studiot

There is still something missing. You say 2ix is defined in the problem as I suspected, but you haven't told us what it is. I did ask for more explanation. A tip about the node Law. At least one of the currents at any node must be of opposite direction to the others, unless they are all zero. The sign that comes out of solving the equations tells you whether you have guessed the direction correctly or not.

Now we have a response from someone who actually knows what they are talking about. Steve you should listen to ZZtop. The purpose of the ruler was to avoid the complication of a 3D object such as a cube and all the arguments that will ensue. The planet observer will not view the cube as a cube, only the rocket observer will do this. The ruler will appear to to the planet observer to grow in length when the rocker observer turns it vertical or horizontal but perpendicular to the direction of motion. Thus the planet observer will be able to witness the effect of length contraction. Because lengths perpendicular to the motion are not contracted but those parallel are directions are affected in a measurable or calculable way.

Three replies (I think) to my post#126 so far. One poster realised that length contraction alone can give direction information. One poster was realised that something would happen on turning the ruler from parallel to the direction of motion to being perpendicular to it, but was unsure what. (The guess was incorrect) One poster completely missed the point that my post was a response to the issue of difficulty in observing length contraction. No it was not a trick question.

I don't understand your labeling in the diagram. You have written 2ix in blue against the controlled current source, which suggests it is defined in the problem. But you have written ix in red as though it was your naming of the branch currents at the nodes. Please explain.

An interesting propositional experiment is as follows: A planet bound observer watches an astronaut approach and fly past in a spaceship at 0.8c relative velocity. The astronaut is holding straight out in front of her a 6 foot ruler, marked in feet. What will the planet observer see? Will he see all 6 foot markings? How long will he think the ruler is? If the astronaut rotates the ruler through a right angle as she passes What will the planet observer see happen to the ruler?

Since you now deny your own words, there is nothing more to be said. Perhaps you would like to posit a relationship between space and time, consistent with your claimed properties. Meanwhile Strange +1 for an excellent set of nits.

So you now partially agree with my comment, in the first part of your reply. Progress. But are you asserting that space alone ​somehow incorporates the time property of 'the present' ? Does it also therefore incorporate the property of that which is not 'the present' ? Or are you saying there was no space in the past and there will be no space in the future? Your overshort assertions need more detailed explanation. Finally please stop the insults and discuss the subject.

The diagram size was fine for its purpose. You are correct in saying that the collector current is almost completely controlled by the (collector) load resistor in saturation. Your question gives you the collector emitter voltage as 0.2 which makes the voltage across the load as (5 - 0.2) or 4.8 volts, by your own (correct) equation. So you have simply done this sum incorrectly. You know the base voltage and you know the supply voltage, this is dropped across the base resistor and you know the gain since the transistor is just at the onset of saturation, ie just leaving the linear amplifier condition. So you can calculate the base current by dividing the collector current by the gain. Ohm's Law will then give you base the resistor value.

Which was rude because you lectured me about reading a post properly, whilst totally ignoring mine in your alleged reply. I had stated clearly that There is no universal present and implied that there is therefore no 'The present', as you had been calling it. Nevertheless you quoted my words and then carried on as if I had not posted anything. I would be happy to explain or expand on my assertion if asked about it, but I was not. It was not even graced with a denial or refutation. It was simply ignored.

1) Rudeness is counterproductive. I am well satisfied that, although I sometimes make grammatical or spelling errors my standard of English compares favourably to that you have shown in posts here. All I am trying to do is find out what you really mean when you make those outrageous claims such as space is time, then disown them 2) I did not say you did make that implication, I was addressing String Junky when I made that assertion.

This is even more incomprehensible than your previous statement.

OK so what exactly does the statement isn't space itself not a universal present mean and does it matter whether it changes or not? Are you asking if space is time? SJ +1 for a correct and nicely short comment. But it also implies something more, it implies instantaneous action at a distance.

Do you not read your own thread? This one is not quite 2 days old. There were references in both my posts, which were quite recent. I could feel quite insulted.

@John Lesser I see you are quite unable to address my comments.

