studiot

Well I agree with you. Glad you are following, don't forget to ask for clarification if you need it. I think it is exchemist who is fond of quoting " The map is not the territory". Certainly a good insight always worth bearing in mind. So let us clarify a few things, especially if you are finding KJW's post rather formal (but correct). It will be necessary for you to distinguish between a graph and a function. They are not the same. Indeed there are graphs that are not functions and functions that are not graphs. A function is very tightly defined in maths and one distinguishing characteristic stands out. You select a particular value as an input from the independant variable or set of values if there are several such. Applying the function yields one and only one result or output as a value of the dependant variable. I can't stress the importance of this enough. On the other hand a graph can show what happens when the may be many possible outputs for a given specific input. Figs 1 and 2 Show the graph of the square root. The square root function only has positive values as shown. The graph allows both the negative and positive. We will come on to why this distinction is made later. Fig 3 shows another sort of graph (which actually is a function as it passes the one value result test) but it does not fit with KJW's dimension statements. It is what is known as an area plot of the function y = x2. The area of the squares represent the value of y at the numbers 1,2,3, ...etc. I have drawn this one because it leads into a very important idea you will need when we come to vectors. A much more complicated graph appears in the next figure, where each value of x has many values of y in a branching tree structure. The are the characteristic curves of a transistor amplifier output. Superimposed on this are some other lines, marked load line, input and output signals. The load line is actually a function, the tree of characteristics is not. My final figure, fig 4, shows a piece of paper representing the x axis. Of course this axis goes to infinity in both directions so I hope you can see that it is not possible to get from region A to region B without crossing the x axis? Now a piece of paper is 2 dimensional. If we allow 3 dimensions the we can approach the x axis, move around it in the third dimension (ie leave the paper) and get from A to B without crossing the line. This introduces the idea of what happens in 4 dimensions and why we can get from inside a 3 D box to outside , without passing through a wall - obviously not possible in 3D alone Some more terminology. The first 3 examples are all about geometry, the fourth example is about topology. Back to MigL here. Graphical representations are usually geometrical. that is how that started. But topology, which grew out of geometry and is now a different subject, has an entirely differnt definition of a graph in terms of connectivity. I'm going to be away for most of next week so take your time to think about these things so here is a recommended book, t6he delightful Things to Make and Do in the Fourth Dimension by a modern mathematician, Matt Parker. Just a small Penguin paperback but well worth the read and loads of fun.

Ok perhaps fair enough but

True but irrelevent. Halley's is an ice comet. The irridium signature in the debris of Chicxelub points to a rocky/metallic asteriod.

But that isn't quite 'graphing', that describes the coordinate system not the 'graph'. So yes the coordinate of a point is described by n variables in n space. But as n increases the types and nature of availbale 'graphs' increase. In 1 dimension n = 1 and you can't reall describe much. just different length segments of the same infinite line. In two dimensions you can play about with lines and get straight and (plane) curved lines as graphs. The idea of a function makes sense as does an independent variale (usually x) and the dependent variable (usually y). In three dimensions you get more scope and can describe surfaces, solids and so on. One type uf graph using 3 dimensions is a countour graph such as is used on maps. This is really a sequence of plane curved sections, ie 2D sections. Recently it has become very import in the technology of '3D fabrication by printing' of objects. You can also have knots and other fancy constructs in 3D that have no counterpart in 2D. Many of these constructs dissapear with the step up to 4 D. How are we doing are you following so far ? Keep asking and we will cover these.

Can you explain woldfires over the Ocean ? @Sensei makes a very good point. +1 One problem a breakup hypoyhesis must answer is this. The meteoriod had been travelling for up to billions of years, so all the part had plenty of time to achieve the same velocity, even if lightly attached. So all the parts will have had momenta and energy proportionate to their masses, and even if only touching wouldhave continued together since there is no friction is space. So a breakup mechanism is required. The only reasonable one I can think of would be impact by another object, which as Sensei points out, would have had to occur fairly close to the impact with Earth as the meteroid was travelling at circa 20km/second. Otherwise much of the material would have been scattered clear of Earth by the side impact. Clearly it would have to have been a side impact.

