studiot

It goes deeper than BODMAS I suggest you just point out to those students how many drug errors happen each year because some medical staff or other puts numbers into a calculator and can't realise they should disbelieve the answer. Some of these drug errors result in fatalities. As a matter of interest, imatfaal, how would or could your 'safeguards' work against this?

Mathematics without understanding can be lethal. Yet we are constantly exhorting others to use mathematics and pushing the doctrine that 'mathematics rules OK'. Being human there are always those who will try to short cut the link between understanding and mathematics and technology, with its ever increasing computing power, is offering the illusion that this is possible by simply inputting data into preprogrammed systems that spit out answers. Here is a recent example from this forum http://www.scienceforums.net/topic/88108-please-help-with-calculating-limiting-reagent/#entry857546 This trend has long (always?) been there. I can remember the scandal when the world famous Hospitals For Sick Children (Great Ormond Street Hospital) new block cracked and nearly collapsed. This happened because data was input to a structural engineering program without understanding (taking a short cut) and the resulting concrete frame was not strong enough. So, in my view, understanding must precede mathematics. Yet we must understand both the nature of the subject and the mathematics we employ. Neither one on its own will do. So how do we ensure that the seductive increasingly easy route is safe, going forward into the future?

+1, John. I can't see how someone can have got this far in organic (or any other sort) of chemistry and be unable to balance a reaction equation. This reference might help. http://www.scribd.com/doc/16594538/2009-03-05-Glucose-Anomers

I am not sure what level you are working at or why you have been given the specific heat. Here is a simple definition of Thermal Energy which leads to a simple equation, where the specific heats cancel in your case and results in an answer of http://www.answers.com/Q/What_is_The_thermal_energy_of_a_solid This definition ignores any expansion due to temperature rise. That is considers it insignificant. To include this you need the coefficent of thermal expansion of silver. If this is enough, post your working and we can discuss the difference between Thermal Energy, Internal Energy, Heat content, Heat capacity and their relationships to temperature, and the statement. The temperatures of both samples of silver lie between what is known as the Debye temperature of silver (-43oC) and the melting point of silver (960oC) We can discuss this as well if you like.

Why did you choose C = 17? Proving the statement [math]17x + 11 = O({x^2})[/math] means find a C and k such that [math]\left| {17x + 11} \right| \le C{x^2}:\left| x \right| \ge k[/math] Echoing what John said, I am not sure why you included discrete in the title? For discrete structures we usually use n as the variable. x usually refers to real numbers in which case the inequality would be true for all x except within an interval determined by C an k. If x was complex then it would all x outside some disk of radius k, as John says.

Which should tell you that there is no solution to your equatiion. That is, it does not happen! So let us look more closely at the question, still thinking about heat lost = heat gained. The maximum heat the 10kg water can loose, and still remain as water is 10 * (10-0) * 1 kcals = 100kc. It takes 3 * (0-(-10)) * 0.5 = 15kc to raise 3kg of of ice to 0oC To melt all this ice takes 3 * 80 = 240 kc. But there is only (100 - 15) = 85kc available from cooling the water so this can only melt just over 1kg of ice, leaving 2kg unmelted. Any mixture of ice and water is at what temperature in equilibrium? You should be able to complete this now.

Processes can be classified into two broad categories (amongst other methods of classification) Analysis and synthesis. Which, roughly translated means breaking down and building up. The term model is applied to both, but synthesis is often forgotten, especially in Science Forums. The essence of a model is that it embodies (we hope) the same properties of some characteristic we are interested in. It will (almost) certainly also have many characteristics and properties that are different from our interest and mostly these will only match of some defined range so it is important not to overstep these when using a model. The process of syntheses is used by designers and constructors; here another word for model is 'pattern'. So a dressmaker, a foundry worker, a woodworker, and others will make a pattern to follow to make a dress, a casting or a cutout. In these cases the property common is shape. A dressmaking pattern is made of paper, but the dress is made of cloth. Economist, sociologists and other disciplines create 'models' that they can impose (synthesis) on an ecomony, a business sonciety etc. For the purpose of analysis we have a similar situation Take a bunch of childs blocks. To the child the important property might be colour. He will sort into red and blue. So his model is 'blocks are red or blue' A geometer would sort them into balls and cubes and prisms, regardless of colour. So his model is about shape. A topologist would say that a cube and a ball and a prisma re all the same, but a doughnut is different. In general the model is a simpler system so that we can handle it more easily, finally translating the wanted property in the model to the target object. In synthesis the model controls that property, in analysis the model reflects that property.

Authur C Clarke, who used to live near me, wrote a short SF story about this, with an interesting punchline about the 'reason'. http://en.wikipedia.org/wiki/The_Nine_Billion_Names_of_God

I see no evidence whatsoever that I assumed anything. I was (and remain) quite sure you understand Physics very well, which is why I am surprised at your rather casual dismissal of my attempt to show Mike that the mechanical dynamics of fluids under loads is different from that for solids. Consequently the bucket of water is a very poor analogy. In particular Mike asked "Why does the water not fall out?". I cannot identify a clear and concise answer to this question, couched in the proper language of Physics. If, for instance, you reached up an seized the bucket at the moment it was above your head, and held it there, the water would indeed fall out and you would get wet. If the water was ice then you would (in theory) be able to hold it up there indefinitely. The short answer to Mike's question about the bucket is nothing more exotic than that the time is too short for it to fall. However you should not dismiss air pressure so lightly either. It was a victorian party trick to place a card over a full beaker of water, invert the assembly and show that air pressure could prevent the water falling out. If one wished one could calculate a time, related to the angular speed, from say about 30o from one side of the vertical to 30o on the other, during which the water would be at risk of falling out and would indeed fall slightly. If this time was short enough (ie the angular speed was high enough) the water would simply slump a bit rather than fall out. If the time was too long, water would spill. And why would the water iinitially remain as a body? For the same reason it does when it falls out of your tap in a stream tube. There are no disruptive forces in action. But I repeat my point that all this is entirely different from the proposed action of Mike's Mechanism (I think they did a Gig at my university in the 1960s , or was it the 1860s I can't quite remember ). So let us return to consideration of all the forces acting on these oscillating bodies and, when then the reasons why it won't work should immediately become apparent.

