Separation Definition and 448 Threads

Homework Statement The Moon and Earth have masses of 7.4 × 1022 kg and 6.0 × 1024 kg, respectively, and the distance between their centers is 3.8 × 108 m. The amount of work required to pull them further apart so that their separation increases by a factor of 1.6 is most nearly Homework...

Homework Statement To an observer in frame S, two events are simultaneous and occur 600km apart. What is the time measured by an observer in frame S' who measures their spatial separation to be 1200km? Explain the sign of your answer. Homework Equations Lorentz Transformation t' =...

Why is the "Separation of Variables" method valid? Hey guys, Lately I have been focusing on some question that have annoyed me for some time. One of these questions is: Why is the method of separation of variables valid when solving some PDE? Usually smmetry arguments are presented, and...

Suppose you have some partiel DE describing a physical system with 2 degrees of freedom (e.g. the SE). If you try separation of variables you get something like: Hg(x)h(y) = Eg(x)h(y) now you can separate this to two equations, but the energy has to go in one of them. Is the final...

Homework Statement Find all solutions. Solve explicitly for y. y^{'}=y^{2}-y Homework Equations The Attempt at a Solution Case where y'=0 0=y(y-1) y=0,1 when y(t)=0 Case where y'\neq0 y'=y^{2}-y \frac{1}{y^{2}-y}y'=1 \int\frac{1}{y^{2}-y}y'dt=∫1dt \int\frac{1}{y^{2}-y}dy=t+c Cant...

The ionization of potassium is 4.34 eV; the electron affinity of iodine is 3.06 eV. At what separation distance will the KI molecule gain enough Coulomb energy to overcome the energy needed to form the K^+ and I^- ions? I'm looking at the solution to this problem and I'm not understanding how...

Homework Statement This is the problem as stated in my textbook: Prove that for a timelike interval, two events can never be considered to occur simultaneously. I thought about two different ways to go about this; both of these ways make sense to me, but I'm not sure if they both make sense...

Hi all, I've written code that takes J2000 equatorial coordinates for 2 objects and calculates (1) the projected separation of between object 1 and object 2 at the distance of object 1, and the Euclidean (3D) distance between objects 1 and 2. The projected separations should be <= the Euclidean...

If Galaxy A drifts apart from Galaxy B with twice the speed of light then how could a Galaxy C next to Galaxy A drift apart from Galaxy A at a similar speed? edit: PS. Wouldn't that need some kind of "universal central observer" to limit Galaxy A from Galaxy C to not drift apart by more than 2*c?

Hi! I'm working on a high Reynold's number model, considering flow over an airfoil with a high angle of attack. I know I want to minimize drag. I'm told that flow separation creates pressure drag---relatively low pressure in the wake of my foil. Q1: Why would flow separation cause lower...

Homework Statement Hopefully no one will mind me posting this as an image. But here it is in tex: Using separation of variables, find the function u(x,t), defined for 0\leq x\leq 4\pi and t\geq 0, which satisfies the following conditions: \frac{\partial^2 u}{\partial...

Homework Statement Solve the diffusion equation: u_{xx}-\alpha^2 u_{t}=0 With the boundary and initial conditions: u(0,t)=u_{0} u(L,t)=u_{L} u(x,0=\phi(x) The Attempt at a Solution I want to solve using separation of variables... I start by assuming a solution of the form...

Homework Statement I must find the oscillations of a circular membrane (drum-like). 1)With the boundary condition that the membrane is fixed at r=a. 2)That the membrane is free. Homework Equations The wave equation \frac{\partial ^2 u }{\partial t^2 } - c^2 \triangle u =0...

Homework Statement Homework Equations Assume the solution has a form of: The Attempt at a Solution It looks like a sine Fourier series except for the 2c5 term outside of the series, so I'm not sure how to go about solving for the coefficients c5 and c10. Any idea?

Homework Statement I'm solving a problem where a conducting pipe with a square cross section is being analyzed to find the potential everywhere in space. The pipe lays along the z-axis, so we're really concerned with the x-y plane. My issue isn't so much the general solution via separation...

Homework Statement V_o varies as V(t) = 2000e^(-100t) volts for t > 0 i1(0) = -6A i2(0) = 1A thus i0(0) = 5A Find i0(t) for t > 0. I found Leq = 4H V(t) = L di/dt I separated variables and integrated, got 5e^(-100t) but the software is telling me it's wrong... supposedly the answer is...

