deriving Definition and 1000 Threads

How does one derive the general form of the Riemann tensor components when it is defined with respect to the Levi-Civita connection? I assumed it was just a "plug-in and play" situation, however I end up with extra terms that don't agree with the form I've looked up in a book. In a general...

Homework Statement I still don't got the hang on Atwood Machines, and i don't know if I am wrong here or just overthinking it. But i got this one exercise where i am kind of stuck in two of the sub-exercises. So I am hoping there is someone here who could guide me in the right direction.Atwood...

Im currently trying to find out how my book took this drag equation (1/2 CApv^2P) and found the x and y component for accelration (x=(-pACv/2m)*sqrt (v(x)^2+v(y)^2)) &y=(-g-(-pACv/2m)*sqrt (v(x)^2+v(y)^2))

Homework Statement HI people, I was trying to derive the stefan-boltzman law from the planc's formula, I kind of got stuck with an integral Homework Equations $$ \int_{0}^{\infty} \frac{x^3}{e^x -1} dx $$ The Attempt at a Solution I tried simplifying it with $$ \int_{0}^{\infty} x^3...

Hello! My professors asked me why we don't usually consider the second Friedman equation. He told me that the solutions for the first always give a solution for the second. He told me that the first equation along with it's time derivative can imply the second equation. I have been trying the...

Homework Statement Please explain why we take the "integral of V^2" when deriving the root mean square of Voltage in alternating current? I do not understand why we integrate at all, instead of taking V as it is and squaring it. Also, when we DO integrate, why do we take the integral of "V^2"...

In Sean Carroll's Lecture Notes on General Relativity (Chapter 3, Page 60), in the chapter on Curvature, he derives the definition of the Christoffels Symbols by assuming the connection is metric compatible and torsion free. He then takes the covariant derivative of the metric and cycles through...

I'm trying to derive the law of reflection for Electromagnetic Waves and Optics. I'm using some lecture notes that my university provided. I'm confused as to why the two sine functions are changed to cosine functions as you don't do the same when you are deriving Snell's law. Refer to attached...

We have a circuit consisting of a charged capacitor and a resistor. First of all, we use Kirchhoff's loop rule to express this circuit in mathematical form. Now one teacher tells me Kirchhoff's loop rule yields iR+q/c=0. Another teacher tells me that the rule yields iR-q/c=0. Is there any...

Homework Statement Derive the Hamiltonian equation in terms of momentum and position ( p and r) for the given system whose lagrangian is stated as L=ř^2/(2w) - wr^2/2 Homework Equations L=ř^2/(2w) - wr^2/2 and H=př-L The Attempt at a Solution Notice here ř means first derivative of r. As i...

Hi, There is a cost of debt formula that goes c = ib(1-T), where c is the cost of issuing debt that firm incurs ( a percentage like interest) i is the interest earned by the investor, and T is the tax rate a firm pays. The key is that the interest rate alone is not really the cost of taking on...

Homework Statement As I've been going through examples in my textbook they are becoming increasingly lengthy to compute and thus I have resorted to using software to complete the task. For example when computing the series for ##\sin{(\ln{(1+x)})}##...

Hi! I have the following problem with some old lecture notes I recently had a look on. I have two different fermions (1 and 2) with masses m1 and m2 and the following Lagrangian (where the mass term for fermion 2 is dropped, because we are only interested in the dynamics of fermion 1) of the...

Homework Statement Hello i am trying to write the Stokes parameters as the amplitude of the averaged EM-wave We know the stokes parameters are {I,M,C,S} or {S0,S1,S2,S3} thus a column vector. And S0 is defined as S0=<E2x0>T+<E2y0>T S0 i understand how it was derived since Filter 0 is an...

I am trying to derive Torricelli's equation, i.e. ##v_f^{2} = v_i^{2} + 2a\Delta x##, using calculus. There are two different ways I have seen. First we start with ##\displaystyle \frac {dv}{dt} = a##. Next, we multiply both sides by velocity, ##\displaystyle v\frac {dv}{dt} = a\frac {dx}{dt}...

Hi all, I am trying to follow the calculation by samalkhaiat in this thread: https://www.physicsforums.com/threads/finding-equations-of-motion-from-the-stress-energy-tensor.547502/page-2 (post number 36). I am having some difficulty getting the equation above equation (11) (it was an unnumbered...

Homework Statement [/B] I'm trying to write a program in MATLAB which demonstrates a tautochrone curve and how the starting point of a ball is irrelevant as to the time it takes to get to the lowest point in the curve (without friction). At the moment I'm just trying to model it using a simple...

Hello, A little something I've been working on for fun today was trying to derive the rocket equation: Δv=V_{e}ln(R) So first I start with F=ma =m\frac{dv}{dt} \frac{F}{m}dt = dv ∫_{0}^{Tco} \frac{F}{m}dt = ∫_{0}^{v} dv Where Tco is the time of engine cutoff, and v is the velocity at that...

