Separation Definition and 448 Threads

Two frictionless pucks are placed on a level surface at an initial distance of 20.0 m. The mass of puck 1 is 0.80 kg and it has a charge of +3.0 X 10^-4 C., while puck 2 is 0.40 kg with a charge of +3.0 X 10^-4 C. the initial velocity of puck 1 is 12.0 m/s (E) and the initial velocity of puck 2...

Homework Statement What is the minimum angular separation an eye could resolve when viewing two stars, considering only diffraction effects? Homework Equations θ=(1.22*λ)/D The Attempt at a Solution I tried estimating with λ=550 nm and D=5.0 mm (pupil diameter) which appeared in...

For my research purpose, I made a wind tunnel which has 0.6m rectangular section [0.2X0.2sq. meter] and 1.4m long diffuser section having porous top [top wall angle is 20deg] as follows: Wind tunnel speed is 15m/s. Even using 20deg inclination of porous top wall, there is no flow...

Homework Statement What is the minimum angular separation an eye could resolve when viewing two stars, considering only diffraction effects? Homework Equations Rayleigh criterion: θ=(1.22*λ)/D The Attempt at a Solution This problem doesn't give very much to go on so I think...

Homework Statement Using the method of separation of variables, obtain a solution of the following PDE subject to the given conditions \frac{du}{dx}+y\frac{du}{dy}=(2x+y)u u(x,1)=5e^{x^{2}-x} Homework Equations The Attempt at a Solution See my attached working the...

This isn't a HW problem, it's more of a general question. I'm reading Griffith's Intro to QM 3rd Edition. On page 134 he uses separation of variables, of which I'm familiar (but by no means an expert). Could someone explain why the separation constant in equations 4.16 and 4.17 changes sign...

Let's say I build a parallel plate capacitor using two metal plates with perfectly smooth surfaces. They are separated by some small distance d, with only vacuum between them. I then apply some AC voltage across the plates. Is there some effect which causes loss in the capacitor (equivalent...

Homework Statement Taking the equation of motion for a rocket launched from rest in a gravitational field g, m\dot{v} = -\dot{m}v_{ex} - mg , and knowing that the rocket ejects mass (fuel) at a constant rate \dot{m} = -k (where k is a positive constant), so that m = m_{o} - kt . Solve...

Homework Statement This is from Calculus for the Practical Man, by J.E. Thompson, 1962 edition. "Two automobiles are moving along straight level roads which cross at an angle of 60 degrees, one approaching the crossing at 25 mph, and the other leaving at 30 mph on the same side. How fast...

Dear Everyone, I have a question about the separation of variables for non-central potentials (r, \theta, \phi). In spherical coordinates, such a potential V(r,\theta)=u(r)+f(\theta)/r^2 can be separated. Who knows it could also be separated in other coordinates? Many thanks.

The cause-effect relationship of timelike events is fairly self-evident. But I was wondering, do non-local effects of QM "synchronise" events that are separated along spacelike intervals? Could there be some kind of co-dependent arising, such that if event X happens in one region of the...

Homework Statement Solve the following separable equation \frac{dy}{dx} = \frac{y}{x(x-1)} Homework Equations \int\frac{1}{x}dx=ln(x) The Attempt at a Solution See attachment Im getting y=(\frac{x-1}{x})^{c} as my answer when in fact the answer the tutor gave is...

Homework Statement Light consisting of two nearly equal wavelengths L and L+dL, where dL << L, is incident on a diffraction grating. The slit separation of the grating is D. Show that the angular separation of these two wavelengths in the m'th order is dTheta = dL / ((D/m)2+L2)0.5...

So I'm having trouble understanding how these two are related, i.e., how one proves the other. I understand the ideas behind both of them: For J-B, you're basically taking R^n and throwing in a sphere, so the inside of the sphere is bounded and everything outside the sphere is unbounded. For...

Dear all, Take my best wishes. I am facing a problem designing my experimental setup for my research. I want to produce flow separation over a flat plate. Here is my experimental setup: Diffuser angle is 16deg. I need some documentation/text book regarding the effect of suction flow rate...

Homework Statement The equilibrium separation of the atoms in H35CI equals 1.27 x 10-10m. Calculate the energy separation between adjacent lines in the rotational-vibrational spectrum Homework Equations E = (n + 1/2)h\omega + h2/ 2I * l(l+1) I = \mur02 \mu = m1m2/ m1 + m2 The...

