Recent content by Froskoy

Thanks very much! It all makes a lot more sense now!

Hi, I'm having trouble understanding what the relation is between the impulse of a force during a collision and the changes in linear and angular momentum during the collision. I know that the principle of conservation of linear momentum says that the total linear momentum before is equal...

Homework Statement Let E be the ellipsoid \frac{x^2}{a^2}+\frac{y^2}{b^2}+z^2=1 where a>\sqrt{2} and b>\sqrt{2}. Let S be the part of the surface of E defined by 0\le x\le1, 0\le y\le1, z>0 and let \mathbf{F} be the vector field defined by \mathbf{F}=(-y,x,0). Given that the surface area...

Homework Statement A particle of mass m moving at speed \frac{3}{5}c collides with an identical particle at rest, and forms a new particle of mass M which moves off at speed v. Find v.Homework Equations E-P invariant: E_1^2-p_1c^2=E_2^2-p_2^2c^2=\mathrm{const.} Momentum...

Homework Statement The question: The function F(θ,k) is defined as F(\theta,k)=\int_0^θ (f(x,k))\mathrm{d}x Find expressions for \left({\frac{\partial F}{\partial \theta}}\right)_k and \left({\frac{\partial F}{\partial k}}\right)_θ Homework Equations Fundamental theory of calculus Chain...

Thanks! I hadn't thought of expanding \frac{1}{\sqrt{x^2-a^2}} and then multiplying my x - that's really cool - thanks!

Homework Statement Find the first two non-zero terms in the Taylor expansion of \frac{x}{\sqrt{x^2-a^2}} where a is a real constantHomework Equations f(x)=f(x_0)+f^{\prime}(x_0)(x-x_0)+\frac{f^{\prime\prime}(x_0)}{2!}(x-x_0)^2+...+\frac{f^{(n)}(x_0)}{n!}(x-x_0)^n The Attempt at a Solution If...

Why? Please can you point me to somewhere that explains how this situation is modeled classically?

Thank you so much! It's all really clear now!

Homework Statement For the case n=1, calculate the probability that the particle is found in within the region a/4<x<3a/4 (n is the energy level, a is the width of the infinite potential well). Compare this result with the case n=8 and with the classical result. Homework Equations...

Homework Statement A network consists of an inductor, capacitor and resistor are connected in parallel and an alternating sinusoidal voltage is placed across the network. Sketch the phase of the total current relative to the voltage as a function of the angular frequency. The Attempt at a...

Thanks very much! Have got it now!

Homework Statement \sin\theta\frac{d^2y}{d\theta^2}-\cos\theta\frac{dy}{d\theta}+2y\sin^3\theta=0Homework Equations Use the substitution x=\cos\thetaThe Attempt at a Solution I started off by listing: x=\cos\theta\\ \frac{dx}{d\theta}=-\sin\theta\\ \frac{d^2x}{d\theta^2}=-\cos\theta\\ But...

Hi, I'm trying to get my head around how velocity vectors work in special relativity. For example, in classical mechanics, the magnitude of the velocity would be given by: v^2 = \sqrt{v_x^2 + v_y^2 + v_z^2} where v_x, v_y and v_z are the x, y and z components of the velocity...

Hi! Thanks very much for confirming what I had is correct - it turned out to be a calculation error. With very many thanks again, Froskoy.