studiot

Is this an exam question? A lot of folks are doing physics exams at the moment. Here is a hint, to explain the difference you should think about energy, both energy sources and energy sinks (dissipators).

OK, plastic theory works like this. Take an irregular (bumpy) horizontal surface. Because it is bumpy it must have a highest point Now place a second perfectly smooth flat surface onto the bumpy one. I am only using a flat second surface for simplicity of explanation the pricciple is the same for an irregular surface. Clearly the flat surface will touch the highest point of the bumpy one first. Now the stress equals the contact force (weight of the second object) divided by the area of contact. But this area is very small. So the high point will deform plastically until contact is made with the second highest point. And so on to the third, fourth etc highest points Until the area of contact is sufficient to support the contact force without further deformation. This plastic deformation joins (bonds) the two objects across the area of contact. Breaking this bond requires a shear force equal to the frictional force calculated from the coefficient of friction. I do not have the time tonight but you can derive that [math]\mu [/math] [math] \approx [/math] [math]\frac{{{S_s}}}{{{S_y}}}[/math] That is the coefficient of friction is approximately equal to the ratio of the shear strength to the yield strength.

I've made my point that I think this belongs in speculations. Yes there are many ways to calculate an average. Again I ask why kinetic friction? Perhaps I have misunderstood, but I thought your model involved considering (adding) all the side thrusts from the local irregularities pressing against each other at random angles (hence the average angle). This would obviously also work for static friction. But my point was that the meshing of the local irrecularities would vary as the two surfaces moved across each other. This has nothing to do with conventional plastic theory. I will explain that if you wish. You can arrive at a reasonable estimate of the coefficient of static friction for metals with it and account for the drop between kinetic and static friction.

This is the first time I have seen you present a plausible theory, so +1. A few questions to help you develop it and compare it with conventional theory. Why have you not posted this not in speculations since that is what it is? Why have you chosen kinetic friction? surely your 'average angles' will change as the object slides? What predictions does your theory make? I can immediately see a testable one, but will leave you the honour of stating it, since it is your theory. How does it compare with conventional plastic flow theory of friction? The two theories are not actually incompatible. I look forward to the development of this speculation with interest.

Suppose I take a journey from A to B and plot a graph of the distance travelled en route. Can I say that this is the shape of any physical object? Of course not. It has a definite shape on paper, that's all. If pushed I could observe that it must never be decreasing, unless I went back towards A at some stage. A shape is a surface in 2 or three spatial dimensions. Like the surface of a football tells us it is round, or more accurately a sewn together polyhedron of flat (ish) sides. My graph above is a shape on paper in two spatial dimensions. I am just using one to represent time. This is the source of my query about what you are asking. Now can you see why the question "What is the shape of a photon?" makes no sense in that context?

It is still essential that if you draw a graph (which your sine curve is) you understand (and preferably label) the units on each axis. You have not done this. I repeat understanding this is the key to understanding your difficulty. Are you with me thus far?

Good evening Ophiolite, Now that it's tea time and you are therefore in a really good mood, please sign the attached bearer cheque for $1million and return it to me.

So I am wasting my time, since you do not wish to address any of my comments.

DParlevliet, Am I wasting my time or do you want an answer to your original question? Swansont et al have told you the truth about waves and slits but their discussion is not about shape. The vibrating string analogy is useful in some respects but fallacious in others. And 'shape' is one of these others. The wave variable in a vibrating string is displacement. Displacement in say the y direction if propagation is in the x direction. So both x and y are distances. This allows the equation to directly display the two dimensional shape (in the x-y plane) taken up by a vibrating string. In sound waves, however, the wave varaible, is pressure at a point. This does not take on a shape in space in the same way. Can you imagine the 'shape' of a sound wave? You can only draw pressure contours of the sound field. The Schrodinger equation is similar in this respect to the sound field equation. The wave variable is a derived quantity, not even as recognisable as pressure. The axis variable is certainly not a distance, so again the solution does not take on a 'shape' in space.

The force field depends upon the source of the force, for example gravity or electrostatic attraction/repulsion. Do you know any that depend upon temperature and if so the temperature of what?

I'm really sorry to rain on your parade, but how many axes did your picture have and how many did you label? I keep nagging at this because the answer is the crux of your question about shape.

That's a pretty wavelet picture. But you need to label your axes. What are you plotting against what, which was in effect my orignal request about your question and the proper basis (I think) for your answer.

Can you elucidate further what you are expecting? I mean the 'shape' of what exactly? The photon is better modelled as a wave packet. It is not a wave in the sense of a sine curve, though it is often drawn as one. In fact a sine curve is one it can never be, simply because the sine curve periodically equals zero and the so called probability 'wave' is never zero anywhere in the universe.

It seems to me that both science and religion put too much effort into contemplating matters for which we have far to little information. An observation summed up in the above famous quotation. The likes of Mother Theresa or St Francis of Assisi in religion or Harvey and Gilbert in science are in the minority.

You are thinking about activation energy, which is often required to start a reaction or process. In your case you provide the activation energy through the friction of the matchead on the box. For an exothermic reaction you eventually get back more energy than you put in so once started the reaction proceeds by itself (is spontaneous). For an endothermic reaction you have to keep putting in energy to keep it going. Note that the terms exothermic and endothermic only refer to the input or output of heat energy. Here is a clear explanation. http://www.gcsescience.com/rc24-energy-level-diagram.htm

That's a very good question. I will have to rethink that part.

If you have an infinite set of linearly independent vectors and take one away, how many do you now have? So for instance in fourier analysis where the vector space is the (infinfite) set of continuous functions. we do not normally include the zero function (y=0 for all x) in the series.

I don't have to tell you anything. But since you asked so pretty please nicely: You asserted You have asserted that a particular complex number Z1 is equal to another complex number Z2 Equality is the most fundamental property definition of a complex number after the definition of the complex numbers themselves. Definition: A complex number Z1 is equal to another complex number Z2 IFF ( if and only if) the real and imaginary parts are separately equal. That is Re(Z1) = Re(Z2) and Im(Z1) = Im(Z2). Your numbers fail to meet this criterion. end of. Incidentally in you playing with complex square roots are you aware that not all complex numbers have square roots? Amaton has started a thead to ask about this, you should perhaps follow it. [math]{Z^{\frac{1}{2}}}[/math] Is only defined on the cut Z plane which excludes the negative real axis? http://www.scienceforums.net/topic/79290-the-12-power-and-square-roots/

In complex analysis the square root function has two branches. By convention, the principal branch maps the Z plane onto the right hand half of the w plane, allowing for cuts.The other branch is equally valid but has no special name and maps the z plane to the left hand half of the w plane in mirror image of the principal.

No, you are doing more. You are asserting something we all know to be false, and then asking what I think. Why are you doing this?

A tad more than just showing me something, I think.

Deidre, I see that you are form the United States. Perhaps that is why your experience of arrogance is different from mine amd you identify it with a feeling of inferiority. Being English, I have a lifetime's experience of the english upper classes where to many (but not all) arrogance comes naturally from a feeling of superiority (deserved or not). I certainly wouldn't propose that this group has any higher level of intelligence than the population at large, though fortune has smiled on them somewhere along the line.

If I write something I know is wrong like 2=3, I work at it and worry at it until I find my mistake (and I always eventually do). What I don't do is to present it to others as a proof that i have discovered something new. In fact i have made some small advances in my time, but always it has then been in accord with what I already know and extended my knowledge.

I prefer to think in pints.

FYI there is at least one more way. http://www.mathwarehouse.com/quadratic/roots/formula-sum-product-of-roots.php