Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Is there a simple way to explain a fundamental representation of $O(N)$? Is there a simple way to explain fundamental representation in Physics? For example, a fundamental representation of $O(N)$?
| The fundamental - or defining - representation of $O(N)$ is a representation where the elements of the orthogonal group, which be definition satisfy $R^T\cdot R=\hat 1$, are represented by $N\times N$ matrices acting on vectors in $N$ dimensions.
The fundamental representation of $SU(2)$ is a representation by $2\times... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/444702",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Goldstein's proof that $W = -\Delta V$: Why is $\nabla_i V_{ij} = \nabla_{ij} V_{ij}$? On page 11 of the third edition of Goldstein's Classical Mechanics, the book claims that
If the difference vector $\textbf{r}_i - \textbf{r}_j$ is denoted by $\textbf{r}_{ij}$, and $\nabla_{ij}$ stands for the gradient with respect ... | Because the potential $V_{ij}$ depends on the difference ${\bf x}_{ij} = {\bf x}_i - {\bf x}_j$, so
$$
\frac{\partial V_{ij}}{\partial {\bf x}_j} =
\frac{\partial {\bf x}_{ij}}{\partial {\bf x}_j} \frac{\partial V_{ij}}{\partial {\bf x}_{ij}}
= \frac{\partial ({\bf x}_i - {\bf x}_j)}{\partial {\bf x}_j} \frac{\partial... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/444819",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Are photons and electromagnetic waves the same thing? I have a little bit of confusion: From my understanding (which could be totally wrong), photons are the same as electromagnetic waves but are called photons because their frequency is in the realm of what we can see.
Seems too simplistic. Can anyone enlighten me?
| It's probably most correct to add a layer of indirection. EM waves and photons both model the same thing. They just model it differently. This thing is what we informally call "light."
The different models are better at handling different sorts of situations where "light" behaves one way or another. Photons are effe... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/444917",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is the function of this complicated tensioning system? I saw this arrangement for tensioning overhead cables from my train window (schematic below). Why not just have one pulley wheel leading directly to the weights? What function do the additional pulleys serve? For that matter, what are the cables for? They're c... | Having more pulleys increases the mechanical advantage of the system. In this case the mechanical advantage is 3. This means that the weights involved need to be a third as massive and the cables passing over the pulleys need to have a third the strength. This makes everything cheaper, smaller, and more tractable: i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/445062",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "25",
"answer_count": 5,
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Eigenstates of the creation operator We know that coherent states $\vert\alpha\rangle$ are eigenvectors of the annihilation operator $\hat{a}$, i.e.
$$
\hat{a} \vert\alpha\rangle = \alpha \vert\alpha\rangle
$$
while the creation operator $\hat{a}^\dagger$ has no eigenvector.
Now, I have few questions:
*
*Would it be... |
Would it be correct to say that $\langle\alpha\vert$ is (left) eigenvector of $\hat{a}^\dagger$ ? Can we use this formalism, and does it have some (physical) meaning?
Hmmm... I am not familiar with a specific physical interpretation of that. However, note that if $u$ is a left eigenvector of $A$, i.e. $uA=\alpha u$, ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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What determines the color of the light emitted in a Tokamak? We see images of Tokamak plasma with all sorts of colours from red to purple. Why do we see any light at all, since the plasma should be so hot to have dissociated all its electrons? It is all from contamination or unwanted cooling?
| As Maury Markowitz mentioned, the color of the edge of the plasma (the core is colorless and transparent) is determined by the composition of the partially-ionized gas that is recombining with plasma electrons and undergoing transitions at the edge of the plasma. Sometimes this gas is purposely injected (as was the cas... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/445571",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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The physical meaning of the derivative $\frac{\partial{L}}{\partial \dot q_i}$ of a Lagrangian The lagrangian is defined as
$$L = T - V$$
where $T$ is kinetic energy and $V$ potential energy.
Then the euler-lagrange-equation is
$$
\frac{d}{dt} \frac{\partial{L}}{\partial \dot q_i} = \frac{\partial{L}}{\partial q_i}.
$$... | Actually it means the generalized momentum of the system.
