deriving Definition and 962 Threads

1. An object of mass, M, is projected into the air with an initial vertical component of velocity, Vo. If the air resistance is proportional to the instantaneous velocity, with the constant of proportionality being, K, derive the equations for the displacement, velocity and acceleration as...

Hi there, i would like everyone to evaluate my working here, this is my attempt to wave equation / vibrating system using vector approach. please correct me if i had made some mistakes. Your help is much appreciated, Thanks, and have a nice day. :smile: Regards, Daniel.

hi, I have a very simple question. I am reading Bernard F. Schutz's A first course in general relativity. after completing the special relativity section I had a goal to sit down with paper and completely derive from square one the lorentz metric, four velocity and momentum, and finally come up...

Homework Statement See the attachment please. The Attempt at a Solution I know the v1 x delta (t) is for the rectangle, I don't see how the second part works? I don't understand why the t^2 and how a replaces the area formula i have written. Thanks for your help, its my...

Hey. I want to derive the conductivity of graphene. I'm looking for a formula of the sort: J = \frac{e}{\hbar} n \frac{dE}{dk} D(E) \Delta E where \frac{1}{\hbar} \frac{dE}{dk} is the electron velocity, D(E) = \frac{dN}{dE} is the density of states, \Delta E might be the applied voltage...

Hello, I read some fluidmechanics and there was something I didn't understand. The shear stress in a Newtonian fluid is tau=viscosity*dV/dy, (no need to be dy, but dx and dz also can do.) A shear component called tau(xx) came up, I have two questions about this component: 1. Shear is...

Could someone help me with this. In pipe flow show that the average velocity is half of the maximum velocity. I have it written in my notes that this is true, but not how to derive it.

Homework Statement Consider the Proca Lagrangian L=-\frac{1}{16\pi}F^2-\frac{1}{c}J_{\mu}A^{\mu}+\frac{M^2}{8\pi}A_{\mu}A^{\mu} in the Lorentz gauge \partial_{\mu}A^{\mu}=0 Find the equation of motion. Homework Equations F^2=F_{\mu\nu}F^{\mu\nu} The Attempt at a...

This formula (E = V/d) has been used to derive the value of capacitance...but how is this applicable?...this is for point charges and here we're dealing with plates. Any derivation to prove this is also applicable for plates?

OMG second time I'm opening a thread in the wrong forum FFS! Damn bookmarks! MODS move it please. Homework Statement Not a home work question, just something i cam across and need a clarification. Could One show me how to derive to the equation that X(cm)=int(X dm)/M int=the deformed S of the...

Hi Folks, I have a quick question about the Biot-Savart Law, I know what it is, but I don't know how to derive it. Could anyone give me either links or show me the derivation with origins. I have tried to google it but to no avail. Thanks in advance for all your help in advance Kipper

Homework Statement Hi, I am trying to write the sum and output of a full adder in terms of XOR logical functions using boolean logic and Karnaugh maps. I've got the expressions from the Karnaugh maps fine but I can't seem to rearrange them into the expected form shown at the end of my...

Homework Statement I must derive Torricelli's law. Homework Equations P+\rho gh +\frac{\rho v^2}{2} = \text{constant}. The Attempt at a Solution I chose the origin of the system as being on the surface of the liquid. I have that P_0 = P_1+ \frac{\rho v_1^2}{2}. But P_1=P_0+\rho...

Im aware that the generalised form of the Marcum Q function, which is Q_{M}(\alpha,\beta)=1/(\alpha)^{M-1}\int_{\beta}x^{M}.exp(-x^{2} +\alpha^{2})/2.I_{M-1}(\alphax)dx and the pdf of the amplitude in rice distribution is f_{r}(r)=r/\sigma^{2}exp( (-r^{2}-A^{2})/2\sigma^{2}...

Hi. I'm trying to derive a = (v^2)/r from the position of a particle moving in a circle. Since the equation for a particle moving in a circle is x(t) = r(isin(wt) + jcos(wt)) where w is constant. I took two derivatives to find it's acceleration. I got a(t) = -rw^2(icos(wt)+jsin(wt)). Now I'm...

Homework Statement Sort of stuck deriving the Klein-Gordon equation from Heisenberg equation of motion \dot{\varphi} = i [H, \varphi ] Homework Equations \dot{\varphi} = \frac{\partial\varphi}{\partial t} H = \int d^3x \mathcal{H} \Pi (x) = \dot{\varphi}(x) \mathcal{H} = \Pi...

Homework Statement Problem is this. I am tasked with deriving a formula or equations that I can then input into an excel format. I am to take an equipment base that has four sides with supports at each of the four corners. I am to find the load that each one will hold base upon the Center of...

