Derive Definition and 620 Threads

I am trying to get the coeficient gamma=1/squareroot(1-(v/c)2) I am trying to do this by my own knowledge starting from scratch. Can someone give me the first step? I want to see if i can get there but i just need a hint i am not sure on where to start Thankyou very much, Fox

Homework Statement Now imagine the two spheres fall toward each other and merge, and that after some time, they equilibrate and end up as a single isothermal sphere. Use con- servation of mass, energy, and the virial theorem, to derive the following (and explain your results in words): the...

Homework Statement Can someone please derive tan(2x) using the definition of the derivative? Homework Equations The Attempt at a Solution I've tried to expand it but I couldn't get anywhere with it thank you,

Homework Statement Find \frac{d^2y}{dx^2} of the following equation: x^2-y^3=3Homework Equations Quotient Rule: \frac{d}{dx}(\frac{f(x)}{g(x)})=\frac{g(x)\cdot f^{'}(x)-f(x)\cdot g^{'}(x)}{g^2(x)} The Attempt at a Solution I solved for the first derivative: \frac{2x}{3y^2} But I'm stuck as...

Hey, can somebody show me how to derive that the lagrangian in classical phyics is L=T-V i have seen this formula so many times, but i have no idea where it really comes from?

Homework Statement \Delta f = \frac{1}{{r^2 }}\frac{\partial }{{\partial r}}\left( {r^2 \frac{{\partial f}}{{\partial r}}} \right) + \frac{1}{{r^2 \sin \phi }}\frac{\partial }{{\partial \phi }}\left( {\sin \phi \frac{{\partial f}}{{\partial \phi }}} \right) + \frac{1}{{r^2 \sin ^2 \phi...

hi, I am trying to derive the group velocity equation (actually its inverse): \frac{1}{v_g} = \frac{1}{c}(n(\lambda) - \lambda\frac{dn}{d\lambda}) where n is the refractive index and depends on the light's wavelength. I have started by saying that if v_g = \frac{\partial\omega}{\partial...

Homework Statement [PLAIN]http://img697.imageshack.us/img697/6702/bungee.png Derive the equations of the motion for the jumper. Consider only the vertical motion of the jumper. (g = 9.81 m/s^2) Homework Equations Straing = (Stated Above) Strain Rate = v / lo = v/25 F = -kx...

Homework Statement Homework Equations equation 37.23 37.30 are the following 37.23 x'=gama(x-vt) x= gamma(x'+vt') t=gamma(t-vx/c2) t'=gamma(t'+vx'/c2) 37.30 u'=(u-v)/(1-uv/c2) u=(u'+v)/(1+uv/c2) The Attempt at a Solution i tried the following... since d=vt... i...

Homework Statement Today I had a physics lab. It involved a hanging mass on a string that hung off the table. It went through a pulley and the string was then spooled around a rotating spool on the table. We first measure the radius of the spool. Then we figured out the mass it took to...

Homework Statement Using: particle velocity, beta particle momentum, p total energy, E Lorentz factor, gamma kinetic energy, KE Derive an equation for momentum as a function of kinetic energy. The functions have to depend either on the variable in the bracket, p(KE), or on a...

Hi, Through some searching and guessing with LogiSim I was able to see how to build a XOR gate from only NOR gates. I would like to know what the process for deriving this would look like. Right now I am lost as to how to proceed given that the NOR function is A'B' and XOR is AB' + A'B. How...

Homework Statement Derive an expression for the temperature of an ideal blackbody so that its radiated light at the peak intensity wavelength has exactly enough energy to excite the ground state to fourth excited state. Homework Equations I = σ*T4 λm*T = 2.9 * 10-3 m * K E = hf = hc/λ...

Homework Statement derive f(x)=x2+2x+1/ x2-3x+2The Attempt at a Solution (x2-3x+2)(d/dx)(x2+2x+1)-(x2+2x+1)(d/dx)(x2-3x+2)/(x2-3x+2)2 =(x2-3x+2)(2x+2)-(x2+2x+1)(2x-3) =(2x3-4x2-2x+4)-(2x3+x2-4x-3) =5x2+2x+7/(x2-3x+2)2 that's what I'm getting... but according to the online derivative...

Let \bar{z} = x+iy. We are given that x = \frac{z+\bar{z}}{2} & y = \frac{z-\bar{z}}{2i}. We are trying to derive \partial F/\partial\bar{z} = 1/2(\partial F/ \partial x + i \partial F/ \partial y), where F(x,y) is some function of two real variables. Using the chain rule I get \partial...

