deriving Definition and 962 Threads

Hi, can you derive Gauss's Law without using Coulomb's Law? If so, how? Thanks

Homework Statement Derive the Laplace transform of the following functions, using first principles 3d) u(t - T) \} = 0, \ t<T \ (= 1, t>T) 3e) f(t) = e^{-a(t-T)}u(t-T) Homework Equations see above The Attempt at a Solution I know I need to derive the transform using by integration...

I would like to derive a relation for shear stress on a conical bore shaped fluid element. Essentially, I have flow going through a converging nozzle. I know variables in this include length of the nozzle, inlet and outlet diameters and pressures and nozzle angle. I've done a force balance on...

Hi, I have a quick question about a derivation that has annoyed me all day. I am trying to prove, from the definition of \otimes that: T(\theta,\tau)=T^{i\alpha}(e_i,f_\alpha) Where \theta \in V^* and \tau \in W^* T: V^* \times W^* \mapsto \mathbb{R} and where V has basis e_i and W has basis...

Homework Statement Derive the moment of inertia for a solid sphere with a uniform mass Homework Equations I= \sum mr^{2} The Attempt at a Solution I decided to change everything to polar coordinates. Since the polar coordinate substitution is \int\int\int_{v} Fr^{2}sin(\phi)drd\phi d\theta...

I have a bit difficulties deriving the equation V in =Vout * R2/(R1+R2) Because I can't see a closed loop here Can someone help with this Thx

How would I go about deriving the cooridinate numbers of both ions in rock salt, and, how could I account for the differences in lattice enthalpy between the following; LiCl (861 kJ/mole) - NaCl (787) LiCl - LiF (1046) LiCl - MgO (3850) Cheers.

Given tanA=y/x.....(1) Can anyone tell me how you get the following relations: =>sinA=ay/sqrt(x^2+y^2).....(2) =>cosA=ax/sqrt(x^2+y^2)....(3) where a=(+/-)1 I know tanA=sinA/cosA and sin^2(A)+cos^2(A)=1...and I can see by substituting (2) and (3) into (1) it works, but I really...

Homework Statement Suppose we lived in a matter-dominated, critical-density universe. The matter density rho of such a universe changes with time t as a power of t. Derive the value of the exponent n in the following equation: Homework Equations rho = At^n where A = constant

Homework Statement We have a straight wire with radius R. What is the magnetic induction through point A at a distance of r? In other words, derive the equation B=\frac{\mu_{0}i}{2\pi r} by using d\vec{B}=\frac{\mu_{0}i}{4\pi r^2}(d\vec{l} \times \vec{u_{r}}) Homework Equations...

Homework Statement Deriv µs = tan θ For when a block is put on a wooden plank and the plank is lifted at one side. Homework Equations tan = sin/cos Ff = µFn The Attempt at a Solution Ff = µFn -mgsinθ= µ (-mgcosθ) µ =(-mgsinθ) /(-mgcosθ) µ = tan θ Where i am confused is why Ff...

when we derive the wave equation for a an o0ne dimensional wave moving at constant speed we assume that the wave move losslessly that is a plot of \psi(x,t) with x at any time t is same to the extent that one can be obtained from the other by translation. similarly what are the assumptions when...

Homework Statement A circular curve of radius R in a new highway is designed so that a car traveling at speed v can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will...

I figured out this one, just thought it was quite nice... We start with the only requirement that the Green's function of the propagator is causal in the sense that it propagates stricktly forward in time, so that the Green's function is zero at t<0. Using the Heaviside step function we can...

Homework Statement x(t)= (7.00m/s)t + (7.00m/s^2)t^2 - (2.00m/s^3)t^3 a) find the expression for the velocity as a function of time. b) plot the graphs of the position, velocity and acceleration as accleration vs time for the interval given. c) At what time(s) btw t=0 and t= 3.00...

Homework Statement I am wondering if someone could give me some insight on how the following infinite series was derived: P_e = \sum_{-\infty}^\infty (1/2)^{2|n|} = -1 + 2 \sum_{n=0}^\infty (1/2)^{2n} = 5/3 Homework Equations See above The Attempt at a Solution I think the -1...

