Applies to questions of primarily educational value - not only questions that arise from actual homework assignments, but any question where it is preferable to guide the asker to the answer rather than giving it away outright. Please READ THE GUIDANCE IN META before asking homework questions.

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44 views

Movement of a gyroscope with non-fixed axis

Assume one has a gyroscope rotating around an axis with both ends leaning on a dedicated semiplane as shown on the picture below. There is no friction either between the rotor and the axis or between ...
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113 views

Derivation of the Hartree-Fock equations. Functional varitation

I asked this question at chemistry.stackexchange.com, but the attendance of that source is a little bit lower than here. I would like to ask a question about mathematical derivation of the HF ...
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237 views

Forces on two boxes

This is a problem from my problem sheet but we haven't yet covered the material or received our books. There is a small box of mass $m_{1}$ resting on a plank, of mass $m_{2}$ and length $L$, which ...
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65 views

Can I transfer electricity through induction?

If I place a solenoid connected to a bulb inside a bigger solenoid which is connected to a power source, will the bulb glow?
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368 views

projectile that splits into two fragments of equal mass

I am studying for an exam, and this is part of a problem in my book. A projectile is launch from level ground and is intended to hit a target 100m away. Instead, it explodes into two fragments of ...
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131 views

A basic question about Heisenberg State Kets (in particular the simple harmonic oscillator)

I know base kets in the Heisenberg picture are $U^\dagger |{a}\rangle$ but if the base kets are the base of the hamiltonian, and the hamiltonian is independent of time, are all of the base kets ...
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31 views

Trouble evaluating an integral arising from particle collision

Assume we have two charged particles colliding. He have particle 1 with mass $m_1$, charge $Z_1 \cdot e$ which travels in $x$-Direction passing by a STATIONARY particle 2 (mass $m_2$, charge $Z_2 ...
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90 views

Understanding unit vectors

Trying to understand how the unit vector ${\mathcal{\hat{r}}}$ defined as $\frac{r' - r}{|r' - r|} $ (where $r'$ is the source point) works in this problem: Work out the electric field, $E$, at point ...
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70 views

An Equality in The Calculus of Many Instantons

I am reading the review on instantons. When I tried to derive formula (2.27) on page 17, I always get the different coefficient of $gF_{mn}$ term. My calculation is just directly expanding the first ...
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126 views

insulator based gauss law questions

My book is incredibly scarce on insulator based Gauss law questions. Conductors seem to handle themselves pretty simply. Here's a question I'm working on that isn't part of my book. where the radii ...
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80 views

Find contact force given sphere's radii and distance

I simulate scenario of two contacting elastic spheres, where their radii and the distance of their centers is known, and repulsive force should be computed. Material parameters are also given. Most ...
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125 views

If a beam of light follows the path $y(x)=y_0\sin(x/y_0)$, what is the index of refraction?

An exam question that showed up while I was studying: A plane wave refracts and follows a ray given by the equation $y=y_0\sin(x/y_0)$ where $y_0$ is a constant. Find the refractive index $n(y)$ ...
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39 views

Question about “quadrupole radiation” vector potential formula derivation

I tried to get an expression for $\mathbf A (\mathbf x )$ in quadrupole approximation. After some transformations of Liénard–Wiechert vector potential I got, as in many books, $$ \mathbf A \approx ...
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46 views

Proton or electron charge in the Weinberg-Salam model?

I read Quantum Field Theory, Ryder, second edition. Relation (8.86) brings us the famous result: $e = g \sin \theta_W$ Here Ryder says tht $e$ is the proton charge. However, according to what I ...
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71 views

Deriving the curve of a cantilever

Essentially, there is a beam of length L and negligible mass sticking out of a wall with a mass Mg hanging at the end of it. We are given an equation for elastic energy (which I don't think needs to ...
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79 views

How did Jackson get the exact solution to potential in polar coordinates

On page 45 of Jackson's Classical Electrodynamics (3ed), He solved a polar potential problem with known source distribution. $$ \frac{1}{\rho}\frac{\partial}{\partial \rho}\left( \rho\frac{\partial ...
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51 views

path planning with invasive measurements

My background is not science, and I hope the question I am about to ask doesn't look like a homework kind of a thing! Anyway, I will try my best to make the point clear. imagine there is a lake, and ...
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1k views