Because of $$V=V ( q )$$ so
$$L ( q,\dot q )=\frac { 1} {2 } m \sum {{\dot q} ^2}- {V (q)}$$ then if we make a partial differentiation with respect to particular $\dot q$,that is , $\dot {q_i}$ :
$$\frac {\partial L}{\partial \dot q_i}=m {\dot q_i}$$
So th... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Why are the volumes above and below the center of mass of a uniform cone not the same? So today in my physics class we derived the center of mass of a uniform cone, and it all made sense, but near the end of class a student asked,
"If you were to split an object into two parts with a plane through it's center of mass... | Because mass that's further from the centre has more rotational inertia than mass closer. If you kick a can in its CM it moves without flipping end over end, if the can had more mass at the bottom its CM is lower. So it's not just the amount but the distance that's important.
| {
"language": "en",
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"source": "stackexchange",
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Domain of symmetric momentum operator vs self-adjoint momentum operator Is there an example of a function that is not in the domain of the 'naive' symmetric (but not self-adjoint) momentum operator $p:=-i\frac{d}{dx}$ but is in the 'true' self-adjoint momentum operator $p:= \left(-i\frac{d}{dx}\right)^\dagger$.
I am tr... | Define
$$
P \equiv -i\frac{d}{dx}
\tag{1}
$$
and
$$
\psi(x) = |x|\,\exp(-x^2).
\tag{2}
$$
Let $D(P)$ denote the domain of $P$. Clearly, $\psi$ is not in $D(P)$, because it is not differentiable at $x=0$. However, $\psi$ is in the domain of $P^\dagger$, because
$$
\langle \psi|P\phi\rangle
\equiv
-i\int^\infty_{... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/446058",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How come $\frac{d}{dt}\left(\frac{\partial {r_i}}{\partial {q_j}}\right) = \frac{\partial {\dot r_i}}{\partial {q_j}}$ in Lagrangian mechanics? It is written in the Goldstein's Classical Mechanics text that
$$\frac{\mathrm d}{\mathrm dt}\left(\frac{\partial {r_i}}{\partial {q_j}}\right) = \frac{\partial {\dot r_i}}{\p... | In the Lagrangian formalism position and velocity are considered as independent variables, so indeed $\frac{\partial \dot{q}_j}{\partial q_j} = 0$. See Calculus of variations -- how does it make sense to vary the position and the velocity independently?
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Maximum entropy at equilibrium for closed system: Local maximum or global maximum? For a closed system at equilibrium the entropy is maximum. Is this a local maximum or is it a global maximum?
I am an undergraduate physics student and it seems that the possibility of entropy having local maximums was not discussed. It... | To quote H.B. Callen Thermodynamics book, his second postulate about the formal development of Thermodynamics is:
Postulate II - There exists a function (called the entropy $S$) of the extensive parameters of any composite system, defined for all equilibrium states and having the following property. The values assumed... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/446850",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
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Is Stokes equation a reduction of Navier-Stokes equations? The following Stokes problem:
$$\begin{cases}-\nu\Delta u+\nabla p=f&,\textrm{in }\Omega\\ \nabla\cdot u=0&, \textrm{in } \Omega\end{cases}$$
is a reduction of the Navier--Stokes equations?
$$\begin{cases}-\nu\Delta u+(\nabla u)\,u+\nabla p=f&,\textrm{in }\Omeg... | We write the Navier-Stokes equation in Cartesian coordinates $$\frac{\partial V_l}{\partial t}+\sum_{k=1}^3V_k\frac{\partial V_l}{\partial x_k}=-\frac{\partial p}{\rho \partial x_l}+\nu \sum_{k=1}^3\frac{\partial^2 V_l}{\partial x_k^2}$$ Multiply it by $a^3/Re_{cr}\nu^2$. Get the equation in a dimensionless form. $$\fr... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/446908",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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At what frequency does a string vibrate? When a string with fixed ends vibrates (e.g. plucking a guitar string) Fourier Theorem says that the vibration can be expressed as a sum of its normal modes, which are sinusoidal vibrations with frequencies that are all integer multiples of the fundamental frequency.
My question... | The content of Fourier Theorem is that every periodic function of period T can be represented as a series of (in principle infinite) harmonics, i.e. harmonic motions of frequencies of the kind:
$$
\nu_i = i \cdot \nu_1 ~~~~~ i = 1, 2,3 \dots
$$
each with its own phase.