Of course. QM is probablistic; it makes amazingly accurate predictions. Or are you asking whether a ToE might resolve the probabilistic aspects ? Did you hear the one about the car salesman who said This car has everything you need for the journey to your destination. It's extra for a tank of gas. Or the old saw A present for the man with everything. Penecillin. If it can't answer a simple question to distinguish between a atom that will decay in 5 minutes time and one which will not so so for 5 million years, to me it is a travesty as a theory of everything.

Consider the following: Unstable atoms, numbered 1 through 100, sit in a row. Would any proposed TOE be able to predict the order in which these atoms will decay ? IOW is a TOE allowed to be probabilistic ?

If the meteorite had broken up into fragments we would have expected to find evidence of multiple smaller impact sites. There is no evidence of this. Just one large nearly perfectly round crater. Folks often concentrate on the sexy impact period of such a disaster. The truth is that the impact itself lasted a very short time, as did the temporary heating of the atmousphere and other immediate effects. The impact itself was sufficiently large as to melt the limestone sediment rock to a glassy material and spray large quantities of glass beads into the air. As a marine disturbance it also spawned a series of tsunamis. In the days following the impact the heavier material fell back to earth and has been found over a wide area of the US, Mexico and beyond. The finer particles remained in the sir for much longer, weeks, months ever years. The resulting winter caused freezing temperatures, rather than elevated ones. Evidence for this has been found in studies of the stems and leaves of plants preserved at the moment of impact. They have had ice crystals growing inwards and bursting the cell walls.

Well I see that there has been other interest in these questions, even if the OP has not bothered to come back. The questions are actually more suble than at first meets the eye because book answers define the sets by listing the members, which is unusual. They have done this because the sets are finite and the only members are from the set of ten digits 0 through 9 that we use in our decimal number system. This listing is the simplest way of definiting the sets, and excluding numbers we do not want included. To make this clear the questions ask for the set of digits, not numbers. So in my last example 0 and 9 are digits with that represent numbers but 90 is not a digit it is only a number.

The Chicxelub meteorite impacted into the proto Caribbean, which was larger then. It penetrated up tp 19 km into the crust, driving molten rock down into the mantle. Today it has a 3 ring structure, the outer ring being 195 km across. So the majority of its energy was extended driving deep into the earth and melting the rock to suevite (A breccia formed by shock metamorphism whose angular fragments are set in a glassy matrix).

Some further figures The estimated mass of the Chixelub metoeroid is between 1015 and 1017 kg say 1016 The estimated speed of this sized asteroid is 2 x104 m/s Thus its kinetic energy is (1016 x2 x2 x108) / 2J =2 x1024 Joules So the meteroid had enough energy to heat the atmousphere up to these levels.

The back of my envelope says Mass of atmousphere 5 x 1018 kg 475 J / oF/kg Temp rise from 100F to 400F (temps averaged a little higher in the Cretaceous) Total energy required = 5x 1018 x 300 x 475 = 7 x 1023 Joules.

This is a fair question. But, as always, the wider world is more complicated than our simplifications. Even Philosophers have to agree what theey are talking about before they can have a useful discussion about 'Truth'. Let us start into it by agreeing the difference between a hypothesis and a theory. What do you mean by these terms and also accuracy ? Also I think gravity is far to weighty an example ans as yet, far from a finished hypothesis. So let me offer some simpler ones, and if you must invoke Newton, then how about the wave/particle duality of light ? Back along Newton's corpuscular hypothesis held sway as 'the truth'. Then Huygens proposed the wave hypothesis. Both hypotheses predicted the same result, for every effect. Then Young showed that the deflection from the normal at a boundary was in the opposite sense for the two hypotheses. Ahaa a test. Young's analysis proved correct upon observation and 'the truth' shifted to the wave camp. Hey brother/sister, my clock has stopped working. Perhaps the battery is flat (low voltage). Well it worked when I first put it in so the voltage must be correct. Yeah but the voltages changes with time, and as you use the battery. So what is 'the truth ' with regards to the battery voltage ?

In what way do you think energy will cause a battery to fail ? Here's a challenge. I have just weighed a standard C cell at 71 grammes say 70 to make the math easy. How much energy do you say you need to add to 'destroy' it ? Please provide a figure, since you think it can be done. I will then tell you how to add more than that amount of energy without destuction, and then take destroy the battery by taking away said amount of energy.

