studiot

Then work is done on or by some agent. You have asked a very reasonable question that often puzzles folks and received a relatively short answer from swansont, as he has many calls on his time here. I have tried to fill in some of the gaps but you don't seem to like responding to more than a small part of posts. I do not wish to indulge in verbal fencing about this subject. I gave you the answer in post#13. The gravitational energy is inherent in the whole system by virtue of the masses and separations of the particles involved, according to the equations being bandied about. It manifests itself as the (gravitational) potential energy of the system. If either the separation or mass or both change then work is done, perhaps on one or more of the masses or perhaps on an outside body. The work done exactly equals the change in gravitational potential energy. In other words that is the available energy from the change. In order for the system to have arrived at its present state energy must have been input in the past in the form of work by some agent. We do not necessarily know the details of this, only the quantities. So that is where the energy came from. We observe the effects as 'the force of gravity' in Newtonian mechanics, or alternatively the acceleration due to gravity, but as swansont has already noted, we do not know how this force is generated. That is one of the big question curently being attempted by modern physics.

The negative sign is so that as objects approach closer to each other positve work is obtained from the potential energy change. So a falling stone does work, but it takes work to raise a stone upwards. You didn't reply to my last post noting that it does not take energy to maintain the presence of a force. You should also note that the potential is inherent in the system ie both the earth and the stone together, along with their positions and motions. It is not a property one part alone.

The classical view (originated by Ampere) is that magnetism is generated by (very) small current loops. This works for Gauss and Amperes law (without relativity). You should look up the 'Rowland Ring' theory, which is the most modern version. The more modern quantum view is that the loops are replaced by the spin of the electrons. By the way I think you are doing very well for your age.

Forgive the obvious, but for a particle is the 'vibration' not transverse, so it is neither moving away from nor towards the centre? Hermite polynomials have radial symmetry and apply to shells which do indeed vibrate in and out, but then shells are the other face of quantum mechanics and not particles.

This assumes you require energy to generate a force. That is not the case. Forces and energy are different, independent physical quantities. You need to get this very clear before proceeding to study types of energy. A simple example is a brick sitting on a table. The table exerts a force on the brick. No energy is involved. Energy is only involved, as uncool said, when something changes.

I should have added that not every section appears in every paper, and some papers may have additional ones I didn't mention. The list is a guide, not prescriptive. Also as mentioned some publishers do prescribe a particular format.

But fractions too are more than just numbers. What number, for instance, is represented by this fraction? [math]\frac{{{x^2} - 2x}}{{x + 6}}[/math] And what about the many types of fraction Algebraic fractions , continued fractions, partial fractions to name but a few more. Continued fractions are good fun becasue they represent an alternative way of thinking about recurring decimals or irrationals that have been discussed in this thread. [math]1 + \frac{1}{{1 + \frac{1}{{1 + \frac{1}{{1 + \frac{1}{{1 + ..}}}}}}}} = ?[/math] Is a definite (irrational) number, but is it a division?

Personally I would say that division is a process and a fraction is one presentation of that process and that Myuncle is correct in observing that they are different, even though his arithmetic is a bit rambling. You can apply division (ie operate the verb to divide) to more objects than just numbers. Indeed engineers perfected 'dividing engines' for just that process many years ago. Dividing a circle is exactly what is involved in creating pie diagrams. So yes I agree with Myuncle that even at early stages in teaching we should distinguish between fractions and division as the latter can and will be applied more widely in later teaching. It is an old saw that, however simplified our treatment, we should never teach something that we later have to say "that was actually false".

quote ajb "Right okay" Hopefully this makes now sense of my other posts for you. I'm sure you recognise the integrals fraction/division I posted that confused john cuthber as the x coordinate for the planar centre of gravity.

Are you sure? http://en.wikipedia.org/wiki/Gravitational_potential

Well as you observed the contact force of magnetic attraction is a direct force. That is to say it is a normal force between the magnet and the object. Newton's 3 rd Law says that this attractive contact force is balanced by a normal reactive force which is equal in magnitude but opposite in direction ie still normal. A lateral force applied to the object is at right angles to this and only faces the force of friction. The frictional force against sliding is the normal reaction force times the coeficient of friction. Since the coefficient of friction is less than 1 (typically 0.3 to 0.5 for a magnet and a piece of iron strip) the sliding force is less than the normall pull force.

Quote ajb All you have done is multiply two numbers together. You can think of any number as a map from the real line to the real line by multiplication. I'm sorry you are not understanding what I wrote. All the examples are written using operator notation. Yes indeed the first two examples boil down to the multiplication of two numbers, but the third example is not multiplication in any sense. Are multiplication or division not operations? In the third example I am operating on a circle with the ratio or fraction a/b. This would give me a sector and is purely geometric.

