deriving Definition and 962 Threads

Homework Statement Derive an equation for velocity based on time with drag. Homework Equations The equation is: v(t) = F/b (1 - e^(-bt/m)) The Attempt at a Solution There's some math on paper, but I got down to: F - bv = ma a = dv / dt F - bv = m*dv/dt dt = m*dv / (F -...

Homework Statement If a string wound around a fixed circle is unwound while held taut in the plane of the circle, its end P traces an involute of the circle. In the accompanying figure, the circle in question is the circle (x^2)+(y^2)=1 and the tracing point starts at (1,0). The unwound...

I am supposed to derive this equation: g=aave(M + m / m) It gives me two pairs of equations: T1-Fr = Ma1 mg-T1= ma1 and T2 + Fr = Ma2 mg - T2 = ma2It also says, "hint: for the first pair of equations, eliminate the unknown tension. Do the same for the second pair of equations. In this new...

How does one begin to derive the resonant frequencies of a multiple mass mass-spring system? (3-mass system) OK, so deriving this isn't a homework problem. I'd just like to know how. It's been a couple of years since I've taken a physics course. I was asked what the resonant frequencies of each...

Wikipedia's 'special relativity' entry gives the following relationship between force, acceleration and velocity: \vec f=\gamma m \vec a + \gamma^3 m \frac {\vec v \cdot \vec a}{c^2}\vec v but without derivation. Could someone tell me how one arrives at this? Thanks.

Homework Statement Find the impedance of the circuit (R and L in series, and then C in parallel with them). A circuit is said to be in resonance if Z is real; find ω in terms of R, L, and C at resonance. Here is the circuit: http://img382.imageshack.us/my.php?image=g...ccircuitgf5.png...

Homework Statement I have been given these two equations: x=2acos^2(x) , y = 2a(cos(x))(sin(x)) where a ranges from 0 to 5 and -2π < x < 2π I need to prove that these equations (when you plug in values for x) create points that when plotted, give you a circle with center (x-a) and radius a...

Homework Statement A thin, circular plate assumed to lie on the xy-plane is rotating about its center, located at (0, 0), with angular speed ω. (ω > 0 means that the plate is rotating in the counterclockwise direction.) Show that the velocity field of of this plate is given by v(x, y) =...

I'm supposed to derive this monster! \frac{1}{2} + \frac{2}{\pi} \sum^{\infty}_{k = 1}\frac{1}{2k-1}sin(2k-1)x = \left\{^{0 \ for \ -\pi < x < 0}_{1 \ for \ 0<x<\pi} I don't even know where to start right now. And no examples to work from. Can anyone get me started? the Chapter is on...

deriving identity - need help! Homework Statement Derive for S^{p}_{n} = 1^p + ... + n^p the identity (p+1)*S^{p}_{n} + (p+1 choose 2)*S^{p-1}_{n} + ...+S^{0}_{n} = (n+1)^(p+1) - 1 Homework Equations Um, I know that the S^{1}_{n} = n(n+1)/2 S^{2}_{n} = n(n+1)(2n+1)/6 S^{3}_{n} =...

Could someone show me exactly how to derive the quadratic equation from the least squares method? I have no idea where to start. I will appreciate it very much. Thankyou.

hello. i need help deriving trig formulas. the first problem i most derive is 51. sin^2 x + cos^2 x = 1 i can use these identities: a. sin(-x) = -sinx b. cos(-x) = cos(x) c. cos(x+y) = cosxcosy - sinxsiny d. sin(x+y) = sinxcosy + cosxsiny thanks for any help

Homework Statement I apologize for the blurriness in my title, I couldn't find anything better to fit within the length limit. The problem I'm stuck with, paraphrased, is to derive the formula for the diffraction pattern of a double slit, as found in the Young experiment, from the Fraunhofer...

Homework Statement "starting from the definition of tanhx in terms of exponentials, prove that... arctanh(x)=1/2log((1+x)/(1-x)) This is such a simple equation but I'm having a hard time proving it, can anyone help? Cheers Homework Equations The Attempt at a Solution

I am having trouble with this derivation. This is where I am at: \frac{d \left< p \right>}{dt} = \int \left[ \left( -\frac{\hbar^{2}}{2m}\frac{\partial^{2} \Psi^{*}}{\partial x^{2}} + V\Psi^{*} \right) \frac{\partial \Psi}{\partial x} + \frac{\partial \Psi^{*}}{\partial x}\left(...

On pages 16-17 of Griffith's Intro to QM, he writes the following: \frac{d\left\langle x \right\rangle}{dt}= \int x \frac{\partial}{\partial t}|\Psi|^{2} dx = \frac{i\hbar}{2m}\int x \frac{\partial}{\partial x} \left( \Psi^{*}\frac{\partial\Psi}{\partial x}- \frac{\partial\Psi^{*}}{\partial...

this lab is very similar to mine basically i can only seem to derive a portion of the formula, I=mgb/al - mb^2 where b- radius, g-gravity, al- angular acceleration. I do not get the right answer: here is what i did do however, Fnet=ma T-mg=-ma (acceleration is downwards) so T=(mg-ma) so then...

