Derive Definition and 620 Threads

Homework Statement A truck of mass M and a car of mass m are traveling at the same speed. Suppose M>m. Now the drivers of both vehicles suddenly apply their brakes and the vehicles slide along the road, which has coefficient of kinetic friction uk. the car stops after sliding a distance d...

Homework Statement 1. Derive the Gibbs function g(T,P) for dry air. T = temp, P = pressure 2. Derive the speed of sound (c) from the Gibbs function. Plot c as a function of temp and pressure. Homework Equations c = gp*squareroot(gTT/(g^2TP - gTT*gpp) I wasn't sure how to type it in...

Hello, I just need help deriving the fundamental equation from Equation of state for wan der waals fluids. P=\frac{RT}{v-b}-\frac{a}{v^2} and u=cRT-\frac{a}{v} where a,b, and c are constants. I know the fundamental equation is dS=\frac{1}{T}dU+\frac{P}{T}dvI solved the u equation so it's...

Homework Statement I was trying to figure out how to derive acceleration in spherical coordinates, and I realized that I need to find the projection of each spherical unit vector [ e(r), e(θ), and e(φ)] onto each Cartesian unit vector [î, j, and k], but I'm not quite sure as to how to do that...

Homework Statement Obtain the accelerations of mass a and mass b. Homework Equations Once i derive the displacement relation constraint, then i just have to diff twice w.r.t time. This part is ok. The Attempt at a Solution I am trying to reason this way: suppose 2M moves up by x...

Homework Statement consider the cascading of two non identical amplifiers stages, each having a low-pass STC frequency response. STage 1 has a low freqency gain of ALF1 and a 3 dB frequency of f1. Stage 2 has a low frequency gain of ALF2 and a 3 dB frequency of f2. Derive a polynomial...

Homework Statement Show how W= (P2V2 - P1V1) / \gamma -1 can be derived using relations between PVgamma = constant, and W(1 to 2) = -\int P(T,V) dV (from v1 to v2). Homework Equations I think we can use R = Cv (\gamma - 1) The Attempt at a Solution Not sure how to start. The...

Homework Statement Show that if a single-component system is such that PVk is constant in an adiabatic process (k is a positive constant) the energy is U = [1/(k-1)]PV + Nf(PVk/Nk) where f is an arbitrary function.Homework Equations Fundamental relation: U = [1/(k-1)]PV + Nf(PVk/Nk). State...

Homework Statement Derive an expression for the current I(t) as a function of time for the following circuit: ____ \____ |..... | &..... - & .....- | ...| ___________ This circuit may be a bit unclear - the && is an inductor L, the - - is a capacitor C, and the top part is a switch that is...

Hi all, I need to derive the space state form of this simple system: http://imageshack.us/photo/my-images/856/system.png/ The two springs end are moving. I derived the equation fo motion: m*ddxm+kl*(xm-xl)+ku*(xm-xu)+cl*(dxm-dxl)+cu*(dxmdxu) where ddxm is the mass acceleration dxm is the...

i.e. thank you very much in advance

Homework Statement Derive the Sellmeier equation n^{2} = 1 + \frac{A\lambda^{2}_{vac}}{\lambda^{2}_{vac}-\lambda^{2}_{0,vac}} from (n+i\kappa)^{2}= 1 + \frac{\omega^{2}_{p}}{\omega^{2}_{0}- i\omega\gamma - \omega^{2}} for a gas or glass with negligible absorption (i.e. \gamma ≈ 0...

How to derive expresssion for coefficient of kinetic and static friction?

Hello, I have a problem with divergence function DIV in DERIVE 6 and canot find anything in help and web forums either. #1. At first, I load utility "VectorMatrixFunctions.mth" #2. when I insert DIV([1/r^2, 0, 0], spherical) I obtain ZERO But it seems wrong, f.e. for Gravitation we...

The Relation between Levi-Civita Density and Kroneckers Delta as follows \sum^{3}_{k=1} \epsilon_{mnk} \epsilon_{ijk} = \delta_{mi} \delta_{nj} - \delta_{mj} \delta_{ni} Logically we can satisfy both sides of the expression but Can anyone tell me how to derive this analytically ?

Homework Statement "Maxwell showed that we can easily do a dimensional analysis on mass, using only Newton’s equations. Mass is [length]^3 [time]^-2 ." (http://milesmathis.com/coul.html) I would like to know how to do the dimensional analysis and derive M = L^3 T^-2. 2. The attempt at...

