DrRocket

Swansont does not know everything. No one does. But he is a for-real PhD physicist and he does know quite a bit. Quite a bit more than do you. Conversation requires listening. You need to listen to people who know more than you do. There are rather a lot of such people. Swansont is one of them. There is no competition, but there is some consideration for lurkers who are actually trying to learn. That means that all opinions are not of equal validity. Yours in particular lack validity. Now we are back to that listening thing. Speaking of reading, try reading a physics book. That is relatively unimportant. What is important is the competence demonstrated in the sum total of swansont's posts and blog. Believe it or not, incompetent PhD physicists do exist. Swansont is not one of them.

You continue with the straw man arguments. I stated rather clearly at the outset that more information is required in order to solve such a collision problem. I then stated that conservation of energy would be a helpful principle to apply in analyzing a collision problem. I further demonstrated how that prinicple applies, though you seem to not understand that point and conventiently ignore it as well. The time-average restraining force is trivially determined from momentum considerations, and that is about as close as one can come to "solving" the given problem. Momentum conservation is useful in such problems precisely because momentum is a vector quantity and there are relatively few mechanisms for change in momentum. An external force is required. Energy conservation, because energy is a scalar, is much less useful as there are a myriad of mechanisms available for energy dissipation, and non-conservative forces are involved in these mechanisms.

For the same reason that two gallons of water cannot overlap one another. It makes no sense.

You are correct. Mistyped. Meant to say energy is not a vector. However, my logic basec on the corrected text is quite correct. Thanks for catching that typo. Please feel free to go do something anatomically unlikely.

Which makes it difficult to maintain the low temperatures necessary to maintain a superconducting state.

You have got to be kidding.

What that says is the special relativity is the localization of general relativity. I don't know if I would call that an axiom, or just something necessitated by globalizing special relativity and thereby formuating a theory of gravitation. Given the success of special relativity to predict non-gravitational phenomena, this is pretty much unavoidable. As I said earlier, I don't find general relativity to be axiomatically derived in any meaningful sense. To me it is just (pseudo) Riemannian geometry and the physics comes in via the field equations. I guess you could call the field equations axioms, but I think that to be not in keeping with the usual spirit of a set of axioms. On the other hand I generally do not find physics to be axiomatic anyway. The axiomatization of physics was one of the original Hilbert Problems from 1900 and remains open. I suspect that physics may never be rigorously formulated in terms of axioms. After all, physics is not mathematics.

Thanks for finding a working link. Reason #2 for not using the Feynman Lectures on Physics (the acronym does not do it justice), that physics teachers are averse to an apparent competition with Feynman, is, in my opinion, one of the best reasons for purchasing and reading that book, and should be a reason for using it in a class. There are very few introductory texts, in any subject, written by a true master. I can think of no other such texts, suitable for freshmen, at the moment. The Feynman Lectures on Physics are a rather unique example. What I have found to be the case, particularly with mathematics and physics books, is that books written by top-drawer scientists and mathematicians are the most clear and insightful. Unfortunately most such books are written at a very high level and are not accessible to the neophyte. In the Feynman Lectures on Physics one finds nearly all of physics, at some level, viewed through the eyes of one of the most insightful and productive physicists of all time. Yet Feynman manages to communicate this insight with no advanced mathematics and assuming no previous background in physics. It is his incredible physical insight that allows him to explain so much with so little. Mark Kac was correct -- Feynman was a magician of the highest caliber. Other introductory physics texts have undergone many revisions and new editions. The Feynman Lectures on Physics have been slightly improved, new illustrations made, digitized, and a very few small errors corrected, but the original text survives nearly as originally published -- there is a reason that classics are classics. Competing with Feynman is both silly and futile. But using Feynman to either enhance one's own understanding or to help one to explain the essence of physics to others is pretty smart. If you are going to steal, steal from the best.

That would be great. To some extent that is addressed by Feynman's "Tips on Physics", but your exercise book would certainly be a valuable addition. However, with or without an exercise book, the FLP remains one of the very best physics texts, at any level, ever published. Thanks very much for maintaining and improving that masterpiece. Please raise your right hand, reach over your right shoulder, and pat yourself on the back. You deserve it. BTW your link does not seem to be working.

