Derive Definition and 620 Threads

[Mentor note: Thread moved from technical forums so no formatting template shown] Unfortunately, I'm completely lost with this question: 1. A particle is moving along the x-axis. Its position as a function of time is given as x=bt-ct^2 Derive an expression for the x- component of velocity...

i get stuck in how to find the magnitude of rotating vector . why say that |dA/dt|=A(dθ/dt) but who we can derive it or interpret this fact

Hello! I'm trying to derive the linear velocity vector from the position vector and the angular momentum vector. I've seen on the internet that V = W x R (V,W and R are all vectors and x is the cross product) but I cannot for the life of me derive it! I've tried doing it by writing out the...

Homework Statement I want to derive these equations Homework EquationsThe Attempt at a Solution But I don't have any idea how can extend cos(summation) and sin(summation) in form of Bessel function or product of Sin(wmt+phim)

Homework Statement D1=6cm D2=2cm ( i have to prove that 2nd moment of area (J) of a circulal plate abouts its polax axis(zz) is equal to piD^4/32 ) Homework EquationsThe Attempt at a Solution J=pi6^4/32 - pi2^4/32 = 125.66 J=r1^2x2pirdr J=Integral 2pir^3d2 = 2pi integral(high 3 , low 1)...

The following derives the relation that for a blackbody radiation the energy density is proportional to the energy emitted per unit area over unit time. The average energy density ##d\psi## is obtained by dividing the radiant energy ##dE## received by the surface ##dB## in 1 second by the...

Consider a surface defined by the equation ##g(x, y, z)=0##. The intersection between this surface and the plane ##z=c## produces a curve that can be plotted on an x-y plane. Find the gradient of this curve. By chain rule, ##\frac{\partial y}{\partial x}=\frac{\partial y}{\partial...

Hi All, Question: How to derive these equations of missile launch? v=∆x√(g/2H) v=√(2gh/β+1) I need to use these formulas: ∆y=voyt - (gt²)/2 ∆x=vxt K=(mv²)/2 + (Iω²)/2 ∆UG=mg∆y I=βmr² β=2/5 Thanks, Carlos.

I was wondering, how can I derive pi without fancy math (fancy meaning too complex. I'm not taking out calculus or trig or anything, just not too advance concepts). Can anyone help me out?

Hello, Could someone provide me with a good proof or explain me here how we can derive Slater determinant for N fermions by starting with the vacuum state and the creation operators with anticommutation equations. I see that the idea of both these structures is similar but I cannot work it out...

I'm a bit stuck on this question (which is homework so hints are more welcome than outright answers). The question is: A very long wire carrying a current I is moving with speed v towards a small circular wire loop of radius r. The long wire is in the plane of the loop and is too long to be...

Given the relativistic equation for energy E2 = (pc)2 + (mc2)2 I want to find the non-relativistic approximation for kinetic energy in non-relativistic terms, Knr = p2/2m I start off with subtracting the rest energy E0=mc2 from the above equation. So K = E - E0 and assume that c is very...

Homework Statement Hi I want to derive the equation of kinetic energy for a mass on two springs .. Here is the figure of the system: http://faculty.ndhu.edu.tw/~clcheng/class-98/gen-phy98/gen-phy98-1-Q2s.pdf Am I doing right for calculating the kinetic energy for the mass on two springs ...

Homework Statement consider the space-time transformation of translation xμ → x'μ = xμ + aμ where xμ is a point in space-time and aμis a constant 4-vector. Assuming translations are generated by the operator U=e-iPμaμ acting on fields Φ(x), derive the representation of Pμ on the field Φ(x)...

I understand that the ansatz to $$(\Box +m^{2})\phi(\mathbf{x},t)=0$$ (where ##\Box\equiv\partial^{\mu}\partial_{\mu}=\eta^{\mu\nu}\partial_{\mu}\partial_{\nu}##) is of the form ##\phi(\mathbf{x},t)=e^{(iE_{\mathbf{k}}t-\mathbf{k}\cdot\mathbf{x})}##, where...

