deriving Definition and 962 Threads

Hello PF, I have once simple (well, not so simple for me) question. I'm trying to derive an equation for the velocity of a falling body with accordance to terminal velocity. The equation incorporates drag proportional to the speed. m*dv/dt=mg-bv and mg/b=terminal velocity vt So the steps...

Homework Statement let f(a)=∫20|x(x-a) dx for 0≤a≤2 a)Find the function f(a) The Attempt at a Solution I think the function can be given by this but what I get does not seem to be the correct answer. ∫a0x(x-a)dx -∫2ax(x-a)dx The correct answer is supposed to be 1/3a3-2a+8\3

can anybody help me to derive eqn. (9.19) of Srednicki's QFT book?

Hello, I am trying to derive the equation for the B-field due to a moving charge. ~ Griffiths Chapter 10, equation 10.66. I have been trying to “do” the del cross A and simplify . Things get messy and I am uncertain on some of my vector operations. In searching the internet I find...

(First post, hi everyone.) I'm reading Griffith's textbook on intro to quantum mech right now. After establishing the following equation $$\left\langle f(x) \right\rangle = \int f(x)p(x)\,dx$$ And thus $$\left\langle x \right\rangle = \int x|\Psi|^2\,dx$$ He goes on to find...

Homework Statement My professor wants to see how to derive the formula. Basically get from the first two lines in the bracket to the two lines that are boxed. Homework Equations I have attached the picture of the relevant equations

Homework Statement A projectile is fired from ground level at time t=0, at an angle of θ with respect to the horizontal. It has initial speed V0. Part A Find the time it takes the projectile to reach its maximum height. Express in terms of V0, θ, and g. Part B Find the time at...

\hbox { Bessel's equation of order p: }\;x^2y''+xy'+(x^2-p^2)y=0\;\hbox { and let}\;y=\sum_0^{\infty}C_nx^{n+r} \Rightarrow\; \left[\sum_0^{\infty}C_k(k+r)(k+r-1)x^k+\sum_0^{\infty}C_k(k+r)x^k+\sum_2^{\infty} C_{k-2}x^k-p^2\sum_0^{\infty}C_kx^k\right]x^r\;=\;0 \Rightarrow\...

Can anyone point me to a derivation of the navier stokes equations in polar? I don't see where the single derivative in theta terms are coming from in the first 2 components.

In this documentation from Nasa a procedure to get to what I guess is the gravitational acceleration according to the post-Newtonian expansion at the 1PN-level for the spherically symmetric case is found: http://descanso.jpl.nasa.gov/Monograph/series2/Descanso2_all.pdf The procedure is...

I was asked to formulate the equations governing the rotation of a body moving without any external moments acting about its centre of mass in terms of a coupled system of first order, nonlinear differential equations. I decided to go with the Euler equations, and I ended up with this...

Homework Statement The question asks one to derive the acceleration vector, $$\vec{a} = [\frac{d^2r}{dt^2} - r(\frac{d\Theta}{dt})^2]\vec{u}_r + [\frac{1}{r}\frac{d}{dt}(r^2\frac{d\Theta }{dt})]\vec{u}_\Theta$$ from the velocity vector. $$\vec{v} = \vec{u}_r\frac{dr}{dt} +...

Homework Statement Find derivative of abs (2x^3 + 8x^2 + 5x +1).Homework Equations The Attempt at a Solution A little confused on how the absolute value changes the method of deriving that equation. When I derive it normally, I get (6x^2+16x+5).

Homework Statement Hey all, I am having trouble following some of the notes that my professor posted with regards to waves inside a blackbody; here is what he posted: (the part in bold is what I am just not understanding) "Inside the blackbody box, we need for the position of the walls...

Homework Statement I'm asked to start from Faradays Law & Ampere-Maxwell law then derive the equation for the magnetic field, B, in the form; del2B = 1/c2 * d2B/dt2 Homework Equations Faraday: curl E = -dB/dt A.M : curl B = ε0μ0 dE/dt The Attempt at a Solution taking curl of...

I have a derivation from a book that says Q = 2π Es / Ed Where Es is the energy stored in the resonant components. Dividing both by the period at resonance gives... Q = ωo Es / Pd This is where I'm stuck. The book says Es = 1/2 LI^2 at the instant that all of the energy is being stored in...

Hi, I'm trying to fill in the gaps in my notes - looking at a poroelastic model of tissue. We have the simple spherical model below. The centre sphere is where liquid is produced, then the two following spheres are brain tissue with different permeabilities, and the final sphere is an...

