studiot

Apart from this, I basically agree with what you have said in post#16. But that does not prevent one of the connections acting as a ground, which was the main point made in posts 12 and 13.

Funny I thought my post#43 quoted exactly Newtons words (at least the English version). And, as I pointed out, they differ significantly from yours. As an example suppose I said I was going to give you some £s, and handed you one £. It really is also instructive to consider the inverted pendulum theorem I mentioned in post#41. In particular I am not the one who started this thread with a link to a professor of history, presenting this subject such that his opening equation is flawed as it does not pass a simple high school dimensional analysis test.

I wouldn't, but then I read very carefully what Newton actually wrote. The real solution to this apparent dilemma is in appreciating that all three of Newtions Laws are necessary. Together they make up complete set that prohibits the sort of difficulty or contradiction that can be otherwise dreamt up. Unfortunately Newtons Laws are all to often presented with one as a special case of another. This is just not so.

The beauty of a ground is that you can take an electron from it and stick it into the other battery terminal (to which it is connected) as many times as you like without reference to something 10mm away, let alone 10 light years.

But the mass in Norton's dome is being affected by (at least) two external forces.

Agreed, I have given Gweedz + in recognition. As a matter of interest the length of the return wire is almost immaterial. It is only the length of the supply wire that counts. There are electric supplies on this planet that are single wire and earth, used in some remote areas. I calculate that the mass of a typical 1mm2 lighting copper cable of length 10 light years to be about 1015 kg. This would be a sizeable enough chunk to regard as a pretty good earth, certainly enough to sink the supply current to a light bulb, arriving from 1 light year distant.

No I don't think that's what Newton's first law says and I don't thing that is the situation in Norton's dome either. Edit here is the generally agreed nearest English translation to N1, which was actually written in Latin.

At the risk of yet another unwarranted bloody nose in this thread I would wish to comment that it is instructive to consider the issue in the light of the inverted pendulums theorem.

san, you have mentioned equivalent weight which is an old fashioned term not often taught nowadays. When you reply to John's question about homework please tell us the circumstances of this question so we can find out if you really need the equivalent weight or another property.

You could make the question more interesting by making one leg of the connetion 1 light year long, but the return leg 10 light years, by a more wiggly route.

One thing I have learned over many years is that when I want to understand something is to start with something simple (and preferably well known) and build up my picture, along with my understanding. That is what I am trying to (help you ) do here. So the next stage is not to jump straight to rotating systems but allow my train to accelerate along the tunnel. This should establish the principle that there is now another force acting on the block, that should be taken into account. A force is (by definition) a line object - A force acts along A line, not two lines or ten lines, one line. What we want to determine is: What line? My train is a simpler system because that line does not change. Introducing rotation is more complicated because that line is constantly changing. This is no different from the normal reaction constantly changing in direction as the objects slips down the dome in the current Norton dome thread (I don't know if you have seen that one, but I have stepped out it of because of the hostile and juvenile reactions I received to my thoughts). Anything that is continuously changing direction must be subject to a rotation.

Are you serious? Is that your only comment on the work I out in to help? Yes the table could be mounted on a railway truck travelling in an evacuated straight level tunnel at a steady 25 m/s. Do you understand what the frictional force must be between the table top and the block in those circumstances?

That just ain't possible within the specification. The contact was specified to be frictionless so you can't roll it up or down the dome. Just because the proposal has a big name behind it doesn't mean we should stop being critical (in the correct analytical sense).

Since there has been some talk of objects being held in place by friction in one direction, whilst being moved along by another force in some other direction here is a simple development of what actually happens. Start by placing a moderately heavy block on a rough table as in Fig1. Apply and maintain a fixed push at A, insufficient to move the block as in Fig 2 This can be achieved qith a spring loaded push rod. The action of the friction force exactly opposes A. Now, whilst maintaining A, apply an increasing second force B at right angles to A as in Fig 3. The fig shows B equal to A and the tendency to move angeled midway between A and B. Note that the opposing friction force is larger than A or B, but still enough to hold the block still. Continue to increase B and the tendency to move rotates round, becoming more nearly parallel to B as in fig 4 Finally the combined push of A and B is enough to move the block along aome line close to B as in Fig 5. Note that the block now moves away from A, (and therefore at right angles to B) although we know that friction is enough to hold the block against A alone. That is the block does not move parallel to B. In fact, so long as A is non zero, the movement is never parallel to B. Measurement of B would show that B alone is also not large enough to overcome static friction. This experiment shows that you cannot have a force moving an object against dynamic friction directly along its line of action whilst another force holds that object from moving off that line by static friction.