Yep you say things. Sometimes they are correct. This is not one of those times. As noted above it gives you the integral of the restraining force over time, from which one can trivially obtain the time-average of the force. But apparently not well enough to see the essence of the problem. I don't think much of your attitude or your claimed "expertise" either. If this is truly an engineering problem, and not some foolish exercise, then one knows the mass and velocity of the car, hence the momentum. That informatioin is also necessary in order to have determined the kinetic energy. The whole point of a collision analysis is that you DON'T know the distance over which the force acts. Here nothing has been stated regarding the second obect in the collision. It might be another car or it might be a large tree. The distances involved could vary quite a bit. Both are reasonable scenarios. The point is that energy considerations don't tell you very much, that detailed analysis takes a lot more information than is given, but that one can obtain a time-average of the force if one knows the initial momentum. A more important issue is why one is particularly interested in the force in the first place. That is not at all clear. There are more important parameters for most applications than either the peak or time-average force. Moreover, conservation of energy does NOT get you the restraining force. The initial kinetic energy of the vehicle is NOT the line integral of the restraining force over the applied path. Energy does not work like that. Energy is NOT a scalar and is not countered by the restraining force. There are lots of mechanisms for the dissipation of the initial kinetic energy of the vehicle -- plastic deformation and tearing of the material of the car, deformation of that with which it has collided for instance -- but the restraining force does not absorb energy. In particular it is NOT true that the restraining force x distance over which it acts is equal to the initial kinetic energy of the vehicle. Let's take an extreme example. Suppose the car hits an indeal (immovable) brick wall. And let's look at the problem in the reference frame of the wall. Then the restraining force (contact forct) exerted by the wall on the car acts through no distance at all, and therefore does no work. Energy tells very little. But the time average of that force is still determined by the momentum of the vehicle. The distance-average of the restraining force is meaningless in this idealization, as the distance is 0. Newton But see above. That energy has nothing to do with the kinetic energy of the vehicle, and that mean with respect to distance could be nearly infinite (in the idealization above it would be infinite). Yep. But not as easily as with AC at the proper frequency with a current path that disrupts the heart. With enough potential and current capacity you can vaporize someone. The Los Angeles Department of Water and Power has a very large DC transmission line that goes from hydroelectric generating stations in Oregon to an inverter station at Saugus, and I would advise against inserting oneself in that circuit. Do you have a point ? That is absolutely absurd. The power system does not define the impedance of the load. The load defines the impedance of the load. 400 Hz is a typical frequency in aircraft applications because of the widespread use of servomechanisms. Servo motors have a significant reactive component to the impedance. But there are certainly other devices that are also served by the power supply, and they will impedances that are characteristic of their configuration. This is getting silly. People survive all sorts of things. People also die from all sorts of things. People survive lightning stikes, and people die from lightning strikes. Damn few people are electrocuted by DC current, but it is not impossible for some idiot to find a way to do it. Yes you can survive long duration current with an associated high energy. You just have to have low enough power that there is no serious immediate effect. People who work with car batteries don't worry a lot about 12 v DC, unless they get a piece of metal across the terminals. Ditto for very low voltage AC power. So what ? You can also survive high power shocks if the duration is so short that no appreciable energy is transferred. Power system electricians have been known to test large busses by tapping them with the back of their hand -- not recommended but it has been done. So what ? You can most certainly have volts without amps. Ever hear of an open circuit ? There is a potential difference between the terminals at each and every wall switch in your house, until you turn that switch to the"on' position and energize an appliance in your home. If this were not the case none of your appliances would work. And you can have amps without volta as well. Ask the Cap'n about the experiment that employed him that deals with superconductors. I was recently asked if I had reason to believe that designated experts might not be quite so expert. Thanks for a sterling example.

