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14
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1answer
945 views

Mechanics + Thermodynamics: Bouncing Ball

In preparation for an exam, I'm revisiting old exam questions. This one seems neat, but also quite complicated: A soccer ball with Radius $R=11cm$ is inflated at a pressure of $P =9 \times 10^4 ...
11
votes
4answers
534 views

Capacitance of two almost-touching hemispheres

This capacitor is composed of two half spherical shelled conductors both with radius $r$. There is a very small space between the two parts seeing to that no charge will exchange between them. So ...
10
votes
1answer
1k views

How do I construct the $SU(2)$ representation of the Lorentz Group using $SU(2)\times SU(2)\sim SO(3,1)$ ?

This question is based on problem II.3.1 in Anthony Zee's book Quantum Field Theory in a Nutshell (I'm reading this for fun- it isn't a homework problem.) Show, by explicit calculation, that ...
9
votes
3answers
408 views

No closed orbits for a Newtonian gravitational field in 4 spatial dimensions

We are supposed to show that orbits in 4D are not closed. Therefore I derived a Lagrangian in hyperspherical coordinates $$L=\frac{m}{2}(\dot{r}^2+\sin^2(\gamma)(\sin^2(\theta)r^2 \dot{\phi}^2+r^2 ...
9
votes
1answer
505 views

exponential potential $ \exp(|x|) $

For $a$ being positive what are the quantisation conditions for an exponential potential? $$ - \frac{d^{2}}{dx^{2}}y(x)+ ae^{|x|}y(x)=E_{n}y(x) $$ with boundary conditions $$ y(0)=0=y(\infty) $$ I ...
9
votes
1answer
298 views

Contracting Indices

Does anyone know how to get from (1) to (2) in the system $$ \begin{align} \mathrm{g}^{\mu\nu}_{,\rho}+ \mathrm{g}^{\sigma\nu}{{\Gamma}}^{\mu}_{\sigma\rho}+ ...
9
votes
4answers
2k views

Density of a proton

I was doing some exercises the other day, when I came across this question in my book: A proton weighs about 1.66 x 10-24 g and has a diameter of about 10-15 m. What is its density in g/cm3? ...
9
votes
1answer
190 views

“Redshifting” of forces in stationary space - times

Here's the problem statement: Let $(M,g_{ab})$ be a stationary spacetime with timelike killing field $\xi ^{a}$. Let $V^{2} = -\xi _{a}\xi ^{a}$ ($V$ is called the redshift factor). (a) Show that the ...
8
votes
9answers
10k views

What's the core difference between the electric and magnetic forces?

I require only a simple answer. One sentence is enough... (It's for high school physics)
8
votes
3answers
379 views

Electric Field inside a regular polygon with corner charges

If we have equal charges located at the corners of a regular polygon, then the electric field at its center is zero. Are there other points inside a polygon where the field vanishes? The simplest ...
8
votes
3answers
315 views

Where does the extra equation come from to determine the forces from an object on a table?

I have a question about basic statics but somehow I cannot manage to find the answer on my own (btw, this is not a homework. It's been so many years since school for me...). The problem is very ...
8
votes
4answers
281 views

Question about canonical transformation

I was going through my professor's notes about Canonical transformations. He states that a canonical transformation from $(q, p)$ to $(Q, P)$ is one that if which the original coordinates obey ...
8
votes
3answers
107 views

Correct expression for experimental data

I am doing practices at the laboratory. I have some doubts about how to express correctly the errors; I read some pdfs in Google but I can't solve these questions: Sometimes, it's correct to write ...
8
votes
5answers
307 views

How to get the position operator in the momentum representation from knowing the momentum operator in the position representation?

I know that $$\tag{1}\hat{p}~=~-i\hbar \frac{\partial}{\partial x}~.$$ How can I get $$\tag{2}\hat{x}~=~i\hbar \frac{\partial}{\partial p}~?$$ I think this simple and I'm just over thinking it, ...
8
votes
1answer
9k views

How do you find the uncertainty of an weighted average?

The following is taken from a practice GRE question: Two experimental techniques determine the mass of an object to be $11\pm 1\, \mathrm{kg}$ and $10\pm 2\, \mathrm{kg}$. These two ...
8
votes
4answers
5k views

Weight on carpet vs. hard floor

Will the scale say I weigh more, less, or the same on a carpet as compared to a hard floor? You can assume the scale works via spring mechanism. Free body diagrams encouraged!
8
votes
2answers
252 views

What is the physical meaning of $|f''(\xi )|\leq\frac{4(f(b)-f(a))}{(b-a)^{2}}$ where $f(t)$ is position as a function of time?

