studiot

Do you mean a transformer? Let us use this device as an example of how not to guess at the physics. By the way looking back, sorry about my poor spelling in the last post.

I have no objection to the namaste greeting. That is really good. I wish everyone was that polite. But your text is permeated with confusions about physics, and these are related to phenomena such as terrestrial plate techtonics, atmospheric effects and so forth. A magnetic field is generated by magnet. This filed only moves if the magent does. Solar winds are streams of charged particles emitted by the Sun. they do move and in doing so interact with the magnetic fields of the bodies of the solar system, according to Lorenz law. Does this help?

If you would like to discuss physics then let us discuss physics. If you would like to discuss far eastern religious philosophy, then surely the physics forum here is not the place. Please do not mix the two, they do not mix well. I suugest you look up the difference between a magnetic field, which is not moving, and a 'wind' which is and start your rethink from there.

OK, that is exactly what we do, only we don't call them points, lines or planes. We call them a small element dx and perform the summation on all the dx 's a small strip dxdy and perform a double summation on all the dx 's and dy 's a small section dxdydz and perform a triple summation on all the dx 's, dy 's and dz 's They do not have to be infinite sums, but if they are then the sums go over into integrals, as mathematic says. I am have tried to avoid this since I don't know your mathematical level, but the notation is A single summation becomes a single integral, which is just called an integral A double summation becomes a double integral, also called an area integral A triple summation becomes a triple integral, also called a volume integral There are some additional complications to this.

It is indeed fun and also very much a live and developing subject. The real question is where do you stop? Alongside the techniques you mentioned should perhaps be placed the calculus of variations and use of generalised coordinates. Probably the most modern developments are the applications to finite and boundary element calculations, powder and granular mechanics.

P and NOTP can only take you so far. Every designer of electronic logic circuits knows (or should know) that although logic circuits are based on the same propositional calculus as P & NOTP, there is a third option, known as tristate.

Acme, I think your Easter hangover must still be with one of us. I think you will find the text you attributed to me was actually penned by SamBridge (post#20) To continues with the geometry example I offered in post#12 Having defined a straight line in definition#4, Euclid went on to define a triangle in definition#19 as a trilateral rectilineal figure, contained within three straight lines. The theorem (he called them postulates) he developed from his axioms and definitions was that the sum of the angles adds up to two right angles. Now Euclid diod not know about spherical triangles, so if I offered a spherical triangle as a counterexample, disproving Euclid it is a good example of what ajb was talking about. Eulcid remains valid, with the terms of the definitions, but spherical triangles failure to observe the two rightangles theorem demonstrates that this theorem should not be applied to non rectilineal figures. So far as I can tell everyone is trying to tell you that the above is not so. Axioms are stated as true statements, without proof and have some independence from each other. Theorems are statements developed from these axioms in such as manner as to be true so long as the axioms are true. This process of development is called proof. A counterexample or other disproof would be of a theorem, not an axiom. You cannot disprove something you start out taking to be true, without proof. Thus a disproof would be against your development process, not the axioms. Of course you could one day find that your axiom has let you down and is indeed not true, which is why so much effort goes into testing them. But it is also possible that you could find conditions/definitions outside the original ones. This is the situation ajb and I are trying to explore here. Does this make sense?

Elsewhere I use the signature Do I look old? I don't feel old I don't feel anything till noon Then it's time for my nap. I definitely reckon that my avatar represents this statement.

imatfaal Agree entirely with your latest post but you mentioned your previous which made me go back and re-read. I cannot agree - there is no such sufficiently complicated system of axiomata that does not produce theorems that cannot be shown to be true and which must produce theorem which are not true but cannot shown to be false. This is Godels answer to Hilbert's Second (?) Question; no there is not a self consistent set of axiomata that produce all possible correct theorem but only produce true theorem. ie Anything complex enough to be interesting and useful will have self-contradictions, anything simple enough to not have problems is so boring to be of academic use only Sorry, I really cannot follow this or what you are getting at. Please explain differently.

Yes but the OP asked something slightly different. Yes, a single counterexample discredits a proof, but proofs are about theorems and the OP asked about axioms. There are no proofs involved with axioms. So all you can say is that a 'counterexample' highlights an area where the writ of one or more axioms does not run. This is what I described in my earlier post.