Homework Statement Homework Equations The Attempt at a Solution I've done all the parts easily. I just don't know how to derive the beat frequency fbeat. I cannot provide any workings because I don't know where to begin. I am not asking for an answer. I am asking for a...

Homework Statement Is it possible to find the vector field line expression without the use of differential equations? Say I've sketched the field and found the shape to be parabolas, how would I find the general expression by just using the points I've been given?Homework Equations The Attempt...

Homework Statement Derive the formula to calculate the angle at which the road should be banked to prevent the car from skidding(Ignore force of friction). Homework Equations tan x = v^2/gr ----- answer mv^2/r = fcThe Attempt at a Solution I get how they derived the formula due to this website...

Is there a simple way of deriving Lorentz transformation? I don't find the typical derivations in textbook so convincing, which seems to use too many intuitive postulations...

Voltage across an inductor at any moment in time can be calculated as the inductance multiplied by the rate of change of current. How is this equation derived? I'm pretty sure it comes from Faraday law -emf = rate of change of magnetic flux but I cannot find the relationship. Thanks!

Hi i have been following Hobson in their attempt to derive the einstein tensor, I have split the varied action into three terms and want to factor out \delta(g^{\mu\nu}) terms. The Riemann tensor R_{\mu \nu} must be expanded to R^{\rho}_{\mu \nu p} and then contracted back to the original...

I am not really sure where to go from here, since T varies. I am guessing this means I am approaching the problem incorrectly, but in that case, I have no idea how to do it. Any help/guidance would be appreciated.

Homework Statement The total intensity I(T) radiated from a blackbody (at all wavelengths λ) is equal to the integral over all wavelengths, 0 < λ < ∞, of the Planck distribution (4.28). (a) By changing variables to x = hc/λkBT, show that ¡(T) has the form I(T) = σT4 where a is a constant...

Hi all, I was going through the derivation for the electromagnetic field of point charges by Griffith(Introduction to electrodynamics page 437). I'm missing minus sign somewhere: The book says that:\nabla(\vec{n}\cdot\vec{v})=\vec{a}(\vec{n}\cdot \nabla...

In K&K's text on mechanics, after they present the derivation of the work energy theorem: \frac{1}{2}mv^2-\frac{1}{2}mv_0^2=\int_x_0^x F(x) dx It is mentioned that since v=\frac{dx}{dt}, we could solve for \frac{dx}{dt} and integrate again to find x(t) I tried that with v_0=0 just to make...

Homework Statement I need to derive an expression for the displacement of light as a function of thickness of glass and the angles. I will post a screen shot of the formula to be derived but it can also be found here...

How would one derive the equation for (dP/dV)H? That is the partial of P over the partial of V, holding H constant. I've tried many different things, triple product rule, maxwell relationships, and nothing seems to work. I appreciate any advice.

Hi, I shall show (using Fourier transform) that the solution to \frac{\partial^2 u(x,t)}{\partial t^2} = \frac{\partial^2 u(x,t)}{\partial x^2}\\ u(x,0) = f(x) \\ u_t(x,0) = 0 is u(x,t) = (f(x+t) + f(x-t))/2 I got it almost: Taking the Fourier transform in the variable x...

Can moment of inertia be derived using just linear dynamics and calculus. Textbooks usually derive moment of inertia using energy equation and and analogy of 1/2mr^2w^2 with 1/2mv^2. I would like to know if it can be approached in a different manner using just linear dynamics.

QUESTION A star of bolometric luminosity L at a distance r will exhibit a bolometric energy flux F given by F = L/4πr2 in the absence of obscurity. A. Assume that all stars have the same bolometric luminosity L and that stars are uniformly distributed in space with a number density n...

Deriving addition of sines from Euler's formula (edit: please ignore) Homework Statement I'd like to derive the value of sin(2πkt + θ) so that I can convince myself that the Fourier sum in terms of sines and cosines works. I found the derivation on Wolfram by using the full Euler's formula...

Say I have a mass m on a non linear spring k with some damping b. I start with the restoring force of the spring F=-kx+x^3... the x^3 is the non linearity. Set that equal to Newtons second law F=mx'' = -kx+x^3 Add in the damping which is dependent of velocity bx' ......mx'' = -kx +...

