deriving Definition and 1000 Threads

Homework Statement I need help finding the appropriate expression to use to add a "new calculated column" to produce a vertical velocity vs time graph in Logger Pro. The lab consisted of a ball tied to a rope, creating a pendulum. The Go! Motion sensor was set up to record the oscillations. The...

Homework Statement Homework EquationsThe Attempt at a Solution In case of uniform E, torque ##\vec N = \vec p \times \vec E \\ U = \int_0 ^ \theta N d \theta = pE \int_0 ^ \theta \sin \theta d \theta = - pE \cos \theta \text { Here, I assumed that the direction of } \vec N ~ and ~ \vec d...

I am looking for litterature that derives mathematically the total energy in a ##H_2## molecule by using quantum physics. Anyone knows a book they can recommend. I have seen derivations for helium atom for example: http://farside.ph.utexas.edu/teaching/qmech/Quantum/node128.html I need...

I don't get how they get Eq. 5. Why is the direction of ##\mu## going outwards from the direction of B? And why does the fact that ##\frac{d\mu}{dt}## is perpendicular to both ##\mu## and ##B## mean that ##\mu## goes in circle?

The equation below (2.9) is also a linear differential equation. This equation also describes the wave phenomena. So, why is this equation not considered as wave equation? I have taken it from the optics book by Chapter two Eugene Hecht,5th edition ,Pearson.

I am looking at this brief derivation of the E cross B drift for a plasma, starting at the top of page 3: http://www.physics.sfsu.edu/~lea/courses/grad/motion.PDF. I am a bit confused as to the justification that the drift velocity is perpendicular to the magnetic field, as stated at the top of...

So i was going through derivations of moments of inertia of objects. For objects like the disk and rod, i was able to assume a relationship between mass and volume and integrate From there like $$ \frac{d_m}{m} = \frac{dl}{l} \\ d_m = \frac{dl*m}{l} \\ \int_{0}^{L}r^2\frac{dl*m}{l} \\...

Hi, I've just gotten started with basic quantum physics in physics class and we've just talked about ionization energy. It is stated that the energy of a hydrogen atom is -13.60eV (or -2.179aJ). I assume this is the potential energy (and that this is the reason the atom has a lower mass than the...

I have been reading Thomas Hartman's lecture notes (http://www.hartmanhep.net/topics2015/) on Quantum Gravity and Black Holes. -------------------------------------------------------------------------------------------------------------------------------- In page 97, he derives (9.4), which is...

I am familiar with the derivation of the resolution of the identity proof in Dirac notation. Where ## | \psi \rangle ## can be represented as a linear combination of basis vectors ## | n \rangle ## such that: ## | \psi \rangle = \sum_{n} c_n | n \rangle = \sum_{n} | n \rangle c_n ## Assuming an...

Homework Statement I am trying to derive an expression for the potential of a positive point charge by bringing in another positive test charge in from infinity to a point at a distance R from the point charge. Homework Equations $$V_f - V_i = - \int \vec E \cdot d \vec r \, dr$$ The Attempt...

Homework Statement I have ##E(w)=w^3(e^{\beta\bar{h}w}-1)^{-1}##, where ##\beta=K_{B}T##, ##K_{B}## boltzman constantHomework Equations Need to solve ##\frac{dE(w)}{dw}=0## The Attempt at a Solution [/B] ##k=\beta\bar{h}##...

Homework Statement I am attempting to derive Caldeira-Leggett's influence functional found in their paper "Path Integral Approach To Quantum Brownian Motion". If you find my following statements confusing, then pages 16-18 of http://web.science.uu.nl/itf/Teaching/2006/MxWakker.pdf show the...

I have a question stating to derive the functions x |-> f_1(x)=x^3 and f_2(x)=thirdrootof(x) on their domains of definition based on the asymptotic relative condition number KR = KR(f,x). I'm not sure where to start with this question, I'm not sure if I even understand it. Do I find the...

Homework Statement Show that ##a \sin x + b\cos x = c \sin (x + \theta)##, where ##c = \sqrt{a^2 + b^2}## and ## \displaystyle \theta = \arctan (\frac{b}{a})## Homework EquationsThe Attempt at a Solution We see that ##c \sin (x + \theta) = c \cos \theta (\sin x) + x \sin \theta (\cos x)##. So...

Consider the following tree-level Feynman diagrams for the ##W^{+}W^{-} \to W^{+}W^{-}## scattering process. The matrix element for this diagram can be read off from the associated quartic term ##\mathcal{L}_{WWWW}## in the electroweak boson self-interactions, where ##\mathcal{L}_{WWWW} =...

