Homework Statement
Consider a thin bi-convex lens with refractive index n which has spherical surfaces with equal radii of curvature r and a measured focal length f. The lens floats horizontally on the surface of liquid mercury so that its lower surface effectively becomes a spherical mirror...
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...
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...
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...
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...