On the attached picture I have started trying to derive the path integral but I don't know how I get further. Can anyone help me? Also I have used that: exp(-iHΔt/ħ) = exp(-i(T+V)Δt/ħ) = exp(-iTΔt/ħ)exp(-iVΔt/ħ) But my book says that this identity is only correct to first order, i.e. there is...

I'm trying to derive a formula for the magnetic torque on a semicircular loop. what I've done so far is this The magnetic force on the non-curved loop is $\vec{F}_{x}=\int Idx\hat{i}\times B_{\circ}\hat{i}=0N$ for the curved loop $\vec{F}_{c}=\int_{0}^{\pi} Ird\phi\hat{\phi}\times...

Hey guys and gals, I'm taking an online physics course just to kind of learn the basics before I take the real thing this summer. The course is from OpenYale for those interested (oyc.yale.edu). Anyways, the professor was talking about some formulas for finding ##\vec{r}(t) = r(i(cos\omega t) +...

How can I derive a contradiction from the following nasty statement: Assume $\sqrt{5} = a + b\sqrt[4]{2} + c\sqrt[4]{4} + d\sqrt[4]{8},$ with $a,b,c,d \in \mathbb{Q}$? *This is the last piece of an effort to prove that the polynomial $x^4-2$ is irreducible over $\mathbb{Q}(\sqrt{5}).$*

Homework Statement Let φ=φ(r) and r=√x2+y2+z2. Find ∂2φ/∂x2. Show that it can be written as (1/r + x2/r3)∂φ/∂r + x2/r2∂2φ/∂r2. Homework Equations Use the identity ∂r/∂x = x/r. The Attempt at a Solution I think I know ∂φ/∂x. Using the chain rule, it's ∂r/∂x ∂φ/∂r. That gives x/r ∂φ/∂r. If...

Homework Statement Given: Ideal gas equations: Find S(T,V) for an ideal gas Homework Equations Ideal gas equations: \begin{array}{l} {\rm{}}\\ U = \frac{3}{2}N{k_B}{\left( {\frac{N}{V}} \right)^{2/3}}\exp \left[ {\frac{S}{{\left( {3/2} \right)N{k_B}}} - {s_0}} \right]{\rm{ }}\\ T = {\left(...

... electron transport. 1. Homework Statement Electron - Phonon scattering, derive the contribution to electron transport. Homework Equations Trig. The Attempt at a Solution Am I being REALLY stupid here, I can't see how the equation matches the triangle. If you resolve KF' doesn't KF'...

Homework Statement Show that: ##B=\frac { 1 }{ 4\pi \epsilon r^{ 3 } } \left[ 3\hat { r } \left( \hat { r } \cdot \vec { m } \right) -\vec { m } \right] ## Homework Equations B=delxA, m=a*I The Attempt at a Solution [/B] I follow my professors derivation. However, she expands the term...

I'm looking at Carroll's lecture notes 1997, intro to GR. Equation 7.27 which is that he's argued the S metric up to the form ##ds^{2}=-(1+\frac{\mu}{r})dt^{2}+(1+\frac{\mu}{r})^{-1}dr^{2}+r^{2}d\Omega^{2}## And argues that we expect to recover the weak limit as ##r \to \infty##. So he then...

In A. Zee "QFT in a nutshell" in chapter I.5 Exercise 1.5.1 on page 39 for spin 2 massive propagator. I know I’m missing something very simple (self-taught beginner). I'm trying to derive equation (13) on page 35, which is G_{\mu\nu,\lambda\sigma} = G_{\mu\lambda}G_{\nu\sigma} +...

Homework Statement Overall reaction: A + F = I + J (just take = as the equilibrium sign) It is first order in both A and B. The following mechanism has been proposed: 1. A + B = C + D 2. C + D = E + B (B is the catalyst) 3. E + F = G + H 4. G + H = I + J These are all...

Just one last question today if someone can help. I'm trying to derive the electromagnetic field strength tensor and having a little trouble with (i think) the use of identities, please see below: I understand the first part to get -Ei, but it's the second line of the next bit I don't...

Homework Statement derive the Fourier sine and cosine transforms of $$f(x) = e^{-cx}$$ by using $$e^{iax}=cos(ax)+isin(ax)$$ and computing the integral $$\int_0 ^{\infty} e^{-cx}e^{iax}dx$$.Homework EquationsThe Attempt at a Solution i'm completely clueless, all i did was evaluate what they...

So basically I was wondering whether it's possible to get the expression of ideal gas using molecular flux equation which is ##\phi = \frac{1}{4}\bar{v}n##. The derivation should be straightforward. I need to get the expression of pressure. Because the flux by definition already gives the rate...