Homework Statement We know that T(2)=1, and T(n+1)=1+2T(n), i.e. T(3)=1+2*1=3, etc. Derive a formula for T(n) from above information. Prove the formula by mathematical induction. Homework Equations ?? I don't think there are any apart from the stuff from above. The Attempt at a...

Homework Statement Derive an expression for the radius of a satellite's orbit around Earth in terms of the period of revolution, the universal gravitation constant, and Earth's mass. Homework Equations The final equation should be: r = \sqrt[3]{\frac{T^{2}Gm_{E}}{4\prod^{2}}} The...

Homework Statement I want to show that: \arccos \,z= \left( -1 \right) ^{n+1} \arcsin \,z+\pi/2\, +n\pi Homework Equations There is a trigonometric identity that says \arccos \,z= \pi/2\, -\arcsin \,z The Attempt at a Solution So far, I have come up to this...

Hi all, I'm studying on the current transfer at quantum level and I have a point that is not so much clear. While reading the Fermi sphere from the book "Current at the nanoscale", I could not understand the expression: The number of electrons in the conductor, N, is the ratio of the...

I'm having a problem with that integration part. The average value of i^2 in one cycle = (sum of all i^2 in that period)/(that period). To derive (sum of all i^2 in that period) we use integration, but that gives the area, how can the area be a substitution for this?...they are different...

Homework Statement Consider 2 magnetic masses, m1 and m2; these 2 repel each other for a distance s with force f (relative to each other)...which applies from m1 to m2. Predict final velocity of m1 and m2. Assume final distance to be v1 and v2 Assume the 2 masses at rest initially...

Some confusions from some recent lectures; I asked the prof, but I still don't fully understand what is going on. We began with the action (tau is some worldline parameter, dots indicate tau derivatives; they are hard to see): S = \int d\tau \; \left\{ \dot x^{\mu} p_{\mu} - \frac12 e(\tau)...

Hi, first post here. I've been trying (out of personal interest, not homework) to re-derive http://www.springerlink.com/content/mm61h49j78656107/" relatively famous calculation on the ground state of Helium from 1929. And I'm stuck at one point. What Hylleraas did, was to parametricize the...

Derive formula #5 using any of the other formulas 1. Vav= d/t 2. Aav= V2-V2/t 3. d= (V1+V2/2) t 4. d= V1t + 1/2 a t squared 5. V2 squared = V1 squared + 2ad *note all the Vav, Aav, a and d have a vector sign ontop and d and t always have the triangle representing change in

I play an online shooter game with artillery that players can use. As best I can tell, the shell exits the artillery at 400m/s, I don't know if that's correct because units aren't listed in the code but it sounds logical. I know the distance to target as well, I only need to know what angle to...

The Problem: Using V2x=V1x+ax(deltat)t and (delta)x=V1x(delta)t + 1/2ax(delta)t^2 derive the formula V2x^2=V1x^2+2ax(delta)t Homework Equations 1st and 3rd x-component Kinematics Equations The Attempt at a Solution Ok, so I attempted to solve it, but it didn't work. I don't want...

There's a flaw in my logic, and I cannot find it. Ok, all you are allowed to use is Charles' Law (V/T = K) and Boyle's Law (PV = K) and you have to derive an equation relating pressure and temperature. V = kT V = k/P kT = k/P PT = 1 Therefore P1T1 = P2T2 But, this is the...

Homework Statement Derive the Following Equations: c = [(m_w*c_w + m_c*c_al) (T_e - T_i)] / m_s*(T_s - T_e) and L = (m_w*c_w + m_c*c_al) * (T_i - T_e) - m_I*c_w * [(T_e- T_m)/m_I] Homework Equations T_i - initial temp of water and calorimeter T_m - melting temp of ice T_e -...

Homework Statement Derive from Demoivre's theorem that cos2theta=(costheta)^2-(sintheta)^2 sin2theta=2sin theta costheta Homework Equations The Attempt at a Solution I really am clueless on this. I considered using (costheta +isintheta)^n, but don't know where to go with this idea.

Hi, everyone:) In my mechanics book a derivation is given for acceleration in rotating reference frames. However, there is one step I don't understand. First of all, it is derived that v=v'+\omega\times r' or \left( \frac{dr}{dt}\right) _{fixed}=\left( \frac{dr'}{dt}\right) _{rot}+\omega\times...

I need help with the electric field of a line of charge, a ring, semicircle, a line of charge at a point that bisects the line of charge, and a uniform disc. The teacher showed us how to derive those equations but he does it so fast that I didn't have time to copy them down. Even if I did I...

Maybe this counts as computational physics, or statistics I don't know where this topic belongs. Ok so I have this nice high quality Thermodynamic measurement data and I have to start the "data raping" for results. Let's call the series A(t), and B(t) and I have a few more. So for different...

