studiot

Alternatively you can look at it like this In the diagram the boat wants to travel straight across from A to B, but has to head towards D because of the current AC Now it is important to place your arrows correctly and also indicate their direction because the boat at A has two components of velocity, its motor at 15 km/hr and the current at 4 km/hr. These vectors are concurrent at A so we cannot draw the triangle ADC as this does not represent the sum or resultant. We have to draw AD first then 'place' DE on the end of AD to and complete the triangle ADE, reversing the arrow AE so that we draw the correct triangle. In the diagram the angle (a) for the other method is shown as is the angle in triangle ADE as (b). (a) + (b) is, of course, a right angle here. Now we calcualte AE = AD2-DE2 = 14.47 km/hr and thus cos(b) = AE/AE = 14.47/!5 and (b) = 15.47 degrees, which agress with the other (resolution) method whichs (a) as 74.53 Perhaps this shows more clearly why the boat should not steer your angle theta. In the case of question above 15 is the resultant, and the hypotenuse of the vector triangle. In the case you propose where the boat heads straight across the 15 is one of the components, and the resultant is sqrt(152+42), not the sqrt(152 - 42), we had in the question. The angles are close because of the big difference between 15 and 4 so sqrt(152+42) is not very different from sqrt(152 - 42) so the triangles are nearly the same.

I asked because a 'quantum state' is defined by a characteristic list of quantum numbers. So a different state is entered when one of those numbers change. That is what Strange was referreing to when he saud 'spintronics' - The spin quantum number. However the charges in electric current in conductors is delocalised. That means they are no longer in orbitals that belong to individual atoms, they belong to what amounts to super orbitals that encompass the whole conductor, split or not. That means that the quantum number defining the orbital does not change wherever the electron is in the conductor, ie it does not change with position. Please note this is a very crude, non mathematical, description to help understanding.

OK Let the boat be headed so as to make an angle (a) with the current, and with the dock assuming the dock is parallel to the current. Then its velocity is the resultant of 15 km/hr in this direction and 4 km/hr in the direction of the current. The component of velocity perpendicular to the current is 15 sin(a) and the component parallel to the current is 4 - 15 cos(a) But to go straight across the velocity parallel to the current must be zero. So 4 - 15cos(a) = 0 So cos(a) = 4/15 Having found (a) you can substitute into the this into 15sin(a) to obtain the crossing velocity and thus the time. Now the triangle you have drawn is not the vector difference of 4 and cos sin(a), it is the vector difference of 4 and 15

What do you understand a quantum state to be, particularly with reference to electric currents?

How can I help if you don't cooperate? I don't want to confuse you by introducing stuff they didn't tell you. Surely it's no big secret whether they told you to add vectors using triangles or parallelograms?

Let's clear this up first, as it will get in your way for the rest of vector analysis. You can only add vectors that are of the same type. You cannot add forces to velocities or accelerations to velocities or whatever. Please also state whether you have been taught the triangle of vector addition or the parallelogram.

For the record here is the complete solution using the method chikis and I were developing. Express the statement as an equation [math]\frac{3}{{10}}y = x[/math] This is an equation expressing x as a function of y. We want an equation expressing y as a function of x so rearrange. Multiply through by ten [math]3y = 10x[/math] Divide through by three [math]y = \frac{{10}}{3}x[/math] We now have an equation expressing y as a function of x so multiply it by 3 to get 3y [math]3y = 3\left( {\frac{{10}}{3}x} \right) = 10x[/math] Now take 30% of this [math]\frac{{30}}{{100}}(3y) = \frac{{30}}{{100}}\left( {10x} \right) = 3x[/math] This gives the answer as 3x. We can shorten this by noting in the second line that we have 3x, but most will bypass this combining lines 2 and 3. ******************************************************************************************************************************************************* My alternative method starts in the same place with the equation [math]\frac{{30}}{{100}}y = x[/math] But this time I multiply the y by 3 straight away and then change the order of multiplication of the 30% and the 3 to find the result directly. [math]\frac{{30}}{{100}}(3y) = 3\left( {\frac{{30}}{{100}}y} \right) = 3(x) = 3x[/math]

I really think it is far more important for you to concentrate on reading the question than on trying to pick holes in your instructor's exercises. You seem to have a fundmental misconception about the addition of vectors. Can you see what is wrong with your statement?

What about equilibrium?

What rubbish. Please calculate t for s = 0 in your equation. Not all functions have reciprocals at all points, some even have no reciprocals at all.

