Derive Definition and 620 Threads

Homework Statement Using dimensional analysis deduce the relationship between the pressure drop per unit length along a cylindrical pipe of radius r, and the radius of the pipe, the viscosity of the fluid in the pipe, η, and the volume flow rate, V ̇ . Homework Equations Δp/l = 8ηV...

Homework Statement Derive Stefan-Boltzmann law from Wien’s law Hint: you can use (without proof) R(T) = -∞∫∞ R(λ,T)dλ , ρ(λ,T)=(4/c)*R(λ,T) Homework Equations wien's law: p(λ,T) = f(λ,T)/^5 Stefan's law : R(T) = σT^4 The Attempt at a Solution Honestly I am having trouble just...

Homework Statement Both Newton's gravitational law and Coulomb's law are inverse-square laws: The force of attraction between the sun (S) and Earth(E) has (G*m_S*m_E)/r^2, whereas the force of attraction between an electron and a proton in a hydrogen atom is (e^2)/(4*pi*epsilon_0*r^2). Derive...

Phase difference between clocks with distance Homework Statement Derive Phase difference between clocks with distance Homework Equations I honestly don't understand how this equation ΔT = vD/c2 is derived/figured out. The Attempt at a Solution We haven't covered Lorentz...

Good day! I am a beginner in Finite Element Analysis and Structural Mechanics. I have problem in understanding the insight of potential energy approach to derive spring element equations. I have already search for similar post and I found this, and agree with the example raise...

Here is the working leading up to this: The circuit is a series circuit, with Ro being the circuit's internal resistance and Rh being the heater's resistance. We're only concerned about the power transfer to Rh. We have an input with a constant voltage V. Ohm's law: V = IR, where R is the...

Edit: well this is frustrating, not sure why the itex things aren't working.. Edit2: I've attached a picture of the question at the bottom as well. Homework Statement The cohesive energy of a solid noble gas may be written as (See picture below) Derive an expression for the...

Homework Statement Derive: R=v^2sin2theta/g Show that R=V0^2/g Homework Equations The Attempt at a Solution This is my first time to take up physics so I have no idea at all on how to do this, to be honest.

Differentiation by first principles is as followed: $$y'=\lim_{h\rightarrow 0}\dfrac {f\left( x+h\right) -f\left( x\right) }{h}$$ So, assuming that ##y= e^{x},## can we prove, using first principle, that: $$\dfrac{dy}{dx}\left( e^{x}\right) =e^x$$ Or is there other methods that are...

Homework Statement Why can't you do integration-by-parts directly on the middle expression in equation 1.29--pull out the time derivative over onto x, note that \displaystyle \frac{\partial x}{\partial t} = 0, and conclude that \displaystyle \frac{d \langle x \rangle }{dt} = 0Homework Equations...

According to wikipedia, "The moving magnet and conductor problem", I stopped at the equation shown in the attachment. It said that the curl of the E` ( electric field in the frame of the conductor) is equal to minus of the dot product of the velocity of the conductor and the del multiplied by...

Given a sphere x^2 + y^2 + z^2 = a^2 how would I derive the surface area by using surface integrals? The method I've tried is as follows: dA = sec\ \gamma \ dxdy where gamma is the angle between the tangent plane at dA and the xy plane. sec \gamma = \frac{|\nabla \varphi|}{\partial \varphi...

Homework Statement I try to derive the expression of ω with respect to t, but the problem is the armature current Ia or the flux is unknown. I don't know how to solve it. Anyone could give me ideas? Thanks a lotHomework Equations τ=J(ω/t) Vs=IaRa+Ea T=KEøIa Ea=KEøω

Hi guys, I need some help on this question: Derive the van der Waal interaction potential between 2 spheres of radius R_1 and R_2 using the Hamaker approach. Take the distance between the center of each sphere to be D. Thank you very much for your help!

I'm wondering how one solves for the quantum harmonic oscillator using matrix methods exclusively. Given the Hamiltonian \hat{H} = \frac {1}{2m} \hat {P}^2 + \frac {1}{2} m \omega ^2 \hat {X}^2 and commutator relation [ \hat {X} , \hat {P} ] = i \hbar \hat {I} is that enough for premises...