Nice straw man. You again miss the points being made with respect to the fundamental physics. 1. As has been repeatedly stated, there is not enough information to solve the problem. Nevertheless the fundamental quantity of interest is momentum. That is because the question was phrased in terms of time and momentum is naturally related to force acting over time, and is a vector, while energy is naturally related to force acting over a distance, and is a scalar. This does not mean that energy is not a consideration as well. You have a complex problem involving non-linear material response, including buckling, fracture and ordinary material failure. There are a great many mechanisms through which the initial kinetic energy of the car can be dissipated and ultimately realized as heat. That is because energy is a scalar. Thus one has no means, outside of a sophisticated computer model, to keep track of all of these mechanisms. Momentum, a vector quantity, is somewhat easier to handle in this situation. While one cannot calculate the peak force, or the precise force-time curve, the resisting force integrated over time will equal the initial momentum (mass x speed) of the car. That much can be said. Using energy considerations alone you can say nothing. But once again, your call to "solve the problem" demonstrates nothing more than a lack of understanding of the underlying physics. As an observation I would note that this problem is somewhat analogous to that of calculating recoil forces when a gun is fired. Without knowing details about how the gun is supported one cannot calculate peak recoil force. Nevertheless, momentum conservation demands that the time integral of the recoil force be equal to the momentum of the projectile and expelled gas. 2. Electricity commonly kills by means of disrupting the rhythm of the heart, and is not simply a matter of either volts or amps. Frequency is also a very significant factor, as is the current path through the body. Frequency near the pulse rate can be particularly problematic and 60 Hz is sufficiently close. Frequency is also a factor in determining the primary current path, and the load characteristics are not just simple dc resistivity.

[math] log(Y-c)=b(log \ x \\ + log \ a)[/math] So now use your favorite method for fitting a line. A least-squares fit is one method. You may get a good idea of the value for c, from the behavior of Y for small values of X. However, the first step ought to be looking at the plot of log Y to see if a power law is even reasonable.

No, Timmer is not the nut job. It is the wacko interpretation of things like this that characterizes a nut job.

You might want to take a look at the book Orbital Mechanics by Conway and Prussing. It is quite accessible. Kepler's laws are derivable from ordinary Newtonian mechanics. In fact the motivating factor for Newton in his development of mechanics was to understand the principles behind Kepler's laws.

I see no reason to expect a simple or elegant expression for the derivatives that you seek. Take a look at simple case, say 2x2 diagonal matrices, and see how messy the expression is. It gets uglier from there.

So much for rockets and spacecraft. You really do need to read a physics book. Several.

Doubt anything that blows your skirt up. But you are wrong. Force acting over time is directly relatable to momentum. Force acting over distance is directly relatable to time. When your question involves force and time the relevant quantity is momentum rather than enrgy. Again this is only true for a linear resistive load. It is in general false.

General relativity is not an axiomatic theory in the sense that special relativity it. Modern presentations of general relativity are not logically reliant on the equivalence principle. It served a purpose in the discovery process of Einstein, but it is largely irrelevant to the logical foundations of the subject. It is absolutely untrue that "The EP is actually one of the axioms of GR, so if it weren't true then GR wouldn't be either."

You are right back to ordinary electrical generators. Some motive power (water turbine, gas turbine, steam turbine, etc) turns the rotor on a generator in a magnetic field and kinetic energy is transformed into electrical energy, my means of the mediating electromagnetic force.

The opposite of entropy is yportne, which makes as much sense as the question.

As you suggest, there are indeed lots of shoddy goods and poor designs on the market. But are they predominantly yours ? I wouldn't have guessed that. The time average of the force (presumably we are talking about the contact force between the car and whatever it hits) is tied to momentum, not energy. Better use a little engineering judgment and go read a physics book. Conservation of momentum will be a helpful principle in this problem. Conservation of energy is not so helpful as there are a lot mechanisms for dissipation of energy -- including material failure in the vehicle, which is a significant design objective in modern vehicle design -- that one cannot estimate without detailed knowledge of the car design and the pramaters of the collision. To make use of energy considerations you are right back to those detailed non-linear mechanics models.

I that case you might want to read a bit about Eugene Wigner. Wigner won the 1963 Nobel Prize in Physics for work in quantum mechanics, primarily for introducing group theoretic methods. http://www.nobelprize.org/nobel_prizes/physics/laureates/1963/ http://www.nobelprize.org/nobel_prizes/physics/laureates/1963/wigner.html While he was not a chemist, his doctorate was in Chemical Engineering. http://en.wikipedia.org/wiki/Eugene_Wigner

As I said that works if and only if the bridge is built at the equator in a perfectly north-south direction. That is an extremely restrictive and unrealistic assumption.

Think about cutting the cube along a few edges so that it can be unfolded and laid flat. That will not change distances of lines and curbes on the cube. If you make the cuts cleverly the answer will become clear.

Please inform me as to anything, anything at all, that has your design imprint, and I will most certainly try to avoid it.