These are just uproven theories, which account for some effects, but fail to account for others. They do not have the status of fundamental principles upon which Physics rests.

This is the typical retreat of those faced with incontrovertible facts and amounts to an act of faith on their part. I have told you how to constuct a clock that does not depend upon time, edit silly me, does not depend upon motion I have told you how to show that time must exist , independent of any movment in the universe, but you have chosen not to answer. Instead you have chosen to try the line of ' we must consider what is possible and there might be something out ther beyond our present knowledge that is possible, so we can never rule any theory out, however daft'. Well there are things we can state with absolute certainty today, using only today's knowledge, that can and will never happen, no matter how much knowledge we aquire. You talk of enigmatic mathematics. There is nothing enigmatic about this. I think you have simply confused the difference between the dependent variable and the independent variable. So the funny thing is, had you stated your proposal the other way round, I think most here would have agreed with you. Namely that you cannot have motion without time rahter than you cannot have time without motion. Time is surely the more 'fundamental' quantity, in that it can exist without any other, although it would be a pretty boring universe if time was the only variable.

Do you really want Chemistry or perhaps Metallurgy?

I offered no explanation of brownian motion. I did, however offer direct observation more than once since you were seeking experimental evidence. Have you ever seen Brownian motion, it is a simple experiment to implement?

Both circles actually follow curtate cycloidal paths and depend upon an elliptic integral for their different path lengths. http://mathworld.wolfram.com/CurtateCycloid.html There is no paradox, but thank you for the link that leads to some interesting and entertaining videos.

Agreed, I have already mention radioactive decay of larger particles. Take a few million uranium atoms and count them count them again count them again You have the basis of a non motional clock. But many changes of state, including chemical ones, that John Cuthber should be better able to point out than I, should pass muster as an example of non motional change

The history in Wiki shows that the ideas behind the Kinetic Theory predate experimental proof by several centuries. Maybe Enthalpy's timing is a bit off, but I take his point and have already commented on Brownian motion, which can be observed directly. I would, however, support Bignose's assertion that the motion is in principle classically deterministic, not random, as claimed in the Wiki article. http://en.wikipedia.org/wiki/Kinetic_theoryI I would also like to add that I consider that the Kinetic Theory, in its various guises and developments, is one of the most important and satisfying theories in classical Physics.

@Bignose, I do believe this is a matter of first language (I don't think English is Enthalpy's) and I think Enthalpy meant accepted in the sense of "taken on trust for granted or without direct proof" not in the more obvious sense. I have made this sort of mistake before in discussions with Enthalpy; some of his statements have a deeper meaning behind them that is not obvious on first glance. There is, however, no question that your summary of the Kinetic Theory is corrrect in declaring that the mechanics of motion of the particles is entirely deterministic in principle within the laws invoked in the Kinetic Theory. If we however, consider from the point of view of a particular area or point being bombarded by these particles, the variable recording the time of bombardment takes on the mantle of a random variable, does it not?

Well personally I would not have tackled it this way, but I was concerned to make chikis method work out, rather than attempt to impose my own.

I skipped through the video and suggest that you haven't missed much.

@enthalpy. It is interesting to learn of the existence of pressure sensors sensitive enough to record the impact of a single molecule. If it is not considered off topic a link to them would be appreciated.

At least tell us why you (or the questioner) think the velocity is different at the top of the circle and 30 below the horizontal. If you think the velocity is different what is different about them?

Well I just wasted a good while preparing a diagram with comments, facts and figures, when the site froze on me.

Of course they apply. Some quantities will become zero, but that is also true of the net force on a body in equlilibrium in our normal universe under the action of many forces. In particular there can be no magnetic field, but there can be an electric one if the particle carries a charge. There will be a gravitiational field if the particle has mass and so on. Yes I agree that relativity reduces to trivia, but so what? Don't we often solve mathematical problems by transforming them into a form where some of the coefficients and/or variables become zero? Talking of mathematics, if we offer a general proposition it means that it holds for every value of our variable(s), so we are entitled to test it by using specific values to calculate the values of coefficients. This often means f(x) when x=0, f(x) when y=0 and so on. So I am doing nothig more than following a very well trod path. I chose Maxwell's equations, just because relativity reduces to trivia, but they do not completely, and because they contain the variable time, which does not vanish in a universe containing only a single particle. Or do you wish to propose that our laws of physics only hold in universes that contain a minimum number of particles and, if so, how many and by what proof?

I didn't say that you did However I am rather concerned at the apparent oscillation of the 'acidity of the ocean' with amplitude greater than the total variation over the timescale.