Homework Statement This is a 3 state machine with one input variable. The input given for x produces the output sequence for z. The machine starts in state A. I am asked to derive the state table. x=010001010010010011010 A z=001000000001001000001 Homework Equations The Attempt...

Hello there, If a mass, m, is placed at one end of an boat of mass M, which is located on a frictionless ocean. If the mass, m, is moved from one end of the boat to the other end, conservation of center of mass position ensures that the boat shifts a small distance in the opposite direction...

I'm not sure if I can ask this question clearly, but anyway... We have this collection of 17 or so particles. Some of them have been known to exist for a very long time and were found when physics was still in its relative infancy, because they were trivial to detect and distinguish. I'm...

I need some help with an equation. I will use to find the value of acceleration due to gravity. With a air track and a spring attached to a glider we should find the value of "g". The track is inclined and with two different equilibria (which are achieved by using two different masses on...

So for starters the area of an entire circle has 360º,right? So we can say that: ##1∏r^2## is ##\equiv## to ##360º## So by that logic ##0.5∏r^2## is ##\equiv## to ##180º## And finally ##0.25∏r^2## is ##\equiv## to ##90º## Divide both sides by 9, and you get : ##0.25∏r^2/9## is...

Homework Statement Derive the energy equation for a van der Waal gas when T and v are the independent variables. Homework Equations I'm required to start from: du=\frac{\partial u}{\partial T} dT +\frac{\partial u}{\partial v} dv The Attempt at a Solution We'll when I first...

Homework Statement Actually this is not from homework. It occurs in my brain this afternoon. Is it possible to derive the analytic expression of a function by its Taylor series expansion? For example, given the following expansion, how to derive the analytic expression of it? f(x) =...

It's easy to get a function from a table that follows a clear pattern, but what if the values for y (or x) don't follow a pattern? For example; x = 1 , y = 13 x = 2 , y = 9 x = 3 , y = 3 x = 4 , y = 8 x = 5 , y = 1 x = 6 , y = 5 x = 7 , y = 12 If you look at these points on a graph...

1. For the past 1 hour, I'm trying to derive lens maker's equation using fermat's principle, which of course is our homework. Any help would be great regarding the topic. 2. According to Fermat's Principle, optical path length OPL = PA + AQ, here PA and AQ are two rays. Now using this I...

Guys, My calculus is really rusty and I need help solving this equation using a time derivative (denoted with a dot) in order to get the relativistic equation of motion for the Universe The equation is: adot^2 = Λc^2a^2/3 where adot is the time derivative of the scale factor, lambda...

Is there any way to derive an equation for compound interest based on effective interest rate instead of the nominal interest rate?

Homework Statement Show that the experiment depicted in Figure 2.11 and discussed in the text leads directly to the derivation of length contraction. Figure 2.11: Homework Equations d=v*t Requested result: L=L0\sqrt{1-\frac{v^2}{c^2}} The Attempt at a Solution In K the...

Homework Statement Assume that the center of mass of the Earth moves with approximately constant velocity with respect to the fixed stars, and that \mathbf{\omega}, the angular velocity of the earth, is constant. Rederive the terrestrial equations of motion...

Homework Statement Derive from the uncertainty principle a formula for the relative spread of the spectral line that corresponds to the longest wavelength of the Lyman series. Homework Equations uncertainty principle: σxσp≥\hbar/2 planck constant \hbar=h/2pi h=λp Lyman series...

The calculation for the maximum bending moment is to be verified experimentally using a strain gauge bonded to the outer surface of the beam, at the point where the maximum bending moment occurs. Derive an equation which could be used to calculate the bending moment from the measured strain...

Homework Statement Find the general solution for the current I(z,t) associated with the voltage V(z,t).Do this by substituting [1] into [2] and [3], integrate with respect to time, and then take the derivative with respect to z. Homework Equations V(z,t)= f+(t-z/vp) + f-(t+z/vp) [1]...

The following is the Planck's derivation for black body radiation $${\rho}({\lambda}) d{\lambda}=E({\lambda})*f({E(\lambda}))*D({\lambda})d{\lambda}------equation 1$$ $$\int_0^\infty{\rho}({\lambda})d{\lambda}$$ is the density of radiative energy. From...

Homework Statement The calculation for the maximum bending moment is to be verified experimentally using a strain gauge bonded to the outer surface of the beam, at the point where the maximum bending moment occurs. Derive an equation which could be used to calculate the bending...

