely inscrutable code. The authors of such code ofttimes learn that being extremely clever can be pretty stupid when they are asked to modify that write-only code six months later. It looks like Erlang is an even better candidate for obfuscation than is C. So, is there an Erlang equivalent to the IOCCC? Answer: Yep. There is. Merged post follows: Consecutive posts merged Apparently some on the talk page about the Wikipedia APL article don't like the primes program cited in the main article. It's hard to understand and employs bad practices. The following, from the talk page, is much better in that it is much easier to understand and it does follow good programming practices: [math](2=+/[1]0=R\,^{\circ}.|R)/R\leftarrow\iota N[/math]

Modern civilization / modern agriculture is the key. Until 100 years ago, only a tiny, tiny portion of the population had the opportunity to indulge in eating to the extent the vast majority of the population of any advanced country can indulge today. Obesity has only become a significant problem in the last 50 years or so: two or three generations. Evolution isn't fast enough to compensate for this sudden switch from feast/famine to perpetual feast. The pounds gained from those feasts at the end of harvest time helped us stay alive during winter. We still have the genes that tell us that a wonderfully marbled steak, a baked potato with all the fixins, buttered green beans, and a slice of pie for dessert not only tastes good but is good. Our genes have not yet been modernized to tell us that that meal is not as good as we think it is.

Is that the best you can do? Use a man's language! [math](\sim R \in R \circ.\times R)/R\leftarrow 1 \downarrow \iota R[/math] Sometimes inscrutability isn't all it's cut out to be.

As far as I know, some if not most scientists are saying something more along the lines of "Move along, move along. There's nothing to see here."

I wasn't referring to the articles. I was referring to Wddikind's mischaracterization / oversimplification of the articles.

Kinetic energy is a thing in and of itself. It is not potential energy. This is a big part of your problem. The gravitational potential energy of a jet flying at supersonic speed at an elevation of 1000 feet over the ocean is exactly equal to the jet's gravitational potential energy when it lands on an airfield with an elevation of 1000 feet above sea level. Gravitational potential energy is a function of height and mass only. Velocity doesn't enter into the picture. The same goes for the chemical potential energy of the fuel in the jet. Whether the jet is traveling at Mach 2 or sitting still on the ground doesn't matter. The chemical potential energy depends only on the quantity of fuel in the jet's tanks. Yes. The change in gravitational potential energy in some packet of falling water is [math]mgh[/math], where h is the distance the packet has fallen. Look at it this way. Suppose you carry a ball to the top of a cliff of height h and release it. The ball starts with a velocity of zero (zero kinetic energy) and falls to the bottom of the cliff. Ignoring friction with the air, what is the velocity of the ball right before it hits the ground at the bottom of the cliff? The answer is easily obtained if you look at the problem from the perspective of conservation of energy. The ball loses mgh gravitational potential energy in falling. Therefore, the ball's gain in kinetic energy must be equal to mgh to conserve energy. The ball's velocity at the end is v directed downwards, so its kinetic energy is ½mv2. Put the two together, [math]mgh=\frac 1 2 mv^2[/math], and the ball's velocity right before it hits is [math]\sqrt{2gh}[/math]. Alternatively, you could use Newton's second law and after considerably more work come up with exactly the same answer. Looking at this problem from the perspective of conservation of energy and the answer pops out.

For crying out loud! You have been told you many times over what form of energy is converted into electricity in a hydroelectric plant. It is gravitational potential energy.

A bit of a reality check, Enigm4. You are still in high school. A couple of consequences: Very few people end up doing in life what they thought they would be doing when they were 18. At your age you should be looking at lots of potential paths. The world 5-10 years (about when you'll be getting out of school) will be a bit different than it is today. Your perception of it will be vastly different. Making your life's goal an extremely narrow field that receives very little funding at age 18 might not be the best choice. On the other hand, physics is a very broad field. Aiming for an initial education in physics is a good plan. Suppose you do get accepted into a prestigious school that happens to have one or two people who are working on time travel. As an undergraduate, do you really think you will be involved in that work? You won't even have started learning the requisite knowledge until you are a senior in college (or later). The fact that you are finishing your exams a less than a month from now and you are asking "where should I go to school" is a bit disconcerting. Most people your age already know where they are going to school. They applied to multiple colleges last fall and accepted an invitation to go to one of them months ago. Reality check #3: If you truly want to go to a prestigious school you will have to wait for a year. The primary reason for going to a prestigious school for your undergraduate degree is to give yourself an initial boost in your opportunities immediately after graduation. When it comes to getting into graduate school or getting your first job, a good GPA at a prestigious school is comparable to an excellent GPA from a second tier school. An excellent GPA from a prestigious school opens a lot of doors. On the other hand, a mediocre GPA from a prestigious school means you (or more likely your parents) wasted a lot of money. Reality check #4: Prestigious schools can be a double-edged sword. You will need a PhD if you want to be a theoretical physicist. The school from which you obtain your PhD will matter a lot. If you do get a PhD, where you obtained your undergrad degree is pretty much irrelevant. Nobody cares. By waiting until just a few weeks before graduation to ask what you want to do with the rest of your life you have cut off some immediate opportunities. All is not lost. You can recover. You can go to a local school next fall (we call them community colleges in the US; I am sure Europe has the same concept). Taking your first year at Joe Blow Community College is not going to kill your career. You can transfer credits and you can take that first year to sort out your priorities.

First, I need to get something off my chest. Are you trying to be a crackpot, navigator? If that is your goal, you are well on the way. You have all the trademarks: Intentional obtuseness, tortured logic, ignoring evidence, intellectual dishonesty. OK. Now that I got that off my chest I can address your concerns. Think of a boat with an electrically powered propeller. You can find these on everything from tiny little toy boats all the way up to supertankers. Electricity powers an electric motor which turns the propeller. The blades on the rotating propeller create a stream of rearward-moving water. Newton's third law: The boat moves forward. An electric boat demonstrates conversion of energy from one form to another multiple times over. The electricity might come from a battery, a deisel-powered generator, a nuclear power plant, or a solar cell. Energy of some sort is converted to electrical potential energy. The electric motor converts this electrical energy to rotational kinetic energy. The rotating propeller, thanks to its blades, transforms this rotational kinetic energy to translational kinetic energy, some of that transfered to the water and some transfered to the boat itself. Now imagine the boat is firmly anchored. Turning the propeller will still transfer energy to the water. It will in fact transfer more energy to the water than was transfered when the boat was free to move. There won't be much energy wasted in making the boat move. Last step: Reverse the process. Instead of the propeller accelerating the water, imagine a moving stream of water hitting the stationary propeller. The propeller will turn, which in turn will turn the motor's rotor. Conceptually there is very little difference between a generator and a motor. Apply electricity to a motor/generator and you get rotary motion out. Apply rotary motion to a motor/generator and you get electricity out.