In Wheeler and Taylor's 'Exploring Black Holes', on pages 3-12 and 3-13, the bookkeeper measure of radial velocity (i.e. radial velocity as measured from infinity) is derived. Basically the equation for 'Energy in Schwarzschild geometry' is established-...

I'm a PhD student (not in physics) working on a research problem where I need to use the Lagrangian/Hamiltonian approach for a problem. Suppose I have a particle/object that I can track the location/trajectory of; is it possible for me to derive or enumerate Hamilton's equations for that...

Hello, I think I've got the right idea on how to perform this question but I just need a little bit of help. Homework Statement Show that for a rigid body rotating with angular velocity \omega the energy of rotation may be written as: E = \dfrac {1}{2}I\omega^{2} where the moment of...

Homework Statement For 0<t<1, v(t) = t +3 For 1<t<2, v(t) = 5-t Assume x(o)=0 A) Draw corresponding displacement and acceleration diagrams. B) Determine the equation for each segment Homework Equations Acceleration is the derivative of velocity. Velocity is the derivative of...

Hi Sorry this may be an obvious one...can anyone help me with getting from the first to the second equation below? I'm particularly stuck with manipulating the terms inside the summations formulas. I can derive to here: \sum_{i=1}^{N}x_iy_i - N\bar{x}\bar{y} - \left(...

Homework Statement Using equations #1 and #2 to derive equation #3 Homework Equations #1- ∆x = (b/2)theta #2- ∆z= L (2theta) #3- ∆x= ∆z b/4L The Attempt at a Solution Now I set equations #1 and #2 equal to each other, but I'm not sure how the thetas end up cancelling or if I'm even...

HI I need help with the steps in between? I am totally confused... So, how to derive the final equation from equation 1 and 2 m1v1i+m2v2i=m1v1+m2v2f (Equation 1) 1/2m1V1i^2+1/2m2v2i^2=1/2m1v1f^2+1/2m2v2f^2 (Equation 2) v1i-v2i= -(V1f-v2f) ( Final Equation)

Homework Statement I need to derive an error equation from the following equation... \frac{e}{m} = \frac{2V}{B^{2}R^{2}}Homework Equations Just... basic... derivation rules...The Attempt at a Solution I did try, just don't know how to put the stupid attempt in LaTeX... I'm stuck at the "2V"...

Homework Statement I need to find the Planck's law: R(\lambda)=\frac{2hc^2}{\lambda^5}\frac{1}{e^{\frac{hc}{\lambda kT}}-1} Homework Equations The Attempt at a Solution I've done most of the derivation, but I got stuck with an integral: R(\lambda)=\frac{1}{4\pi^3 \hbar^3 c^2}...

Homework Statement 2x^2+5xy-y^2=1 Homework Equations d/dx(f(u)x))=df/du * du/dx The Attempt at a Solution i got (2y-4x)/5x but I'm almost certain that its wrong...can anyone help me?

I am trying to derive the electromagnetic wave equations from Faraday's law of Induction, and the Ampere-Maxwell law. But, I am having a problem with the 1/c^2 disappearing. This is what I am using: \nabla\times\vec{B}=\mu\vec{J}+\mu\epsilon\stackrel{\partial\vec{E}}{\partial t}...

Hi all, There are a few doubts I hope I can get enlightened. If we were in a lab in outer space, free of gravitational influence and the lab accelerates downwards, what will we experience? do we 'move' to the top of the lab? What I'm confused about also is, why is that when you have an...

When setting up this derivation one assumes a chain of identical atoms. The interatomic interaction between atoms is short ranged and so only affects neighbouring atoms (see Hook and Hall, "Solid State Physics" chapter 2.3.1). The potential V(r) is expanded as a taylor series about r = a to...

Homework Statement Find the commutators [P^\sigma,J^{\mu \nu}] The answer is part of the Poincare algebra [P^\sigma,J^{\mu \nu}]=i(g^{\mu \sigma}P^\nu-g^{\nu \sigma}P^\mu) If someone can convince me that \partial_i T^{0\mu} = 0, (i.e. the energy-momentum tensor has no explicit spatial...

When working with Fourier transforms in Quantum mechanics you get the result that \int_{-\infty}^{\infty}e^{-ikx}e^{ik'x} = \delta(k-k') I understand conceptually why this must be true, since you are taking the Fourier transform of a plane wave with a single frequency element. I have also...

Homework Statement Derive the error expression \delta v_{}x from the equation v _{x}=\frac{s}{sqrt(\frac{2h}{g})} The Attempt at a Solution I've derived error expressions before, but I have a history of getting the calculations right and the error equations wrong. So, if possible I'd...