studiot

Good morning Deepak, I really thought you had cracked this issue with your earlier thread about basically the same thing, where you answered Delta1212 But you don't seem to have been back to that one. The point is that equations such as F = ma need all the variables to be there to make sense in the physical world because they have units or dimensions. So whilst in mathematics we can write 6 = 3 * 2 and be OK, in physics we must ask 6 What? 3 What? 2 What? In the above equation we have a units of force = b units of mass times c units of acceleration If we set b or c equal to 1 (as you have done in both these threads) we cannot just drop that physical quantity out of the equation. the equation now becomes a units of force = b units of mass times 1 unit of acceleration so, whilst the number as might be equal to b in mathematics, F is never equal to m in Physics One further consequence is that nowadays units are arranged so that If b = c =1 then a = 1 So 1 unit of mass times one unit of acceleration gives 1 unit of compatible force units. It was not always so as Strange has pointed out.

Despite 74 posts in this thread no one has shown any laws to be broken.

You need to observe forraging bird counts at different height intervals, by species. The null model is clearly going to be that there is no stratification of species so any differences you observe will occur randomly. You then test to see if the observed level of stratification could have occured randomly, within the chosen confidence interval.

What I think swans means is that the first and second time derivative of r are both discontinuous at r = 0.

What doesn't violate N2, that you seem to imply violates N1?

Because it doesn't. Nor is it a correct equation, since you deliberately missed something out. What do you think that might be?

Is there any good reason for not discussing the mathematics of the situation? What is the equation of motion of the point mass on the dome? Can it be proved that this equation satisfies the Lipschitz conditions?

Well for a start the force is not its force. The force is the external force required to accelerate it at 1m/sc2.

Good snappy response deta1212. +

I find it disappointing that this thread has fallen short of the usual high standards at ScienceForums. This is on two main counts. Firstly: I do not expect to have to go trawling the net to unearth the main thrust of the issue for myself, I expect that presented in the opening post. Secondly: The issue is essentially one of the mathematical analysis of the situation and no mathematics has been presented. When posted the originator's first equation it was ignored. Now both of these counts are frequently used to rebut wooly posts so why is this thread any different? In point of fact there are several possible ways to continue Norton's analysis mathematically. Since there are inconsistencies inherent in his mathematics, whichever way one proceeds, we need to have at least one approach presented for proper (mathematical) discussion.

Don't worry about posting it in the wrong place, the mods will easily fix that. What I was trying to find out is if you know what equivalent weight means, given that it is a (nearly) obsolete term. Or if you like do I need to explain that part to help you solve the question? The actual calculation is trivial, do you know the normal valency of magnesium? You will also need to look up the atomic weight of magnesium, if you haven't already done so. Here is a sample equation of the type in the question, the reaction of permanganic acid with magnesium to form a salt plus something else. Mg + 2HMnO4 = Mg(MnO4)2 + H2

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.