It's good that you understand it now.

I started this reply before ajb and imatfaal posted further, however the comments are still valid. I suggest you reread ajb's post#2. This was proved in the early part of the 20th century. But we need to go back a lot further. A system of mathematics (there are many, there is no single one) is a logically self consistent construct that builds on axioms to create theorems and other results. However it is not built on axioms alone. Axioms in isolation cannot provide sufficient information. The history of geometry is a good example. The original 5 axioms (he called them propositions) of Euclid were supported by 23 definitions and 5 what he called 'common notions', without which we could not have Euclidian Geometry today. Without definition 4 (a straight line) the rest is nonsense. If the analysis is not restricted to straight lines many of the results can be negated by a curved line as a counterexample. Exactly as ajb has indicated. In the 18 century (I think) one of the axioms was changed and projective geometry was born. (Some of) The theorems and results of projective geometry are at variance with standard Euclidian geometry, but the new system is consistent within itself and its altered axiom. In the 19th century, the fifth axiom was removed altogether to found Riemanian geometries. In the 20th century Geometry moved from discussion of figures and shapes as being the fundamental to discussion of sets, symmetries and groups.

Yes. Incidentally a 'series' is already a sum. A 'sequence' of points is just a list.

None of the laws of Thermodynamics refer directly to efficiency. Mechanical systems (machines) Efficiency is output work divided by input work. This also equals the mechanical advantage divided by the velocity ratio. http://www.slideshare.net/jbishopgcms/mechanical-advantage-and-efficiency and http://www.learneasy.info/MDME/MEMmods/MEM23041A/dynamics/simple_machines/simple_machines.html

Agreed. Don't forget that General Relativity (which deals with gravity) operates in 4D Minkowski space. In Newtonian physics (that you are describing) the gravitational effect and contant G is due to mass density in 3D space. In General Relativity these effects are due to momentum density in 4D Minkowski space.

If you weren't so commited to attack me for reasons that I don't understand, I'm sure we could cooperate a great deal better. This should not be contest as to who can pick the most holes.

Enthalpy post#89 At very high pressure swing, acoustics get nonlinear because P*V is a product. It stays nonlinear whatever the gamma. Anyway, sound is linear at the sound pressure levels produced by a bell. Using the product P*V is incorrect, although even Newton made this error. That is a pity since there is inverse proportionality ie if you double the pressure you halve the volume and so on. In this sense the P*V relationship is linear. The ratio is independent of the starting values and is constant. Using the correct adiabatic expression does not enjoy this cosy relationship of ratio, it depends upon the actual values. Enthalpy post#89 It is perfectly known that flexural waves become shear waves at higher frequencies, at about the frequency where both propagation speeds get equal. You almost got away from compression waves, go on, that's the right direction. Sound is slower in usual austenitic stainless steel, and by less than 20%. Wrong figures somehow. 6000m/s would be very much. Anyway, compression waves are irrelevant in a bell. 5000m/s would give a resonance outside ear's range, so it's about time to change your opinion. No compression wave. Extract from Kaye & Laby, for speeds of sound in solids all in m/s Mild steel Longitudinal bulk waves 5960 Waves in thin sections 5196 Shear waves 3235 Rayleigh Waves 2996 Stainless Steel Longitudinal bulk waves 5980 Waves in thin sections 5282 Shear waves 3297 Rayleigh Waves 3045 Penn University rated its sample as mild steel with a velocity of 5000m/s I keep repeating this, the action of the bell is a (complicated) vibration, not a wave. But you do not hear this action. You only hear the sound in the driven air. As to the frequency in the air, I was suprised that so many higher frequencies were present, but measuement shows that they are, and not all harmonically related. This implies that the mode of vibration of the bell is acting in 'panels', with small panels of bell wall producing the higher frequencies. This is consistent with the images in the articles I linked to. Enthalpy post#89 If a tuning fork is alone in air, it's a bipolar souce. Though, its bottom is commonly put on a wood part that radiates more strongly for being bigger - and sometimes at a resonator. The bottom (middle of the U shape) vibrates with a small displaceent that fits the wood part better. This movement can result in a monopole source if a resonator is used, often a quarterwave box. The ouptut from a tuning fork can be biploar, quadripolar or more up to full spherical. Clearly if there is a close plane or other boundary things will be different. Here is a good discussion. http://www.acs.psu.edu/drussell/publications/tuningfork.pdf