Problem: The adjacent lines in the pure rotational spectrum of 35CI19F are separated by a frequency of 1.12 x 1010 Hz. What is the equilibrium separation of the atoms in this molecule? The attempt at a solution So, the equation I think I need to use to find the equilibrium separation...

two frictionless pucks are placed on a level surface, as shown, at an initial distance of 20.0 m. the mass of puck 1 is 0.80 kg and it has a charge of +3.0 X 10^-4 C., while puck 2 is 0.40 kg with a charge of +3.0 X 10^-4 C. the initial velocity of puck 1 is 12.0 m/s (E) and the initial velocity...

Homework Statement Sorry don't know how to use the partial symbol, bear with me partial u wrt t=2*(2nd partial u wrt x) Boundary conditions: partial u wrt x (0,t)=partial u wrt x (1,t)=0 Initial conditions u(x,0)=x(1-x) Homework Equations I get an answer that is different...

For water separation purposes, what's the difference between steam and fully saturated air? I was looking at a certain product: http://www.nciweb.net/combinat.htm And I'm not sure if such a thing would be suitable for separating the water from a fully saturated air stream at about 60degC...

How might one try to separate water from air at high temperature (say, 75degC) - if the gas if fully saturated? I understand that you should try to cool it down first to do so, but other than putting it though a heat exchanger is there any other approach you can take? Thanks

One particle has a mass of 3.00 10-3 kg and a charge of +7.50 µC. A second particle has a mass of 6.00 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 between them is 0.100 m, the speed of the 3.00...

\frac{\partial z}{\partial t}=\frac{\partial z}{\partial x}+\frac{\partial z}{\partial y} \mbox{Let }z=T(t)X(x)Y(y) T'(t)X(x)Y(y)=T(t)X'(x)Y(y)+T(t)X(x)Y'(y) \Rightarrow \frac{T'(t)}{T(t)}=\frac{X'(x)}{X(x)}+\frac{Y'(y)}{Y(y)} \Rightarrow \frac{T'(t)}{T(t)}=A \wedge...

Homework Statement http://i.imgur.com/mgIkS.png Two long parallel wires carry currents of 2.03 A and 8.83 A. The magnitude of the force per unit length acting on each wire is 4.49*10^5 N/m. Find the separation distance of the wires expressed in millimeters. Homework Equations I'm not...

Im doing separation of variables now and I am stuck...ive come up to this stage -5 ln 2-3i = t^2/2 + C my problem is do i need to divide the C and t^2/2 by -5? or don't divide the C? please help me.. thnks

Can anyone help me solve this ODE: ..in other words, find a general solution? dy/dx = e^(x+y) I use a separation method, but i can't take the natural log of -e^(-y). So, help?

Supposed you want to send an electron to a double slit. What must be the separation of the slits if they are say 1 meter away? What is the size of the initial electron field? When it travels to the slits, does the electron field expand in size? Why? I'm asking this because I'd like to know...

a) Derive a formula for solutions of the ode equation b) If (t0, x0) lies in the subset of the (t,x)-plane given by x>1 write down a formula for the unique solution of the equation below through this point. c)Give a formula for two solutions to equation below through the point (0,1) in the...

See attached image for the question and my working. Hopefully you can read it OK, I had to resize it to fit to the allowed dimensions. I'm unsure how to proceed or if I have done something wrong previously - the initial and boundary conditions are tripping me up. The boundary conditions in red...

I've taken a first semester course on PDEs. Basically all we learned was separation of variables and method of characteristics. I understand that there are transforms out there, such as laplace and fourier. However, it looks like there aren't many analytical ways of solving PDEs. Mind you, I'm...

Just quick question about sep of variables.. say have function U(x,y)=X(x)Y(y) when do separation of variables end up with some generic case that looks like: X''/X=Y'/Y=lamda my question is (and I think I know now the answer but would like confirmation), is what sign should the lamda...

http://img835.imageshack.us/i/anmol.png/ the graph is as per the link but my question is that at a particular point the potential energy becomes zero...is thre any significance for it?

Homework Statement Use separation of variables to find a general series solution of u_t + 4tu = u_{xx} for 0 < x < 1, t> 0 and u(0,t) = u(1,t)=0. Homework Equations The Attempt at a Solution Looking for a solution of the form u(x,t) = X(x)T(t) implies that \frac{T'}{kt} - \frac{X''}{X} = 0...

Homework Statement Help solving this separation of variables. M(dv/dt) = [k*(v^2)] - Mg Homework Equations As above The Attempt at a Solution dv/(kv^2-Mg)= dt/M Intregrate both sides; (1/2kv) ln |kv^2-Mg|= t/m + c? Then what to do..? Something to do with with Ae^(-kt/M)..?

