DrRocket

I have seen all sort or total nonsense assumed under the heading of "engineering judgement". I have had to overrule it, and in the process saved many milliions of dollars, and likley a life or two. Your approach is just more nonsense. There is nothing in the problem statement to indicate that the car meets an "immovable object", and hence the distance traveled by the CG need not be bounded by any reasonable function of the length of the car. Moreover, even if the car were to collide with the proverbial immovable object, the net force on the car will hardly be constant, so an average of force over distance traveled by the CG and an average over time will be totally different things. Better take the hard way. Silly solution based on unfounded and unrealistic assumptions is often much worse than simply admitting that you don't know. If you want to get fancy then maybe you even need a hydro code (e.g. Epic) and high-rate material properties. Been there, done that.

You are missing elfmotat's very valid point. "Now" in special relativity is a surface of simultaneity -- the events that an observer "sees" as being simultaneous with his time 0. That surface is not the same for all observers. This is what is colloquially called the "relativity of simultaneity". "Now" varies with the reference frame. It is not true that nothing can tell the difference between the views. The events in spacetime are invariant. All observers will agree on the existence of the events. They do not agree on the specific coordinates of the events, and in particular they do not agree on which events are simulataneous. So to distinguish between the two views one must merely compare the perceptions as to what events are simulataneous.

How do you determine that ?

Not quite. Given that the invariance of the speed of light means that the speed is the same in ALL inertial reference frames, no experiment can prove that. There are too many invariant reference frames. There are in fact uncountably many inertial reference frames and one simply cannot check all of them directly by experiment. However, the alternative, assuming that Maxwell's equations are correct, is that either Maxwell's equations apply in only a single preferred reference frame, by definition the ether frame, or else the speed of light is indeed invariant. The former was the consensus prior to the Michelson Morely experiment. The experiment supported the latter alternative. If one wants to be picky, and you are being picky, then strictly speaking the existence of the ether has not been disproved. In fact there is a perfectly valid theory, the Lorentz Ether Theory, that includes an ether and is experimentally indistinguishable from special relativity -- it makes exactly the same predictions as does special relativity. So, again strictly speaking, the Michelson Morely experiment and special relativity did not and do not disprove the existence of an ether, but rather simply make an ether irrelevant in classical electrodynamics.

Apply the theorems that you should know that pertain to finite groups.

A sphere, in whch case the geodesics are known to every school child -- great circles. This is pretty clearly a class assignment, or should be. You need to show your work in a reasosnable attempt to solve this problem. Then we will help you.

The equivalence principle was philosophically useful to Einstein in the discovery and development of general relativity. However, unlike the axioms of special relativity, it is not central to the logical structure of general relativity, which is based on (pseudo) Riemannian geometry and the relatioship between the stress-energy tensor and the Einstein curvature tensor. It is still useful in some situations, but one must be careful not to confuse onself with it. That said, light follows a geodesic in spacetime. So does any object influenced by no force other than gravity. Consider a ball floating in your spacecraft in free fall (eg. in orbit around a massive body). That ball also follows a geodesic in spacetime, as does the spacecraft until thrust is appplied. Now fire your rockets and accelerate the spacecraft. The ball will continue to follow a spacetime geodesic until it hits something. But from the perspective of a passenger in the spacecraft, that ball will follow some more or less arbitrary path determined by the acceleration of the ship around the ball. The only significant difference between light and the ball is that that light follows a null geodesic in spacetime, while the ball follows a timelike geodesic. From the perspective of an observer with a coordinate system referenced to the body of the spacecraft that path can appear to be almost anything.

Titled "Stone Cold Crazy" ? (with apologies to Queen)

Of course. One expects scientists to be honest and objective. When they appear not to be it is a shock and the reaction to that shock can be pronounced. Credibility is lost largely because there was credibiliity to begin with. No one expects politicians to tell the truth or to act out of anything except self-interest. When they lie it is just another day at the office, and since there never was any credibility there is nothing to be affected.