I have a question about the velocity of a mass that is being accelerated from its resting position, for deriving its energy according to ##E=mc^2## The energy needed for accelerating a mass is: ##E = F \cdot s = m \cdot a \cdot s##. Where s is the distance over which the mass is moved. Now, I...

In classical mechanics, the Hamiltonian and the Lagrangian are Legendre transforms of each other. By analogy, in quantum mechanics and quantum field theory, the relationship between the Hamiltonian and the Lagrangian seems to be preserved. Where can I find a derivation of the Lagrangian...

Homework Statement Hi guys, would just too make sure my derivation and insight to why is correct. Question: a) only Homework EquationsThe Attempt at a Solution $$dU=-wd_{ext}$$ $$dU=-F_{ext} \cdot dx$$ Now as the ##F_{ext}## is in the same direction and the direction vector { have not...

Homework Statement A uniform spherical ball of mass M and radius R, initially spinning about a horizontal axis with angular speed ω0, is placed gently on the floor. The initial center-of-mass velocity of the ball is zero. Derive that the moment of inertia ICM of the ball about an axis passing...

Hello, In deriving the energy-momentum equation: E^2 = (pc)^2 + (mc^2)^2 the following equations are used: p = ymv E = ymc^2 But both equations are equations that depend on mass, while the final result does not and applies to massless particles. Besides the energy-momentum equation is...

Homework Statement "Derive the equations for position (in terms of acceleration, initial position, initial velocity, and time) and velocity (in terms of constant acceleration, a, initial velocity, v0, and time, t) from the definitions of position, velocity, and acceleration (derivative...

I've always heard that maxwell's equations contains essentially all of eletromagnetic theory. However, there's one thing I'm having trouble doing for myself: deriving the magnestatics equations from the maxwell's equations. Of course: it's clear that if you put ∂[t]E=∂[t]B=0 (partial derivative...

Hey guys, I got this problem: We had the derivation of the ekman transport today in class. And what I wondered about is this: Usually the equation for the ekman transport looks similar to this (depends on the author) u = V_0 e^{az} cos(\frac{\pi}{4}+az) v = V_0 e^{az} sin(\frac{\pi}{4}+az)...

Is it correct to state that a progressive wave, originates when a simple harmonic motion is imparted continuously to adjacent particles from one direction to another moving with a velocity v. Using this idea, substituting (t - x/v) instead of t is the simple harmonic motion function...

Hello, I’ve been trying to derive Posseuille’s Law and I’m very close. However there seems to be a small difference between my concluded formula and the real one but I don’t know why. Here’s what I get: Picture a cilindrical tube with a radius ##R## in which a fluid is flowing. From what I...

Hello everyone! I am reviewing the derivation of the Virial Theorem from an introductory Astrophysics book (Carroll and Ostlie's) and found a step I couldn't follow. I've attached a photo of the step. Can anyone explain how Newton's Third Law brings about eqn 2.41? I don't see how that first...

How do I use the double angle identity in order to derive this expression: cos6(u)?

Hello, I have a question regarding the following picture: Here, person B is moving in his S’ reference frame with a speed of u relative to Person A, who is in his reference frame S. An event shown by a star (*) happens after tA time according to A. The distance of that event is a distance...

Hi, So I am aiming to derive the continuity equation using the fact that phase space points are not created/destroyed. So I am going to use the Leibiniz rule for integration extended to 3-d: ## d/dt \int\limits_{v(t)} F dv = \int\limits_{v(t)} \frac{\partial F}{\partial t} dV +...

## L(x) = L(\phi(x), \partial_{u} \phi (x) ) = -1/2 (m^{2} \phi ^{2}(x) + \partial_{u} \phi(x) \partial^{u} \phi (x))## , the Lagrange density. ## S= \int d^{4}(x) L (x) ##, the action. ## \phi -> \phi + \delta \phi ## (just shortened the notation and dropped the x dependence) I have ##...

Apologies if this question has already been asked, but is it not possible to derive the formula of a sphere by imagining a circle sliced in two, then rotating this semi-circle about the flat side (imagine the flat side is stuck to a skewer) by 2Pi, so as to sum up the semi-circles to "create"...

Hi Can I derive the expression for Z_PDF(z) where: Z = t(X,Y) = X + Y By starting with: Z_PDF(z)*|dz| = X_PDF(x)*|dx| * Y_PDF(y)*|dy| Z_PDF(z) = X_PDF(x) * Y_PDF(y) * |dx|*|dy|/|dz| and then substitute the deltas with derivatives and x and y with expressions of z?