Here is the full problem: I was able to prove the given expression; but the interpretation part is giving me a bit of trouble. Here is my interpretation: The average acceleration in $(a,b)$, is ...
7
votes
6answers
68k views

How to calculate average speed [closed]

I recently encountered a puzzle where a person drove 120 miles at 40mph, then drove back the same 120 miles at 60mph. The average of the speeds is (40mph+60mph)/2 = 50mph, so the total trip time ...
7
votes
4answers
306 views

Distribution of point charges on a line of finite length

How will $N$ freely moving charges confined to a line with length $L$ be distributed? What are their equilibrium positions?
7
votes
3answers
470 views

Bird flying in a cage

Assume that you are holding a cage containing a bird. Do you have to make less effort if the bird flies from its position in the cage and manages to stay in the middle without touching the walls of ...
7
votes
4answers
580 views

Integrating radial free fall in Newtonian gravity

I thought this would be a simple question, but I'm having trouble figuring it out. Not a homework assignment btw. I am a physics student and am just genuinely interested in physics problems involving ...
7
votes
1answer
239 views

Is there any usage of $x^x$ in physics? [closed]

I am so excited about the function: $x^x$. I would like to know if there is any usage in the physics world of this function. Is there any formula that uses $x^x$?
7
votes
1answer
1k views

One strategy in a snowball fight

Here's a common college physics problem: One strategy in a snowball fight is to throw a first snowball at a high angle over level ground. While your opponent is watching the first one, you ...
7
votes
2answers
292 views

Why does the quantum Heisenberg model become the classical one when $S\to\infty$?

The Hamiltonian of the spin $S$ quantum Heisenberg model is $$H = J\sum_{<i,j>}\mathbf{S}_{i}\cdot\mathbf{S}_{j}$$ I have read that when the spin quantum number $S\to\infty$, quantum fluctuation ...
7
votes
2answers
2k views

Transformation of angles in special relativity

My question is about the problem below Depicted are two space ships (the USS Voyager and the USS Enterprise), each with velocity $v=c/2$ relative to the space station (Babylon 5). At the exact ...
7
votes
1answer
208 views

Virial theorem and variational method: a question

I have an hydrogenic atom, knowing that its ground-state wavefunction has the standard form $$ \psi = A e^{-\beta r} $$ with $A = \frac{\beta^3}{\pi}$, I have to find the best value for $\beta$ ...
7
votes
3answers
2k views

Charge density in concentric spheres

Question: If there are two conducting spherical shells and the inner shell is grounded, what will be >the charge density in the inner shell if there is a charge Q placed on the outer shell? ...
7
votes
2answers
119 views

Find the minimum value of velocity [closed]

Find the minimum value of the initial velocity $u$ of the particle such that the particle crosses the wheel of radius $R$. Details and assumptions $R=2m$ $g=9.8m/s^2$ Neglect air resistance. All ...
7
votes
1answer
245 views

Causality for the Dirac Field

In Peskin & Schroeder page 54, they are trying to show how far they can take the idea of a commutator for the Dirac field instead of anti-commutator. To this end they are examining causality, ...
7
votes
2answers
185 views

A problematic integral in calculating the entanglement entropy in 1+1 D free massive bosonic field theory

I encountered a curious integration identity when I was reading the paper by Pasquale Calabrese and John Cardy on the entanglement entropy of 1+1D quantum field theory (arXiv). The identity is given ...
7
votes
2answers
362 views

Equivalence principle and radiation from falling particle

I am currently having a hard time solving a problem of GR from Lasenby's book. I can't make it more clear than by quoting the exercise: 7.2 A charged object held stationary in a laboratory on the ...
7
votes
1answer
362 views

What will be different if the spring is not massless?

In almost all text, it uses the massless spring as example to illustrate the idea of elastic potential energy. I wonder what's really being changed if we consider the mass of the spring? I saw a ...
7
votes
0answers
93 views

Simple argument for unexpected behavior in SUSY model

Consider a supersymmetric theory with 3 chiral superfields, $X, \Phi_1$ and $\Phi_2,$ with canonical Kahler potential and superpotential $$ W= \frac12 h_1 X\Phi_1^2 +\frac12 h_2 \Phi_2\Phi_1^2 + fX.$$ ...
6
votes
4answers
17k views

What is the relationship between kinetic energy and momentum?