This is nonsense as it is physically impossible to apply a force to the rope greater than required to break it. By definition. In the practical real world the real world breaking force will be greater than 100kg for statistical reasons. But statistical reasons don't enter into our consideration of circuits. I gave you a graph of the characteristics of a general voltage source. What do you think would be the correct circuit equation to describe it? It is important to use observable quantities.

I keep telling you that the only way to correctly and accurately analyse such problems is to use measured properties or parameters. Those analysts with suffieient experience may be able to guess or estimate suitable values for at least some of the variables. Consider this simple question I have a length of rope specified at 100kg breaking stength. What force is rquired to break it ? In other words if I hang it up and add weights to the bottom what weight will I require to break it ?

I never said it does, nor does millman's theorem. Forget the ground. The circuit analysis must also describe the situation where there is no ground.

What is very clear is that you have not understood it. What I can't understand is why you would wish to argue rather than expand your knowledge and understanding. Firstly I haven't assumed anything (except linear circuit theory. Non linear theory gets exceedingly hairy) Secondly you haven't understood the most basic property of all real world voltage sources. I have already been through this. It is impossible to specify the output of a real world voltage source without reference to the load current, which is something you are trying to do. Thirdly U1 and U2 cannot be anything but equal since they are connected across the same pair of circuit terminals.

It's probably called the ~Dark Web because there is no electric voltage coming from the ground. So there are no electric lights in the Dark Web. Forget it. This suggests to me that you still don't appreciate the nature of electrical quantities. Since you haven't answered my comments. Further I still have no idea what level to pitch the next bit at. At the end of this discussion I was going to point you at Millman's theorem (also known as the parallel generator theorem). This represents the general case and was developed for three phase elctrical supply where the three phases are often connected to a single load in what is known as a star connection. So help me to help you here

Well I for one don't accept that premise. What 'laws' do you think are different at these scales ? So you chose not to answer my question.

The most important lesson any student can learn is Read the question and answer it, not some other question that was not asked. Added to this in a wider context for life is RTFM - Read the frigging manual. So did you read the rules for the forum you have posted in ? I gave you a hint in the form of a question. - since we may not do your homework for you But you ignored it and argued instead, like a smart alec. Here is another comment/hint. There is no requirement for 0 or 9 to appear in every set of numbers or digits. If you still don't understand - ask.

This looks really promising, you have some idea about voltage sources. +1 Electrical engineering is an intensely practical subject. It is very fortunate that we are able to model the behaviour of electrical systems by carefully defining a few ideal or perfect components or elements. But we should always keep in mind that there are no such things as ideal or perfect elements in the real world. Note this is true in other disciplines as well as electrical enginering. When we measure the performance of real world voltage sources we find the graph in fig1 applies without exception whether we are talking about alternating or direct, pulsed or steady and whatever their source of EMF (electromotive force). So it applies to generators, dynamos, batteries thermogenerators etc. Looking at fig1 we see that the ideal voltage source output remains constant, whatever the current draw. But the output of the real world voltage source fall proportionately with increasing current from a maximum at zero current. So we construct a model of a real world voltage source by combining an ideal voltage source with an ideal resistor in series, as shown in fig2. The ouput of this real source appears between terminals A and B and is called the terminal voltage. In the next post or two I will go on to show how to use this extra information to determine the effect of combining two batteries of different voltages and capacities across the same load. We can also discuss conservation laws in the light of this new information. The situation there is somewhat more complicated than a simple answer. You will need to be clear upon the difference between an EMF and a Potential Difference (pd) and also the difference between voltage and current. There are circuits which are called voltage to current converters, but they are not rectifiers and act quite differently from what we are talking about.

See my answer to your other question then come back for more help if you still can't answer it yourself.

Zero is an even digit. Ask yourself what is a the difference between a digit and a (whole) number ? What is your definition of an even number ? A side note other numbers and digits are either positive or negative. Zero alone is neither (or both) So don't mix up sign and even/odd.

Well I for one don't accept that premise. What 'laws' do you think are different at these scales ?