Hi i am trying to derive the Dirac equation of the form: [i\gamma^0 \partial_0 + i\frac{1}{a(t)}\gamma.\nabla +i\frac{3}{2}(\frac{\dot{a}}{a})\gamma^0 - (m+h\phi)]\psi where a is the scale factor for expnasion of the universe. I understand that the matter action is S=\int d^{4}x e...

Homework Statement In general, I know that you can use the equation ωn=[k/m]^0.5 to calculate the natural frequency of a hanging spring and mass system. However, for a non-ideal spring (where the mass of the spring isn't negligible) a correction factor is added to the equation and it...

Homework Statement There is a diagram in the problem statement so here is a link to the image of the problem: http://imgur.com/KDrRsyO Homework Equations Snell's Law: n_{1} * sin(\theta_{1}) = n_{2} * sin(\theta_{2}) The Attempt at a Solution My attempt using Snell's law...

Hi I am using the metric ds^{2}=c^{2}dt^{2}-a^{2}(t)[\frac{dr^{2}}{1-kr^{2}}+r^{2}(dθ^{2} + sin^2θd^{2}∅)] and am subsequently trying to derive the christoffel symbols: \Gamma^{\sigma}_{\mu\nu}=\frac{1}{2}g^{\sigma\rho}(\partial_{\nu}g_{\rho\mu} +\partial_{\mu}g_{\rho\nu}...

Homework Statement A long string of linear mass density μ_1 = 1.0 gr/cm is joined to a long string of linear mass density μ_2 = 4.0 gr/cm and the combination is held under constant tension. A transverse sinusoidal wave of amplitude A _i = 3.0 cm and wavelength λ =25 cm is launched...

deriving equation for minimum height in projectile motion with two give me's :) Homework Statement A ball is launched at a 45 degree angle and lands 152.4 m away. What is the maximum height the ball will reach during its flight. I Know the answer, what I need is to find a way to derive an...

Problem deriving "failure of simultaneity at a distance" Homework Statement I'm trying to derive the failure of simultaneity at a distance from the spatial part of the Lorentz transformation. In his treatment of the subject, Feynman glosses over the algebra/derivation and produces the...

Hello, I've seen several derivations of it and I understand them, specially the one in two dimensions with the right angled triangle, but when I try it in 1 dimension, I always find that the condition that the speed of light is the same in all the inertial frames, isn't enough to specify what...

In Stewart's calculus text, the way he derives the tangent plane equation at some point is to divide the general plane equation a(x-x_0)+b(y-y_0)+c(z-z_0)=0 by c This must mean c is always non-zero right? But isn't c is the 'z'-component of the normal vector to the surface at some point...

The equation can be obtained from the fact that the "canonical momentum of the ground grstate of superconductor is zero", but where does this fact follow from. P.S. Jackson gives a vague reference to Kittel, which I couldn't find in his Introduction_to_solid_state/Quantum_theory_of_Solids.

Say we were given an expression for the energy-momentum tensor (also assuming a perfect fluid), without getting into an expression with multiple derivatives of the metric, are there any cases where it would be possible to deduce the form of the metric?

Our professor derived a Minkowski force like this: F^\mu = \left[ \gamma(e\vec{E} + e(\vec{v}\times \vec{B})) , \gamma \frac{e \vec{E} \vec{v}}{c} \right] Does this mean that i can write 4-force like this? F^\mu = \begin{bmatrix} \gamma(e\vec{E} + e(\vec{v_x}\times \vec{B}))\\...

Homework Statement There's a short introduction saying that honing missiles can determine their position by utilizing their acceleration, then the problem says: Suppose that the missile's acceleration obeys the following equations: \\ a_x = 0.8\\ a_y = -6.0 - 3.0t Knowing that, in t =...

Homework Statement A driver sees the red light, and instead of braking the car, changes the gear to neutral. Suppose that velocity obeys this equation: v = v_0 * e^{-bt} Where v_o = 20 m/s and b = 0.150 s^{-1} a)Acceleration when time equals 0;(Answer:-3.0 m/s^2) b)Displacement when t=5.0...

Homework Statement A quasi-3 level solid-state laser gain medium consists of a ground state manifold containing two energy levels within which a single electron can be promoted, with the second energy 10meV above that of the lowest level. A. Where the gain medium is not optically pumped...

Hello, I'm new here and this is the first thing I ever write on this forum, hence the question if this is the wrong place to post anything remains unanswered on my part. I came across this forum doing something on the internet, I can't remember what. I'm certain though that it was related...