Of course, the supported object could be quite large, eg an inverted dome and there would be a theoretical contact point of zero dimensions. However you would need to take into account the distribution of mass for any non zero mass point or particle (arguing a difference is a diversion) even an infinitesimal one.

Coulomb's first law of friction. It is important to realiise that a body can only move in one net direction. You can resolve that net tendency to move in as many ways as you like, but there is only one net direction. the net Friction always acts in that direction and is equal to the static or dynamic coefficient times the reaction depending upon whether the object is moving or not. You cannot have the static coefficient in effect in one direction and the dynamic in another.

Here is an discussion due to Glauert that explains it rather well.

Of course, "Not necessarily", in appropraite circumstances. But equally of course, necessarily in other circumstances, including this one. The issue is that the notion of a 'point mass' is contingent upon its definition which includes the phrase "much smaller than the smallest significant dimension of the system under consideration" or words to that effect. Since the smallest significant dimension in this system is zero that is a very severe constraint.

It's not the when that matters, is the wacking great pole in the density distribution and the contact forces that the analysis starts off with. A point mass has infinite density and if balanced on a point support is subject to infinite contact forces in a gravitational field. How's that for a kick-off? Edit : Actually I should have said contact stresses, not contact forces.

Does the OP not agree with me that the proffered analysis commences with fallacy? Small wonder it leads immediately to a singularity, we would ordinarily be able to ignore, but cannot because of the shape of the dome. I like delta1212's analogy of the discontinuity in time that is also presented. +1 I see no conflict with Newton's Laws, properly applied.

I don't follow. Of course a pupil had to be able to decipher chemical names and show some understanding of the chemicals themselves, even in the context of chemical reactions. For example "Underline three substances that dissolve in dilute sulphuric acid from Copper, Chalk, Zinc, Iron, Copper Sulphate, Zinc Oxide." But this was not about a word equation. The closest I can come is Acid plus Base = Salt plus Water Remembering also that I only have access to some much more general General Science papers, not the more specific Chemistry ones. What does that have to do with it?

With the greatest respect, do you have any (first hand) experience of the exams that preceeded GCSE? I do and I can remember taking GCE Chemistry. I can also remember our chemistry teacher (we called her Granny) harping on about accuracy and stochiometry. I'm pretty sure that stating the reaction as a word equation would have resulted in failure at GCE. But then I can remember a time before the "No one can fail an exam" doctrine became de rigeur. Looking up some questions here are two from, not a full Chemistry paper, but just the GCE General Science paper from the 1950s Yes, they used the phrase "word equations" thusly "Write a word equation to illustrate the process of fermentation by yeast." For a chemical equation they asked "CaO + H2O = ............................"

Did I somehow not post my reply? I was not impressed with the inadequate analysis of the mechanics of the dome. What do you expect if you divide a singularity in space by a discontinuity in time?

Since I didn't have the luxury of those ridiculous exams that are at the root of all today's educational evils, I don't doubt you. Perhaps the idea came in with the GCSE?

You are quite entitled to be puzzled about the use of the term 'word question' This is a new idea as presented nowadays and seems to be causing much trouble in teaching and learning circles if the new crop of question from posters who say they have trouble with 'word questions' is anything to go by. However it was specifically not just a chemistry paper, but a GCSE chemistry paper, and I posted the specification for 'word question' on GCSE chemistry papers showing they specifically exclude numbers. So chalk it up to experience. I too am finding new challenges since 'word questions' appeared in the current guise. I was even thinking of starting a disussion thread about the subject since so many are experiencing difficulty it is making matters worse, not better.