studiot

You have not yet addressed my question as to why there is no outward push (as you earlier asserted) on any link in my chain or any object attached to it.

Well before you open it, you can see that there is a (nearly) clear liquid almost filling the bottle. This liquid is still, that is it is not fizzing or showing significant activity or evidence of gas, if you do not shake it. When you release the lid the fizzing starts. You can clearly see bubbles of gas in the liquid. Where did they come from if they were not dissolved? The obvious (and correct) conclusion is that they were dissolved.

Yeah, that's good. You need a clear bottle of the stuff to see what it is like before you open the lid. That is why a can will not do. Before you open it are there any / many bubbles? After you open it there is clear visible evidence of gas being released. You do not know that this gas is carbon dioxide, from this evidence. Further tests would be needed to establish that.

Perhaps you should review your history sources? I have already pointed out that Einstein, in particular, is not a good example for this thread, and offered some who might be, for discussion.

Chemistry is a practical subject. Do you know some practical tests you can subject the water to? For instance what happens to litmus paper in pure water and water containing dissolved carbon dioxide, sulphur dioxide or nitrogen dioxide? What happens if you take a clear bottle of a fizzy drink and open the top? I am not sure what you mean by "bubbles are formed in a liquid solution"? Under what conditions? Bubbles will form if you boil that liquid, but they are not indications of dissolved gas. But they could be under other circumstances. Does this help?

You are asking what a rotating body 'feels'. Try this. Consider a rotating chain. Start at the first link by the pivot. The first link 'feels' a centrally directed inward force - the centripetal force. So it pulls inwards on the second link, to which it is attached. The second link therefore 'feels' an inward pull , so it exerts a reaction force on the first link which is also a pull, by Newtons third law. In turn the second link pulls inwards on the third link; it does not, however, push outwards on the third link. In turn it receives a reactive pull from the third link. This process continues all the way up the chain to the outer link. The outer link, or weight or whatever has no attachment further out so does not pull inwards on anything. No animals were harmed in the production of this post and no centrifugal force was involved.

I thought the presenter explained quite well. She said that you have Area as a function of two variables, x and y. You can't differentiate this to find a minimum, so you introduce a second equation connecting ,x, y, and a single variable or parameter m. This second equation is the equation of the line through the point 8,4. Now we know the values of x or y for two other points on that line. That is when x=0 or y=0. So we can substitute this (she did this at 3 mins 15 seconds) to find twio equations, one connecting only x and m and the other connecting only y and m. Then you can substitute for x and y in the original equation obtaining an equation connecting only Area and m. This you can differentiate to find a minimum. Does this help?

Of course, I could also offer Ramanujan as a prime (pun intended) example of an unknown but then we would have to accept the premise, Galois excepted, that to be such a super being your name would have to begin with R.

If imperial measure offends you, then call them all kg and metres - the numbers don't matter it is the principles that count. And the principle you have correctly observed is that the larger, 100unit , mass does not exert a centrifugal force on the breakable link. So why should the smaller 1 unit mass exert a centrifugal force on anything?

Not at all similar, no. Yes you mentioned acceleration and that is the problem. I said that none exists if you apply a balancing force. That is a definition of a balancing force. You did, however, correctly identify that the centripetal force pulls the rotating mass away from its inertial straight course, inwards towards the centre of rotation. Unfortunately you are also mixing up motion and acceleration. Motion (velocity) is a vector and has direction as well as magnitude. Change of either of these constitutes acceleration. What you are suggesting is because the radius is not changing there must be a balancing force. This is not so. The mass accelerates because it deviates its course from a straight line to maintain a constant radius. This deviation requires a net force to be acting or there could be no acceleration. If the centripetal force is 'balanced' by another, how could the acceleration be generated? Since you correctly answered my last question here is a more tricky one that an engineer ought to be able to answer. A 100lb mass is attached to one end of a 1 ft substantial chain and the other end anchored at a pivot. A second mass of 1lb is attached to the larger one by means of a single 1 inch link that breaks at a force of 10 lbs. The whole assembly is set in motion, rotating about the pivot as shown in the diagram. What are the forces on the link and when will it break?

This is the whole crux of the matter. I said, in my first post in this thread, that the rotating object is not in equilibrium. It cannot be or it would not be accelerating. It must be accelerating because it's motion is deviating from a straight line. Because it is accelerating it must be subject to a resultant or unbalanced force. Or because it is not in equilibrium is must be subject to an unbalanced force and therefore it must be accelerating. This acceleration is called the centripetal acceleration because it is directed towards the centre of rotation. So I repeat no balancing outward force is required, in fact one cannot be present. ************************************* You can, however reduce the analysis from one in Newtonian dynamics to a (often) simpler one in statics by introducing a fictitious balancing force called centrifugal force. In this analysis nothing is then considered to be accelerating.

