deriving Definition and 962 Threads

This is essentially the problem. And this is what I did. Realizing the following: E = -▽V I simply took the derivative in regards to the vertical component, in this case "a". So: -dV/da [the above formulae] And I got the following: Κλl/(a sqrt(l^2+a^2)) Does that seem about right...

Homework Statement The pressure of a non-interacting, indistinguishable system of N particles can be derived from the canonical partition function P = k_BT\frac{∂lnQ}{∂V} Verify that this equation reduces to the ideal gas law. The Attempt at a Solution I have a very poor...

Hi all, First, I hope this is in the right place, apologies if it isn't. I'm looking into the possibility of deriving sound from the simulated actions of simple bodies in a 3D space. As a toy example of my aim, I hope to be able to compute the sound that would be generated by a metal...

Homework Statement Derive equation below. It is the potential energy of an electron inside a nucleus assumed to be a uniformly charged sphere of R. Homework Equations V'(r) =( -Ze2/4∏ε0R)(3/2 - (1/2)(r/R)^2) The Attempt at a Solution So I understand that I need to find the ∫ from infinity...

Homework Statement 1. Suppose two masses are arranged as shown and released from rest. There is no friction. Suppose we have a certain mass m1 and we want to cause a certain acceleration a. How big should m2be? (In other words, derive a formula for m2in terms of m1, a, and g.)...

So, there are two things in Quantum Mechanics that I understand are axioms: the first is the schrodinger equation, which cannot be derived. Okay fine, we have to start somewhere. The second axiom is that the integral from a to b of the wavefunction-mod-squared gives the probability of finding...

So i was wondering how the curl of the magnetic field is derived since Feynman just introduces it from nothing in his second volume of Feynman's lectures on physics: c2∇xB=j/ε0 or the other one where ∇x B=μ0j

Here is the question: I have posted a link there to this thread so the OP can view my work.

On the book "Introduction to Solid State Physics" by Kittel, on page 98 he derived the roots for optical and acoustical branches for the equation: M_1 M_2 \omega^4-2C(M_1+M_2)\omega^2+2C^2(1-cos(Ka))=0 where the roots are: \omega^2=2C(\frac{1}{M_1}+\frac{1}{M_2}) and...

so we used an equation in class to basically describe the relationship between some quantities of a vibrating string held fixed at both ends. and i noticed (just now...) that this was.. well.. i don't want to say that it's 'wrong' yet but, the expression does not make sense to me; and just to...

Well, I was doing a problem the other day, inserting the complete interaction QED Lagrangian into the Euler-Lagrange equations, in order to obtain the field equation governing the interacting electromagnetic field, with the Dirac field. The problem is that, by doing so, I got the equation, but...

Hi When we talk about shear stresses in a fluid, we find that the shear stress is given by \tau_{xy} = \mu(\partial_y u + \partial_x v) = \tau_{yx} This relation we get when only looking at one side of our fluid-"cube". Now, in order to take into account the opposite side we assume that the...

Homework Statement By considering small changes in enthalpy, and using the central equation, derive the Maxwell relation \left (\frac{\partial S}{\partial V} \right )_{T}= \left (\frac{\partial p}{\partial T} \right )_{V} Homework Equations H=U+pV dU=TdS-pdV The Attempt at a...

Homework Statement I have a 13 foot long beam supported by a pin at x = 0 feet and a roller at x = 9 feet. There is a triangular distributed load of 50 lb/ft from 0 ft to 9 ft. (Increasing as it approaches 9 ft) At the end of the beam there is a moment of 200 lb-ft counter-clockwise.Homework...

Lately I have been interested in the many-worlds interpretation, and in particular the way it is described by Wallace in his latest book The Emergent Multiverse. In the book he tries (or succeeds) to derive the Born rule from unitary dynamics by using game-theoretic arguments. But for this he...

I have been trying to derive the different ultimate 'fates' of the universe from Friedman's equations, for the different possible values of k (shape parameter) and ##\Lambda## (cosmological constant). There are nine possibilities, according to whether each of k and ##\Lambda## are negative...

Orthogonality of spherical bessel functions Homework Statement [SIZE="5"]Proof of orthogonality of spherical bessel functions The book gave \int_{0}^{a}\int_{0}^{2\pi}\int_{0}^{\pi} j_{n} (\lambda_{n,j}r) j_{n'} (\lambda_{n',j'}r) Y_{n,m}(\theta,\phi)\overline{Y}_{n',m'}(\theta,\phi)...