Homework Statement How would I derive Gauss' law for gravity from Newton's law?Homework Equations \mathbf{g}(\mathbf{r}) &=& -G\frac{m_1}{{\vert \mathbf{r}\vert^2}}\hat{\mathbf{r}} to \nabla\cdot\mathbf{g} = -4\pi G \rhoThe Attempt at a Solution I have no reference material outside the wide...

So I am trying to derive the continuity equation: \frac{\partial}{\partial x^{\mu}}J^{\mu} = 0 From the Dirac equation: i\gamma^{\mu} \frac{\partial}{\partial x^{\mu}}\Psi - \mu\Psi = 0 And its Hermitian adjoint: i\frac{\partial}{\partial x^{\mu}}\overline{\Psi}\gamma^{\mu} -...

[SOLVED] Amperes Law Homework Statement Deriving the magnetic field through a solenoid. Homework Equations dB = mu0/4pi x Idlsintheta/ r^2 where I = current dl= a tiny change in length dB = a tiny change in flux density sintheta is the angle to the normal r is the radius mu0 is the...

It's been a while since I've taken calculus. I was going through the derivation of the work-energy theorem and came across this: dv/dt = (dv/dx)(dx/dt) which is supposed to be a result of the chain rule. Anyone care to explain and please simplify it as much as possible. Thanks!

Hey, Homework Statement How do you derive the equations of the parabola from the general equation of a Conic Section? Homework Equations General Equation of a Conic Section, {{{A}{{x}^{2}}}+{{B}{x}{y}}+{{C}{{y}^{2}}}+{{D}{x}}+{{E}{y}}+{F}} = {0} Where (for a parabola)...

Here are some papers on the covariant entropy bound conjectured by Raphael Bousso http://arxiv.org/abs/hep-th/9905177 http://arxiv.org/abs/hep-th/9908070 http://arxiv.org/abs/hep-th/0305149 It would be a significant development if the conjectured bound could be proven to hold in LQC...

As i know there are several diffrent way to derive the canonical equations. Some of them starts from a physical principle like Hamilton's principle or the Lagrange equations. But it can be derived also by simply make a Legendre transormation on the Lagrange function and then make...

help deriving this elliptical orbit equation?? Hi guys, this is my first post on these boards. just found out about this forum and I am really happy because i often find i need a place like this to ask questions and my prayers are answered! im a physics/computer science major in my second year...

Homework Statement An object of mass m is at rest at equilibirum at the origin. At t=0, a new force \vec{F}(t) is applied that has components F_{x}(t) = k1+k2y F_{y}(t)=k3t where k1, k2, and k3 are constants. Calculate the position r(t) and velocity v(t) vectors as functions of time. Homework...

Why does du/dT = Cv, and same for Cp? Also, i don't understand how Cp/Cv = v, where v is the specific volume. It is derived from: Cv + R = Cp, how is PV=nRT used to get from Cv + R = Cp to Cp/Cv = v? I know n is replaced by m/M to leave Pv=RT where R would equal R(universal gas const)/M...

So in my book, it derives the expression for power in a traveling transverse mechanical wave. P= Sqrt[(mu)F].(omega)^2.(A)^2 It reduces this from: P=k^2.omega^2.F.A^2.(sin(kx-omega.t)^2 Where all symbols are the standard ones in dealing with waves. Could someone please go thru how it...

Derive the following equation: (mV^2/r)cos(x) = mgsin(x) I don't know how you would exactly derive the equation but you can simplify it to: tan(x)mg = mV^2 /r You can also divide by the m and get tan(x)g = V^2/r ... Any help is appreciated.

Homework Statement I am doing some research and reading this: http://www.csuohio.edu/ece/theses/2004/Bhavin.pdf I don't understand how the equation 4.1.11 on page 67 is derived. Can anyone help clarify? Homework Equations (As in the pdf file) The Attempt at a Solution I have...

can anyone help me derive the poynting vector from energy density of electromagnetic waves? and how we obtain average value <S> thanks

I knew i should have paid more attention in class =/ anyways, We have been studying Newton's second law. And I have a question on my lab that asks for me to "derive equation for a (acceleration) vs F (force) and a (acceleration) vs m (mass)" a vs F and a vs M are two graphs which we did...

Deriving Expectations (i.e. means) I'm looking at my Introduction to Econometrics book and trying to figure out the derivations in the 2nd Chapter. First, E(Y^{2}) = \sigma^{2}_{Y}+\mu^{2}_{Y} The derivation goes like this: E(Y^{2}) = E{[(Y - \mu_{Y})+ \mu_{Y}]^{2}} = E[(Y- \mu_{Y})^2] +...