I am doing a lab this week where the objective is to use acids and bases and a microscale extraction to separate three solids in a mixture. The mixture in question is a mixture of naphthalene, benzoic acid, and ethyl 4-aminobenzoate. It will then be put through a series of solvents and...

Is it possible to separate out the oxygen from atmospheric air by centrifugal force. I am not asking theoretically but practically. In other words is there any device that will act as a gas centrifuge which can separate air molecules in real time? A continuous process as opposed to a batch...

Homework Statement A wave of wavelength 75 cm has velocity 375 m/s. a. What is the spatial separation between two points that are 30° out of phase at a particular time? b. What is the phase change at a particular position for a time change of 0.5 ms? Homework Equations u = λ / T...

Please forgive me, I don't really know how to properly ask my question, so I'll just do my best. I want to learn how sound is processed. More specifically what math goes into figuring out what individual frequencies are within a single sound signal. Like if I had a recording of say 5 separate...

Hi all Quick one, if one had an equation y' = x on could simply separate the variables and integrate. Now it the equation y'' = x you would use separation of variables what drives this? Also y'' =0. Is the same as. y''dx =0 dx Why is this legal?Thanks in advance

Would it be true to say that boyancy, as in helium rising and liquids of different densities separating, with the densest at the lowest point, is an indication of gravity's natural tendency to attract the most dense mater to its centre point? If so is the Schwarzschild radius a natural...

Could somebody point me in the right direction on how to go about starting this question please? In need of some guidance on where to begin. Homework Statement Calculate the separation between the two lowest energy states for an electron confined in an infinite potential well of width 1nm...

Hi all. I have been looking for a formula that gives me the angular separation of two stars. So far I just found this one :http://www.skythisweek.info/angsep.pdf but it uses the RA and DEC of the 2 stars, and I need to use the hour angle and DEC. Is it the same thing? Do I just replace HA by...

"separation of variables", but for 2nd order Ok, I know how to separate variables in solving an ODE. I am unable to understand a solution I have for a problem which was the result of reduction of order- we end up with u''*sinx-2u'*cosx=0 so turn this into u''/u'=-2cosx/sinx At this point I...

Not really a specific problem, but just a general question: Does anyone have any good references (preferably online) for solving E&M problems with this method? I'm using Griffith's Electrodynamics book for my class and I'm trying to get ready for a final. This is the only part I'm having...

Hi I know that for an airfoil, it's typical to describe stall in terms of angle of attack. I'm wondering, how does Re play a role in flow separation of an airfoil (and for objects in general such as a plate, sphere, or cylinder)? One Wikipedia (http://en.wikipedia.org/wiki/Flow_separation) it...

Homework Statement solve dy/dx=e^(3x+2y) by separation of variables The Attempt at a Solution \frac{dy}{dx}=e^{3x+2y} \frac{dy}{dx}=e^{3x}e^{2y} e^{-2y}dy=e^{3x}dx \int e^{-2y}dy=\int e^{3x}dx e^{-2y}=-\frac{2}{3}e^3x + C -2y = ln(-\frac{2}{3}e^{3x}+C)...

Homework Statement I can't answer to that question, and I don't know how to. I have to calculate the average separation between H2O molecules in pure water. Homework Equations The diameter of the molecule is 0.29 nm I think we can use the bohr equation to resolve it? r = (ε0*h2)...

Homework Statement Use separation of variables to find the solution to Laplaces equation satisfying the boundary conditions u(x,0)=0 (0<x<2) u(x,1)=0 (0<x<2) u(0,y)=0 (0<y<1) u(2,y)= asin2πy(0<y<1) The Attempt at a Solution I am able to perform the separation of variables...

The normalization condition is: ∫|ψ|^{2}d^{3}r=1 In spherical coordinates: d^{3}r=r^{2}sinθdrdθd\phi Separating variables: ∫|ψ|^{2}r^{2}sinθdrdθd\phi=∫|R|^{2}r^{2}dr∫|Y|^{2}sinθdθd\phi=1 The next step is the part I don't understand. It says: ∫^{∞}_{0}|R|^{2}r^{2}dr=1 and...

I think I understand much of SR and some GR, but I'm always stuck when this thought comes to mind.It looks like a stupid proposition and never appears in discussions, but want it cleared up. Consider two objects separated by some distance comparable to the speed of light. Thus each observer...

Homework Statement dP/dt=P-P^2 Homework Equations The Attempt at a Solution I know you can separate this and after i did that and did my partial fractions i got t + C = ln(P) + ln(1-P) but i don't know what to do from here i figure you take the e of both sides at some point...