Homework Statement Find vrms from the Maxwell speed distribution. Basically what I need to solve is the integral a\int_0^∞ \! v^4e^{xv^2} \, \mathrm{d}v Where ##a## and ##x## are constants. Homework Equations $$a\int_0^∞ \! v^4e^{xv^2} \, \mathrm{d}v $$ Where ##a## and ##x## are...

Homework Statement Derive m*= mM/(m+M) *hint* total angular momentum Iω=m*r2ω equals the sum of the individual angular momenta, where r = re + rn; re and rn are the distances of the electron and nucleus respectively from the center of mass. Homework Equations Angular Momentum = mvr...

So,here we have a graph.For every unit of 1(x axis),the unit of the previous y-axis is multiplied. Like this. (0,2),(1,4),(2,8),(3,16)... I don't know how the formula will be,and had never seen this kind of graph. The y seems to be a geometric sequence,on which we can use, ## ar(n-1) ## .r is...

hello, im trying to do this homework, where i have to derive Plancks constant using an experiment where we used some LED lights of different wavelengths to work out voltage at different wavelengths. From that i worked out the frequency and ekmax of the electrons given out. however i have no...

Homework Statement Question is hereHomework Equations Shown in the image, but just to restate: Vc(t) = A+Be^(-t/τ) n/m=e^-1 OR p/m=1-e^-1 The Attempt at a Solution First thing I tried to do was solve the Vc(t) equation for e, which comes out to e=(-A/B)^(-τ/t). I'm not even sure if...

Hi Please see table below GDP growth rates of a group 5 countries. I am trying to derive some conclusions from this small sample. 1. can I conclude that countries in the group have very similar growth rates and there is no significant difference between their growth rates? 2. As...

I'm looking at this scenario where a car is moving and then shifts into neutral. Knowing the initial velocity, how can I derive a differential equation? I know the air drag and the frictional force... are there any other forces, like gravity, that should be included to make it realistic? I...

I may be being stupid here... But I'm trying to derive such an equation to no avail. Maybe such a formula requires more than one variable - but I would like to easily display this graphically. To start out the derivation I stated that the Surface Velocity = (2pi/T)-(v/r) where v/r=angular...

original question: Consider light passing from one medium with index of refraction n1 into another medium with index of refraction n2. User Fermat's principle to minimize time, and derive snell's law (n1sintheta1=n2sintheta2). here is part of the solution key http://i.imgur.com/S1Pg9jC.png...

Homework Statement We want to fin an expression for \theta, the Rutherford scattering angle. I have an expression that I derived for a hyperbolic trajectory, of the form \frac{(x+x_0)^2}{A^2}-\frac{y^2}{B^2} = 1. We wanted it in terms of α, ε, where α is a constant ( \alpha =...

I am currently redoing grade 11 physics and they have introduced the following formula, \Delta d = v_1\Delta t + \frac{1}{2}a\Delta t^2 I am trying to find this equation using calculus. So from what I understand, \Delta d is the area under the curve for v(\Delta t). We can define v(\Delta...

https://dl.dropboxusercontent.com/u/22024273/vectorpotential.png In the above passage, can someone explain to me where (3.102) comes from?

Homework Statement http://puu.sh/4M7BE.png Homework Equations ln(ax) = x*ln(a) The Attempt at a Solution ln(y) = cos(x)*ln(ln(x)) dy/dx * 1/y = -sinx*ln(ln(x)) + cosx/(x*lnx) No clue how to solve this, there's no ln(ln(x)) in the possible answers Attempt 2 y =...

Homework Statement In a damped harmonic oscillator, show that |R(\omega)|^2 = \gamma at full width half maximum. 2. My attempt at a solution This is another one of those questions that I feel like I am almost there, but not quite, and it's the math that gets me. But here goes: For a...

Homework Statement For some work I am doing I wish to be able to define the potential distribution as a function of the radius (ρ) between two concentric electrodes. Homework Equations One solution (from reliable literature) defines the varying radial potential as: V(ρ)=2V0(ρ0/ρ...

Problem: Material scientists have discovered a new fluid property called "radost" that is carried along with a fluid as it moves from one place to the next (just like a fluid's mass or momentum). Let ##r(x,y,z,t)## be the amount of radost/unit mass in a fluid. Let ##\rho(x,y,z,t)## be the...

Hello, I have few question for deriving the Lorentz transformation (LT): While deriving the LT, we draw a graph as x,y,z in one frame of reference and x',y',z' in the other frame of reference as S and S' as two frames of reference. Now the factor ct comes in, which is the flash of...

Homework Statement OK, we've been asked to derive the equations of motion in spherical coordinates. According to the assignment, we should end up with this: $$ \bf \vec{v} \rm = \frac{d \bf \vec{r} \rm}{dt} = \dot{r} \bf \hat{r} \rm + r \dot{\theta}\hat{\boldsymbol \theta} \rm + r...