I'm trying to get from the magnetic vector potential \vec{A}(\vec{x},t) = \frac{1}{\sqrt{\mathcal{V}}}\sum_{\vec{k},\alpha=1,2}(c_{\vec{k}\alpha}(t) \vec{u}_{\vec{k}\alpha}(\vec{x}) + c.c.) where c_{\vec{k}\alpha}(t) = c_{\vec{k}\alpha}(0) e^{-i\omega_{\vec{k}\alpha}t}...

An extremely elementary question but... Lets say we had a spaceship sitting on Earth under the influence of gravity. Light travels from the ship's floor to the ceiling. An observer 'A' stands near the ceiling. Hence the light loses gravitational potential energy, and therefore decreases...

Homework Statement The De Broglie Wavelength of any object in motion is given by \lambda=\frac{h}{P} where h is Planck's constant and P is the body's momentum. for heavy masses this wavelength is too small to be observed, nevertheless it is still there... I have seen a derivation for this...

[SOLVED] Deriving the head-on collision equation in terms of v2' and v1' I think I'm having an algebra issue here, but how is the momentum equation (where v2=0): m1(v1-v1')=m2v2' combined with v1+v1'=v2' to give: v2' = v1 [ 2m1/(m1+m2)] and v1' = v1 [(m1-m2)/(m1+m2)] I'm...

Something has always bothered me about the way the de Broglie relation is derived and I've never seen anyone address this, so I'm hoping someone here can. As I understand it, the derivation begins with two of Einstein's equations: E=hf, and E=pc. E=hf was experimentally obtained by Einstein...

Homework Statement Derive the equation for angular frequency for simple harmonic motion of a spring. Homework Equations Derive omega = sqrt(k/m) from F = -kx (sorry i don't know how to use notation) The Attempt at a Solution I asked my teacher how to do this, and he used some...

This is probably more Calculus than it is physics. The voltage at a point X produced by a uniformly charged rod is V = (Ke*Q/l)*[ln(l+sqr(l^2+a^2))-ln(a)], in which point X is right above the left end of the rod by a distance a, l is the rod's length, Q is the charge of the rod, and Ke as the...

If the Ricci-scalar R is constant for a given spatial hypersurface, then the curvature of that region should be homogenous and isotropic, right? A homogenous and isotropic hypersurface (disregarding time) has by definition the following line element (due to spherical symmetry): d\sigma^2 =...

Homework Statement I am trying to show how the Lorentz factor is derived but i am unsure how to get past a certain stage.. 2. Homework Equations / attempt Let: c = velocity of light. v = the velocity as observed from where time t is measured. D = distance AB. t = time light occupies to...

Homework Statement Derive... x(t)=(exp^(-\zeta\omegat))*(a1(exp^(i\omegasqrt(1-\zeta^2)*t)))+a2(exp^(-i\omegasqrt(1-\zeta^2)*t)))) into x(t)=(exp^(-\zeta\omegat))*(A sin (\omega*t + \varphi)) Homework Equations n/a The Attempt at a Solution I've managed to get x(t) =...

Hello, First post. Thank you for letting me be a part of the discussion. My question is, can the Law of Conservation of Energy, http://upload.wikimedia.org/math/2/7/3/273abc16486177bf6cc4c8ec4a4a5fc9.png, be derived using E=MC2. I understand that the E=MC2 can be derived using the LoCE...

I have been trying to show that the Einstein ring radius R_e = 2[GMx(L-x)/(Lc^2)]^1/2 to no avail. can someone who knows this show me, or at least point out the direction. I have a strong hunch that i'll have to use the light bending formula for small angles
delta_phi = 4GM/(bc^2), and...

Homework Statement I found on Wikipedia the formula for energy density of an electric field in a vacuum to be U = \frac{1}{2}\epsilon_0 E^2. I was wondering if someone could point me in the right direction to figure out how this was derived. Homework Equations The Attempt at...

Ok, so I'm really at a loss as to how to do this. I can prove the formula by just using determinants, but I don't really know how to do manipulations with the levi-civita symbol. Here's what I have so far: (\vec{B} \times \vec{C})_{i} = \epsilon_{ijk}(B_{j}C_{k})\vec{e_{i}} And I'm...

Homework Statement I have a problem that asks to derive the doppler effect for the two different cases of a moving observer and a moving source. Homework Equations I should get f' = f*(v +/- vo)/(v +/- vs) as my general equation, where f' is the observed frequency and f is the...

Projectile Motion! Please Help! Homework Statement The acceleration due to gravity can be measured by firing a projectile upward and measuring the time it takes to pass two given points in both directions. The figure below is a plot of height versus time and shows that the time the...

Homework Statement There is a uniform electric field E, and a uniform magnetic field B in space. A particle of mass m, and charge q, at the origin is released from rest at t=0. The only acting force on the body is the Lorentz force. Derive the trajectory of the particle for t>=0. Homework...