Gladly, except when it comes to science. Scientists also philolosophize, as part of the creative process of research. They just don't pay any attention to philosophers. Science seeks only to descrive HOW nature behaves, quantitatively and predictively. WHY it behaves that way is a question to be contemplated by philosophers and theologians. I did not mean to imply that philosophers or theologians were in any danger of reaching a conclusion, or of actually answering such questions. I definitely agree that any actual answers will come from science. But those answers, again, will simply describe how nature behaves and not why it behaves in that manner.

You are better off with a good book than something questionable on line Any book with something like "Real Analysis" in the title should do. Two very good ones are: Elements of Real Analysis by Robert Bartle Principles of Mathematical Analysis by Walter Rudin Earlier editions are affordable at Amazon or Alibris and are fully adequate.

You have a false set of premises. Therefore, according to the simple rules of logic, you can deduce literally anything from them, including the negation of anything that you show to be "true". Religious arguments regarding scientific theories are like that. Pointless at best. No, I am not an atheist. Neither am I an idiot.

Science answers "How". "Why" is for philosophers and theologians.

You are basically asking that science transform itself into something that it isn't so that people who are not scientists can understand it completely as it is. That is pretty much a self-contradiction. There is a reason for the language used in various branches of science, and that reason is precision. It is also the same reason that much of science cannot be fully understood without recourse to mathematics, which is, after all, the language of much of science. So, you will either have to be satisfied with over-simplificataions and imperfect analogies or you will have to study the subjects that interest you intensely, and in the language in which they are properly expressed. There is no royal road to understanding.

No. Implosion of a structure like a cylinder is a function of the applied load on the boundary -- in this case the differential pressure between the interior and exterior. If it did not implode on Earth it will not implode in space. In fact the differential pressure in space vs on Earth will be both lower in magnitude and differ in sign and this will be reflected in the stress state of the cylinder. On Earth the cylinder will be in compression as the outside pressure is greater than the inside pressure, while in space the reverse will be true initially and in any realistic situation (laboratory vacuums are not as complete as the vacuum of space). So in space the skin of the cylinder will be in a state of slight tension. Cylinders more easily survive an internal pressue load than an external crushing load. Now, even in the idealized situation in which one might achieve a more complete vacuum inside the cylinder than that of space, the net pressure difference will be nearly 0 -- the difference between two very small pressures -- and the stress will be extremely low. The cylinder will have survived a much more severe stress state on Earth.

You have a bit of a "chicken and egg" problem. If you assume that the laws of physics are the same in all inertial reference frames and that any phenomena propagates at the same speed, call it x, in all inertial frames, then it is a logical consequence that time and length transformations between reference frames are described by Lorentz transformations with "x" in the usual role of "c". So time dilation and length contraction come with the assumption. Lorentz transformations, not surprisingly, also carry the speed "x" in one frame to the same speed "x" in any other frame. So, basically everything follows from the constancy of "x". You now have special relativity, except for a need to find something that propagates at some fixed speed in all inertial frames. Enter light. Maxwell's equations show that light meets the requirement of propagating at the same speed in all inertial frames. So do many experiments, starting with the well-known historical Michelson-Morley experiment. Thus light fills the bill for the required phenomena used in deriving special relativity and the Lorentz transformations and the speed "x" is the speed of light in a vacuum, "c". With this train, it is the constancy of "c" that results in time dilation and length contraction. Note that as a result of the logic used, there can only be one such invariant speed. So any phenomena that propagates at the same speed in all reference frames must propagate at the same speed as does light. It is thought that gravitational waves also propagate at c, so one might equally call c "the speed of gravity". It just happens that light is a more easily measured phenomena and so we deal with "the speed of light". Conversely, if you start with time dilation and length contraction, hence the Lorentz transformations you find that there is a unique speed that is the same in all reference frames. With the standard Lorentz transformations, that speed is the speed of light "c". So in that sense you might say that the constancy of the speed of light results from the Lorentz transformations, and those transformations are based on so-called time dilation and length contraction. Take your pick as to what "caused" what. But you either get the whole package or none of it.