Problem: Starting from the gradient of a scalar function T(x,y,z) in cartesian coordinates find the formula for the gradient of T(s,ϕ,z) in cylindrical coordinates. Solution (so far): I know that the gradient is given by \nabla T = \frac{\partial T}{\partial x}\hat{x}+\frac{\partial...

Homework Statement An object has a position given by r-> = [2.0 m + (1.00 m/s)t] i + [3.0m−(5.00 m/s2)t2] j, where all quantities are in SI units. What is the magnitude of the acceleration of the object at time t = 2.00 s? Homework Equations All I am thinking here is that I can find...

I am given Z = f (x, y), where x= r cosθ and y=r sinθ I found ∂z/∂r = ∂z/∂x ∂x/∂r + ∂z/∂y ∂y/∂r = (cos θ) ∂z/∂x + (sin θ) ∂z/∂y and ∂z/∂θ = ∂z/∂x ∂x/∂θ + ∂z/∂y ∂y/∂θ= (-r sin θ) ∂z/∂x + (r cos θ) ∂z/∂y I need to show that ∂z/∂x = cos θ ∂z/∂r - 1/r * sin θ ∂z/∂θ and ∂z/∂y = sin...

Homework Statement Trying to derive the work-energy theorem, without manipulating differentials.Homework Equations a=\frac{dv}{dt} v=\frac{dx}{dt} W=\int F dx =ΔKE=\frac{1}{2}mvf^{2}-mvi^{2} The Attempt at a Solution F=ma \int F dx=m\inta dx =m\int\frac{dv}{dt}dx <-- I cannot continue...

Homework Statement I'm stuck at one of the derivations for relativistic energy. I've figured out every other single step, but I just can't wrap my head around this one: Prove that: {\frac{d}{dt}} {\frac {mu} {\sqrt{1-u^2/c^2}}} = {\frac {m {\frac{du} {dt}}} {(1-u^2/c^2)^{3/2}}}...

Homework Statement Wow LaTex fail... anyone know how i make this look like not ****? I had it looking all pretty on http://www.codecogs.com/latex/eqneditor.php and it gave me these codes as my latex markup but it didn't come out right... why do they look like source code and not the pretty...

This is an attempt by a novice to do something neat. Please feel free to correct me. I am trying to see if one can derive the Hamiltonian equations of motion from a simple statement of the conservation of energy for mechanical systems. My attempt: 1. For a system S with position q and a...

Hi, I think I need a sanity check, because I've been working on this for a while and I can't see what I'm doing wrong! According to several authors, including Sakurai (Modern QM eq 3.3.21), a general way to write an operator from SU(2) is...

Hi guys, So I'm starting to learn about magnetic fields and electrics fields, one of the equations we use is v= -L*di/dt ... I've been trying to figure out how it's derived, in my book it says: it starts off like this: 1. v=-dθ/dt (faraday's law) <- why is there no N(no. of turns)...

I am studying Bessel Function in my antenna theory book, it said: \pi j^n J_n(z)=\int_0^{\pi} \cos(n\phi)e^{+jz\cos\phi}d\phiI understand: J_m(z)=\frac{1}{2\pi}\int_0^{2\pi}e^{j(z\sin\phi-m\theta)} d\theta Can you show me how do I get to \pi j^m J_m(z)=\int_0^{\pi}...

Hello, There is this formula ∆t=Lv/c^2 I can't remember how it's called, but it is used to determine time difference between two clocks (one is at rest and the other is moving speed of v). L is the distance between two clocks. How do you derive this formula using special relativity...

Much like Simpson's Rule, a.k.a. the prismoidal method, improves upon the trapezoidal method by fitting parabolic arcs across known discrete points on some function $f(x)$ rather than line segments, Newton-Cotes formulas of order 1 and 2 fit cubic and quartic curves across points on the curve...

Can anyone give me the proof or point me to a link to derive this First Integral of Bessel's Function. J_n(x)=\frac{j^{-n}}{\pi}\int_0^{\pi}\cos(n\phi)e^{jx\cos \phi}d\phi I have been searching all over and can't find the derivation. In fact, other than some basic Bessel's identities that is...

I'm terrible at calculus and am trying an exercise to hopefully help me understand it better. I want to derive the equations of acceleration, velocity and position of a car with known power and mass. As the car's speed increases, the acceleration will decrease. force = mass/acceleration...

(My last https://www.physicsforums.com/showthread.php?p=4424810#post4424810 post did not get much attention so I try again without all these formulae. Think this will be more clear...) To derive the local field in a non-polar dielectric you assume a very small spherical cavity in which (since...