Homework Statement Prove that ## [L_a,L_b] = i \hbar \epsilon_{abc} L_c ## using Einstein summation convention. I think I have achieved the solution but I am not sure of my last steps, since this is one of my first excersises using this convention. Homework Equations [/B] ## (1)...

I'm looking at Lecture Notes on General Relativity, Sean M. Carroll, deriving the FRW metric, and I'm a little confused with the use of eq 8.4 . I thought instead it should be using the general form of a spherically symmetric metric, not a vacuum spherical symmetric - eq 7.13 has been derived...

Homework Statement Hi my question is whether an SOP = POS for a given function F(A, B, C, D). Or is the SOP a complement of POS?Tasked to convert derive a simplfied SOP from a 4 var Kmap with don't cares. My answer was, F = C'.D' + A'.B'.C which is correct. Then for part B they asked for the...

Homework Statement Consider particles in a gas centrifuge. This device is used to separate gases of different molar mass by rotating a cylinder at high rates. Derive two equations: one for the pressure (P) and one for the particle number density (nv) as functions of M, r, w and T, where r is...

Hi dear forum members, I'm an undergrad. physics student(freshmen),i've learned that Galilei found g.t^2=s formula(a free falling object's position function with respect to time)without using physical foundations,by using him blood impulses for count time not utilizing acceleration etc,i've...

Homework Statement Derive ∫(dr/dθ)^2 + R^2 )^0.5 dθ Homework Equations x = Rcosθ y = Rsinθ The Attempt at a Solution Arc length is the change in rise over run, which can be found using Pythagorean's Theorem. Rise is dy/dθ while run is dx/dθ. The arc length is [(dy/dθ)^2 + (dx/dθ)^2 ]^1/2...

I am trying to derive the gravitational red shift effect but I think I am going about it all wrong. Specifically, I want to derive the change in frequency/ wavelength when a photon moves away from the surface of a star mass M and radius R. So I tried to use relativistic mass of the photon and I...

I am looking at derivations of the Doppler effect for sound and light, and I am very confused about what stays the same when it comes to sound. In this video, at 5:10, it is said that the wavelength will be the same. I'm not sure I agree with this because I'm pretty sure both the observed...

In Schwartz QFT book, while explaining the Faddeev-Popov procedure, he presents this following observation at (25.99): Can someone help understanding me why this expression equals one? THANK YOU!

Homework Statement A dog accelerates from 2.0 m/sec to 5.0 m/sec while covering a distance of 14.0 m. How long did this take Homework Equations d=(Vi+Vf/2)t The Attempt at a Solution 2(-Vi-Vf)d=t I am doing something wrong. Please help. Thanks[/B]

Homework Statement Using the Boltzmann distribution for a small system in contact with a heat reservoir at temperature T, find the Maxwell-Boltzmann distribution. Homework Equations The Boltzmann distribution states that the probability density of a system in contact with a heat reservoir at...

Can anybody out there show me how the sine wave formula y=Acos(kx - ωt + φ_{0}) or y=Acos(kx + ωt + φ_{0}) is the direct solution of the wave equation \frac{\partial^2 y}{\partial t^2} = v^2 \frac{\partial^2 y}{\partial x^2} ? I mean I looked it over on the Internet but everybody keeps...

I have a projectile that can only launch at 30 degrees and a target exactly 100m away at the same elevation on flat ground with 1g (9.8m/s2 meters per second per second?) What velocity without (then with) air resistance would the "muzzle velocity" need to be? (with a droplet shape for...

Hey I'm having an issue deriving the calculus of variations because the chain rule i use ends up different to the one in the textbook. Firstly I assume we have some function of 3 variables Y=y+alpha eta with grad Y'=y'+alpha eta' and x. Secondly we have an integral of this function over x and...

Hello there, I want learn to do homogenous differential equations and I cannot work out what is wrong in this example. Hope you'll be able to tell me why my DE is unsatisfactory. Assume that a capacitor is has charge Q and that the terminal with the high voltage is connected to a switch in...

1. Derive (∂U/∂P)V=-T(∂V/∂T)S 2. I must use dU=TdS-PdV 3. Derivations are my weakest part of math. I checked many wikis about Total differentials, partial derivatives, Maxwell relations and derivations. I can use the Thermodynamic Square, I know how to find different Maxwell relations but I am...

I am at the very last part of a relatively long derivation of the Casimir effect, and I just don't understand the final step D: So far, I have derived the ground state energy to be \langle 0| \hat{H} |0\rangle = \delta (0) \int _{-\infty}^{\infty} dp \frac{1}{2} E And for a massless field...

Hi guys, I was wondering if anyone knows of a good source/paper that I can find online that details how to derive the MSW Hamiltonian from a field-theoretic approach, or from an effective field theory approach or anything like that? Every time I study the MSW effect, the Hamiltonian...