Therefore, although made by many different freque... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Is the Big Bang a naked spacelike singularity? While reading some answers on similar topics, I was wondering about the nature of the Big Bang singularity in the standard cosmological model. I know it's a spacelike singularity that have a causality horizon, but I have read several contradicting answers and comments abo... | The big bang is certainly spacelike. If you use the definition in Penrose 1973, then the big bang is not a naked singularity. See pp. 85-86 of that paper. He defines a naked singularity as one that can be in both the past and future light cones of the same observer. He describes how this is specifically formulated so t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/447308",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Can a battleship float in a tiny amount of water? Given a battleship, suppose we construct a tub with exactly the same shape as the hull of the battleship, but 3 cm larger. We fill the tub with just enough water to equal the volume of space between the hull and the tub. Now, we very carefully lower the battleship into ... | The question you ask is a good one, and a common one. The phrasing of Achimedes' principle you use is most apropos in situations where you have a large body of water compared to the size of the vessel, so that you don't noticeably raise the water level.
The full mathematical phrasing of the principle holds true in all... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/448673",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "39",
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Energy dependence on boundary conditions for particle in a box I am taking a course in solid state physics, and I have some trouble with the "hard wall" and the periodic boundary conditions for a particle in a box.
The thing is that we obtain, for a box of length L, $k= n \pi/L$, $n\in \mathbb{N}$ for the hard box, w... | The energies for periodic boundary conditions and hard wall boundary conditions are not precisely the same. However, they have basically the same statistical properties. That means that the energy spectra are similar enough that they give the same results for macroscopic phenomena (such as in statistical mechanics).
... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/448882",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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What do "broad" and "narrow" mean in the context of spectral lines? For example, at this page: http://pages.astronomy.ua.edu/keel/agn/spectra.html
it talks about some lines being broader than others. But they all look the same width to me. I feel like this is something very obvious that I'm just missing.
| Imagine you try to fit a Gaussian profile to different lines, you will find that the width of each profile (line) is different. Here's the image you linked, I annotated two lines with two very different widths
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/449005",
"timestamp": "2023-03-29T00:00:00",
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How is pressure an intensive property? I've seen this question asked before but I can't find an answer to the specific point I'm troubled with. From the kinetic theory of gases, pressure results from molecules colliding with the walls of a container enclosing a gas, imparting a force upon the wall. Now, if we split the... |
But If we split the container into two, isn't there effectively half the number of molecules striking the wall on each side so the pressure should also be halved? Shouldnt pressure be dependent on the number of molecules?
The pressure is not dependent on the number of molecules alone. You can simply examine the ideal... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/449201",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Derivation of Covariant Maxwell's Equations I am trying to derive the covariant formulation of Maxwell's equations.
I understand that all four of Maxwell's equations can be written compactly as
$$\partial_{\mu}F^{\mu\nu} - j^{\mu} = 0 \;, \tag{1}$$
and
$$\partial_{[\mu}F_{\alpha\beta]} = 0\;. \tag{2}$$
However, the s... | Since the Levi-Civita symbol is antisymmetric, contraction with it extracts the antisymmetric part,
$$\epsilon^{\mu\nu\alpha\beta} \partial_\mu F_{\alpha \beta} = \epsilon^{\mu\nu\alpha\beta} \partial_{[\mu} F_{\alpha \beta]} = 0.$$
However, the Levi-Civita symbol is also invertible, i.e. we can remove it by contractin... | {
"language": "en",
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If you take 200 rods of plutonium what would happen due to it’s half-life? If you take 200 rods of plutonium then stick them together would 100 full rods worth of plutonium be remaining? And after half-life #2 here would be 50 rods worth of plutonium left and then after half-life #3 would there be on 25 rods of plutoni... | If it is plutonium 239, you most probably will have a melt down the minute you stick them together, because of the critical mass of plutoniumPu-239
Of all the common nuclear fuels, Pu-239 has the smallest critical mass. A spherical untamped critical mass is about 11 kg (24.2 lbs),3 10.2 cm (4") in diameter.
11kg/20... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/449419",
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Does the external leg contraction of gluon in QCD carry group generator index? While I am trying to compute the amplitude for the following Feynman diagram
I realized that the external leg contraction of $g$ should carry group generator index $A$ or $B$, is that right? If so, what would their polarization sum be
$$
\s... | No, there can only exist colorless final states, and so cannot carry a color index. The external leg factors only care about the spin of the particle. Namely, spin-0 particles get unity, spin-1/2 get the eigenspinors $u(p), \bar{u}(p)$ (or $v$), and spin-1 particles the polarization vectors.
