studiot

I agree with Strange +1 Your explanation doesn't make sense so please reword it. When you do this please consider what happens to the charge when it arrives at 'Earth' - shell A? 'There is a conservation of charge law'

With regard to post#5 I agree that the OP has been misunderstood. I also think that Lord Antares has misunderstandings of his own so the replies are not wrong, just at cross purposes. This quote for swans states the general Newtonian formula, but the response does not address what LA is trying to say, since he is proposing that r in general is getting larger, for two general bodies. Assuming G does not change over time. So yes, if and as astronomic bodies move further apart, the net force on each will diminish. This is entirely consistent with a geometrical interpretation that the larger the radius of a circle the flatter the circumference. But it does not mean that the effect we call gravity is 'weakening' in an Asimovian sense.

Dear old Leibnitz. His notation is so convenient and flexible. The main difficulty was typng the text, but no longer with modern computers or handwriting. Writing f'(x) can be done on a single line. That was a good reason to introduce it. Thank you for referring to Thomas & Finney (I have the 9th edition). I think I have spotted your difficulty. The differential defined on page 251 is dy, not dx Using Leibnitz makes this more obvious [math]y = f\left( x \right)[/math] [math]\frac{{dy}}{{dx}} = f'\left( x \right)[/math] differentiate with respect to x [math]dy = f'\left( x \right)dx[/math] [math]df\left( x \right) = f'\left( x \right)dx[/math] but isn't dy clearer than the last line which is your original definition in post#1? Note also that both dy and dx are classed as variables.

A slight digression but you might like to try to get this book from your local library. The Self-Made Tapestry by Philip Ball Now issues in three volumes there's lots of accessible stuff in there for you including discussion of sand flow, up to and including why you should not overload a cement mixer. https://www.amazon.co.uk/s/ref=nb_sb_noss?url=search-alias%3Dstripbooks&field-keywords=philip+ball+tapestry+of+nature

Science Forums are obviously bestest but here is also good http://chemistryhelpforum.com/

Hello, ILikeChemistry and welcome to Science Forums. I see you are in Oz and now offline. Sorry I missed you. The phenomenon you describe is called 'liquefication' and is a purely physical action. No ghoulies or ghousties are involved. I'm sure it was pretty frightening and I understand (perhaps the biologists here will give more information) that some marine organisms use this effect. But I do not think that an animal source would be more than quite local. Liquefaction occurs through both saturation of the sand and vibration. I'm sorry I can't find a year 8 explanation here is a much more advanced one. http://web.hku.hk/~junyang/pdf/Yang_Savidis_JGGE.pdf Essentially sand can support loading pressure when dry but when wet or vibrated the sand grains flow away from the source of loading like a liquid. Sand is a non cohesive soil. This means that there is no chemical interaction between the grains so any transmission of force is like a dry stone wall. (Dry stone walls are made without mortar) Such a material cannot support tension. It can only support compression. So when the material is loaded by your weight, the bursting force under your feet (which is tensile) pushes the grains aside. Hope this helps.

There are plenty more criticisms that can be levelled against that vid. The front of the train hits the unbreakable door huh? And then what ? Well it stops. Stops, you say? Well yes it is at rest relative to the track. So what is the train length now as seen by the bloke on the train v the train length as seen by the girl on the track?

Yes I watched with the sound off. But I wasn't convinced either by the proposed events or the proffered explanations. I am particularly suspicious of this comment Isn't that contradicted by the observed fate of cosmic pi mesons?

Hello sensei. Maybe there is a thermal effect. I don't know but I think perhaps there is a polarity effect here to build the branching dendrites. Like charged particles repel so form the extending but branching structures. You can also see this on the structures built by iron filings on magnets. The individual filing particles are attracted to the magnet but repel each other and the resulting balance is branching.

Good to see the interest. An English note: we say the "derived function" or just the "derivative" we do not usually say the derivative function It is, however, difficult to guess the level to answer at since you are discussing a very simple function of a single variable but some of your comments hint at a much higher level of mathematics. For example you mentioned differential forms and your answer about the definition of a function. There are a lot of different notations about for calculus. Further many different sorts of people use calculus for different purposes. Some of the people are much more rigorous than others. Many people mix up the notation and/or terminology. None of this really matters for the calculus of a single variable and people muddle through. More rigor becomes important with multivariable calculus. This is where the 'differential becomes important. The differential is really defined as a transformation from Rn to R where n is the number of independent variables. I don't know if your studies are ready for this or where to start for you so I am going to post two pages from different textbooks. Please say if anything is familiar. Or do I need to start further back? I will be away for a few days now so see what you can make of these pages.

Quote working here today. I think dendrification might be the correct word. https://www.google.co.uk/search?q=dendrification&sa=X&biw=1366&bih=679&nfpr=1&tbm=isch&imgil=M7xNRoKqBuX7tM%253A%253BsnkLg87mR0oxVM%253Bhttps%25253A%25252F%25252Fkarczmarczuk.users.greyc.fr%25252FTEACH%25252FProgSci%25252FTD01.02.html&source=iu&pf=m&fir=M7xNRoKqBuX7tM%253A%252CsnkLg87mR0oxVM%252C_&usg=__-U1cFmc2pnohD8_7YGAKgM5DcGA%3D&ved=0ahUKEwj62szYrK7RAhUFBBoKHQjVAmkQyjcIKw&ei=y_xvWLrJCoWIaIiqi8gG#imgrc=M7xNRoKqBuX7tM%3A It is certainly an interesting extension of kirlian photography.