I am not interested in your squabble with others here, but I am disappointed in your total disinterest in my (only) post#109 before this one. Eddington was the first man to articulate that there is no 'Universal Present', even if he was not the first man to realise this. (Faraday was the originator in his famous letter deposited with the Royal Society March 12th, 1832 An observer at one point in the universe will record a different 'present' from the 'present' recorded by an observer at any other point. Einstinian relativity is not necessary to understand this. I am trying to dig out the Eddington reference for you, where he develops this idea very clearly.

I like Eddington's story of the cigars as a way of avoiding the acceleration in the twin's 'paradox'.

I'm glad to see strange mentiones manifolds, though I haven't looked into his references. This is because you can't have an everywhere smooth vector field on a spherical shell. (The Hairy Ball Theorem) This is important for instance in applying the NS equations to the Atmosphere. The reason for the ban on divergent (and convergent) fields is that there must be a singularity at the point of divergence (convergence) ie a sink or source

Yes I know the mass starts off in its initial position. That is a definition of initial position. But where is this initial position? And what of the spring? What is its condition? Come on, all the equations on earth are useless without the proper boundary conditions as well. I suggest you leave the location of the zero point (origin) until after the boundary conditions are fully specified, there is much to be said for measuring from the charged plate. Usually when analysing a system either The system is in a neutral condition in which case an outside agent acting once only is invoked to provide an initial displacement and the system then follows its trajectory controlled by the system forces. or The system is held at some point in the trajectory and released at time t = 0 and the system again follows its trajectory. A linear system will repeat the same trajectory over and over. But this system is non linear and I think there is the possibility that the neutral point will be displaced along the horizontal axis with each cycleand that each cyle will be different. So what I think you are saying is. The mass is attached to the unstretched spring (although you have not said if the spring can work in compression. Before t=0 no forces are acting The charge is somehow 'switched on' at t=0. The electric attractive force E causes the mass to move towards the plate, stretching the spring which provides a restraining force S. Now E increases as a second order quantity of displacement, whilst S increases as first order. So even if E starts from a lower base than S (depending upon the constants involved in the boundary conditions) it will eventually overtake S and from that point S will not be able to return the mass towards its original position.

Upon rereading all the posts and the title, I owe you an apology, Sriman. Nowhere have you mentioned simple harmonic motion, just harmonic motion which is different. However as I already indicated you have not convinced me that the mass will move at all, let alone oscillate. You should start by considering the Physics, before throwing in equations of any sort. I think this applies to some other posts as well. For example the nature of charged plate is important, certainly the distance dependence of the electric force is not as anyone has as yet stated. If the plate is large enough to be considered 'infinite', then the force is independent of distance, ie it is a constant. If the plate is of finite dimensions then at a large enough distance from it the attraction does indeed approach Qq/z2, but the true relationship is subject to [math]\left[ {\frac{z}{{\sqrt {\left( {{a^2} + {z^2}} \right)} }} - 1} \right][/math] Where z is the distance from the plate and a is the radius of a circular plate. Then we must consider the spring. Is the spring able to be compressed or not? If so then the spring force may reverse in direction at some point in any motion. Finally there is the starting position. Are we starting from an unstretched spring and, holding the mass in position and then releasing it, or somehow suddenly switching on the electricity? Or are we starting from a position (if one exists) where the restraining force of the spring exactly equals the electric force of attraction. If so why will the mass move at all? It is clear that there could be different equations in operation at different points along the axis connecting the spring foundation and the charged plate and that some of them may depend upon the dimensions of the system. So this is the last time I will ask you to specify properly.

I think a big problem for students is relating theory to practice. A few practical examples can bring out the important principles and provide a lot of fun. A hammer, nails, a wooden post and a lamina to nail to the post can demonstrate the difference between what happens when you apply a moment, (via a single force) and when you apply a couple. A more sophisticate experiment is as follows. Consider sharpening a chisel of thickness 4mm. The chisel is applied tangentially to a rotating grindstone of diameter 200mm and coefficient of friction 0.6. The chisel is pressed against the surface of the stone with a force of 10N and the frictional force is resisted by axial support at the other end of the chisel. Now the normal force pressing against the grindstone produces a normal 10N reaction on the chisel blade. Neither produce moments in the stone or chisel. The frictional force of the blade against the stone is 6N and acts tangentially so it applies a moment of 6*0.2 = 1.2 N-m, opposing the rotation of the stone. The counter frictional force acting on the chisel blade, also 6N, is balanced tangentially by the axial support force supplied to the other end of the chisel. But these two forces are not coaxial. The support acts along the centreline 2mm from the contact surface. The friction acts in the opposite direction along the contact surface. These two forces form a couple about the tending equal to 6*.002 = .012 N-m So the turning effects are not equal by a long margin.

