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    Work required to assemble charged particles

    I take it that the charges come from infinity. The work required to bring them in from infinity is the sum of the electrostatic energies of the pairs of charges. With 8 charges there are 8*7/2 = 28 such pairs. These can be viewed as the 12 sides of the cube, its 12 surface diagonals and its 4...
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    Time Dilation/Proper Time Question

    The twin paradox involves a set of twins, or rather a set of two watches set to an equal time and traveling at different velocities. After some interval they are supposed to read different times. Now the time measured by a watch is its proper time, whatever route it has traveled; there is no...
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    How much curvature are we talking about?

    I am unsure about the source of the confusion. There are three things to be considered: 1. To calculate the time needed to fall from a certain height in Earth gravity. 2. To calculate the length of a line segment in spacetime. 3. To calculate the radius of a circle, if a chord and...
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    Quantum Physics and the Pensions Crisis

    I have sometimes feared that, by a chain of events which steadily become more improbable, I would live forever, though in steadily declining health. Think about it. To observe oneself as being alive, one doesn't need much of one's faculties. The idea is nightmarish enough to keep one awake at...
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    Electron 'orbits' question

    This is a question to which different people will give different answers. For example, the theory of Bohm would imply that the electron does trace a kind of orbit, but a very intricate one, which isn't at all like a circle or an ellipse. The Many Worlds theory would have the electron trace...
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    How much curvature are we talking about?

    In space, a circle touching the bullet's track on the inside would have a much larger radius (hence less curvature) than a circle touching the ball's track on the inside. However, the problem is to be solved in spacetime. Now, the bullet takes less time to complete its track than the ball (which...
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    Prime Numbers

    Prime numbers have exactly two (positive integer) divisors: 1, and the number itself. after all, N = 1 * N, and N = N * 1. As far as I know, some patterns have been found which generate only prime numbers, but no pattern has been found which generates all of them. In general, to see if some...
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    Infinite Of Infinates, whats the solution?

    Infinite expressions, like 1 + 1/2 + 1/4 + 1/8 + ... , may or may not refer to existing mathemathical objects. If one wants to reason about such an object, one must first ascertain its existence. (For a finite expression, such as 3 * 1/5; the existence of the object is usually "prewired" in the...
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    Nostradamus and the LHC

    Multi-quote still doesn't work. I did not think of asteroid impacts, but of nuclear bombs. Perhaps I should translate: Fire which is sleeping in the abyss of matter, Will be unchained by the ingenuity of ONE STONE Devastation to an entire city Great kingdoms turned into cemeteries...
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    Nice way to find the integral

    Oh, yes. Gn(0) = (-1/n)*(6/n3)*e0=(-6/n4). Not zero at all. But Gn(x) does tend to zero if x increases without bound. So, the integral of gn(x) from 0 to infinity would be (+6/n4). Strangely, because someone had earlier suggested zero as the answer, I accepted a result of zero without...
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    Nostradamus and the LHC

    The problem with "supernatural" claims, such as prognostication, is that there is so much fraud going around. And the problem with Nostradamus, specifically, is that his quatrains are so unclear. Thus he opens himself to the suspicion of fraud. A fraudster would be unclear on purpose, in order...
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    Nice way to find the integral

    Last night, I have thought about it some more. x3/(ex-1) = (x3/ex)*1/(1-e-x) x3/(ex-1) = (x3/ex)*(1 + e-x + e-2x + e-3x + e-4x + ...) x3/(ex-1) = x3 * (e-x + e-2x + e-3x + e-4x + ...) Let Gn(x) = (-1/n)*(x3 + 3x2/n + 6x/n2 + 6/n3)*e-nx gn(x) = dGn(x)/dx = (x3 + 3x2/n + 6x/n2 +6/n3)*e-nx...
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    Nice way to find the integral

    This is an improper integral, because the integrand x3/(ex-1) is not defined at the edge of the integration domain, x=0. e0 - 1 = 1 - 1 = 0. 03/0 = 0/0 is undefined. So one must first ascertain whether it converges. To find a primitive function, one might substitute ex = u, or x = elog(u)...
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    Nostradamus and the LHC

    I continue wondering why Nortradamus would urge the inhabitants of Geneva to flee from their city, if they cannot also flee from their planet. In an earlier post I suggested that the initial black holes, spraying from the installation, might already be harmful to human beings, in spite of their...
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    A mass sliding down an incline plane with a pulley attached