The color index will only o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/449545",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Electromagnetic current operator using Feynman rules In the calculus of the electron anomalous magnetic moment some text books usually calculates the forms factors from $\Gamma_{\mu}$ in the expression bellow
$$\left<p',s'|J^{em}|p,s\right> = \frac{e^{iq.x}}{\sqrt{2EV}\sqrt{2E'V}}\bar{u}(p')\Gamma_{\mu}u(p)$$
and then... | Recall where this $\Gamma^\mu$ comes from. If you look at the top of page 185 in Peskin, he introduces it using the diagram
$\phantom{\qquad \qquad\qquad }$
The $\Gamma^\mu$ is just the "blob" (i.e. effective vertex), meaning that it represents everything that happens in between an electron entering and leaving the ver... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/449692",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Could gravitational wave permanently distort a region of spacetime? Imagine a flat spacetime being disturbed by a gravitational wave from a very distant source, say given enough time would that flat spacetime recovers meaning it must be at the same state as before, flat? Please assume a static universe because I simply... | No. If you think of spacetime as a fabric, and a huge mass (such as a blackhole) as a marble, then as soon as you lift the marble then the fabric changes back into its original curvature, which is zero (Or at least think based on our current observations). In addition, based on LIGO's observations, astronomers have cre... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/449780",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Is gas flow always compressible? From Franz Durst's Fluid Mechanics: An Introduction to the Theory of Fluid Flows:
When a fluid element reacts to pressure changes by adjusting its volume and consequently its density, the fluid is called compressible. When no volume or
density changes occur with pressure or temperatu... | At the steady state, the density of a flow will be constant. That's tautological.
Fluids like water can be treated as incompressible because its response to a pressure change is negligible for most practical calculations.
For more information see here.
| {
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I have a question regarding the Painlevé-Gullstrand (PG) metric with factor 2 I have a question regarding the Painlevé-Gullstrand (PG) metric.
If we have the line element in a radial fall we get:
$$d\theta = d\phi = 0$$
$$ds^2 = -dT^2 + \left(dr+\sqrt{\frac{r_s}{r}}dT\right)^2.$$
Writing out the binomial formula we obt... | No, in general the differentials are not really "multiplication" as such (I can go into it if you'd like). So when you expand, you need to write
$$ds^2 = -dT^2 + dr^2 + \underbrace{\sqrt{\frac{r_s}{r}} dr dT}_{g_{r
T}} + \underbrace{\sqrt{\frac{r_s}{r}}}_{g_{Tr}} dT dr + \frac{r_s}{r} dT^2 .$$
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/449959",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Why do we care only about canonical transformations? In Hamiltonian mechanics we search change of coordinates that leaves the Hamilton equation invariant: these are the canonical transformations.
My question is: why we want to leave the equations invariant? I mean: we want to solve a differential equation (the Hamilton... | *
*See What's the point of Hamiltonian mechanics? for a closely related question. The answers in that thread mention various benefits with the Hamiltonian formulation, among other things:
*
*Analysis of structural patterns, symmetries & conservation laws, separability & integrability, Liouville theorem, Hamilton-Ja... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
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Is the second law of thermodynamics a "no-go" theorem? As defined here, there are several no-go theorems in theoretical physics. These theorems are statements of impossibility.
The second law of thermodynamics may be stated in several ways, some of which describe the impossibility of certain situations.
The question i... | From the perspective of statistical mechanics, the second law is neither an axiom nor a strict no-go theorem. It's a practical no-go theorem in the same sense that getting $10^{100}$ heads when flipping a fair coin $10^{100}$ times will never happen. It's not strictly impossible (in contrast to the strict impossibility... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/450313",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "19",
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Potential Difference of a battery - What does it mean? I have studied current electricity for a while now. When I look back at basic concepts, I am quite clear about what current, electron, resistance is. But I cannot imagine about the potential difference or voltage of a battery. Or in a circuit, it is said that poten... | We can consider almost all concepts By water in tank.As water in pipe as electrons , tank as battery or energy source , Pressure difference as potential difference ,resistors as changed area of cross section of pipe etc.In images,the Charges are moving From higher point to lower points,this difference is potential dif... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/450445",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 5,
"answer_id": 1
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Superconductive magnet as a source of energy? Could we charge a superconductive magnet and use it as a source of energy?
| Yes. The energy expended in producing the magnetic field can be recovered during the field's collapse, which occurs after the current producing the field is shut off.
