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4
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3answers
149 views

Effect variable cylinder radius has on airflow

Can someone shed some light on the following problem? I'm unable to get any traction on it as I know nothing about fluid dynamics (I'm a computer engineer). It's a problem I made up over a lunch ...
4
votes
1answer
2k views

Solving a statically indeterminate truss

I'm trying to solve the statically indeterminate truss shown below and I'm having a little trouble. $H$, $P$ and $\beta$ are given. The material is aluminum (density is 2700 ${kg/m^3}$) and has a ...
4
votes
1answer
2k views

Force on Earth due to Sun's radiation pressure

I have been asked by my Classical Electrodynamics professor to calculate the force that the Sun exerts in the Earth's surface due to its radiation pressure supposing that all radiation is absorbed and ...
4
votes
1answer
3k views

Shouldn't the electric field in a solid insulating sphere be linear with radius?

I am a senior in High School who is taking the course AP Physics Electricity and Magnetism. I was studying Gauss's laws and I found this problem: A solid insulating sphere of radius R contains a ...
4
votes
1answer
203 views

Transpose Map Positive, But Not Completely Positive?

I am reading Introduction to Quantum Computing by Kaye, Laflamme, and Mosca. Here is a question I am struggling with: Exercise 3.5.6: Prove that the transpose map, which maps $\rho \mapsto ...
4
votes
1answer
261 views

Projection of states after measurement

Continuing from the my previous 2-state system problem, I am told that the observable corresponding to the linear operator $\hat{L}$ is measured and we get the +1 state. Then it asks for the ...
4
votes
1answer
878 views

Finding the position of a planet between two other planets of known mass and distance

Here is the question: A planet with mass $m$ and a second with mass $M$ are separated by a distance $d$. A third planet with mass $m_3$ happens to be midway between $M$ and $m$. Where could ...
4
votes
1answer
95 views

Simple Commutator question

For some reason this is really tripping me up: $$[q_rq_sp_r,q_sp_rq_s]$$ Where $r$ and $s$ are different. Is this just zero because $p_r$ on $q_s =0$. I am trying to simplify this and I feel like 0 ...
4
votes
1answer
141 views

Derivation of the quadratic form of the Dirac equation

I am asked to derive the quadratic form of the Dirac equation in an electromagnetic field, $\left[\left(i\hbar \partial - \frac{e}{c}A\right)^2 - \frac{\hbar e}{2c} \sigma^{\mu\nu} F_{\mu\nu} - ...
4
votes
1answer
271 views

Problem in Youngs double slit experiment

This is from Young Double slit experiment. But How to prove the the two $\theta$ are equal, I meant, how $\angle EAD= \angle PEC$? I see from the both triangle have $90^0$ but what about others?
4
votes
1answer
387 views

Chemical Potential of Ideal Fermi Gas

In Wikipedia's article on Fermi Gases, they have the following equation for the chemical potential: $$\mu = E_0 + E_F \left[ 1- \frac{\pi ^2}{12} \left(\frac{kT}{E_F}\right) ^2 - \frac{\pi^4}{80} ...
4
votes
1answer
51 views

Charge in a layered ball

A ball (radius $R$) has three layers. For $0<r<a$ it is a conductor with free charge $+Q$. For $a<r<b$ it is a linear dielectric $\epsilon$ with free charge embedded in it with density ...
4
votes
1answer
492 views

How much negative charge do I accumulate by touching the earth?

The Earth carries a negative electric charge of roughly 500 thousand Coulombs (according to different sources I've seen). If I touch the Earth I should therefore pick up some of this electric charge ...
4
votes
3answers
141 views

What is the difference between material fatigue test with 1 sec cycle and 1 hour cycle?

Assume I have two pieces of metal. I want to test the material fatigue (e.g. how many cycles can the material stand before it will break). Onto one of them I apply a tension force every second. Onto ...
4
votes
2answers
311 views

How to directly calculate the infinitesimal generator of SU(2)

We commonly investigate the properties of SU(2) on the basis of SO(3). However, I want to directly calculte the infinitesimal generator of SU(2) according to the definition $$X_{i}=\frac{\partial ...
4
votes
1answer
151 views

Wald problem 11.4

Consider a stationary solution with stress-energy $T_{ab}$ in the context of linearized gravity. Choose a global inertial coordinate system for the flat metric $\eta_{ab}$ so that the "time direction" ...
4
votes
2answers
730 views

Quantum Mechanics: Show that the expectation value of angular momentum does not change with time

The potential is given by $V\left(\left\|(x,y,z)\right\|\right)$, so $[\hat{L}, \hat{H}] = 0$. Using the definition of $\langle \hat{L} \rangle$ and the time-dependent Schrödinger equation, show that ...
4
votes
2answers
627 views

I have a slight problem understanding the concept of “work”?

