studiot

No it is still not correct. It is not correct becasue it starts with the word 'when' This demonstrates that my efforts have still not been understood. The proportionality of the (magnitude) of the force is totally independent of the acceleration. So it is true that "when an object moves with constant acceleration....etc" BUT It is also true that "when an object does not move with constant acceleration....etc" So what is the point of the half-a-statement?

Did you guys read my mind? I just finished a mammoth post on this subject in your last thread Deepak. +1 for encouragement.

Good Morning Deepak, What did you make of my post# 28. It was quite short. But you have not mentioned anything about it, just repeated your earlier list of options. Post#28 did indeed explain what was wrong, but perhaps as it was also short, it was too short. It is difficult to get the length of answer right. Asking questions to enable understanding is good. But you need to ask questions about what other people as thinking and saying as well as what you are thinking. Perhaps they can see something you haven't thought of? So asking Is just fine. Further, and unlike some here, I am willing to discuss equations in English as well as maths. So let's do that. F = ma is a common modern statement of Newton's Second Law off Motion. Newton himself did not state it this way. In his day he (people) usually thought in terms of proportion, not equations. Equation theory was nor really developed then, like it is nowadays. Today discussion of proportion has nearly fallen into disuse, in favour of using equations, which is a pity becasue proportion is a powerful tool that can be easier to use. Enough background waffle, the title of your thread is equations in general and since this subject is important for lots of equations I will use another example and then return to Newton. Let us go back another two thousand years to Archimedes and the principle of the (simple) lever. Two quite independent physical quantities determine how much turning effect or moment you can generate with a lever. Let us call this moment M. You can vary the lever arm or distance from the pivot. Let us call this distance d You can vary the force applied at the end of the lever. Let us call this force P (to keep it separate from other equations). The key point in my post#28 is that you can vary these two quantities quite independently. Now the longer the lever the greater the genrated moment or M is directly proportional to the length of the lever arm, d That is M = k1d But also The harder you push or pull with the same length of lever, the greater the moment. That is M = k2P So we can achieve the any given value of M by changing the value of P and keeping d constant or by changing the value of d and keeping P constant. In this situation the equation for M is M = k1k2Pd and we combine the two separate constants of proportionality into a single one and adjust the units of P and d so that k1k2 = 1 So now can you tell me why I said in my post#28 that your option 3 was wrong? As added value, and to show how powerful the idea of proportionality is, think about this. The kinetic energy of a moving body is Directly proportional to the mass and also directly proportional to the square of the velocity. A note on terminology. Directly proportional means 'multiplied by' Inversely proportional to means 'divided by' But you can also have proportional to the sine of something or even the square of the sine of something, as in electrical theory.

That was Mama Cass not making it, not the battery. Though you were quite right to note that transit time is important in modern circuitry.

Hi Strange, This is the problem with Deepak trying to force his 'list' of views on us, instead of listening to the many who have tried to tell him the same truth.

Daniel +1 by way of encouragement. You are showing substantial appreciation of electric circuits. As a matter of interest, the small differences in signal paths between the various bits on a parallel data bus are sufficient to cause computer 'glitches' at the speeds of modern computer circuitry. That is why design has moved to serial data transfer and away from parallel, for example with hard drives. Look up 'race conditions' http://en.wikipedia.org/wiki/Race_condition

True. But that is just stating one particular case and so is of no real value. Not true. The fact of proportionality of the force is not contingent on the value of the acceleration, which is why we have an equation such that we have the force proportional to two independent quantities and which are multiplied together. Any quantity A that is proportional to another quantity B and also proportional to a third quantity C and a fourth D and so on is given by the equation A = k(B*C*D.....)

The 1 is a coefficient. That is a simple number, like 2,3, 4 etc. so if we have 2kg of mass the 2 is a coefficient (of mass) So if we have an acceleration coefficient of 4 and a mass of 2kg the equation says that (The coefficient of force) x Force = {(The coefficient of mass) times mass} times {(The coefficient of acceleration) times acceleration} So the coefficient of force is 2 x 4 = 8 But the force is 8 Newtons. Does this make it any clearer?

You are wasting my time and yours since you are not makeing the effort to follow what others are telling you. The answer to your rephrased question is 4)Something else. None of the others are actually true.

It means that you have written an invalid equation. Several have told you this, besides me. The valid physics equation is F = ma. you said (wrongly) a =1 acceleration can never ever be 1 in any system. of units a can be 1 m/sc2 then F = m times 1m/sc2 is a valid statement.

Well yes of course, but the force is the mass times the second derivative of r w.r.t.t. , which we already have in the sequence, just as momentum is the first derivative scaled by the mass.

The discontinuity is a t = 0. It is discontinuous at t = 0 because the value of the each function has different limits from the left and limits from the right. So the limit at t = 0 if it exists except by convention can only equal one of them and and convention would have it that the the limit is 0.5{(Lt+) + (Lt-)}, which is neither of these anyway.

Are you familiar with the particular Zeno paradox I am referring to? Since we are using r as a measure of position, If you plot position v time, the first time derivative, dr/dt (ie the velocity) v time and the second (acceleration) and subsequent derivatives v time, there is a jump discontinuity for each function at t = 0. There is some interesting mathematical discussion of both Norton's Dome and Newton's Laws http://physics.stackexchange.com/questions/39632/nortons-dome-and-its-equation?lq=1 and http://physics.stackexchange.com/questions/13557/history-of-interpretation-of-newtons-first-law

First, My apologies. In my post#72 I meant and should have said t = 0. I realised this last night, just after I shut down ( as one does) along with the thought that this issue and what Swansont proposed earlier was effectively one of Zeno's paradoxes. No object can ever move. The question appears to be how does the motion get started and using distance as the independent variable (as Zeno and Swansont did and I did in error) leads to a Zeno's paradox. The discontinuity is in time not space. ydoaPs, I am not saying your analysis is flawed, (I haven't seen one yet), I am saying Norton's is in the paper linked to, insofar as results are derived that rely on continuity that is not there. Swansont, I did not address my remarks to your set of infinite balls but to the original problem but I suppose the question of initiation is the same. Incidentally there is nothing in Newton's law to suggest that time can or cannot run backwards. However the nature of a discontinuity is the limits from the left do not equal limits from the right, which is what happens at the instant of commencement of motion. This therefore rather suggests that you can only run time equations backwards in piecewise fashion between points of discontinuity but never include the points themselves.

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