Separation Definition and 448 Threads

Homework Statement Two events occur at the same place in a certain inertial frame and are separated by a time interval of 4 seconds. What is the spatial separation between these two events in an inertial frame in which the events are separated by a time interval of 6 seconds? Homework...

Homework Statement dx/dt=3x(x-5); x(0)=2 Homework Equations dx/dt=F(x)G(t) dx/dt=x' The Attempt at a Solution First I separated the variables using F=3x(x-5) and G=3 x'/(3x(x-5))=3 Applying method of quadrature: \int\frac{x'}{(3x(x-5)}dt=\int3 dt On the right hand...

Here's my understanding of the Force /Separation graph, I'm open to criticism/ridicule if I've got it wrong: If the two atoms are pushed together, then there is a repulsive force between them of a positive magnitude. If they are separated by a distance r, then the two forces...

Homework Statement x^2y'=1-x^2+y^2-x^2y^2 Homework Equations n/a The Attempt at a Solution I am trying to separate the y terms on one side and the x terms on the other so I can solve this differential equation. I've tried everything I can think of, but cannot get them on their...

Homework Statement The lenses are separated by 250mm. Where should the object be places so that the final image is formed at infinity? I'm confused.

Hi. This is my first post in PF. I'm an undergraduate student of Electronics Engineering with strong interest in math & physics (and weak understanding of them :P). One of the things I always hate is when in some book (or some lectures) ODEs or PDEs are solved after the magic words "[...] and...

Homework Statement y' + (2/x)y = 3/x^2 Homework Equations separation of variables The Attempt at a Solution First I turned it into dy/dx + (2/x)y = 3/x^2 dx then multiplied both sides by dx dy + (2/x)y = 3/x^2 dx I then tried to divide both sides by 2/x and got...

Homework Statement du/dt=d2u/dx2, u(0,t)=0, u(pi,t)=0 u(x,0) = sin^2(x) 0<x<pi Find the solution Also find the solution to the initial condition: du/dt u(x,0) = sin^2(x) 0<x<pi The Attempt at a Solution From separation of variables I obtain u(x,t) = B.e^(-L^2t).sin(Lx)...

Hi. I believe I understand separation of variables for a first order DE. But can anyone tell me how to use it on a second order DE? In particular I have been looking at this example http://en.wikipedia.org/wiki/Integrating_factor#General_use" where it is claimed that one can use separation of...

I'm writing code to check if polygons intersect, but I've ran into a problem. I have two "vectors." Each has an origin and x and y components. They are facing towards each other. I need to write code that determines if there's a perpendicular axis that separates them. Here's a picture of what...

Reduce the equation (equation is attached) to a set of ODEs by the method of separation of variables. kindly help me with the solution, i m unable to solve.

It is said that all humankind is at most six social relationships removed from each other. How many blood relationships at most currently remove every human from each other?

1. using differentiation,find the angular separation in arc minutes in second order for two wavelengths 589.0 and 589.6 nanometers 2. d sin(\theta)=m (\lambda) 3. i try to use D=\delta\theta/\delta\lambda by differentating d sin(\theta)=m (\lambda) i got d/m sec(thetha).this...

Homework Statement Given that the total cohesive energy, U, in an ionic crystal as a function of nearest neighbor distance, R, between two ions +e and -e is given by: U(R) = \frac{A}{R^n} - \frac{\alpha e^2}{4 \pi \epsilon R} show that at equilibrium: U(R) = \frac{\alpha e^2}{4 \pi...

Homework Statement Considering only orbital angular momentum, estimate the energy level separation between electron states in a magnetic field of 1 Tesla applied along the z direction. Homework Equations I am confused by how to even start this question! Isn't orbital angular momentum...

Homework Statement Light with two wavelengths (510.0 nm and 525.6 nm) is spread by a diffraction grating. On a screen 4 meters behind the grating we observe that the diffrence between the two second order maximum is 1 cm. What is the grating constant (d) ?Homework Equations I think i only need...

Homework Statement If the energy separation of two states is known for some atom, how can the same energy separation be calculated for the same two states for an ionized atom? i.e. if we know that the difference between the 1s^2 and the 1s2s states in Helium is something like 25eV, how could...