For example, the amount of energy stored in the superconducting magnets that steer the particle beams in CERN's Large Hadron Collider is equal the the k... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/450543",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 2,
"answer_id": 0
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What does it mean for an oven heating element to burn out? The heating element in my oven has just burned out and I needed to replace it with a new one, because it simply wouldn't heat. When I took it out it looked pretty much OK (at least no huge difference to the replacement item).
What does the "burning" mean from p... | An oven element usually consists of a long, single-layer coil of wire packed in an electrically insulating powder inside a protective metal tube. At each end of the tube there are terminals making connections to the ends of the wire, so that a current can be passed through it. This makes the wire hot (probably to a dul... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/451077",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Which heat equation should I choose if I want to toggle between conductive and convective heat transfer? I have a science project where I have an aluminum cylinder, filled with oil, with a diode chain floating inside of it. The diode chain has a bimetallic temperature switch on it that turns off the current once the di... | If you want to know how much heat is produced over time, why not just use the power (watts) delivered by the dc power source (2 amp x dc voltage) during the on time of each thermostat cycle and average it out over the cycle.
As far as the aluminum can temperature is concerned, your graph shows the temperature of the o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/451315",
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Why does the chain yield in nuclear fission sum up to 200%? The table of nuclides states the fission yield, or chain yield $Y$, the percentage of decays of $^{235}$U that lead to an isotope with mass number $A$. Why do they sum up to 200%?
Wikipedia just states
Yield is usually stated as percentage per fission, so th... | It took my probably longer than necessary, but now I understand why it sums up to 200%. An example illustrated it to me. Let me enlighten you with a nuclear power plant. But first, the answer:
Let us assume that $^{235}$U would only split into 1 specific isotope. So when it splits, 2 nuclei are created. $2=200\%$
So, ... | {
"language": "en",
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Electronic band structure I want to know why the bands like valence or conduction splits up into two parts as shown in this diagram. why the energy gaps exist with in these bands? As you can see in this diagram that their is an energy gap with in conduction as well as valence band. what are their physical significanc... | The reason is that electron orbitals are quantised. In a crystal an electron can have linear momentum, $\hbar \vec k$. This is described by crystal orbital, which are basically linear combinations of atomic orbitals at crystal site $\vec r_i$ with coefficients $e^{i\vec k \cdot \vec r_i}$. The energy of such orbitals d... | {
"language": "en",
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Missing link re: how does kelvin relate to temperature when talking about color temperature? I am an electrician at a commercial electrical company. There is an in-house training program that posits the datum that when talking about the designations of color temperature for lights (for example an LED light with a 5000 ... | Your intuition is correct.
For a normal filament type bulb we run current through a narrow wire and the current heats it up due to ohmic resistance and it achieves something like thermal equilibrium - and the physical temperature and the color temperature are the same. This means that there is a lot of infra-red which... | {
"language": "en",
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Direction of gravity General Relativity explains the path a falling body makes (ex. An apple falling toward the center of the Earth) as a geodesic in curved spacetime. What explains the direction the apple falls? In other words: why doesn't the apple follow the same geodesic away from the Earth? What provides the kinet... | *
*For a given timelike geodesic that would be the direction that points into the future light-cone in spacetime.
*The geodesic itself depends (besides on the geodesic equation) on conditions, such as e.g., initial conditions or boundary conditions.
| {
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Can neutrinos change chirality by oscillating? Active neutrinos are left-handed while sterile neutrinos are right-handed. There are speculations that active neutrinos can oscillate into sterile neutrinos. Can neutrinos change chirality by oscillating?
| If right handed neutrinos exist the neutrino dirac mass term
$$-\mathcal{L}_D = m_D\overline{\nu}_L\nu_R +h.c.$$
couples left-handed to right-handed neutrinos and will therefore lead to left handed neutrinos "oscillating" into right handed ones and vice versa.
So yes there would be such oscillations. There are hints to... | {
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Are forces of gases intensive or extensive? What am I wrong at in here:
I read that pressure is an intensive property.
According to this and to $P=\frac{nRT}{V}$, can this be true:
$(1)$: When $V$ is constant, increasing $n$ won't increase $P$, but rather will decrease $T$.