Hi there, I just wanted to know how to find out where the separation point is on a Pressure Coefficient against Angle Graph ? I did some research and found out something called an adverse pressure gradient what does it mean ? I know that it does promote a separation point so would a separation...

Homework Statement Solve the following equation by separation of the variables: y' tan-1x - y (1+x2)-1 = 0 Homework Equations The Attempt at a Solution I am not sure if tan-1x stands for arctan x or (tan x)-1. (This has been taken out a book.) Any help on this would be...

Hi all, I am looking to learn more about boundary layer control devices that can delay boundary layer transition (Laminar to Turbulent) and also BL devices that can delay flow separation. I have already found loads of info on Vortex Generators but i am having trouble finding info on things...

Solve the following first order, ordinary differential equations using separation of variables: dy/dx = y^2 x subject to y=-1 when x=0 the correct answer is: y = -2/x^2 + 2 i cannot seem to get this answer, after i separate the variables and integrate both sides i get: y^2 x^2/2...

Homework Statement Given the partial differential equation: ∂2u/∂x2 = ∂2u/∂t2 , where x[0;L] Use separation of variables to find the solution that satisfies the boundary conditions: ∂u/∂x (x=0) = ∂u/∂x (x=L) = 0 Homework Equations The separation of variables method. The...

Homework Statement Solve the differential equation: y' + cos(x)y = cos(x) The Attempt at a Solution y' = cos(x)(1 -y) \frac{dy}{1-y} = cos(x) dx -ln|1-y| = sin(x) + C \frac{1}{1-y} = e^{sin(x)} + C 1-y = \frac{1}{e^{sin(x)} + C} y = \frac{-1}{e^{sin(x)} + C} + 1 Have I done this...

Why does flow separation give less lift? A separated "suction side" would in my pov give zero pressure (which is the lowest possible). And low pressure on suction side is, of course, beneficial. I think I got it now; as the pressure can not drop further a increase in angle of attack will...

Homework Statement Two frictionless pucks are placed on a level surface with an initial distance of 20m. Puck 1 has a mass of 0.8 kg and a charge of + 3x10^-4 C while puck 2 has a mass of 0.4 kg and a charge of +3 x10^-4 C. The initial velocity of puck 1 is 12 m/s [E] and the initial...

Homework Statement I have sinusoidal waves traveling along the surface of the water. I'm given the relation v=\sqrt{gh} where h is the depth of the water. I'm given that when the water is 5 m deep the wavelengt of the waves is 1.4 m. I"m asked how far apart the wave crests are near the...

Homework Statement if i have source separation between 2 light sources, d, and wavelength, λ, what is the highest order node and antinode? Homework Equations The Attempt at a Solution im not sure where to start for this question I am leaning towards division to cancel out the meters

Homework Statement use separation of variables to solve the differential equation x^2dy/dx=y-xy with the initial condition of y(-1)=-1 Homework Equations The Attempt at a Solution after i separated and integrated i got the answer y=e^(-1/x-lnx+c) the answer in the book is y=e^-(1+1/x)/x i...

\displaystyle\frac{dN}{dt} = rN\left(1-\frac{N}{K}\right)\displaystyle\int\frac{KdN}{N\left(K-N\right)} = \int rdt \displaystyle K\int\frac{dN}{N}-K\int\frac{dN}{K-N}=r\int dt Now, I obtain: K\ln\left(\frac{N}{K-N}\right) = rt+c \left(\frac{N}{K-N}\right)^K=C_0r^{rt} The final solution is...

Hello, Just out of curiosity, where would following "seperation axiom" fit in? So far I'm only acquainted with the T1, T2, T3 and T4 axioms (and the notion of completely regular in relation to the Urysohn theorem).

This semester while taking Linear Programming (Linear Optimization Models), we talked about using a linear program to separate two sets of points A and B. The general program is: Max d s.t. yA ≥ axA+b+d yB ≤ axB+b-d It can be expanded into finding a polynomial that passes between the...

Homework Statement I made this problem up as an example for a bigger problem I have to do. P = {(-2,4),(1,3)} and Q = {(-1,1),(0,0)}. I need to use linear programming to find the best line to go between them. Homework Equations Max d subject to: y_{i}≥ax_{i}+b+d (for all points above...

Homework Statement I am having trouble understanding the concept of induced charge separation. In my textbook, there is a diagram that demonstrates the procedure, but it gets confusing because the first image is normal, and then it gets inverted? I don't understand in the second set-up if it...

I was just wondering if there are any written documents which give the views of the United States founding fathers' views towards separation of church and state. The constitution reads, "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof"...