Homework Statement Integrate v_{y} = v_{t} (1 - e^{-(\frac{k}{m})t})) to get y as a function of time. Homework Equations y = v_{t}(t - \frac{m}{k} (1 - e^{-(\frac{k}{m})t}))) is the solution. v_{t}=\frac{mg}{k} The Attempt at a Solution Well, when I integrate I get the following: y =...

Is there a practical utility to derive the electric field produced by a charged rod (and the 1/r dependence at great distance)? I know it can be useful to derive the electric field produced by a large plate since you can then show that the field between close parallel plates that are oppositely...

1. An infinitely long cylinder of radius R contains a uniform charge density Rho. Calculate the electric field using Gauss' law for r> R and R>r 3. I attached a pdf with my attempt at r>R. My answer doesn't agree with those given...

Homework Statement I wanted to know how this equation is derived. Thanks. Homework Equations {v_{f}}^2 = {v_{i}}^2 + 2a\Delta d The Attempt at a Solution v_{f} - v_{i} = \frac {\Delta d a} {\Delta v}

Hello all, I am currently studying multivariable calculus, and I am interested in the Taylor series for two variable function. I am not sure where to begin; I cannot understand any of the proofs (which are apparently sparse) on the internet; they all just state it using a sigma sum; not...

Homework Statement Show that it follows from \frac{dV}{V} = \beta dT that, for small changes, density has a similar linear relationship to thermal expansion, namely \frac{d\rho }{\rho } = - \beta dTHomework Equations The Attempt at a Solution Well, at first glance this one seems ridiculously...

I know you need to use some spacetime geometry to solve some conservation equations but what is the simplest way you derive the following equation about energy and momentum: E2 = (pc)2 + (mc2)2

"Definition" of Curl. Can anyone derive the gradient operator? Can anyone prove why this equality is true? http://en.wikipedia.org/wiki/Curl_%28mathematics%29#Definition Wikipedia says it is defined, however that's BS since the gradient operator was already defined so this needs to be proven...

I'm programming a minesweeper game, and I'm trying to come up with an equation to determine the maximum number of mines a board can have dependent on the amount of rows and columns given. I pulled some numbers from the Windows 7 version, but I'm not sure how to derive an equation from them...

Does anyone know how to derive a fraction? I want to be able to differentiate f(x)=\frac{x(20-x)}{36} Ill show you what I've done but think I've just simplified it. f(x)=\frac{x(20-x)}{36} f(x)=\frac{(20-x-x)}{36} f(x)=\frac{(10-x)}{18} Is this correct?...although not sure what...

When deriving equations, do you look at the diagrams and derive the equations from there. Could you please tell me how you would derive the equations?

Using these two formulas derive the third formula: D/l = (D+f)/(l+alpha) D/r = (D+f)/(r+beta) D=(fb)/(alpha+beta) where D is the distance of the point from the line between the viewer's eyes; f is the focal length of the lens in the eye; b is the distance between the two eyes; and...

Homework Statement Starting with the Planck distribution R(\lambda,T) for blackbody radiation. (a) Derive the blackbody Stefan-Boltzmann law (ie total flux is proportional to T4) by integrating the above expression over all wavelengths. Thus show that R(T) =...

Homework Statement The motion of various shaped objects that bob in a pool of water can be modeled by a second order differential equation derived from F = ma. The forces acting on the object are: 1)force due to gravity, 2)a frictional force by water, 3)and a buoyant force based on...

:smile:Hi I have been wrestling with this situation for a while, trying to derive an equation for it...A sphere is placed in a fluid of viscosity n and density p, outside any gravity. The sphere is instantly beamed out (perhaps by Capt Kirk?). At what volume rate will the fluid rush into the...

Homework Statement Is there a univeral conversion formulae to convert Azimuth and Elevation to Lat Lon or Cartesian X,Y,Z? Homework Equations So far, I have only been able to source out and successfully convert Cartesian X,Y,Z to Lat Long Alt. The Attempt at a Solution No findings...

Hi, I was wondering why the wave-function in quantum mechanics is complex. There are a lot of threads in the physics section and I've downloaded a lot of papers, but they seem quite technical. So I'd like to examine the following idea (sorry if I use sloppy terms ;) ): I have an orthonormal...

hello suppose a eqn is given as y=x/(ax+b). which we can linearize as: (1/y)=a+b/x and therefore Y=A+BX where A=a, B=b and X=1/x .Another example is y=ax^b this can be written as ln y=ln ax^b or ln y=ln a+bln x therefore Y=A+bX where Y=ln y,A=ln a and X=ln x thus it is linearized now. I...