$(2)$: When $T$ is constant, increasing $n$ w... | I think you are confused as to what an intensive property is.
As an example, suppose that we have a room filled with some gas with $(P, V, T, n).$
Now let us say that we consider only half of the room. The new state will be $(P, \dfrac{V}{2}, T, \dfrac{n}{2})$.
The quantities which did not change(P & T) are called inte... | {
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Stone skipping does spinning help? I have tried to hurl a stone with some added rotation and it performed slightly better but I have great difficulty replicating this feat for consistency, my question is should I add angular momentum to my throw or it was just a waste of energy?
| Try thinking of your stone as a spinning top. Its angular momentum will stabilize its orientation in the air, flat side down, which in turn will make it skip across the water more evenly. Without the angular momentum, it would topple over, just like a spinning top that has stopped spinning. That would make it hit the ... | {
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Is spacetime-curvature relative? Velocity is relative, which means kinetic energy is. Since, according to general relativity, energy bends spacetime around it, wouldn't this mean observers moving in different inertial frames measure different values of curvature?
I think this is slightly different from this question: I... | Locally, yes. Globally no.
The Equivalence principle tells you that you can always find a local Inertial reference frame, which means that given a point in spacetime you can always find neighborhood of this point where spacetime is flat, and special relativity holds.
Globally you can't do that because spacetime is, m... | {
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Why is a temperature gradient set up in a heated rod? Suppose a cylindrical rod is maintained at 100 degree Celsius and the other at 0 degree Celsius. My book says that after reaching "Steady State" the rod will have developed a constant temperature gradient all throughout the rod.
Why does the rod reach a steady state... | I think you want a conceptual answer, so:
Heat flows into the end of the rod that's in contact with the 100C source, and flows out of the end that's in contact with the 0C sink.
Unless forced by a heat pump of some sort, heat can only flow from a warmer place to a cooler place. The rod is passive (does not contain any... | {
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Voltmeter has high resistance If voltage remains constant in parallel combination then why doesn't the voltmeter with low resistance give correct reading if there is only one resistor?
If there are two resistors then the one on which we are calculating voltage would be less but if there is only one resistor in the cir... | You would be right if your circuit looked like the first picture (that is, the voltage source is indeed a "pure voltage source" with zero internal resistance).
Any "real" voltage source has some internal impedance which I indicate in the second diagram (the dotted line is "the real voltage source" which consists of an... | {
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What is the low level magmatic frequency to be used to get signal out from a metal faraday cage? I need to track the inventory kept in a sealed metal container at the Gate level before delivery.
I am not sure if RFID tracking can help since the signal tends to bounce on and will not reach the antenna / reader kept at ... | Is this just one piece per container? If so, isn't the easy solution to RFID (or even bar-code) the container run the inventory off that?
| {
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Why is the composite fermion not included in the anyon contents of FQH topological orders? For example, both the $\nu=1/3$ Laughlin state and the Moore-Read state has a simple interpretation in terms of composite fermions, which are bound states of an electron and two fluxes.
Both the Laughlin states and the Moore-Read... | The question is: Where are composite fermions in the anyon content of FQHE? The answer is that composite fermions cannot be derived from the anyon content. Anyons, on the other hand, can be derived from composite fermions. In view of certain remarks made above: It is not debatable that composite fermions are physical p... | {
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What are wave-functions in QM. corresponding to? I was learning about a particle trapped in a double well potential
$$V(0) = \infty, V(x1)=\infty$$
which can be described by $\psi_n$ for n=0,1,...,$\infty$ with corresponding Energies $E_n$.
Just conceptually I understand that in qunatum mechanics a particle can be desc... | You cannot.
The product of the wave function and its complex conjugate gives a real value which is the probability. There is no "physical analogue" of a wave function and no way to understand this intuitively
| {
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Boiling point of water in microwave oven My textbook says that water heats so well in a microwave oven that people might be able to heat a cup of water as much as $8~C^{\circ}$ above the normal boiling temperature of water without causing it to boil.
Normally, the boiling point changes with atmosphere pressure, but I ... | Microwave heating does not stir or shake the water. If the water is left quiet as it heats in the microwave, it is not hard to superheat it. At that point, the slightest disturbance will cause the water to explode into vapor all at once.