Equations of motion for a pendulum and spring system

The question is available here: I've modeled the building as a rod on a torsional spring (with a pendulum hanging from the top). $\phi$ is the angle from the centre for the pendulum and $\theta$ ...
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60 views

Transformation of $t=0$ line in moving frame of reference

How does $t=0$ transform into $t - vx/c^2 = 0$ if a frame of reference is moving as given in here? It seems that the relativistic transformation is given by $$ \begin{bmatrix} x' \\ ct' ...
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84 views

Motion on a smooth surface

A particle of mass $m$ is moving on the inner side of smooth circular cylinder of radius $R$ whose $Oz$-axis is vertical and directed downwards. The particle started its motion from the $x$-axis with ...
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129 views

How to prove Eq. (2.4.5) in Polchinski's string theory book?

I got one more stupid question in Polchinski's string theory book. In p. 44, it is said The currents $$j(z)=i v(z) T(z), \tilde{j}(\bar{z}) = i v(z)^* \tilde{T}(\bar{z}) \tag{2.4.5}$$ are ...
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73 views

Preservation of a scalar along geodesic trajectory

Let $u^\mu$ be the velocity of a particle , and $\xi^\mu$ be a killing vector. would taking a contravariant derivative of to scalar product $\xi_\mu u^\mu$ , and showing that it equals to 0 shows that ...
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61 views

How to absorb a characteristic line in a spectrum

I have an x-ray tube. When I see the spectrum, I notice the characteristic lines of the anode. What do I have to do if I want to absorb a characteristic line? I have thought that I can add a filter. ...
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80 views

Superradiance of electromagnetic waves

I have to do a calculation (problem 5 of chapter 12 in Wald) verifying the super-radiance of electromagnetic waves incident on Kerr black holes and have a few preliminary questions. As background: ...
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40 views

Calculate the acceleration of the trailing muon bunch

Two separate suitably short but intense bunches of muons, "A" and "B", are both supposed to be constantly accelerating (in an otherwise sufficiently flat region) with constant proper acceleration ...
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53 views

Hamiltonian system: match transformations and constants of motion

I have a problem about the interpretation of an exercise. Given the following Hamiltonian $$H=\frac{\mathbf{p_0}^2}{2m}+\frac{\mathbf{p_1}^2}{2m}+\frac{\mathbf{p_2}^2}{2m}-2V(\mathbf{r_1}- ...
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80 views

A quicker way to verify that a function is a constant of motion?

I have three particles that we can indicate with $\alpha$ ($\alpha$=0,1,2), they are identified by the $r^i_\alpha$ coordinates and $p^\beta_j$ conjugata momenta ($\beta=0,1,2$ and $i,j=1,2,3$). I ...
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135 views

Proving conservation of angular momentum in an elliptic billiard problem

This is for a course focusing on the connections between Newtonian, Lagrangian and Hamiltonian formalisms. We're given an elliptic billiard table with foci 1 and 2, where $L_1$ and $L_2$ are the ...
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79 views

Calculate heat loss of aquifer with unknown shape

I am trying to calculate the heat loss of an aquifer. An aquifer is basically a hot-cold storage $80\: \mathrm{meters}$ under the ground. It is an open system and utilizes groundwater. By pumping for ...
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154 views

Maxwell-Boltzmann distribution

The short story is, that I have to calculate some transport coefficients, but using the the MB distribution as my distribution function. What I currently need to solve is: ${{\mathcal{L}}^{\,\left( ...
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153 views

How to find outflow pressure/force of air through a pipe

I have been trying to find the correct method for determining the outflow force resulting from a certain amount of air being forced into a pipe of a certain dimension. Essentially i'm trying to ...
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226 views

Gradient involved commutator in $\phi^4$ theory

In a phi fourth theory, the Hamiltonian density is: $$\mathcal{H}=\frac{1}{2}\pi^2+\frac{1}{2}(\nabla \phi)^2+\frac{1}{2}m^2\phi^2+\frac{\lambda}{4!}\phi^4$$ Now I impose the usual equal time ...
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129 views

Maxwell-Boltzmann distribution for transport equations

I have to calculate the transport coefficients for the Maxwell-Boltzmann distribution. But I'm not sure what distribution I have to use. As far as I know it should not be the MB distribution for ...
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142 views

Mercury's Orbital Precession in Special Relativity

I am researching Mercury's orbital precession. I have considered most perturbations and general relativity. I am still not satisfied. I need your help. I need a solution to Exercise 13, Chapter 6, in ...
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140 views

Stress-energy tensor of point particle when the trajectory is a transcendental equation?