Homework Statement As part of the solution to a HW problem of mine, I have to solve the PDE p_t = -vk^2 p - k \delta p_k, where p = p(k,t) and v,\delta are known constants. Homework Equations I tried to look for a solution of the form p(k,t) = K(k)T(t) and found one, but I'm not sure if I...

Homework Statement In the midst of Forced Vibrating Membranes and Resonance Utt = c^2*delsquared(U) + Q(heat source) Arrive at eigenfunction series solution where the coefficients are given by d^2/dt^2 (A_n) + c^2*lambda_n*A_n = q_n Homework Equations according to the book, I am supposed to...

Try not to fly too far over my head if you answer this. I'm just an amateur chemist who spent three years in the chemistry department until I hit a wall (Calculus!) and ended up with a writing degree. So be gentle please. I'm trying to dry oil (vegetable oil) in a process (rather than a...

Homework Statement Calculate the slit separation (d) given that: Wavelength = 650 nm (Plugged in 6.5*10^-7 m) m = 1 (plugged in 1) Distance to screen (D) = 37.5 cm (plugged in 0.375m) Distance between centre to side order (y) = 0.7 cm (pluged in 0.007m) Homework Equations We were only given...

As everybody I have read or heard on the matter claims, the Axiom Schema of Separation was concocted to resolve a paradox that results from the Axiom of Unrestricted Comprehension. The Axiom Schema of Unrestricted Comprehension as I understand it is stated as follows (forgive my lack of...

Hello my name is Colin Wilson and I am the inventor of a new mineral separation process. http://www.coldgold.rotoquad.com I am looking for help and/or a partnership in this endeavor. As a group I can not think of a better place to start. To test this new method of mineral recovery 3...

I don't even know where to start.. Two styrofoam balls with the same mass (m=9.0x10^-8 kg) and the same positive charge Q are suspended from the same point by insulating threads of length (L=0.98 m). The separation of the balls is (d=0.020 m). What is the charge Q??

Homework Statement Solve the boundary value problem for a string of unit length, subject to the given conditions. f(x)=0.05sin \pi x, g(x)=0, c=\frac{1}{\pi} Homework Equations Model: u(x,t)=X(x)T(t) Which yields two separated equations by the one dimensional wave equation. X''-kX=0 and...

Assuming that theories regarding the existence of multiple universes are true, what would separate said universes? If multiple universes exist, it can be assumed that there is some form of separation between said universes. This could be in the form of a barrier, or a kind of "space" between the...

We are considering a stationary curved spacetime fabric. Temporal separation[Physical]is given by: {T}_{2}{-}{T}_{1}{=}{\int \sqrt {g}_{00}{dt} [Limits of integration extending from t1 to t2which are of course the coordinate times] The above integral is path dependent,in the general...

Homework Statement I'm supposed to find a nontrivial solution to tx'' + (t-2)x' + x = 0, x(0) = 0. You don't really need to know that but just in case. I got to this point: (s+1)X'(s) + 4X(s) = 0 Now I need to separate variables to find a solution but I've been working on this for two...

dy/dx = 3[(y-1)^(1/3)] with initial values: y(0)=1 ultimately I end up with y=sqrt((2x)^3) + 1 or ((2x)^3/2) + 1 book answer: y= 1+((3x)^3/2) steps: separation of variables... ((y-1)^-1/3)dy = 3dx after u-subs, where u = y-1... 3/2((y-1)^2/3) = 3x + C...

Two protons that are very far apart are hurled straight at each other, each with an initial kinetic energy of 0.15 MeV, where 1 mega electron volt is equal to 1x10^6 (1.6x10^-19) joules. What is the separation of the protons from each other when they momentarily come to a stop? i got 4.58e-13...

Homework Statement A cubical box (sides of length a) consists of five metal plates, which are welded together and grounded (Fig 3.23). The top is made of a separate sheet of metal, insulated from the others, and held at a constant potential V0. Find the potential inside the box...

Homework Statement We have a 2-dimensional box with only one side at a potential V0. The other 3 sides are grounded. The box is a square with top and bottom at y=a/2 and –a/2 and sides at x=±a/2. Find V(x,y) (it should contain cos and sinh). Homework Equations The Attempt at a...

Consider the separation of the Riemann Zeta function in two terms \begin{flalign*} \zeta(s) &= 1^{-s} + 2^{-s} + 3^{-s} + 4^{-s} + 5^{-s} + 6^{-s} + ... = & \\ &=(1^{-s} + 3^{-s} + 5^{-s} + 7^{-s} + 9^{-s}+ ... ) + ( 2^{-s} + 4^{-s} + 6^{-s} + 8^{-s} + ...)&=& \\ &= (1 - 2^{-s}) \zeta(s) +...