I can't seem to figure out the relationship between $E_k$ and $p$ or $F$. I understand that the units are pretty different. But for example: A bullet with a mass of 10.0g is moving at the speed of ...
6
votes
4answers
5k views

Derivation of self-inductance of a long wire

Currently I am stuck, trying to derive the self-inductance of a long wire. According to literature it should be $$L=\frac{\mu_r\mu_0l}{8\pi}$$ and in literature its derived by looking at the energy ...
6
votes
3answers
492 views

Gauge invariant Chern-Simons Lagrangian

I have to prove the (non abelian) gauge invariance of the following lagrangian (for a certain value of $\lambda$): $$\mathcal L= -\frac14 F^{\mu\nu}_aF_{\mu\nu}^a + ...
6
votes
3answers
282 views

Commutator with a square root

How to find the commutator $[a, \sqrt{a^\dagger a}]$? Here $a$ is a usual bosonic annihilation operator, and $[a, a^\dagger] = 1$. The first thing I tried is $$ [x,A] = [x, \sqrt{A}]\sqrt{A} + ...
6
votes
3answers
692 views

Force between two charged rods?

Suppose that we have two rods of length $l_1, l_2$ connected at one end but free to rotate. These rods have charge density $\lambda$ uniformly distributed, so the total charge of rod $i$ is $\lambda ...
6
votes
2answers
338 views

Infinitesimal Lorentz transformation is antisymmetric

The Minkowski metric transforms under Lorentz transformations as \begin{align*}\eta_{\rho\sigma} = \eta_{\mu\nu}\Lambda^\mu_{\ \ \ \rho} \Lambda^\nu_{\ \ \ \sigma} \end{align*} I want to show that ...
6
votes
4answers
568 views

Symmetry in resistor circuits

Given 6 points that are connected with each other with a resistor of resistance $R$, find the resistance between any two points. (Answer: $R/3$) (All the conducting wires have the same ...
6
votes
2answers
292 views

How to show that every Killing vector field is a matter collineation?

Various texts make this claim, but no proof is given. Explicitly, let $L$ denote the Lie derivative. Suppose $L_X g_{ab} = 0$ for some vector field $X$, called a Killing vector field. Suppose that ...
6
votes
2answers
1k views

Galilean transformation of wave equation

I have this general wave equation: \begin{equation} \dfrac{\partial^2 \psi}{\partial x^2}+\dfrac{\partial^2 \psi}{\partial y^2}-\dfrac{1}{c^2}\dfrac{\partial^2 \psi}{\partial t^2}=0 \end{equation} ...
6
votes
2answers
223 views

Can the process $u\overline{u} \rightarrow s\overline{s}$ be mediated by the EM interaction?

I’m working on a homework problem which asks for the dominant contribution (e.g. EM, strong, or weak) to the process $p + \overline{p} \rightarrow \Lambda + \overline{\Lambda}$). I know that the EM ...
6
votes
1answer
189 views

Integral in $n$−dimensional euclidean space

I've asked this question in Mathematics Stack Exchange, but unfortunately there is no answer yet. I repost it because this integral comes from QFT and maybe someone here did it before or could help ...
6
votes
2answers
231 views

Harmonic oscillator modified by infinite well: are analytic solutions possible?

I'm trying to find solutions to a harmonic oscillator that sits within an infinite square well. I haven't spent too much time yet, and I've had no success so far. I'm wondering how possible or complex ...
6
votes
3answers
268 views

Induced current using a reference system bound with a moving charge

Suppose we have a charge moving at velocity $\mathbf{v}$ in the same plane of a square wire. If I sit in a reference frame where the square wire is still, since the charge is moving with velocity ...
6
votes
2answers
627 views

High school double lens optics question

This is a first year high school homework question (in the Finnish high school), and I'm having serious trouble solving it. I apologize for possible non-standard terms: I'm doing the translation from ...
6
votes
2answers
217 views

Radioactive Decay

Problem:Nuclei of a radioactive element $\Bbb X$ having decay constant $\lambda$ , ( decays into another stable nuclei $\Bbb Y$ ) is being produced by some external process at a constant rate ...
6
votes
1answer
105 views

Doubts about the ideal gas law

EDITED AND SOLUTION: In fact my stupid mistake was to take the wrong value for my $P_1$ and I was getting an 1.2998 that finally is a 1,9178 within just a difference about 7%. So at the end they are ...
6
votes
3answers
184 views

Angular momentum of particle rolling around inside of sphere

I have a hemispherical bowl in which I roll a small particle around the edge, starting from the top at point A with a velocity $v_o$. It travels halfway around the sphere and reaches point B, which is ...