It is easy to superheat water like this if the heat deposition rate is high enoug... | {
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Schwarzschild geometry for negative masses Imagine that in a part of our universe there exists negative masses $M=-|M|<0$.
The metric around this object -- say a black hole -- will be of the form
$$
ds^2 = -\Big(1+\frac{2|M|}{r}\Big)dt^2 + \Big(1+\frac{2|M|}{r}\Big)^{-1}dr^2+r^2d\Omega^2,
$$
where I have put $G=c=1$ f... | The Schwarzschild metric with negative mass describes an object that repels test objects, whether they have positive or zero mass. The geodesics of those objects, including massless ones, will not be the same as they would have been for an ordinary Schwarzschild black hole. (In the geodesic equation $\ddot x\sim\Gamma\... | {
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Varying a scalar field Lagrangian density I was varying a scalar field density and I look at this term $${\cal L}~=~-\frac{1}{2}\partial _\mu\phi\partial^\mu\phi.$$
The result that I need to come is $$-\frac{1}{2}\delta(\partial _\mu\phi\partial^\mu\phi)=\nabla_\mu\nabla^\mu\phi\delta\phi.$$
But I can't find a way to d... | Hint: The square root $\sqrt{|g|}$ in the measure is here important. The infinitesimal variation of the action term is
$$\delta \left( \int \! d^4x~\sqrt{|g|} \frac{1}{2}\partial_{\mu}\phi ~g^{\mu\nu}~\partial_{\nu}\phi\right)
~=~ \int \! d^4x~\sqrt{|g|} \partial_{\mu}\delta\phi ~g^{\mu\nu}~\partial_{\nu} \phi $$
$$~\... | {
"language": "en",
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What happens when we cool down the gas of non-identical particles? For gas of identical particles, when we cool it down to extremely low temperature we can see one of two types of behaviour depending on the symmetry of wavefunction with respect to argument interchange, fermion and boson. This happens because particles ... | At some point, confinement and quantization will become important, and this will make that the Maxwell distribution does not apply.
For example He-4 which has six distinguishable particles: two electrons, two protons, two neutrons (two different spins of each), all in the ground state of a potential well.
| {
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Water mixture at different temperatures Let's say that we mix homegeneously and instantly cold water at $t^\circ $ C and hot water at $T^\circ$ C (like in a water tap) in ratio $p:1$. My question is the following: What is the instant temperature of this mixture? Is there a law in that sense?
I am a mathematician, not ... | If you mix cold water at temperature $T_c$ and hot water at a temperature $T_h$ in a ratio $x:1$ then the mixture is going to end up at a temperature:
$$ T_{mix} = T_c + \frac{1}{x+1}(T_h - T_c) $$
If we graphed the temperature as a function of time we'd get something like:
I've represented the part of the graph where... | {
"language": "en",
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How does measuring the location of one entangled photon affect its pair? If you have two entangled photons that are moving in opposite directions and you measure the location of one of them, what happens to the wave function of the location of the other photon?
| Nothing happens to it.
If you know how the two photons are entangled, and if that entanglement has anything to do with the locations of the two photons, then you now know what would happen if you tried to measure the other photon's location in the same manner. This is possible because you combine the measurement resul... | {
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Why are my interference patterns completely out of phase? DIY physics enthusiast here doing a double slit eraser experiment at home with a laser pointer, double slit diaphragm, and few linear polarizers (horizontal at one slit, vertical at the other, +/-45 degrees for the eraser).