Homework Statement Outside the International Space Station, a 60 kg astronaut holding a 4.0 kg object (both initially at rest) throws the object at 10 m/s relative to the space station. A 50 kg astronaut, initially at rest, catches the object. What is the speed of separation of the two...

Homework Statement evaluate the integral cos^-1 2x dx? Homework Equations The Attempt at a Solution let u = arc cos du = -1 / (sqrt 1-x^2) dv = 2x v= x^2 arc cos * x^2 - the integral of -x^2 / (sqrt 1-x^2) then i don't know what to do

Homework Statement Show that the time-dependent Schrodinger equation is separable when V depends on time only and is uniform in space (i.e., V = V (t)). Homework Equations The Attempt at a Solution In the attached document

Homework Statement Is there a formula for calculating the rate of separation (per degree) for two planes beginning at a common point, traveling at the same speed, performing turns with two different turn radiuses? Homework Equations See linked image for better understanding...

How does rubbing separate positive and negative charge on neutral objects?

Okay, I'm stumped at what seems like a very simple mathematical step I start with Then, the next step is I see what changed, but I don't understand exactly what happened. Can someone please explain? Thanks in advance!

So I've always done simple ODEs by the method of separation of variables. You know, dy/dx = A*y dy/y = A*dx IndefiniteIntegral[1/y dy] = IndefiniteIntegral[A dx] ln(y) = A*x + Constant y = Constant*e^(A*x) It's easy to remember and it usually works. A lot of the PDEs I know how to do...

Homework Statement The differential equation I have is dy/dx = (xy + 2y - x - 2)/(xy - 3y + x - 3). I need help getting started. Neither the top nor the bottom can be factored, so I don't know what to do next. Can anyone give me a push? All I know is that I need to use separation of variables.

1. Solve the wave equation u_(tt) = 4u_(xx) on the interval [0, π] subject to the conditions u(x, 0) = cos x, u_t(x, 0) = 1, u(0, t) = 0 = u(π, t). Homework Equations 3. Hello. This appears to be a common separation of variables question. Only problem is after using...

When solving a pde using this method how do you know what ORDER to use the initial/boundary conditions given to you? E.g. if you are asked to solve the wave equation given u(x,0), u'(x,0), u(0,t), u(l,t) how do you know what order to use these in (particularly the first two)

Hi all, I'm trying to nail very precisely the effects of a battery in terms of charge separation. In particular: when and what points are excess charges seen in a typical circuit powered by a battery. A. Prior to wires being attached to the battery, you just have the battery itself. My...

Hello, I'm studying for an exam tomorrow and am facing a question I can't for the life of me fathom. " A PP air capacitor is made by using to plates 16 cm squared, spaced 4.7 mm apart, connected to a 12V battery" Find Capacitance, charge on each plate, electric field between plated...

Homework Statement Use separation of variables to solve (x+2y)y'=1 y(0)=2Homework Equations u=2y+x >>I did not know how to start this, so i looked at the back of the book and it said to use that substitution y=(u-x)/2, du=2dy+dx, dy=(du-dx)/2 The Attempt at a Solution so i got the following...

Homework Statement In detail, explain the theory behind the use of chromatography as a a.)separation technique. b.) identification technique. Homework Equations The Attempt at a Solution I know that chromatography can be used as a separation technique and also indetification...

Homework Statement Alpha particles of kinetic energy 9.6MeV are incident on a silver foil of thickness 7.0 micro meters. For a certain value of the impact parameter, the alpha particles lose exactly half their incident kinetic energy when they reach their minimum separation from the...

Understandably so, certain isotopic separation techniques are going to be sensitive (U-235, U-233, Li-6) because of their relationship to nuclear weapons. Would any other isotopic separation techniques fall under the wing of any regulating agency in the United States (NRC, NNSA, etc.)? For...

Homework Statement Solve the given differential equation by separation of variables. Homework Equations \frac{dy}{dx} = \frac{xy + 2y - x - 2}{xy - 3y + x - 3} The Attempt at a Solution \frac{dy}{dx} = \frac{xy + 2y - x - 2}{xy - 3y + x - 3} = \frac{(x + 2)(y - 1)}{(x - 3)(y + 1)} (x -...