What I understand is that work is not the same as a car using gas or a crane lifting a car high up into the air. Let's use the crane as an example. And let me write out a few lines from the book. ...
4
votes
1answer
238 views

Voltage drop over a cell membrane

Again, a problem from exam preparation: [A] cell's membrane allows sodium ions to pass through it, but not chlorine ions. The cell is placed in a salty solution with a ten times higher ...
4
votes
1answer
102 views

$\tau$ pair production question

There's a question on my homework about the process $e^{-} e^{+} \rightarrow \tau^{+} \tau^{-}$. Specifically, it is claimed that the minimum energy required of the colliding positron and electron ...
4
votes
0answers
105 views

Action of Parity operator on Impulse representation

Is my derivation of the action of the parity operator $\mathbb{P}$ on the $|p\rangle$ representation correct? $$\left( \mathbb{P}\tilde\psi \right)(p)= - \tilde\psi (p).$$ Obtained from $$\left( ...
4
votes
0answers
146 views

Hamiltonian function for classical hard-sphere elastic collision

I'm trying to find the Hamiltonian function for a system consisting of a single particle in one dimension colliding elastically with a wall at x = 0. Everything I've read on the topic (e.g. this ...
4
votes
0answers
62 views

Is the relative atomic mass directly proportional to the size of an atom? [closed]

I have a piece of homework, i have to make a pair of models depicting pure metals and alloys. I want it to be as accurate as possible, and so i'm asking this: Is the relative atomic mass directly ...
4
votes
1answer
449 views

Paramagnetism Spin-1/2 Particles - Partition Function

I'm trying to come up with an expression for the partition function of a system of spin-1/2 ideal gas particles on a line of length $L$. The total number of particles $N$ is fixed, with $N = ...
4
votes
1answer
662 views

Wien's displacement law in frequency domain [duplicate]

When I tried to derive the Wien's displacement law I used Planck's law for blackbody radiation: $I_\nu = \frac{8 \pi \nu^2}{c^3} \frac{h \nu}{e^{h\nu/k_bT}-1}$ Asking for maximum: $\frac{dI_\nu}{d ...
4
votes
3answers
164 views

Finding the equation of motion of anharmonic potential [closed]

If I have a potential given by: $$U=U_0\left[2\left(\frac xa\right)^2-\left(\frac xa\right)^4\right]$$ It says that at $t=0$, the particle is at the origin ($x=0$) and the velocity is positive and ...
4
votes
1answer
161 views

$\require{mhchem}$ $\ce{\beta^{+}}$ decay for $\ce{_9^18F}$, computing $\Delta m$

For the decay: $$\require{mhchem}\ce{_9^18F\to_8^18O +e+ +{v}}$$ To compute $E$, I need $\Delta m$, the provided answer looks like: $$m_i = 18.000938~u$$ $$m_f = 17.999159~u + 2~(5.49 \times ...
4
votes
1answer
921 views

Application of Archimedes Principle

A candle is floating in a liquid placed in a container. The container is a cylinder of diameter $D$, and the candle is of width $d$. ($D>d$) The height of the liquid from the bottom of the ...
4
votes
0answers
527 views

Friction in circular motion [closed]

A circular horizontal table spins around its axis of rotation with a constant angular speed. It completes one revolution in 2 seconds. An object whose mass is $M = 0.8 \ \text{kg}$ is placed on the ...
4
votes
0answers
166 views

Thermodynamic relations from Gibbs-Duhem

Given the Gibbs-Duhem relation $V dp = S dT - N d \mu$, I am having trouble deriving the following identity: $\ (\frac{\partial N}{\partial \mu})_{V,T} = N (\frac{\partial \rho}{\partial p})_T$ ...
4
votes
0answers
268 views

Derivation of the oil drop experiment [closed]

The oil drop experiment performed by Robert Millikan in 1909 enables us to calculate the elementary charge. The following forces have effect on the droplet: $F_\mathrm{G} = m g = \frac{4}{3} \, \pi ...
4
votes
1answer
879 views

Infinite-range 1D Ising model + Hubbard-Stratonovich-Transformation

I have a probably quite simple question RE the HST. After some work, I obtain as the partition function for the infinite range 1D Ising model $$Z = \int_{-\infty}^\infty \frac{dy}{\sqrt{2\pi / ...
3
votes
4answers
922 views

Paradox- Object thrown parallel to the ground will never fall down

Suppose an object is thrown parallel to the ground. The gravity acts downward (ie. perpendicular to the direction of motion of the object). The work done by gravity on that object will be given by : ...
3
votes
4answers
316 views

How are we able to view an object in a room with bulb..?