Agreed. I was referring to this particular thread. (Added in edit: And at the time I wrote it. I am not responsible for the effect on the truth of my assertion that may be caused by any latecomers.) If you were to trawl Philosophy your net might not take the load.

Not quite everything.

Only because you were wrong. Not likely. My definition of an expert, in some specified area, is someone who knows everything that is known, knows the major open problems, knows who is investigating the open problems and their general approach, and has a feel for which areas of investigation are likely to pan out. I was once an expert in a very tiny area, but am no longer an expert in anything. NO ONE is an expert in "physics", "mathematics", "chemistry", "biology", etc. and probably no one has been an expert in any such broad areas since Gauss. They have simply grown to be too big and too diverse.

Without working the problem through in detail I cannot find the precise mistake, but it looks to me like you are relying on pre-derived formulas. The basic idea is as follows: 1. For a "properly banked" track at 63 km/h the bank angle and radius of curvature are such that gravitational and centripetal forces are precisely matched and the car would stay on the track with a coefficient of friction of 0. This will determine the bank angle, since the radius of curvature is given. 2. Now with the bank angle as determined above you re-analyze the situation for a car traveling at 90 km/s and assume a condition of impending slip -- so that the centripetal force, the gravitational force and the frictional force precisely cancel. That will allow you to solve for the coefficient of friction. Note that in this case that the frictional force prevents the car from sliding up the incline. You should also be able to determine, with that same coefficient of friction, the minimal speed allowed to prevent the car from sliding down the incline.

The entire peer review system is based on "appeal to authority". In fact all of science, in contrast to mathematics, is based on induction and on "appeal to authority" in some form. An appeal to authority is not part of a valid argument in formal logic. Formal logic deals only with pure deduction. But appeals to authority are used with validity and rather commonly in other contexts. Science is such a context. In mathematics one starts with a set of axioms, which are accepted without proof of any kind, and uses purely deductive arguments based on those axioms to prove theorems. But it should be noted that mathematicians actually use induction to discover the theorems that are then proved deductively. And mathematics is not science, and need not describe anything having to do with natural processes. In science we have no set of axioms, and science deals with evidence, not proof. ALL of science is fundamentally based on inductive reasoning. It can be no other way, for in science one cannot accept a set of axioms purely on faith. The fundamental tenets of science are based on empiricism, not faith. The only arbiter of "truth" in science is consistency with experiment and observation -- and that is inductive. So how are scientific theories accepted ? They are accepted on the basis of consistency with a body of experimental and observational data and that in turn is determined via reliance on the published word of experimenters, perhaps a large body of experimenters replicating one another's work, and by reliance on the peer review process. All of that is nothing more than a very disciplined and controlled argument by "appeal to authority". You are perhaps perplexed because your typical arguments are appeals to authority without any corresponding reference to the actual data produced and evaluated by those authorities. A more scientific and valid use of authority normally includes reference to actual data as well as the analysis and opinions rendered with regard to that data. Arguments of the latter type are ubiquuitous in science. It would be pretty damn clear from the content of your posts that you had no such qualification. Absolutely. But this is neither the time nor the place. Some are much better than others.

Usually. http://instrumentsofpleasure.com/wp-content/uploads/hitachi-magic-wand24.jpg

Good luck. Owl started the thread with a false dichotomy and experience tells me that he cares neither for logic nor evidence. This thread will most likely be garbage. You might, just possibly, have detected a wee note of sarcasm in my statement.

d No. The force that causes the acceleration (change in direction is an acceleration, even at constant speed) is supplied by the reaction force of the structure acting on the tires of the motorcycle. The force that results from the torque applied to the drive wheel is tangent to the path of the motorcycle and hence does not cause a direction change. But the moltorcycle is in fact constantly accelerating. It is just that the acceleration need not be due to the action of the motorcycld engine. Any object traveling in an arc is constantly accelerating. That includes the Earth in orbit around the sun. Incorrect. He is in fact constantly accelerating by virtue of change in direction. This acceleration will be measured by any 3-dimensional accelerometer that he might have. Centripetal acceleration is real acceleration.

Nope. There is only one person here dumb enough to call any such nonsense a "proof".