deriving Definition and 1000 Threads

Homework Statement Show that the energy-momentum relationship, E^2 = p^2 * c^2 + (m*c^2)^2, follows from the expressions E = (gamma)*m*c and p = (gamma)*m*u where (gamma) = 1 / sqrt(1 - (u^2)/(c^2)) the lorentz transformation factor. m is the rest mass. c is the speed of light u is the...

I'm a bit confused by the following: We can derive the equation of motion for a particle traveling on a timelike worldline by applying the Euler-Lagrange equations to the Lagrangian \mathcal{L}=- g_{\mu \nu}(x(\tau)) \frac{d x^\mu}{d \tau} \frac{d x^\nu}{d \tau} However, to derive the...

Homework Statement I want to derive the square of the total angular momentum as shown here: http://en.wikipedia.org/wiki/Angular_momentum_operator#Angular_momentum_computations_in_spherical_coordinates Homework Equations The x,y, and z components of angular momentum are shown in the...

The energy-momentum tensor for a perfect fluid is T^{ab}=(\rho_0+p)u^au^b-pg^{ab} (using the +--- Minkowski metric). Using the conservation law \partial_bT^{ab}=0, I'm coming up with (\rho+\gamma^2p) [\frac{\partial\mathbb{u}}{{\partial}t}+ (\mathbb{u}\cdot\mathbb{\nabla})\mathbb{u}]=...

I'm going through Landau/Lifgarbagez's book II of theoretical physics. In it they have a derivation of the equation of motion from the principle of least action, however I don't understand one step. Homework Statement Derive the equation of motion: \frac{d^2x^i}{ds^2}+\Gamma^i_{kj}...

Hi guys, I can't find my notes on Fresnel diffraction and I have my Optics exam on Monday... Does anyone know how to derive F=a2/λL where L=1/z+1/z' I've googled it to death, checked here and tried in Optics 4th edition by Hecht with no luck... I'd really appreciate any help...

Homework Statement Show that \frac{\partial\overline{\mathcal{L}}_G}{{\partial}\mathfrak{g}^{ab}_{,c}}=\Gamma^c_{ab}-\frac{1}{2}\delta^c_a\Gamma^d_{bd}-\frac{1}{2}\delta^c_b\Gamma^d_{ad}.Homework Equations...

Hello, I am reading this paper about quantum gravity, trying and failing to follow along in the derivation of this, eq (204) p. 72, expression for the scale factor: a(t) = a_1 \left( 1 + \frac 3 2 ( 1 + \omega ) H_1 (t - t_1) \right)^{\frac 2 {3(1+\omega)}} (I'm not sure what the...

Hi, I'm a graduate student in the life sciences seeking to use entropy maximization to describe ecosystem processes. I have a decent understanding of why S= -k Ʃ pi ln(pi) is a generalized form of S= k ln W, but get stuck in the algebra. Maybe I'm going about it the wrong way. S= -k Ʃ pi...

Homework Statement Assuming that ∅ is a differentiable scalar valued function and F a differentiable vector field, derive the following identities. a)∇(dotted with)(∅F) = ∇∅(dotted with)F + ∅∇(dotted with)F b)∇(crossed with)(∅F) = ∇∅(crossed with)F + ∅∇(crossed with)F Homework Equations The...

A car can accelerate 0-60 mph in 8.6 seconds and 0-100 mph in 26.1 seconds. How far (in feet) would the car have to travel in order to accelerate from 0-81 mph?

hi guys i was wondering how the coordination numbers for the atomic positions of atoms in crystals such as NaCl are derived ...more specifically why is Na at (0,0,0) and Cl at (1/2,1/2,1/2) and not (0,0,0) and (1/4,1/4,1/4) of course this is in fractional coordinates

I'm trying to derive T= 2π√m/k to become k= 4π2m/T2 How is that happen? Can someone please explain it to me? Thanks in advance!

Homework Statement Derive the expressions for the i_r and i_θ components of velocity and acceleration. Homework Equations r=|r|i_r \omega=\frac{dr}{dt} \alpha=\frac{dω}{dt}=\frac{d^2r}{dt} The Attempt at a Solution r=|r|i_r \omega=\frac{dr}{dt}i_r+r\frac{di_r}{dt}...

Question: Derive the formula y = arcsinh(x), the inverse hyperbolic function. I thought the question was asking to find the derivative of the inverse function but my teacher marked it 0/10 points because he did not want the derivative... Can "derived" mean derivative? If so... Is there...

Hello all, I'm wanting to learn how to derive all of the trig identities (well, not all, but the most common) rather than memorizing them. Perhaps someone here could provide me with a list of "essentials" that are the framework for deriving others. For example, I know there are a few that can...