Just to show we all make mistakes this line in post#73 Should read d = ut + 1/2 at2, Your approach will get you into greater difficulty when you come to more advanced dynamics like motion in a circle and impact/collision. There is no potential energy involved, for instance, when two billiard balls collide on the table, or a bullet hits a target. gravity is not directly involved. How does your analysis handle the interchange of KE here?

I went through your questions and working in great detail. Following a complete failure to address even one of my questions, why would you expect me to answer yours? The above is just a load of waffle.

First thanks to imatfaal for sorting out the Augean stable. Then to return to just before we left off. A previously missing question and answer was Yes delta [anything] is defined as [anything2] - [anything1] So what? That is just notation for the difference between the value of anything at point 1 and point 2 So the previous statement defines a notation for delta f(x). Then the statement says (your words) "a good approximation" is given by (defined by if you like) the expression with the approximately equals sign. This says exactly what I wrote out previously. Whether you realize it or not, you included both functions and the values of those functions in your question and mixed them up in your thinking. I have said this before and already indicated that there are two functions involved The derived (not derivative) function and the original function. (That by the way is how the name derivative came about) Both of these are functions in their own right and therefore have values. You can only subtract values to obtain a Delta [something] Because you introduced additional quantities that were not in the original definition you posted as a question.

For those who might be wondering what this is all about, Posting a reply went badly wrong for me this afternoon in this thread. http://www.scienceforums.net/topic/102139-rigorous-definition-of-differential/ and imatfaal is very kindly helping out. Please note there is still something wrong there.

Thank you for drawing the short straw. This proves the text entry editor is behaving normally for me in other threads. Of course the concepts of stability also apply to particles, great and small. So yes given the vagueness of the word 'stable' as used here the scope could easily be extended. I do think, however, it is important to emphasize the difference between stability and equilibrium, which are different things.

The rest of the site seems to work normally but this post is obstinate. The whole page changes when I open this thread and the text entry box is wider. Also it did not correctly post your quote, on my screen at least. ************************************************************************************************************************************************************************** Edit it is still playing up for me so the following should have been in a separate post. Hamed Here at least is one part of quite a long explanation I wrote. I am sorry that much of it is missing: I will try to add back more later. I had broken it into parts before as promised. There is no reason to expect an explanation or definition of how to form d (f(x)) in the definition of a differential any more than to expect a definition of how to form say x3+x2+x+3 or sin(x) in the definition of f(x). In fact d(f(x)) is quite rightly not mentioned at all. So why bring it up? You have not even acknowledged my comment about the difference between a function and the value of a function at some point. I did indicate that this was key to answering your question. Do you actually know what a function is?

Neither Post#1 nor the title mention atoms on my screen. And it is posted in the Chemistry section.

I think itoero made the same point I did earlier in post#3 What do you mean by stable? Further surely this is a chemistry question since it refers to all these compounds reacting with each other, not isotope decay.

Let's do this a bit at a time shall we? Yes delta [anything] is defined as [anything2] - [anything1] So what? That is just notation for the difference between the value of anything at point 1 and point 2 So the previous statement defines a notation for delta f(x). Then the statement says (your words) "a good approximation" is given by (defined by if you like) the expression with the approximately equals sign. This says exactly what I wrote out prevciously.

The definition you quote is a bit ambiguous (though whether most textbooks use it or not depends upon which ones you have read) This version brings out the meaning more rigorously. [math]\Delta f\left( {{x_1}} \right) \approx f'\left( {{x_1}} \right)\Delta x[/math] Basically in words it states The change in the value of the function of x, f(x) at the point x1 is approximately equal to the value of the derived function f'(x) at x1 multiplied by the change in the value of x. There is nothing circular about that definition. All you need to do is distinguish between functions and their values.

A good readable source for this is Contemporary Quantum Chemistry J Goodisman Plenum publications The main reason you need Legendre is the integration of the spin in an electric field.

Was the negative vote here a mistake? This could certainly have been better phrased, but deserving of a negative vote? I have added +1

If this nonsense if left unchallenged others trying to understand this subject may think it authoritative and get the wrong idea. So let us look at your 'algebra'. Formula? What formula? This clearly comes from the correct full formula d = u + 1/2 at2, with u = 0 If u can equal zero then so can a so what is distance for a body that is just moseying along at velocity v? Does it not cover distance or enjoy a kinetic energy by virtue of its motion? I notice you said if you apply a force. And if you don't? It would be better if you said that the change in KE is the additional energy gained by the accelerating force if one is applied. This was already discussed earlier in the thread. By the way what distance? Is moment energy? I ask because Newtons times metres also defines moment. And if a = 0 Oops division by zero. Many false results can be 'proved' using division by zero. What theorem states that PE = KE? What variables do you think are vectors and what do you think are scalars?

Sorry about the link it is the University of Chicago. I wasn't directing my thoughts particularly at sub atomic particles, or parts of them. Shape is important in the properties and therefore the interactions of some molecules eg cis and trans isomers. Orbitals can be 'bent' by lone pairs - the most famous example being the bond angle in water Molecular sieves can be blocked up by long thin molecules, that could pass through length ways, but not width ways, just as effectively as sticks crossways can block culvert grids, although they are thin enough to pass through end on.