I am stuck with this (d) all the other (a),(b),(c) were just like (a) E= −∇φ (b) ∇ · E= −∇2φ (c) ∇ × E I know only very basic about Gauss' law, the problem is not from Electrodynamics course. I don't know what should I do to solve (d)

Homework Statement Homework Equations Work energy theorem The Attempt at a Solution .5mv2 - .5mv2 = (kx - μmg)d final velocity is 0 ½mv2 =(kx - μmg)d solve for v2 ((kx - μmg)d2)m When this was wrong I tried integrating Fx but it was still wrong

Derive Vacuum permittivity and permeability using Quantum Field theory or String theory! If QFT or String theory is real fundamental theory, it can be derived the permittivity and permeability of vacuum. << Moderator's note: personal contact details deleted>>

Hello, I'm trying to study a settingless relaying scheme for Power System protection. The method is fairly well known and requires that one model a piece of equipment (like a transformer) with differential equation sets and compare that computational model with the actual operating behavior. If...

Homework Statement I would like to know how to derive the quantum commutation relations in matrix form, $$i \hbar \partial_t x(t)= [x(t),E]$$ $$i \hbar \partial_t P(t)= [P(t),E]$$ Where X(t), P(t) and E are the position, momentum and the energy of the particle, respectively. 2. Homework...

Homework Statement "Cars A and B move in the same direction in adjacent lanes. The position x of car A is given in Fig. 2-27, from time t = 0 to t = 7 s. The figure's vertical scaling is set by xs = 32 m. At t = 0, car B is at x = 0, with a velocity of 12 m/s and a negative constant...

I'm talking about equation 22, Does anyone know how to derive this? It's Marin Mersenne's formula for fundamental frequency, but I'm perplexed as to how he derived it. L would be the length, F would be force, and μ would be mass per unit length. f is the frequency Thanks

I'm taking an engineering heat transfer course as an elective. 1. Homework Statement Copper tubing is joined to a solar collector plate of thickness t, and the working fluid maintains the temperature of the plate above the tubes at To. There is a uniform net radiation heat flux q”rad to the...

Homework Statement The formula being derived is N=No*e^k*t, from the equation Nn=No/2^n where No is the initial number of particles and the lowercase n in the second equation is the number of half lives. The n in Nn just indicates the number of particles after so many half lives. You might also...

in particular f=Gm1m2/r^2?sorry if my question sounds very irrelevant.if f is proportional to m1m2 it implies f=some constant times m1m2.okay.at the same time f is inversely proportional to r^2 .so force = some other constant times 1/r^2.okay.but in most places i see that what is done is they...

Homework Statement "An automobile travels on a straight road for 40-km for 30 km/h. It then continues in the same direction for another 40-km at 60 km/h. (a) What is the average velocity of the car during the full 80 km trip? (Assume that it moves in the positive x direction.) (b) What is the...

Homework Statement Arbitrary derivative of inverse trigonometric function: (sin-1x) = 1/(√1 - x2) Homework Equations f-1(f(x)) = 1/f`(x) The Attempt at a Solution So basically I learned about derivatives of trigonometric functions in class, and I thought maybe this would work: deriving the...

Homework Statement Compute the radiation pressure exerted by a gas of photons (according to kinetic theory). There are N photons, each with energy hf, the momentum is hf/c, and the walls are perfectly reflecting. Express the pressure in terms of N, V, and the product hf. Homework Equations...

Just curious are cubic functions dirvel from just having the zeros, does that always determine where the local min/max is. I notice many cubic graphs given on homework show where the zeros are but the local min/max is not given. For example...

Please explain in detail how to derive formula for capacitance of spherical capacitor?

I'm trying to understand how the Navier-Stokes equations are derived and having trouble understanding how the strain rates are related to shear stresses in three dimensions, what a lot of texts refer to as the 'Stokes relations'...

hi i had doubt in hereditary and evolution chapter class 10 CBSE India So now I know that the phenotypic ratio of the pea ( with reference to dwarfness and tallness) is 3 : 1 which can be interpreted as : for every 4 pea plants obtained by a peapod, there are 3 tall plants and 1 dwarf plant...

So I have to derive f(x)=2x^x I know I first set i equal to y y = 2x^x then take the natural log lny = ln(2x^x) lny = 2(ln2x) but here I get a bit stuck. Do I take the derivative now?