Homework Statement I am currently studying the optical Michelson Interferometer and I am in need of help with a derivation. The equation I need to derive is that for the intensity of the light arriving at the viewing point. The equation is given below.Homework Equations I(Δ)=I/2 +...

Homework Statement I've been given a series circuit with a .5H inductor .01F cap, .5H inductor and 10Ω resistor in series. This circuit is connected to a source i(t) = 10cos(10t) and I need to find v(t) across Z Homework Equations From the givens I've found the Z(s) to be s+100/s+10 and...

When you derive the time dilation equation, and you see the light move straight down in one frame and in the other frame you see it move on a diagonal because the object is moving. My question is in the moving frame when you use the horizontal distance to derive the distance that the...

Homework Statement Use a Free body diagram to show that :Tanθ=static friction, on an incline plane Homework Equations FF/FN= coeficiant of friction The Attempt at a Solution I know I must get an angle to have a tan of the Force of friction and a Normal force, but I don't...

Hi, I am struggling with the heat equation ut = kuxx with the boundary conditions u(0,t) = u'(L,t) = 0 and initial condition u(x,0) = f(x) 0 ≤ x ≤ L 0 ≤ t I want to derive it's eigenvalue using complex analysis. After separating the variables...

Homework Statement State the Maclaurin series for sinx and cosx. Hence derive the Maclaurin series for tanx. Homework Equations sin(x) = x - x3/3! + x5/5! - x7/7!... cos(x) = 1 - x2/2! + x4/4! - x6/6!... The Attempt at a Solution I know you divide the series for sinx by the...

Homework Statement A popular model for the mass distribution in a spheroid (such as a bulge) is the Hernquist model, with density ρ(r) = M(total)*a / 2πr(a+r)^3 M(total) is the total mass. a is constant with dimensions of length. Derive the enclosed mass M(r) The Attempt at a...

Homework Statement I am not sure that my work is correct, and some guidance would be much appreciated. An electric toy car has mass m and has a power source of constant power P. The power source converts electrical energy directly into kinetic energy. If the car is initially stationary and on...

Homework Statement If a signal f1[n] begins in a moment N1 and ends in moment N2, and signal f2[n] begins in the moment M1, and ends in the moment M2, derive the formula which states in which moment begins and ends the signal f1[n]*f2[n] Homework Equations The Attempt at a Solution I...

How do I go about deriving the thermal conductivity of graphene (specifically, in the low temperature limit) when I'm given the phonon dispersion relation? I haven't been able to find anything explaining how the dispersion relation relates to the thermal conductivity in materials. (this is...

Homework Statement I should derive the Hubble law redshift from Maxwell equations in closed Universe. Homework Equations The metric of closed Universe is ds^2 = dt^2 - a^2(t)\left(d\chi^2 + \sin^2 \chi d\theta^2 + \sin^2 \chi \sin^2 \theta d\phi^2\right). The Hubble law redshift: \frac...

Folks, I was checking to see was it possible to determine the bending moment diagram from the shear force diagram. Seemingly one can do it for simply supported beams but if we consider a rigidly supported beam on either end its not possible to derive the bending moment diagram from the shear...

Homework Statement Derive y= \sqrt(2x^4) - \frac{5}{3x^2} The Attempt at a Solution I am still at the first part of the function (the root): First I tried to derive inside the root like this: \sqrt(2x^4) = \sqrt(8x^3) = 2 \sqrt(2) \times \sqrt(x^3) = \sqrt(2) \times x^2...

Homework Statement A curve has equation y=(x^2+1)^4 + 2(x^2+1)^3. Show that \frac{dy}{dx}=4x(x^2+1)^2(2x^2+5). Homework Equations \frac{dy}{dx}=(\frac{dy}{du}\times \frac{du}{dx})+(\frac{dy}{dv} \times \frac{dv}{dx}) The Attempt at a Solution y=(x^2+1)^4 + 2(x^2+1)^3 let u =...

Hey all. I am taking my second college physics course (electromagnetic physics) and am looking for some help deriving the equations. I found it very helpful to know how to derive many of the equations in my first physics course. So far we have studied e fields, guass's law, capacitors...

Homework Statement In a lab experiment about Gravity Waves and Dispersion, one of the preliminary questions is: Show that for gravity waves the group velocity is: C_{g} = \frac{C_{p}}{2}\sqrt{1 + \frac{2kh}{sinh(2kh)}} Homework Equations C_{g} = dω/dk ω = \sqrt{gktanh(kh)}...