Homework Statement Derive equation of torque: G = p X E from equation U = -p\cdotE Homework Equations G = \int x \times \rho(x)E dV U = \int \rho(x)x \cdot \nabla\varphi dV The Attempt at a Solution I tried to figure how to represent G in a way that better express the nature...

Let \;\vec r\;'\; be position vector pointing to the source. \;\vec r\; be the position vector pointing to a field point. Therefore the distance from the source and field point is: \vec {\eta} =\vec r -\vec r\;' \;\hbox { and }\; \eta = \sqrt{r^2+r'^2 - 2rr'cos\theta}= r \sqrt{1+\left...

Homework Statement Derive equation (1) from equation (2): (1) \nabla \cdot D = \rho_f (2) \nabla \times H = J + \frac{\partial D}{\partial t}Homework Equations [PLAIN]http://img198.imageshack.us/img198/4645/maxwell.png The Attempt at a Solution \nabla \times H = J + \frac{\partial...

because it seems the Lorentz transformations constitute special relativity itself

Hi! I am looking for some help using Derive. I have a differential equation, you can see it in the third image (I wanted to use LaTeX to render it but apparently I can't post LaTeX in this section of the forum). The value of lambda is given in the first image. I know the function...

?How to derive the equation of motion F=ma, given this info Homework Statement http://img861.imageshack.us/img861/1557/2009b5a.gif Homework Equations The Attempt at a Solution Is my attempted solution correct? [PLAIN][PLAIN]http://img42.imageshack.us/img42/2465/2009b5asol.gif

Hi I would appreciate some help on this question please. Derive the basic equation for the voltage across a capacitor as a function of time for a circuit that includes a resistor and capacitor connected in sereis to a battery through a switch. I know the formulas but haven't the slightest...

I know the derivative of arcsin and that I should use the chain rule, but I was wondering if I should use (1 - 2 e ^-t) for the chain rule portion?

Is it possible to derive a formula for the equivalent resistance of n such sections in cascade? Show your analysis. Series: Reqv = R1 + R2 +...Rn Parallel: Reqv = 1/{(1/R1) + (1/R2) + (1/R3) +...(1/Rn)}

r' = 4r - rf f' = -3f + rf In this question, there was three parts: a) find all the critical points of this system. b) Derive the linearised system about each critcal point... c) Use the chain rule to derive the path equation of the trajectories in the phase plane. I managed to get a...

I am not sure how to format in LaTeX; I apologize for that. The Hermite polynomials Hn(x) (physicist's version) satisfy the recurrence relation, H_{n+1}(x) - 2xHn(x) + 2nH_{n-1}(x) = 0; H0(x) = 1 and H1(x) = 2x: Use this to derive the generating function for the Hermite polynomials...

Hi.everybody How do I derive viscosity equation F=6π*r*μ?

Homework Statement In Atkins's physical chemistry textbook it is written that Debye considered atoms to oscillate from 0 up to a nu max. It is explained further in the text that the complication (i.e., not all atoms oscillating at same frequency as shown in Einstein's formula) is accounted...

Could anyone derive an assertion found in "light and matter, a strange theory"? Feynman writes in his book that the propagator of the Klein Gordon photon is proportional to 1/(r2 - t2) Have you ever read the proof?

Putting together a spreadsheet to calculate the hydrogen spectrum, cannot seem to get the right mix of units to get the Rydberg constant of 13.605... eV also, what is the significance of R (1/n^2-1) converging to R as n gets large? can anyone put this together or refer me to a source that...

Homework Statement Using Fermat’s principle, derive the spherical mirror formula in paraxial approximation: \frac{1}{s_o} + \frac{1}{s_i} = \frac{-2}{R} where so and si are object and image distances, R is the radius of curvature of the sphere. Homework Equations As far as I know you...

This is a homework problem and I thought about putting it in the homework section bu since its very materials science specific I decided to put it here: For a transversely isotropic material, the “plane strain bulk modulus”, K23, is an engineering constant that is defined by the stress...

Homework Statement Imagine a narrow pipe, filled with fluid, in which the concentration of a certain type of molecule varies only along the length of the pipe (in the x direction). By considering the flux of these particles from both directions into a short segment \Deltax, derive Fick's...