    I think it might be well to define what you mean by T, w, N, x, and so on, because that would make the problem easier to understand. The way I understand it, there is an inclined plane, and theta is the angle between the plane and the horizontal. Mass m1 is lying on the plane, while mass mass...
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    Speeds of a Person

    The kinetic energy (KE) would not be helpful here, becase chemical energy is being converted into kinetic energy when the gun is fired. Momentum, however, is helpful. Think of the system (man plus pistol plus bullet) splitting in two. The two parts (man plus pistol) and (bullet) will have...
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    Projectile Help Please

    After 10 seconds, the flare will have a vertical speed (vertical component of velocity) of 10 s * 9.81 m/s2 = 98. 1, m/s. (Its vertical speed was initially zero, as it was fired in a horizontal direction. Unless they mean horizontal relative to the ascending helicopter. I assume they don't mean...
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    Double integration calculation

    I assume that it is the volume of the sphere which you wish to calculate. In polar coordinates, the volume element is dr * (r * dtheta) * {r * sin(theta) * dphi}. Or r2 *dr * sin(theta) * dtheta * dphi. This must be integrated for r between 0 (the midpoint) and R (the surface), for theta...
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    Rule or law for absurdity

    The number of hydrogen atoms in the observable universe has been estimated as being around 1080.
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    Domain Issues

    fg, f+g and f-g are defined everywhere, where f and g are both defined. f/g is defined everywhere, where f and g are both defined and g does not equal zero.
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    A mass sliding down an incline plane with a pulley attached

    The two masses are attached to each other by an unstretcheable rope, so any force acting on one of the masses will accelerate both of them. To find the acceleration, the force must be divided by the sum of the masses. (That is, if the force would tend to accelerate them away from each other if...
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    Mechanics of Solids - Crandall,Dahl, Lardner

    Would the answers not be in the back of the book?
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    Air Resistance of bicyclist problem

    Now we must calculate. Work on the first leg of the journey is 6.2 km * -2.7 N. Work on the second leg is -5,5 km * 2.2 N. -16.74 kJoule + -12.10 kJoule = -28.84 kJoule. (A Joule is a Nm.) However, this is being too exact. The distances and forces were given in two decimals, so only the...
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    Proof of constant acceleration

    If the acceleration is the vector product of the velocity and something else, the acceleration is at right angles to the velocity. The scalar product of acceleration and velocity must then be zero. (The scalar product of two vectors is the product of their magnitudes and the cosine of the angle...
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    TORQUE calculations for Brushless dc motor.

    It seems to me that you would want the motor to deliver the maximum amount of work per second. That means using it at a number of rotations per second where the number of rotations multiplied by the torque reaches the maximum value. So you would first need to make a graph of torque versus RPM...
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    Air Resistance of bicyclist problem

    work (a scalar) = the scalar product of distance and force (two vectors). Of course, the work for the second leg of the journey must be added to the work for the first leg of the journey. The scalar product of two vectors is the product of their magnitudes and the cosine of the angle between...
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    Black hole in LHC?

    This is a sequel to post 403. Previously I argued that there must be a minimum size and mass for any black hole carrying an electric charge, and I calculated the mass to be in the microgram range. To do this, I used an integration of the mass of the electric field in a shell around the event...
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    Linear Algebra-Fields and axioms

    The zero vector is a vector which, if added to another vector, gives this other vector as a result. (x,y)++(0,a) = (x+0,y+a-a) = (x,y). So (0,a) seems a reasonable zero vector. If I multiply (x,y) by 0, I get 0(x,y) = (0x,0y-0a+a) = (0,a), so that's okay, too. If I multiply (x,y) by 1...
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    Black hole in LHC?

    Anyone reading this: I tried to multi-quote, but it doesn't seem to work, so I did a normal quote. Vanesch refers to a post of mine about a calculation of the minimum mass for a charged black hole. Vanesch: You are right. Using a normal Euclidean volume element for an integration in the...
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    What is the minimum distance she can be from the waterfall?

    To jump to a certain height, she must start out with a certain kinetic energy, equal to the potential energy she will have on reaching that height. Her mass is unimportant, because if (1/2)mv2 = mgh, then (1/2)v2 = gh Happily, the kinetic energy for vertical and horizontal motion add, by...
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