Jamsmith wisely asked about "the turning effect of forces" and it is quite true that there are several different and distinct mechanical effects associated with turning. So it would seem to me highly sensible and desirable to identify each of these effects with a unique name. Unfortunately too many mix up the available different terms to create the general confusion, particularly for beginners, that holds today. So Perhaps a little history might help? Ca 250 BC The mechanics of turning effects was known to the ancient world for example the principle of levers attributed to Archimedes. 1725 The term moment was introduced and formally defined by Varignon in his book 'Nouvelle Mechanique.' “The moment of a force, P, about a point O is defined as the product of that force into the perpendicular OM drawn to its line of action from O, this perpendicular being reckoned positive or negative according as it lies to the left or right of the of the direction of P." Varignon's theorem holds to this day and may be found on Wikipedia. 1750 – 1804 St Vennant investigated the torsion of prismatic bars and posed St Vennant’s Problem. He did not however introduce new concepts in turning. 1804 -1806 Poinsot published his book 'Elements de Statique' and the theorem that bears his name. This introduced two things. He defined and introduced the term ‘couple’ and the theorem which states that in 3 dimensions any system of forces may be reduced to a single force plus a couple, in a plane perpendicular to the line of action of the force. He clearly defined his couple to exist in a plane. 1912 Lamb, one of the most prominent applied mathematicians of his time, proposed that the term ‘torque’ be introduced to replace ‘couple’ Lamb 'Statics' p52. “Since a couple in a given plane is for the purposes of pure statics sufficiently defined by its moment, it has been proposed to introduce a name torque or twisting effect which shall be free from the irrelevant suggestion of two particular forces.” This suggestion was not, however generally adopted. Indeed the three most influential texts ( in this subject) of that era and since carried on as before. 1926 Love ‘A Treatise on the Mathematical Theory of Elasticity’ 1936 Southwell ‘Theory of Elasticity’ These both refer to ‘Torsional Couples’ for the 3D effects described in St Vennant’s Problem. 1934 Timoshenko published the third standard text, ‘Theory of Elasticity’ and clearly establish torque in this 3D role. In fact most authors in the second part of the 20th century have followed the notation set by Timoshenko in elasticity. I haven't ventured beyond the first half of the 20th century because nothing new has been added since. It does bring out one other source of confusion. The difference between twist and turn, which is even less often correctly stated. I usually try to associate the Ts Torque, Torsion and Twist.

And I thought perhaps you were using the European convention, not the American one, which is confusing. A couple has the property stated in your last line. The moment of a single force is the different about nearly every point in a plane containing the line of action of the force. It is zero at every point along the line of action. A couple is the same about every point in the plane in which it acts. There does not have to be any material body at the point of action of a moment or couple.

In the water sprinkler, the water exits tangentially to the spin circle of the spinner. Consequently object A (the water) exerts a moment on object B (the spinner) , about its central mounting. However, as you have just observed, the spinner exerts no moment on the exiting water. Normally the spinner incorporates balanced pairs of nozzles so actually generating a couple rather than a simple moment. In the catherine wheel, there may be only one exhaust and therefore a simple moment, rather than a couple, is generated.

Go on?

I am guessing that you are referring to the resonant frequencies of pipes due to standing waves in the pipe. A closed end must have a node of the standing wave An open end must have an antinode. So for your question the fundamental occurs when you have one node in the middle and two antinodes, one at each end. The distance between adjacent antinodes (or nodes) is one wavelength, so the length of the pipe corresponds to one wavelength of the fundamental. Obviously the first harmonic you can have has two nodes and so on. Can you work out the relationship between the length of the pipe and the wavelength of the harmonics now?