Hi, Using conservation of energy $$m\cdot\ g\cdot\left(h_0-h\right)=\frac{1}{2}m\cdot\ v^2$$ it's easy to find the exact velocity of a pendulum $$v\left(h\right)=\sqrt{2g\cdot\left(h_0-h\right)}$$ at height ##h## above the minimum when it was let go from the inital height ##h_0##. Is it...

In physics lab course I measured equivalence conductivity of NaCl in infinite dilution Λ0 as a function of temperature T. So I have observations (T, Λ0) and fitted a line using the least squares method in Ms excel (lol :oldbiggrin:). The formula of the line is Λ0(T)=c0+c1T, where c0 and c1 are...

Please help, I've put this is true on my personal statement, but I'm now fairly sure that it is not, but a more expert opinion would be extremely helpful.

Homework Statement In your design of an experimental spring powered model car, you note that the speed of the car (mass Mc) increases as the car travels further. The exact relationship is that v(x) = C|x|, where C is a constant and x is the position of the car with respect to the starting...

In an earlier thread of mine, another physics forums member was nice enough to point out that there is an uncertainty relation between photon number and wave phase for light. https://www.physicsforums.com/threads/is-there-a-frequency-eigenstate-for-light.727141/ Now I am wondering, where does...

Hi, I need some help with a problem in my Classical Mechanics undergrad course. We were assigned a problem in which we were given a one dimentional potential (some sort of a parabola). We were asked to determine the velocity's direction at different point, and even though it is somewhat...

Homework Statement The frequency of a simple pendulum depends only on its length and the gravitational field strength. Use dimensions to derive a possible form for the equation for this frequency. Homework Equations [/B] Not sure. I was looking at f = 1/T as a starting point and g = F/m The...

Homework Statement Homework Equations The picture is all we know about the entire system, we need to derive an expression for the acceleration of ramp M. There is no friction anywhere. The ramp is free to move on the surface beneath it. The Attempt at a Solution I drew the free body...

I recently read a paper titled : " The Saros cycle: obtaining eclipse periodicity from Newton's laws " My question is, more or less: " Is it possible to obtain an approximation of G by observing Saros periodicity ? " I'm currently studying the derivations of the Lunar , Solar, and Stellar...

> The isothermal compressibility $\kappa_t$ of a substance is defined as $$ \kappa_t = -\frac{1}{V} \left ( \frac{\partial V}{\partial P} \right )_T $$ Obtain an expression for the isothermal compressibility of an ideal gas. (PV = RT) in terms of p. I believe that the ideal gas law equation...

I listened to a lecture the other day that some anomalies in observations compared to theory caused Max Plank to derive his famous Constant.

I am trying to derive the Kepler equation: M = E - e * sin(E) where M=Mean Anomaly, e=Eccentricity and E=Eccentric Anomaly. If you drop a perpendicular down from the object to the Perihelion-axis you can take: a * cos(E) = a * e + Recl * cos (TA) where Recl is the Ecliptic radius to the...

Hello Is it possible to derive the Euler–Bernoulli equation: \frac{d^2}{dx^2} \left(EI \frac{d^2w}{dx^2} \right) = q from Navier-Cauchy equations: \left( \lambda + \mu \right)\nabla\left(\nabla \cdot \textbf{u} \right) + \mu \nabla^2\textbf{u} + \textbf{F} = 0 I don't really know where to...

Homework Statement [/B] This graph shows an infinite string on the x-axis. The middle part is deformed as shown. The string is released at time t=0 - give the analytical solution of the problem, i.e. find for t>0 - sketch the string displacement \xi(x) for a sequence of times t. (I'd like...

Homework Statement Hi, I am stuck with this homework. I have been asked to make an equation out of a diagram for V(z) using V=kQ/r equation, where z is a positive axis centred with four negative charges. Here is the diagram. 2. Relevant equation E=F/q F of point charge: F=kQq/r^2 E=kQ/r^2...

On page 51 Peskin and Schroeder are beginning to derive basic Fierz interchange relations using two-component right-handed spinors. They start by stating the trivial (but tedious) Pauli sigma identity...

Homework Statement there are a lot of mathametical and graphical derivations of the three laws of motion but i have been trying to derive the second equation of motion from the first one but i always end hopeless. please help Homework Equations 1st equation v[f] = v + at 2nd...