The analogies presented in post #1 are logically inconsistent. For example if I stand on a thick steel plate on the elevator floor, both the plate and I are pressed to the floor, the addition of the plate does not provide any shielding or interference effect. Suppose further that gravity were a 'universal field'. Then in order to "interfere with this field" as stated, a massive object would perforce have to produce a counterfield of its own, contrary to the stated premise. Actually I prefer the term interact, rather than interfere, which has some specifically different connotations. Finally in suggesting that a massive object can interfere with the field to the side of the body and at a distance from it is contrary to the suggested notion that massive objects just block it by being in the way. Note that we know light is deflected in passing massive bodies to the side.

Bearings are measured clockwise from the vertical axis on paper. This is the north axis on the ground and on the paper. I have started your sketch off by drawing a north axis from P due north and positioning Q on it 20km north. Then I have drawn a line from Q at 140 clockwise from this north axis towards R. Then I marked R on this line (which is the bearing of R from Q) at a distance of 8km. At this point I will leave you to carry on with the diagram to draw in the three extra lines needed to complete both parts of your problem, which is then just an exercise in trigonometry. Post your results when you have done this.

We have to be careful not to be too all embracing. What would happen if all the schoolkids were exactly the same height and you told them to line up in order? Or, since I can take any members what if I ask four hydrogen atoms to line up in order? How about a mathematical example, the set of 4 rotations by degrees {0, 360, 720, 1080} ?

You are talking about the phenomenon called 'real and apparent depth'. Look here http://www.physicstutorials.org/home/optics/refraction-of-light/apparent-depth-real-depth

I'm trying to avoid the thorny isse that strictly speaking the answer to the question "What work is done by the oil ?" is zero. So strictly speaking the question is faulty since it does not offer zero in the list of options. The next part is really a language question. Although the oil does not do any work, there is work done. This work is done by the ball. Both the ball and the oil cannot do work on each other or the two amounts of work would cancel out and there would be not net energy exchange. If you wish to consider this in terms of forces then the ball rubs against the oil as it falls and in so doing applies a frictional force to the oil. Also in falling the ball moves its point of application of this frictional force. Remember there are two conditions for a force to do work. Both these must be met. Not only must a force be applied but it must also move its point of application.. Now the oil also applies a frictional force on the ball But the oil does not fall. So the oil does not move the point of application of the frictional force on the ball. So the work done by the oil = force times zero movement = zero work. So the only work done is by the ball and energy passes from the ball to the oil. What the question wants is for you to calculate this energy and call it negative since it is from the ball to the oil.

According to your original sketch the 5A current is flowing in the opposite direction from the 20A current. Therefore the magnetic field circles the wire in the opposite direction. Note that you should not say "the 5A conductor"; rather say "the conductor carrying 5A", because both conductors could be identical, just one is carrying more current than the other.

The force and distance act along the same line in this case so the cosine is not invoked. That is the angle between the line of movement and the line of action of the force is zero and the cosine is therefore unity. The positive or negative sign is relative to our statement of which way the energy flows or what force does work on what body. This depends upon our statement. In this case the question was what work does the oil do on the ball? Well it doesn't. Where would it obtain the energy? What actually happens is that the ball looses some potential energy in falling. This energy is transferred to the oil as work done by the ball on the oil. Since the oil does no work, we can call the energy it receives, by way of work done on it, negative work. This idea is important because it is the cause of many errors in the application of the first law of Thermodynamics.

Here is what I think you your professor might be saying. Two long straight parallel wires pass currents in opposite directions of 20amps and 5 amps. Given the distances apart find the null points in the combined field. Now the fields are additive and the field around a single wire is circular and inversely proportional to the diatance from it and given by the equation at the bottom of my sketch. The sense of the fields is given by the right hand screw rule and is as shown. This allows a section or plan to be drawn through any plane at right angles to the wires where the resultant field may be calculated. Can you see how to do this? Note the cross and point should really only be used for the current in the wires. (imagine looking at an arrow and seeing either the feathers or the tip)