My textbook is describing a 3-body situation where there are two large masses rotating around their barycentre, and a third much smaller mass experiencing gravitational forces from the two larger masses. If the frame of reference is the one in which the barycentre is at rest, then it is not...

Homework Statement A device called a capstan is used aboard ships in order to control a rope which is under great tension. The rope is wrapped around a fixed drum. The load on the rope pulls it with a force ##T_A## and the sailor holds it with a much smaller force ##T_B##. Show that ##T_A = T_B...

Could someone please assist me in deriving the following projectile motion equations from the following kinematics equations? Kinematics Equations: Δx = v0xt + ½at2 ; Δy = v0yt + ½at2 vx = v0x + at ; vy = v0y + at Δx = ½(v0x + vx)t ; Δy = ½(v0y + vy)t vx2 = v0x2 + 2aΔx ; vy2 = v0y2 + 2aΔy...

Assume: Hydrostatic Situation, ideal gas Use empirical formula T = T0 - Bz I have rechecked my work several times and can't seem to find a mistake. The answer is supposed to be: p2 = p1((T0 - Bz)/T0)(g/Bz) dp/dz = -ρg Now substitute ideal gas equation for ρ dp = -(p/RT)g dz ∫(1/p) dp...

I am attempting to understand how I can derive a new expression as a function of another variable in this existing expression. This is a college undergraduate course but I can't recall doing this much before, maybe in high school. I have taken all the way up to ODE's and PDE's. The confusion...

I have never had to use the English Engineering System so I am having a bit of a struggle here. I understand the concept of an inconsistent system of units. I understand the following 2 statements: 1lbf = 1lbm x 32 ft/sec^2 1lbf = 1slug x 1 ft/sec^2 When given a problem that is asking for the...

Homework Statement This problem relates to the two body problem of two rotating point masses, where one is much larger than the other. Equate the orbital energy per unit mass ##\epsilon## with the moments of momenta at the apses to get: ##\epsilon = -\mu/2a## Homework Equations The orbital...

I am trying to derive the law of signs from the cross product. First, we have three vectors ##\vec{A} ~\vec{B} ~\vec{C}## such that ##\vec{A} + \vec{B} + \vec{C} = 0##. This creates a triangle. Then, we label the angles opposite the respective sides as a, b, and c. I am not sure where to go...

I'm nearly at the end of this derivation but totally stuck so I'd appreciate a nudge in the right direction Consider a set of N identical but distinguishable particles in a system of energy E. These particles are to be placed in energy levels ##E_i## for ##i = 1, 2 .. r##. Assume that we have...

Hello PF! I am trying to find out how the formula for the magnetic field of a dipole magnet is derived, so far I've delved into maxwell equations, but I am finding the math too complicated to read. My state's education system is very far behind, and I am not accustomed to characters and symbols...

Homework Statement Going through a lecture recording from a lecture I missed the lecturer says "to get the relationship between translational speeds and angular velocities we will take a differential" what is that relationship she is talking about? does she mean converting between the two? The...

Homework Statement Okay, in Carrol's Intro to Spacetime and Geometry, Chapter 4, Eq. 4.63 to 4.65 require a derivation of a difference between Christoffel Symbol. I did the calculation and found my answer to be somewhat correct in form, but the indices doesn't match up Homework Equations So...

I'm trying to derive the conservaton of energy for electromagnetic fields with currents from the action principle, but I have some trouble understanding how the interaction term in the Lagrangian fits into this. The approach I have seen so far has been to express the Lagrangian density as...

I have a particle that travels in the cartesian plane with the maximum velocity of A units along the x-axis and B units along the y-axis per unit of time. How do I go about deriving the maximum velocity of my particle in the rotated uv plane? (the maximum distance the particle can along the u...

I am trying to derive the strain at the base of a cantilever beam with a known deflection. I know the bending stress is equal to Mc/I, so the strain is Mc/IE, where c is the distance from the neutral axis. For a point load ,P, the strain would then be PL/IE. Since the deflection is known I...

Assume that i have a wave function of holes in a solid, can we derive the wave function of electrons? If can then how?

Hello all, First of all I want to let you know that my question is very basic and that it involves discrete changes in velocity due to acceleration for every given Δt. I was trying to derive the relationship between the distance and acceleration in a formula and here's what I came up with: 1...