Homework Statement Automotive engineers refer to the time rate change of acceleration as the Jerk. Assuem an object moves in 1 dimention such that it's Jerk is constant. a) determine expressions for it's 1. acceleration ax(t) 2. velocity vx(t) 3. position x(t) given initial...

I'm looking for a good book for graduate students that indicates how one can obtain a (classical) potential from a tree-level Feynman process. For example, how can one go from the S-matrix of e.g. Compton scattering and derive the Coulomb potential. Any help would be appreciated.

I was going through the derivation of the Taylors series in my book (Engineering Mathematics by Jaggi & Mathur), and there was one step that escaped me. They proved that the derivative of f(x+h) is the same wrt h and wrt (x+h). If someone could explain that, Id be really grateful.

Homework Statement Okay, this lab has had me stumped for the last few hours. This is our first lab for AP Physics BC. Problem: Determine the position vector that describes the locatino of the water that is launched by a drinking fountain. Your position vector needs to be in unit vector...

How do you derive the equation for the launch angle using the range and peak equations? This isn't a homework problem but something i want to know for my own general knowledge for solving physics problems. Is there a site that has physics equations solved for different variables? Hyperphysics is...

Homework Statement Derive (v_f)^2 = (v_i)^2 +2ad Homework Equations (v_f)^2 = (v_i)^2 + 2ad (v_f) = (v_i) + at d = (v_i)t + \frac{1}{2}at^2 The Attempt at a Solution I have attempted to replace the variables with others from other kinematic equations such as v_f = v_i + at...

How do we come to 4.pi.r^2?

hi frenz i want to how to derive mathematical relation between dependent(output) and independent(input) variables when i know the relation between them at few samples. cud someone help me out? thanks in advance

Homework Statement I need to derive some equation that are on the paper "does the inertia of a body depend on it's energy content". http://www.fourmilab.ch/etexts/einstein/E_mc2/www/" I just don't know where to start and if someone can point me to the right direction, it will be so much...

For a homework assignment I'm supposed to prove that sin(x)^2+cos(x)^2=1, using only the following identities (along with algebraic operations): sin(-x)=-sin(x) cos(-x)=cos(x) cos(x+y)=cos(x)cos(y)-sin(x)sin(y) sin(x+y)=sin(x)cos(y)+cos(x)sin(y) I can't figure this out, because as far...

Homework Statement Basically I am given an image showing a test charge tied to a string where there is the ball is stationary. I need to use the fact that there is no net force on the ball to derive an equation for the electrostatic force in terms of g, the angle, and the mass of the ball...

Two ladders, one red, and the other green, are 2 and 3m long respectively. The base of the red ladder is resting on the side of a narrow hallway and leaning on the wall of the other side of the hallway. The green ladder is doing the same, but on the opposite side, such that the two ladders cross...

I am having a huge problem with understanding the derivation of velocity profiles for these type of problems. The one i am having the most difficulty is the flow of oil going down vertically along the surface of a glass rod. Where p=900 kg/m^3 and u=120 mPa's. How do I start this problem?

Homework Statement Water is filled to a height H behind a dam of width w. Determine the resultant force exerted by the water on the dam. Homework Equations P=pgh = pg(H-y) (where p is density, greek rho) dF = PdA = pg(H-y)wdy (where dA is a narrow horizontal strip of the dam with...

Homework Statement n_1 moles of a monatomic gas and n_2 moles of a diatomic gas are mixed together in a container. Derive an expression for the molar specific heat at constant volume of the mixture. My answer can only use the variables n_1 and n_2, and I'm assuming constants. Homework...

Homework Statement Hello everyone, I'm in need of some assistance in regards to deriving an equation from a graph. I have been tasked to graph information which I've collected through experimentation and then write an equation to represent the graph. I'm stuck at steps 3 and 4 and I am not...

I am supposed to derive 4\,\arctan \left( 1/5 \right) -\arctan \left( {\frac {1}{239}} \right) from the complex product of \left( 1+i \right) \left( 5-i \right) ^{4} I do see how the argument of product of the complex expression is equal to pi/4 - 4 arctan(1/5) but I am totally lost. SO how...

