studiot

Just as a matter of interest, how many pump and hose systems do you know that require a return hose to the reservoir? Also what happens at the cut end if you suddenly cut a hose that has water being pumped through it, does the flow from the pump stop? Electricity in cables is not (very) like water is a hosepipe.

Scenario 1 is the nearest to common sense. Scenario 2 basically says that the current leaves the battery, arrives at the lamp and passes through it, but the lamp does not light until 1 year later, when the current has arrived back at the battery. That is ridiculous. Scenario 3 is even more against electrical theory. What are the agents of the two currents - they can't be the same can they? How about scenario 4? You switch on the battery and half a year later I come and switch if off again. Will the lamp light briefly? Or even worse suppose that scenario 2 was actually true and the lamp will not light until the current returns to the battery after 2 years. Now for scenario 5 suppose I come along and switch off the battery after 1.5 years, ie after the current has left the battery, arrived at the lamp and is on its way back to the battery. So where does the current or energy go now since it is not dissipated in the light and does not return to the battery?

Rainwater collection and storage is a great idea. Just a few practical thoughts. You are intending to store it for long periods in a hot climate so you will need to think of ways to stop it going rancid or putrid and ways to clean the storage reservoir. Like emptying a swimming pool you would need somewhere to put the water whichilst you did this, or some seasonal cycle to carry the cleaning out. If you dig a hole below the level of your garden you will also have to pump the water back out. I'm sure there are some here with tropical gardens who can tell you better than I can the amount of water you would need to store. You can calculate the available volume by taking the collection area and multiplying this by say 1/4 the average total rainy season rainfall.

Why do I get the impression you are trying to catch people out, rather than gain understanding? By itself the question in the above quote is perfectly reasonable and understandable. Indeed I considered mentioning this link to where mass is used as the constant of proportionality. However as part of the too-clever complete post above, all it shows is that you are not thinking because one part contradicts the other. If applied force is to be proportional to mass, then it must be allowable for mass to vary. So mass cannot be a constant. If we we are going to hold mass constant and vary the acceleration, then we can say the applied force = a constant mass times the variable acceleration (in suitable units) So in those circumstances we can say that mass is the 'constant of proportionality'. And yes you will find plenty of references to this as it is a way of introducing inertia or inertial mass and it is one of the great unifying triumphs of Physics that we have been able to show that the quantity 'mass' as defined in Newton's second law is the same as the quantity 'mass' as defined in Newton's Law of Gravitation. This is also an equation of the form [math]F = G\frac{{{M_1}{M_2}}}{{{r^2}}}[/math] Would you say mass is the 'constant of proportionality here, or would you say something more complicated is going on?

Yes this is just fine. It actually tells us what you have written after. So that part is not really needed. It actually tells us even more than this because it says that even if a body has mass, the force applied to it is zero, if the acceleration is zero. (Which, of course, is what we want) And of course we don't have any accelerating bodies with zero mass in classical physics to bother with thoughts of zero mass. This means that there are no additive constants in the equation.

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?