This is a very basic question on optics. How are we able to view an object kept in a room with a bulb? From what I understand, light rays from bulb will hit the object and some colour will be ...
3
votes
4answers
2k views

Divergence of $\frac{\hat{r}}{r^2}$

In David J. Griffiths's Introduction to Electrodynamics, the author gave the following problem in an exercise. Sketch the vector function $$ \vec{v} ~=~ \frac{\hat{r}}{r^2}, $$ and compute ...
3
votes
2answers
203 views

Commutator of $L^2$ and $X^2$, $P^2$

In our quantum mechanics script, it states that $[L^2, X^2] = 0$ and $[L^2, P^2] = 0$, therefore for the following Hamiltonan $$H = \frac{P^2}{2m} + V(X^2)$$ it is that $[H, L^2] = 0$ therefore $H$ ...
3
votes
1answer
800 views

Equivalent resistance in ladder circuit

I have stumbled upon a given question I really have a hard time to solve. Basically I need to find an equivalent resistance in some form of "ladder" configuration. Where the chain is an infinite ...
3
votes
1answer
265 views

Find the Hamiltonian given $\dot p$ and $\dot q$

I have these equations: $$\dot p=ap+bq,$$ $$\dot q=cp+dq,$$ and I have to find the conditions such as the equations are canonical. Then, I have to find the Hamiltonian $H$. To answer to the first ...
3
votes
3answers
358 views

Is this interpretation of $\psi=\frac{1}{\sqrt{\pi a^{3}}}e^{-r/a}$ correct?

Apologies if this is stating the obvious, but I'm a non-physicist trying to understand Griffiths' discussion of the hydrogen atom in chapter 4 of Introduction to Quantum Mechanics. The wave equation ...
3
votes
2answers
1k views

First integral of an equation of motion: $\mu\ddot r=-\frac{k}{r^2}$

I've got an equation of motion (EOM), which is $ \mu\ddot r=-\frac{k}{r^2} $ How do I find the first integral of this EOM? I'd appreciate it if someone could show me the steps involved. I should ...
3
votes
2answers
156 views

Wave function with a delta potential

I have a particle and a potential $V(x)=\frac{\hbar^2}{2m}k\delta(x)$. Where $\delta (x)$ is the Delta function, and I am interested in the solutions of the stationary Schroedinger equation. If ...
3
votes
4answers
1k views

Time period of simple pendulum with varying mass

How do you find time period as a function of time for a simple pendulum that is in the form of a hollow sphere that is filled with mercury and there is a hole in the bottom through which the mercury ...
3
votes
3answers
3k views

Transverse Magnetic (TM) and Transverse Electric (TE) modes

I'm reading and working my way through "Plasmonics Fundamentals" by Stefan Maier and I've come across a step in the workings that I'm struggling to understand when working out the electromagnetic ...
3
votes
4answers
391 views

The Expansion Coefficients for a Particle in a Box

This is an expansion of two previous questions I had before (I am very confused by it). I am now encountering a problem with an integral. We want a general expression for the probability of finding E. ...
3
votes
2answers
111 views

Do I think or listen - physics talks [closed]

I am just a student, still I have already listened to a few talks on physics. In my study program everyone has to give a talk of about 45 minutes what he did in his about 1-2 month reach project ...
3
votes
3answers
737 views

Irreversible process

I have this problem. I have an ideal gas that goes through an irreversible adiabatic decompression. I have the initial state (P,T,V), and the final pressure, and I have to calculate the entropy ...
3
votes
3answers
380 views

waves on water generated by a falling object

Let an object of mass $m$ and volume $v$ be dropped in water from height $h$, and $a$ be the amplitude of the wave generated. What is the relation between $a$ and $h$. How many waves are generated? ...
3
votes
3answers
3k views

Maximum range of a projectile launched from elevation “dumbed down”

I am trying to conceptually understand why the angle which produces the greatest range for a projectile launched with an elevation is not 45 degrees. I have exausted all other options, and I hope that ...
3
votes
1answer
446 views

Do the trigonometric functions preserve units?

I saw an exercise where you had to calculate the units of $C_i, i=1,2$ from an equation like this: $v^2=2\cdot C_1x$ and $x=C_1\cdot \cos(C_2\cdot t)$ where $x$ means meters, $t$ means seconds ...
3
votes
2answers
137 views

Derivatives of delta function and equation of continuity for a single charge…

For a single charge $e$ with position vector $\textbf R$, the charge density $\rho$ and and current density $\textbf{j}$ are fiven by: \begin{equation} \rho(\textbf{r},t)= ...