Hey guys was hoping someone could give me a hint for the derivation of Newton's Law of cooling stated in the following equation form:http://img263.imageshack.us/img263/3143/a6e5a27835e9e5738016606.png http://img716.imageshack.us/img716/8728/75784887.jpg Thanks in advance!

Homework Statement How do you derive the following equation given I/Io= (I/N2)[(sinNØ/2)/(sinØ/2)]2 given that Ø= (2πdsinΘ)/λ Homework Equations Ø= (2πdsinΘ)/λ d=λ/sinΘ The Attempt at a Solution I have tried substituting Ø into the equation as well as d=λ/sinΘ, but I...

Hello, I'm having trouble to derive Eq. (3.110) in Peskin's QFT book. In the book, it's said to use u(\Lambda^{-1} \tilde{p})=\Lambda^{-1}_{1/2} u(\tilde{p}) But I ran into trouble to derive this. Here is my try: The equation is equivalent to u(p)=\Lambda^{-1}_{1/2} u(\Lambda p) To...

Please derive equation 2.27 in Goldstein(3rd ed.)

[b]1. The problem statement, all variables and given/known For a a uniformly charged sphere of radius R with total charge Q, show that the potential energy of a point charge q' varies with r U(r) = Qq'/4\pi\epsilonR * (3/2 - r2/2R2 if r < R Homework Equations \DeltaU = - \intE(r)q'dr...

Homework Statement Derive p(r) = \frac{A}{r}e^{j(\omega t - kr)} from pV = nRT Homework Equations The Attempt at a Solution From ideal gas law I have p(r) = \frac{nRT}{V} R and T are constant, so I can pull them out now and replace them with A. If V is the volume of a spherical shell of...

Homework Statement The problem is to find at what distance the ball has to be placed at on a ramp given a certain angle measurement of said ramp. The cup's position will be given a few minutes prior to testing so there are more unknown variables. Table Height: .73M Cup Height: 10cm Angle...

Homework Statement I have attached a jpeg image of a karnough map of a rs flip flop. How can i derive the logic equation? Homework Equations The Attempt at a Solution

Homework Statement A regular pendulum is swinging back and forth. Assuming it starts from a horizontal position, find an expression for its tangential velocity. (I don't know if the question is posed right, I just asked myself it as a challenge) 2. The attempt at a solution using a freebody...

Homework Statement The mass of a rocket, including a full chamber of fuel, is M. Its net mass without fuel is m. The products of combustion are ejected with velocity c. If the rocket starts from rest, derive Ciolkovski's formula. Homework Equations N/A. This is actually from differential...

Hi, I don't know if this should go in a Math forum or a Programming forums, but y'all here seem quite handy with mathematics, so I'll give it a shot. If this is totally not what y'all are about, just let me know. I have two computer images... one of them is an "original" image. The other one...

Homework Statement A uniform stick of mass m and length L, initially upright on a frictionless horizontal surface, starts falling. The circle at the center of the stick marks the center of mass. Derive an expression for the speed of the center of mass as a function of y and θ if the stick falls...

Homework Statement Derive the period of a sphere oscillating in a hemispherical concave surface at small angles. Homework Equations Net Torque = I x alpha Delta E_m = 0 The Attempt at a Solution The thing is, tried using the conservation of mechanical energy to get an expression...

Homework Statement Derive the Oseen tensor from the Navier-Stokes equation, Consider an incompressible fluid where the velocity field \vec{v}(\vec{r},t) is given by \nabla.\vec{v}=0 (1) Assume inertia forces are negligible. Homework Equations The Navier-Stokes eq becomes...

Homework Statement Two wires are tied to the 300 g sphere shown in figure. The sphere revolves in a horizontal circle at a constant speed of 6.50 m/s. What is the tension in the upper wire?What is the tension in the lower wire? Write an equation for the sum of the forces along y. Use it to...

Homework Statement I am trying to derive the transfer function for the circuit (figure 6). I have what the final transfer function is supposed to be (figure 7) but I can't derive it. Homework Equations ((v2+) - 12)/12k + (v2+)/12k + ((v2+) - v1)/c2= 0 (v2-)/c1 + ((v2-) - Vout)/15k =...

Homework Statement A very long, solid cylinder with radius R has positive charge uniformly distributed throughout it, with charge per unit volume \rho Derive the expression for the electric field inside the volume at a distance r from the axis of the cylinder in terms of the charge...