Good evening Myuncle, No it isn't, but a fraction is always the same thing as a division. That is because 'a division' applies to a wider class of things than just numbers. For instance my earlier comment A line divides a plane into two regions. It makes no sense to attempt to write this geometric statement as a fraction. But all fractions imply that you have to divide the bottom into the top, or divide the top by the bottom if you prefer. Of course you should distinguish between proper fractions that are numerically less than or equal to 1, and improper fractions that are greater than one. You should also note that there are numbers that cannot be expressed as a fraction (if you count fractions as being only of the form a/b where a and b are single numbers) unless the bottom number is one. These are called irrational numbers, and their existence greatly troubled the ancient Greeks.

So you actually agreed with me all along. Thank you for confirming that.

No I don't think I am being lazy, I am agreeing with you that either the word division (noun) or divide(verb) or the ratio symbol a/b have more than one meaning in mathematics, and I have been trying to demonstrate some of these. eg " A line divides the plane into two regions" However I am also suggesting that the particular meaning is normally very clear from the context. This is unlike many of the other words in my mathematical dictionary that benefit from multiple meanings and give rise to far worse confusion IHMO.

I wasn't suggesting that / is an operator. I was suggesting that the expression 3/10 or more generally a/b can be considered an operator. Not only on numbers, but on other objects such as circles. That is how a pie diagram is generated. So I repeat my question. What in the definition of operators prevents a/b being an operator? [math]\frac{a}{b}(1)[/math] [math]\frac{a}{b}(10)[/math] [math]\frac{a}{b}(\bigcirc )[/math] All have valid meanings if a/b is regarded as an operator IHMO.

What about the definition prevents it being an operator? Obviously it could be generalised from specifically 3 and 10. edit: This is not to say that it couldn't also be something else in another context.

Consider the following [math]\frac{3}{{10}}[/math] What does it say? Well it could say I have divided something into 10 (equal) parts, but that I only have three of them, So do the other seven parts exist, did they ever exist? Can I consider 3/10 as an operator that carrys out the operation of dividing into 10 and discarding seven of the parts?

Pity you have started mud slinging again. I am quite well aware of the difference between dividing in half and by half. That is the whole crux of the question, that even in mathematics, it (edit : dividing ) has at least two meanings. I notice, incidentally, that you have avoided my questions about dividing pies or integrals.

What is the difference between the surface of a (polished) metal and a piece of paper at a microscopic (not molecular) level? What is the difference between their material structure?

Why is division to be restricted to integers? Even more interesting is to consider the dual propositions: Take 6 oranges and divide them by 2, which come out at 3 as noted by others. But compare Take 6 oranges and divide them by 1/2. This comes out at?? Or what about [math]\int {xydx} [/math] divided by [math]\int {ydx} [/math] How do these examples play with the idea of parts, equal or otherwise?

Sorry, can't agree old bud. and that goes to the heart of Myuncle's question. The quotient formed by dividing 6 by 3 is 2. It is a single pure number, not a number of parts, each comprising a pure number. However it is perfectly respectable mathematics to divide something into a (not necessarily equal) number of parts, which may or may not be numbers. For example a pie diagram. I note that john cuthber's interpretation of repeated subtraction also end up with three parts, not a single number. Myuncle wished to distinguish between these two uses.

To a large extent it depends upon the dictats of the publishing house or conference where you intend (hope?) to publish. These may be obtained from the publisher, sometimes online on their website. The first thing to do is to create the Title and draft abstract, which states the objectives and results, but not the detailed method. It should also contain keywords that will be used by archivists in future subject searches. The importance of this is it is your sales pitch to the publisher. (S)he will then tell you the required format details. The meat of the paper will follow conventional lines: Introduction Development and presentation of work Results and discussion/conclusion References Recommendations for further work Appendices. Here is a short example Title : Greens Functions For General Disk-Crack Problems Abstract : The two dimensional elasticity problem of a circular disk with an embedded edge dislocation is considered. Using Mushkelishvili's variable method and reducing the case under consideration to a Hilbert problem, a closed form solution is obtained. The dislocation solution may be used as a Green's Function to tackle general disk-crack cases. As an example, a disk containing a slant crack subjected to point loads is studied, numerical procedures for calculating the stress intensity factors for both internal and edge cracks are presented. I have highlighted some keywords, but the author has squeezed many more into the abstract.

Do you? Are you quite sure? Where was division into equal parts mentioned? Why can you not divide 6 oranges into three (still whole) parts thus: 4 + 1 + 1 ? Are not the meanings of the terms 'division', 'rational' and 'fraction' usually apparent from the context? Not always. I understand what Myuncle is saying. Division has different meaning in mathematics, inheritance and physics where dividing a whole into parts is often meant. Strangely you can multiply by dividing. For example : The general divided his force into two. Meaning he now had two forces!

When you get your quota sorted, I recommend using greyscale for preference, they automatically take 1/3 the memory size of colout. You can get even smaller if you use 2 colour gif format, but I don't know if this forum supports that.