Is any of this on topic? IMHO Riemann's story would provide better example of an 'unknown' offering a startling new theory that was not fully formed or without error at presentation, but yet lead us into non Euclidian geometry. Incidentally, Delta, special relativity does not conflict with Maxwell's equations. Further, Maxwell himself realised that c was independent of the speed of the source, as it is with any wave.

Mike, it might help to consider the question If a person on the edge of your roundabout dropped a ball, we all know it would fly off. But in which direction? tangentially or radially or in some other direction? It is perhaps easier to rephrase as If I whirl a stone around my head on a string and suddenly cut the string, which way will the stone go?

Congratulations you have just conceived of Peano's space filling curve. http://en.wikipedia.org/wiki/Space-filling_curve PS you can also use it to fill 3 or more dimensions.

I do not propose to enter a childish debate with someone who is labelled a resident expert on this site, so I am reporting the issue and personal way it has been presented for moderation. I did not in any way dispute what would happen with your hydrogen chloride - water system. I simply used a simple example that has been part of the UK chemistry syllabus since before GCSE was invented. In that case the process is different. Is the UK secondary school chemistry realistic? Well I have personal experience of measuring this effect in bridge post tensioning cables at different temperatures and the rate of corrosion is markedly lower in winter. go well.

I do not know if this is a question about thermodynamics or ? It is perfectly possible to describe a physical system that converts 100% of its energy from one form to another in theory. A perfect pendulum is such a system, converting kinetic energy to potential energy and back again in an indefinite cycle. But the energy is not transferred from one system to another, it remains in the one system.

Indeed??? I think I have it all right. However I was suitably vague about the case when there is a chemical reaction involved, because I do not know the circumstances. I do know that two (or more) substances undergoing a chemical reaction are not in equilibrium. I do not think bringing in more advanced thermodynamics adds to clarity. Let us suppose that we have an inert sealed container, partly filled with water and having an oxygen containing atmosphere above. Some of the oxygen will dissolve in the water, there will be no chemical reaction so my first condition will pertain namely that the % dissolved oxygen will decrease with increasing temperature. Now let us introduce a quantity of finely divided iron into the water. Over time there will be a chemical reaction between the iron and the hydrated oxygen (the iron will rust) which will remove oxygen from the water, allowing further oxygen from the atmosphere to dissolve. Eventually it is possible that all the oxygen will be removed from the sealed atmosphere this way. The rate of this process will increase with temperature. But things are more complicated and the rate of solution involving a chemical reaction may increase, decrease or show a definite maximum at some preferred temperature. I did wonder if this was about the solubility of aerial carbon dioxide in seawater.

So given the information I have offered, your thoughts are? Is an electric fire bar more efficient at converting energy to heat than a gasoline engine?

The solubility of gasses that dissolve in water, but do not react with the water, decreases with increasing temperature. An example of this would be oxygen, which has a solubility of 1.5 mg/L at 0C and 0.8 mg/L at 30C If, however, the gas chemically reacts with water and this reaction speed increases with temperature, then the solubility will increase.

Well what do you think? Have you taken several known examples of energy transfer and compared their efficiencies?

Those who wish to trace the history of the atmosphere and its relationship to conditions, and life, would be advised to read the Oxford University book The Emerald Planet by David Beerling. As far as I know it is the only modern book dedicated to this subject. In particular Professor Beerling discusses and answers the headline question of this thread. go well

Because there are more of them?

Nice pictures, good job your visit wasn't today.

swansont, thank you for these thoughts, I will look into them. It is a pity no one else wishes to chip in.

Look more closely at my previous post. Point 1 states quite clearly: start with the set with no members and I used the conventional symbol for this - [math]\emptyset [/math] It is officially called the empty set and is literally nothing. Note there are no brackets. This is the first term in the sequence. Now point 2 describes how to create the sequence. The brackets are a common mathematical notation for enclosing the specification of a set. This can either be by enumerating all the members, as I have done, or by providing a rule or formula for identifying members. Create a set that does have members, in fact create a sequence of sets linked by the rule that each succeeding term contains all the previous terms as members. So each term is a set with one more member than the previous term. To show they are sets enclose them in brackets. So the second term in the sequence is a set with precisely one member. This member is the empty set described above. The next term has one more member, ie precisely two members and these are the empty set and the set with one member. the next term has one more member, ie precisely three members and these are the empty set, the set with one member and the set with two members. You can, of course, proceed indefinitely with this process. And each term is constructed from - nothing.