# Tagged Questions

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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
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### A question on charge renormalization in QED

Let us work with charge renormalization in QED. Consider 2-point photon correlation function $\Pi_2(q^2)$ at one loop level. We normalize the coupling constant at $q^2=0$ (point of normalization). ...
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### Neglecting friction on a pulley?

So, this is how the problem looks: http://www.aplusphysics.com/courses/honors/dynamics/images/Atwood%20Problem.png Plus, the pulley is suspended on a cord at its center and hanging from the ceiling. ...
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### Massless Dirac equation is Weyl covariant

Does somebody know how to show that the following equation is Weyl invariant? $$\gamma^ae_a^\mu D_\mu \Psi=0$$ where: $D_\mu \Psi=\partial_\mu\Psi+A_\mu^{ab}\Sigma_{ab}\Psi$ is the spin-covariant ...
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### Potential energy of a spring

I have a little problem with the potential energy of a spring... I hope you can help me! I have two coupled pendula, given by two masses $m$ fixed to two rigid bars (that haven't any mass) and with ...
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### helmholtz free energy of a polymer

You have a polymer chain of $N$ units, which is represented by $N$ independent springs in series. The springs are Hookean, with spring constant $L$, and the end to end vector is $\mathbf r$. So the ...
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### What is the angle of the string with the vertical?

A heavy uniform sphere of radius $a$ has a light inextensible string attached to a point on its surface. The other end of the string is fixed to a point on a rough vertical wall. The sphere ...