This is a revision question rather than homework as I have the answer and working. I have attached the block diagram and first part of the answer which explains how to derive the transfer function from first principles. I understand the principles behind this and how the RHS of the equation...

Homework Statement [/b] The attempt at a solution[/b] I have done the first bit but don't know how to show that phi(r,t) is a solution to the equation of motion.

Homework Statement Hello! I have two graphs which I need to find if there is relationship between them (all in one). I have to create a formula/equation that can show and prove that there is this relationship between them.I am really confused at the moment since I do not know if there is...

Hi there, I'm trying to derive the following equation, but despite internet searching haven't been able to figure out what to do with the multiplier, D. D * dθ/dz + k = C I need to derive the equation and then plot the graph θ(y-axis) against z (x-axis). Any help greatly appreciated...

Hello all, In Carroll's there is a brief mention of how to get an idea about the curvature tensor using two infinitesimal vectors. Exercise 7 in Chapter 3 asks to compute the components of Riemann tensor by using the series expression for the parallel propagator. Can anyone please provide a...

Hi, We have: \beta(a,b)=\int_0^1 t^{a-1}(1-t)^{b-1}dt,\quad Re(a)>0, Re(b)>0 and according to Wikipedia: http://en.wikipedia.org/wiki/Pochhammer_contour we can write: \left(1-e^{2\pi ia}\right)\left(1-e^{2\pi ib}\right)\beta(a,b)= \int_P t^{a-1}(1-t)^{b-1}dt valid for all a and b where P...

Homework Statement Derive from Maxwell's equations these Hill equations for 's' and 'p' mode waves; s\hspace{3mm} modes: E(r,t) = \Psi_{s}(z)e^{i(\beta x - \omega t)}y \\ \hspace{10mm}Hill\, Equation for\, \Psi_{s}(z)\\ \hspace{17mm} \dfrac{d^{2}\Psi_{s}(z)}{dz^{2}} +...

Homework Statement http://imageshack.com/a/img580/682/z3mt.jpg Derive a linear differential equation for the above LTI system. Homework Equations i_C=C\frac{dV_C(t)}{dt} V_L=L\frac{di_L(t)}{dt} The Attempt at a Solution Using KVL, I can get the following equation...

Can someone explain this proof of the moment of inertia of a sphere? And how you can use the same principals to solve for other formulas? https://www.physicsforums.com/attachment.php?attachmentid=62987&stc=1&d=1381895479http:// I understand each individual variable. But I don't understand...

can you show me derive cross product from dot product?

Homework Statement Derive the equation v^2 = u^2 + 2as I have no clue how to do this please can someone help! Thank you!

Homework Statement Derive the differential equation from the following circuit Homework Equations The solution needs to be a differential equation in standard form, so that I can solve the equation for the characteristic modes, zero-input response, zero-state response, etc. The...

Can anyone derive the p.m.f. of Poisson distribution without mentioning the binomial distribution? The binomial deriving method put lambda = np and finally the binomial p.m.f. become the Poisson one as n goes to infinity. It seems that this is only proving that binomial distribution will...

Hi, i am trying to develop a CDF from a given MGF. The standard way of using the inverse Laplace transform etc.. is not feasible due to complexity of MGF. I was woldering if there is another straighforward direction via integration or differentiation method to produce the CDF (or PDF)...

Homework Statement The formula for divergence in the spherical coordinate system can be defined as follows: \nabla\bullet\vec{f} = \frac{1}{r^2} \frac{\partial}{\partial r} (r^2 f_r) + \frac{1}{r sinθ} \frac{\partial}{\partial θ} (f_θ sinθ) + \frac{1}{r sinθ}\frac{\partial f_\phi}{\partial...

Homework Statement Derive he Laplace Transform of the third derivative of f(t). Homework Equations The Attempt at a Solution So, I'm not at all sure how to do this. I think I can start with: L{f'''(t)} = But I'm honestly not sure how this works. Any guidance would be...

Homework Statement 1. (a) Find the equation of the circle with the straight line joining A(1;-1) and C(3; 4) as diameter. (b) Hence or otherwise, derive the general formula (x - x1)(x - x2) + (y - y1)(y - y2)=0 of the equation of a circle for the points A(x1; y1) and C(x2; y2): Homework...