Homework Statement Consider a star made up of ionized hydrogen. First, take the electrons to be non-relativistic. If the mass of the star is M, derive an estimate for the radius R. As the mass increases, how does the radius change Homework Equations p~(h2 /Me) n5/3 The Attempt at...

Apparently one can deduce the form of divergence in polar (and spherical) coördinates using the theorem of Gauss and Ostrogradsky, namely that the volume integral over the divergence is equal to the flux integral over the surface. I can't see a way to do that, do you?

Homework Statement Derive an equation that relates the velocity of a freely falling particle to its altitude. Assume that the particle is released from rest at an altitude from the Earth's surface. Express your answer in terms of the variables and , constant gravitational acceleration at...

1. Using V(x)= -max, in the following equation: \int_{x_0}^x \frac{dx}{\pm \sqrt{{\frac{2}{m}\{E-V\left( x\right)\}}}} \ = t - t0 to get: x = x0 + v0 + at2/2 E is total energy and V(x) is potential energy. I have tried hard integrating it in various ways but do not seem to get the...

After watching the video below, I came up with the idea of using a piece of paper as a keyboard much like Mistry did for a mouse. I am only in high school, but I'm sure you can measure position via sine waves which relates to the sin trig function (the reason I posted here; if wrong thread, mods...

I'm in my second year of a physics degree and my QM lecturer showed us how to calculate the RMS around the expectation of an operator by considering the E of a system in equal superposition of two energy eigenstates u_1 and u_2. He then says "This gives some measure of how far off we would be...

Homework Statement For a downtime analysis the spectrum of motion has to be calculated with the wave spectrum and the RAOs (given) for several frequencies. Given is a wave scatter diagram with the significant wave height (Hs) and the peak period (Tp). How convert the significant wave height...

Homework Statement Needs to be in TODAY (yeah I know I am cutting it close!) Derive an expression for the moment of inertia of the masses at the ends of the arms in terms of l, θ and m Is the example question asking for the derivative or is it asking to use the terms above in an equation...

I am reading the H. A. Bethe's book ---quantum mechanics of one and two electron atoms. In section 39, it is shown how to go from general form to pauli approximation form through momentum space. who knows how to go directly in position space?

How do we come to the formula for Conservation of Mechanical Energy? [Initial Kinetic Energy + Initial Potential Energy = Final Kinetic Energy + Final Potential Energy] It's not a part of our syllabus, but I'm just curious how to derive that formula. Also, could you please clarify to me...

Ok, I am really stuck on this one. I tried using the first principles formula and everything, but I don't get two separate terms like I am supposed to in the actual derivative. I always end up with -1/(3x-1)^2 when I try. Can someone please help me out?

Homework Statement Calculate the minimum radius ratio for CN = 3. Givens: Minimum radius ratio for CN = 4 is 0.225, so that's also the max for CN = 3. The Attempt at a Solution I know that the radius ratio determines the CN, which is related to the geometry, and that for a CN of 3, the...

What is the trick to derive the ideal gas law and gas constant from the "combination" of Charles', Boyle's, and Avogado's laws? The general chemistry books I have seen tell me this is how they derived the ideal gas law and constant but they do not show how that is achieved. I tried to go about...

x^2 y'' + x y' + n^2 y = 0 \; Is Euler equation and solution is y=x^m I understand the three cases with different solution. But my question is if n=0. If I use y=x^m \;\Rightarrow\; m(m-1)+m=0 \;\Rightarrow m^2 = 0 \;\Rightarrow m=0 That would not work. I know the answer is y=C_1...

[/tex]1. Homework Statement [/b] Given: \phi(x)=\phi^+(x)+\phi^-(x) Where: \phi^+(x)=\sum_{\mathbf{k}} \sqrt{\frac{\hbar c^2}{2 V \omega_{\mathbf{k}}}} a(\mathbf{k}) \mathrm{e}^{-\mathrm{i}kx} and \phi^-(x)=\sum_{\mathbf{k}} \sqrt{\frac{\hbar c^2}{2 V \omega_{\mathbf{k}}}} a^\dagger...

Homework Statement That's basically the whole question in the title there, ie; Derive an expression for the fermi energy of a 2d structure at 0 kelvin. 2. The attempt at a solution Basically the first part of the question had us sketching the Fermi-Dirac distribution function at 0K for...