I'm working through Carroll's GR book, and Problem 7.8 is not coming together. I'm missing something idiotically simple, but I'm not sure if I can cleanly write a stress-energy tensor for a point ...
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99 views

Proton scattering off electrons

I'm looking at a question which starts off as: A proton is travelling through a material and scattering the electrons in the material. Express the scattering angle in terms of the impact parameter, ...
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0answers
33 views

Henry's Law in metals

For fixed temperature the concentration of a gas dissolved in a solution is directly proportional to the gas pressure $p$, i.e. $c_s (T,p) = f(T)p$. Since $H_2$ only dissolves in metals as single ...
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1k views

Joule-Thomson effect of Van der Waals gas

I'm supposed to calculate the inversion pressure $p_i$ of a Van der Waals gas. The state equation of the Van der Waals gas is: $$(p + \frac{a}{V^2})(V-b) = RT.$$ To get a hold of the inversion ...
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128 views

Dust generated static space-time implications on fluid 4-velocity

Imagine we have a perfect fluid with zero pressure (dust), which generates a solution to Einstein's equations. Show that the metric can be static only if the fluid four-velocity is parallel to the ...
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195 views

linear response for a simple harmonic oscillator

Really sorry for this simple question, but I think it will be useful/interesting in general. Consider a quantum simple harmonic oscillator. Add a perturbation $H_I = -\lambda \hat{x}$ Calculate ...
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91 views

Feynman Diagram for Interaction of Deuteron with Oxygen-16

I have to draw a Feynman diagram for the interaction of a deuteron with Oxygen-16. The interaction is as follows: $ d + {}^{16}O \rightarrow p + {}^{17}O . $ I am generally ok with Feynman ...
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127 views

Use of Principle of Equivalence

Let $x^\mu$ be the coordinates of a reference frame, $K$, where all bodies feel the same constant and uniform acceleration $\textbf{a}=\textbf{g}=-\nabla\varphi$; let $\xi^\mu$ be the coordinates of a ...
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74 views

Concentration of Proteins

You release a billion protein molecules at position $x = 0$ in the middle of a narrow capillary test tube. The molecules’ diffusion constant is $10^{−6} \ cm^2 s^{−1}$. An electric field pulls ...
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0answers
291 views

Rotational Constant and Moment of Inertia of Fluorine gas

I have come across some homework question on thermodynamics which needs me to calculate $B$ of $F_2$ My attempt: $B= \frac{h}{8\pi^2cI}$ where $I=\mu r^2=\frac{m_1m_2}{m_1+m_2} r^2$ Atomic mass of ...
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225 views

How to Analyze Applied Forces/Torques of System With Multiple Massless/Frictionless Pulleys of Different Radii

I have been reviewing the basics of mechanics in preparation of studying Spivak's text book on mechanics (I am from a more mathematical background and I am taking an advanced analytical mechanics ...
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31 views

How do I find the force from drop shock using material properties?

I am dropping a cylindrical cast iron bar with a know elastic modulus and poisson's ratio, $E_{1}$ and $v_{1}$, onto a flat beam of elastic modulus, $E_{2}$ and $v_{2}$ so there is tangential drop ...
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190 views

Getting pairs of angle and velocity for a projectile to a given destination

I'm trying to calculate the initial velocity $v_0$ and angle $\theta$ for a given destination $(x, y)$ with a launch height of $y_0$. Obviously there will be a set of pairs of velocity and angle that ...
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85 views

Problem in average height

Let, diameter of cylinder hole of height 30m and diameter 2m filled with water. In a book, when author tried to find out the power for lifting all of the water then he used average height. why is ...
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364 views

Point charge moving towards a conducting plane

A point charge $q$ of mass $m$ is released from rest at a distance $d$ from an infinite grounded conducting plane. Show that the charge hits the plane after an amount of time given by: $ \Delta t= ...
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49 views

Height of a piston in a heated cylinder containing H2O

I'm a first time user and I hope I won't be too enigmatic asking the following question: I have a cylinder (radius= $6$ $\text{cm}$) with a frictionless piston on top of it and inside $30$ $g$ of ...