Ok so the equation I picked out is a heat balance Heat gained = Heat lost. But Heat gained by what? = Heat lost by what? Heat gained by raising 3kg ice from -10oC to 0oC, plus heat gained by converting 3kg ice to water at 0oC, plus heat gained raising 3kg of water fom 0oC to +xoC degrees centigrade. Heat lost by lowering 10kg water from +10oC to +xoC Can you now put the correct figures into this ?

Sorry to harp on about this, but, under gravity, the water would be travelling in something approximating to a parabolic arc, not a circular path. It is the bucket which imposes a circular path and the bucket is being forced round by the forces in the string or whirling arm, not gravity. Suppose the bucket suddenly rotated or opened to release the water, the water would separate from the bucket and fall in its parabolic arc, whilst the empty bucket would carry on round on its tighter circular arc.

Or you could put a hole in the bucket and sing that immortal song There's a hole in my bucket, dear Lisa. I would also observe that the bucket and its contents are not in equilibrium so we should not expect the forces to "balance". This is often forgotten.

Think again about this. Can you say why it's wrong?

What works? And of course there is no air pressure on 5 of the six sides of the water. I believe it was an emperor who told Van Guericke that 'air pressure doesn't matter'. Doesn't any fluid act differently from a solid in a centrifuge, shapewise? I think the shape of the parcel of water will be quite different from the shape of a block of ice in the same place. And are you also suggesting there is zero contact force between the water and the bucket? This must be complete nonsense. Sorry to be so pedantic but the string is tied to the bucket, not the water. The water is constantly being forced to travel in the arc by the bucket, not by the string. I could see you being able to use a string to circle a block of ice, but not a parcel of water by itself.

I beg to differ, although I am not suggesting that these are enough to hold the water aloft, just that the applied forces are complicated in the case of the water. There are a variety of forces acting on the water. There will be air pressure, the contact forces with the bucket, surface tension, to name but a few. A good physics question might be "What are the static and dynamic pressures inside the water?"

This should not be an argument about continuity. The calculus you require for the floor and ceiling functions is called the finite calculus. In this calculus the derivative operator D is replaced by the difference operator [math]\Delta [/math] and the integral operator [math]\int {} [/math]is replaced by the Summation operator [math]\Sigma [/math] You can find out about these and the maths of floor and ceiling function by reading Graham, Knuth and Patashank Section 2.6 deals with the finite calculus and chapter 3 with f&c functions.

Perhaps you would explain how that would produce a force at right angles to the motion?

I'm confused by this. Are you now saying the oceanic ridges were not created, in stages, by upwelling magmatic material? What you you mean by the extraordinary elevation? What is extraordinary about it? And what about my question concerning the pattern of horizontal distribution of rock age away from the centre of the ridge? Once again you have put a lot of effort into unconnected pretty pictures instead of responding to statements by others in this conversation. So how is it a conversation? I posted some examples of useful experiments I thought you might like to do for yourself, but you have not even acknowledged that post. Finally here is another question for you to ignore. The surface of the Earth is constantly going up and down by a measurable few inches. Have you heard of Earth Tides? Here are some measurements. http://www.colorado.edu/ASEN/asen6090/SolidTides.ppt I am rather disappointed.

I am testing a new (to me) tool jrt.exe Anyone got any experience of this one?

Mike here is my concern regarding your vibrating doodads. Newtonian mechanics requires a force acting towards the centre of curvature on any body following a curved path. (If you like it pulls the trajectory in towards the centre off the straight line path) Now you maintain that, as a result of your vibrational dance there is a force which counteracts gravity. So what force is acting to create the partial arcs you describe?

I should start by thinking about what heppens on a non icy sidewalk. As you walk forward your whole body, including your feet has a foward velocity (relative to the ground). You lift one foot off the ground and extend it forwards, placing it back on the ground. What (whose) law says it will keep going forwards? Yet as soon as it touches the ground your foot stops and does not move forwards. So what stops it?

It depends what you understand the words, Entropy, Order and Disorder to mean. That's a rather extreme view. Why would disorder being at a maximum make a system completerly unpredictable? Could there not be a scale of predictability?

CAD software is as accurate as your computer can be.

There was a program called Design View, written for Windows 3.1 that could do what you ask. Mathsoft had a somewhat less capable program, linked to MathCAD, called Imagination Engineer. There are AutoCAD plug-ins that allow AutoCAD to display moving vector resultants, but I can't remember the name. You should reasearch "Linking spreadsheets to drafting programs"

Good morning, pavel. I am not sure why you have resurrected this thread, but the answer to what was wrong with the original reasoning is simple. Inappropriate mixing of information from different frames. There is one and only one frame in which the centre clock can count simultaneity. That is its own frame. The whole train, and everything on it including the end clocks, remain in the frame of the centre clock for the entire experiment. The OP took pains to establish that the transfer of the end clocks from the centre has insignificant effect. Other observers, not any the train, will see the simultaneity differently, ie they will not see it simultaneous, from their point of view (frame). The error in the reasoning is thinking that they should see the flashes as simultaneous in their frame, instead of applying relativity of simultaneity, which is, of course, what they should do to obtain the correct answer.