Homework Statement I am trying to derive the mass of \Xi using the formula: M\left(baryon\right)=m_1 + m_2 + m_3 + A' \left[\frac{S_1 \cdot S_2}{m_1 m_2} +\frac{S_1 \cdot S_3}{m_1 m_3} + \frac{S_2 \cdot S_3}{m_2 m_2\3}\right] Homework Equations We have: S_1 \cdot S_2 + S_1 \cdot S_3 +...

Homework Statement Derive Bateman equation for a decay chain a->b->c->d where each decays with a given mean life let decay constant be L, where L=1/mean life Na(0)=No, Nb(0)=Nc(0)=Nd(0)=0 Homework Equations Want to derive Nb(t)={(No)(La)/(Lb-La)}*{exp[-La*t]-exp[-Lb*t]} extend for...

Hello everyone... can someone help me with this problem please: The rotation curve V(r) for a mass distribution characterizes the rotational velocity of a test particle in orbit in its gravitational field as a function of radius from its center. Suppose you have a spherically symmetric mass...

Suppose I had a random variable, X, that followed a Gamma distribution. A Gamma distribution can be defined as \Gamma(\alpha,\beta) , where \alpha and \beta are the 'scale' and 'shape' parameters. Now suppose if \alpha was a random variable, say following a binomial distribution, how would...

Hello again everyone Part of a problem I've been set is to show that the equation: B(r) = \frac{1}{2}\mu_0 (J x r) from Ampere's law: \nabla x B = \mu_0 J. The problem presents no... uh... problem thereafter, but I'm at a loss where to begin. I've been playing around with random...

Homework Statement I have solved the equation for the neutron density as a function of position and time. I need the boundary conditions to change my infinite number of solutions (the varying separation constant) into one value so that my answer for the critical radius does not contain a...

How are the Planck length, Planck time, and Planck mass "derived"? I know their values, but I don't understand where we get them from.

I am having trouble finishing this problem. I am supposed to first derive an equation for V_5 in this circuit: http://img292.imageshack.us/img292/599/picture3qy2.png I applied a Delta-Wye transformation to get here: http://img292.imageshack.us/img292/9672/workot8.jpg From there I am...

Could someone show me a derivation of the Weyl tensor or link me to a good site?

I am curious how you derive this law. It seems that you could derive coulomb ` s law from gauss ` s law, but are there are no similar analogy for Bio-Savart law.

Homework Statement Use the thermodynamic identity to derive the heat capacity formula C_V=T\frac{\partial{S}}{\partial{T}}_VHomework Equations C_V=\frac{\partial{U}}{\partial{T}} T=\frac{\partial{U}}{\partial{S}} dU=TdS-PdV+\mudN The Attempt at a Solution I used...

Homework Statement I have the following question to answer: Show that (X^2/h^2)*((1/2*y1) - y2 + (1/2*y3)) + (X/h)*((-1/2 y1)+(1/2 y3))+y2 (sorry about the format) is equal to (taylor expansion): y = y2+(x(dy/dx)¦0 + (x^2/2*((d^2)y)/(dx^2))¦0 Homework Equations also given in...

Homework Statement A uniform rod of mass M and length L is free to rotate about a horizontal axis perpendicular to the rod and through one end. A) Find the period of oscillation for small angular displacements. B) Find the period if the axis is a distance x from the center of massHomework...

I read somewhere that the whole of magnetism, and in particular the lorentz force, can be found merely by applying the lorentz transformation to transform the coordinates of the electric field of a charged particle from the frame in which the particle is at rest to a frame in which the particle...

Given the following formulaes prove that maximum speed (Vmax) of a mass on a spring is given by 2(pi)(frequency)(Amplitude) (constant k) A^2 = mv^2 + (constant k) x^2 ma = -(constant k)(x) f = 1/2(pi) sqrt (a/-x) and f = 1/2(pi) sqrt (constant k/m) i just don't...

A line charge of liner charge density lambda=4.5 nC/m lies on the x-axis and extends from x=-5cm to x=5cm. Derive an expression for E_y. I have started with this question and it seems that I have to sum the electric fields in the y direction caused by each dx along the line with a charge dq...

Hey... Could someone help me out with deriving the LaPlacian in spherical coordinates? I tried using the chain rule but it just isn't working out well.. any sort of hint would be appriciated. :) \nabla^2 = \frac{1}{r^2} [ \frac{\partial}{\partial r} ( r^2 \frac{\partial}{\partial r} ) +...