Homework Statement This is from Exploring Black Holes, Query 1, page G-3. It involves a one dimensional creature on a two dimensional circle. Constant dl but different dx. Collect terms in equation [5]. Show that the result can be written dl^{2} = \frac{dx^{2}}{1 - x^{2}/r^{2}} Equation...

How can one derive the relationship for a cubic crystal: d= \frac{a}{\sqrt{h^2 + k^2 + l^2}} It is shown here. This is probably trivial but I am having trouble proving it as the Miller indices are reciprocals but the reciprocal is not distributive. This isn't for homework by the way - I...

A certain program, that shall remain nameless, tells me that the integral of cos(tan(θ)-2θ) from 0 to pi/2 is pi/e. Does anyone know of a variable transform or contour that would help me to derive this result? I'm really interested in integrals of the function cos(a tan(θ)-b θ), but, I'd be...

Homework Statement You drop a baseball from the roof of a tall building. As the ball falls, the air exerts a drag force proportional to the square of the ball's speed (f=Dv2). (a) In a diagram, show the direction of motion and indicate, with the aid of vectors, all the forces acting on the...

Homework Statement I have to derive an equation with the following variables: T= period m= mass Theta= angle l= length and I was told to think of the period as the perimeter of a circle.Homework Equations The Attempt at a Solution C=2\pi r,C/2=\pi r,d=\pi r,(at^2)/2=\pi r,t=\sqrt{\frac{2\pi...

Homework Statement You borrow money from a friend at a continuous interest rate of r% per month. You want to pay your friend back as quickly as you can at the beginning, but reduce your payment rate over time. You decide to pay off at a continuously decreasing rate given by K₀e^{-at}, in...

Homework Statement I recently finished a test that asks you to derive Power = \frac{dE}{dt} = F \times v from the energy equation: E^2 = E_{0}^2 + (pc)^2 Homework Equations Power = \frac{dE}{dt} = F \times v E^2 = E_{0}^2 + (pc)^2 p = \gamma m v The Attempt at a Solution I got...

Tired and not understanding Calculus. So, velocity equals dx/dt and acceleration is dv/dt But to derive the constant acceleration equations, my professor took the integral of vdt = dx, which we got from v = dx/dt. I follow all of the math that comes after that, but I don't understand...

Homework Statement Show that the range R can be expressed in terms of maximum height h, and in particular that R=4hcot\Theta. Show that, when range is at a maximum, h=R/4 Homework Equations R=(v(o)^2*2sin\Thetacos\Theta)/g v(y)^2=v(yo)^2-2gh The Attempt at a Solution I used the second...

The teacher told us to start with Bohrs equation, E=-2.18x10^-18(z^2/n^2). Then using ΔE= E_f - E_i , and E=λv. Also what are the limitations of using Rydberg's equation? Thanks

I didn't know where to put this and it didn't apply to the template. As a study aid and to sate my masochism, I wanted to know, where can I see an exhaustive, step by step process of all of Maxwell's Equations (Gauss, Faraday and friends) being derived? Differential form, integral etc.

Homework Statement Assuming that the rate of the mass (m) of an object is proportional to its total surface area, derive a D.E for the rate of change in the mass. Arbitrary constants may be included. The objects in question are expanding peat discs. The discs absorb water through their...

Homework Statement At a distance of 45 meters from a traffic light, a car traveling 15 m/s is brought to a stop at a constant deceleration a) What is the value of Deceleration (-5m/s) b) How far has the car moved when its speed has been reduced to 3 m/s c) How many seconds would the car...

How would I go about showing \prod_{k=1}^{N-1} \sin{\frac{k\pi}{N}} = \frac{N}{2^{N-1}} I've tried using Euler's equation to substitute sin, but it just gets messy.

d/dx (sin-1x) = \frac{1}{\sqrt{1-x2}} But using chain rule, I got: dy/dx = -sin-2xcosx Why?

Homework Statement At which minimum height atoms or molecules are able to leave Earth’s atmosphere to space? To obtain an approximate estimate use the assumption that molecules can leave if the mean free path, λ, is larger than the scale height H. Write λ and H as a function of height and...

im doing my traffic analysis homework and i don't understand how they went from "1" to "2" in the picture below. more specifically i don't know if I am taking the derivative wrong or if they are (those who wrote the solution). if you distribute the "k" that's at the beginning of the equation...

Homework Statement I was shown a formula by a physicist I met through a friend when I asked for help with a homework problem. I needed to find y final for a motion in 2 dimensions problem. He showed me this: Y1 = X1 * tan(Theta) + (Ay * X1^2) /( 2 * V0^2 * cos^2(Theta)) Y1 = Y final X1...