Homework Statement Solve the problem. utt = uxx 0 < x < 1, t > 0 u(x,0) = x, ut(x,0) = x(1-x), u(0,t) = 0, u(1,t) = 1 Homework Equations The Attempt at a Solution Here is what I have so far but I'm not sure if I am on the right path or not. u(x,t) = X(x)T(t)...

Please have mercy on my non-mathematical mind... I am struggling so hard with Differential Equations. This is my third time to take the class and I still feel like I am walking through the woods at midnight on an extremely dark night. This is the problem that I am working on: dy/dx =...

Homework Statement This is a try for the solution of Laplace Equation. We have to calculate the potential distribution in a cylinder coordinate. However, there is a step really bring us trouble. Please go to the detail. You can either read it in the related URL, or in my PDF attachment...

Homework Statement A car and a truck are heading directly toward one another on a straight and narrow street, but they avoid a head-on collision by simultaneously applying their brakes at t=0 . The resulting velocity-versus-time graphs are shown in the figure . What is the separation...

Homework Statement One particle has a mass of 3.00 \times 10^{-3} kg and a charge of +8.00 \mu C. A second particle has a mass of 6.00 \times 10^{-3} kg and the same charge. The two particles are initially held in place and then released. The particles fly apart, and when the separation...

If I am using vortex generators in an attempt to delay diffuser separation what would the consequence be of the vortex generators stalling? For instance if I set them at and angle of attack to the flow that was past the stall point.

this may seem like a simple question but how does one know that separation of variables for solving linear PDE's will work. What i mean is that it seems to pick out a form of the solution to a given problem (I have heard that linear PDE's have an infinite number of functions of a particular...

Since I first leaned of the concept of social networks it has fascinated me but I never really studied the topic. It seems to me a huge topic but is not widely studied compared to other areas of mathematics. What better way to study such things as the spread of information, political views...

\int^{B}______________{A}\int^{\infty}_______________{0}\frac{t^{N-1}x^{s-N-1}dtdx}{e^{t+x}+1} With the restrictions that that B>A, 0<Re(s)<1 and N is a natural number>1. I think t=ab and x=a(1-b) would work, but I'm not sure how to go from there. I don't need to solve the integral; just...

Does anyone know of a way to calculate the point at which flow separation occurs?

Homework Statement Solve the heat flow problem using the method of separation of variables: Homework Equations PDE:\frac{\partial u}{\partial t}=k\frac{\partial^{2} u}{\partial t^{2}} for 0<x<L, 0<t<\infty BC's:\frac{\partial u}{\partial x}(0,t)=0,\frac{\partial u}{\partial x}(L,t)=0...

Hi all, For my thesis I would like to solve the following second order nonlinear PDE for V(x,\sigma,t): \frac{1}{2}\sigma^2\frac{\partial^2 V}{\partial x^2}+\frac{1}{2}B^2\frac{\partial^2 V}{\partial \sigma^2}+a\frac{\partial V}{\partial \sigma}=0, subject to the following boundary...

Homework Statement Hi, I don't really understand separation of variables very well, and I was hoping to do get my mind more clear on the following question: (Q) Use separation of variables to find all the separable solutions of the equation: d²y/dt² -c²(d²y/dx²) + w²y = 0 where 'w'...

Homework Statement The green line of gaseous mercury at 546nm fals on a double-slit apparatus. If the fifth dark fringe is at 0.150 degree from the centerline, what is the slit separaton? Homework Equations d sin (theta) = m* lambda The Attempt at a Solution ok i used the...

So my book says that to solve a PDE by separation of variables, we check the three cases where λ, the separation constant, is equal to 0, -a^2, and a^2. But in this particular problem, instead of substituting λ=0, λ = a^2, λ= -a^2, they substitute the entire coefficient of X, (λ-1)/k =0, (λ-1)/k...

Homework Statement (a)What is the mean free path for oxygen molecules at 300K and atmospheric pressure (105 Pa) and the average frequency of collisions for a particular molecule? (The diameter of an oxygen molecule is 0.29 nm). (b)What is the mean free path of oxygen molecules at an...