When I angle the eraser polarizer at -... | The diagrams represent light coming out of the screen towards us. There are therefore oscillating electric and magnetic fields in the plane of the screen. We don't need to consider the magnetic field, so I've left it out. I'm assuming (to make things easy) that linearly polarised light from one slit has an electric fie... | {
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Where does the factor of one half come from in the delta-vector equation involving the Riemann Curvature Tensor? In Einstein's Theory, A Rigorous Introduction for the Mathematically Untrained, by Grøn and Næss:
The change of the covariant components a vector by parallel transport around an indefinitely small closed cu... | The explanation of the apparent contradiction is that the infinitesimal surface area embeds a factor $2$. In fact in your link it is stated:
$d\sigma^{\nu \alpha} = (a^\nu b^\alpha - a^\alpha b^\nu) d\xi d\eta$
where:
$d\sigma^{\nu \alpha}$ infinitesimal surface area
$(\xi, \eta)$ parameterization coordinates of the su... | {
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Height of water fountain due to pressure difference This was a question on a fluid dynamics exam: the pressure $p_A$ on a plane is lower than the atmospheric pressure. We fill a water bottle with a straw on the ground and open it in the plane. Water will come out due to the pressure difference. Calculate the maximum he... | Use Bernoulli's Principle: the energy equation for incompressible, inviscid fluid flow:
$$p_{bottle}+\frac12 \rho v_{bottle}^2+\rho gh_0=p_A+\frac12 \rho v_1^2+\rho gh_1$$
Because the bottle is much wider than the straw and with the continuum equation:
$$A_{bottle}v_{bottle}=A_{straw}v_{straw}$$
Where the $A$ are cross... | {
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3D perfectly elastic collision between two points There is a high probability, I think, that this question is a duplicate of some other question ... but to may knowledge, it hasn't been posed in this exact manner:
Assume we have 2 points, $P_1$ and $P_2$, of mass $m_1$ and $m_2$ in a world coordinate system $(O, \vec{i... | Because there is an infinite number of solutions. Even if you assume conservation of the energy, a given collision that results in final components of the momentum outside the line of initial motion, will be degenerated by a rotation around that axis. The degeneracy is double (six variables, four equations), because yo... | {
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Why we neglect the $\hbar ω/2$ in the Hamiltonian of the the Electromagnetic Field? After the quantization of the electric and the magnetic field, we get the Hamiltonian of the electromagnetic field:
$$H= \hbar ω(a^{\dagger}a +1/2) .$$
with $\hbar$ the planck constant and $a^{\dagger}$ the creation operator.
Why can w... | If the number of oscillators is finite, the term is finite and usually constant (if frequencies do not change). Thus it is just an additive constant in the Hamiltonian, which never changes anything important, so it can be dropped to make analysis less cumbersome.
If the term changes (such as due to changing boundary co... | {
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Violation of Virial theorem as indication to ergodicity breaking Under which conditions the break of virial theorem implies break of ergodicity?
I've seen this question, but it is very limited and not sufficient. To constrain the discussion I'm interested in 1D hamiltonians of the form (2 degrees of freedom)-
$$H=a p^2... | I tried to learn a little about the subject, so here is my attempt at an answer. According to van Kampen
https://doi.org/10.1016/0031-8914(71)90105-4
the system is ergodic if and only if all autonomous functions of position in phase space have time averages (for trajectories on an energy surface $E$) equal to phase spa... | {
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Length dimension in the Lane-Emden equation I was deriving the Lane-Emden equation from the hydrostatic equation and the polytrope. I was following the procedure presented by Carroll & Ostlie's book. I was stuck on this part, it said that the collective constant
$$\left[(n+1)\left(\dfrac{K \rho_c^{(1-n)/n}}{4\pi G}\rig... | The constant $K$ is defined by the polytropic equation of state
$$P=K\rho^{1+\frac{1}{n}}$$
so $K$ has strange dimensions that cancel out the strange dimensions of $\rho_c^{(1-n)/n}$.
Since
$$[P]=[M][L]^{-1}[T]^{-2}$$
and
$$[\rho]=[M][L]^{-3}$$
one has
$$[K]=[P]/[\rho]^{1+\frac{1}{n}}=[M]^{-\frac{1}{n}}[L]^{2+\frac{3}{... | {
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Is there any constant with unit meter-second? I wanted to know if there exists a constant with a unit meter-time or say length-time. Dimensionally [LT].
I have searched browsed a lot. Is there any quantity arising with such a unit?
| One can probably always derive some contrived example.
If I characterize flow in a pipe by the property of "residence" $R$, for example, where the time required for some slug of liquid to pass through a pipe of length $L$ and cross-sectional area $A$ is $t=RL/A$, then this property would have units of meter-second.
If... | {
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$\hbar \approx 0$ and the spread of QM wave function Is there a direct mathematical method to show that if a quantum wave funtion is initially sharply localized, then it will stay sharply localized if $\hbar \approx 0$? In that case the Ehrenfest theorem implies the transition from quantum mechanics to classical mechan... | The propagator for a one-dimensional free particle is, for example,
$$ K(x'-x, t'-t) = \sqrt{\frac{m}{2\pi\mathrm i\hbar (t'-t)}} \exp\left( -\frac{m(x'-x)^2}{2\pi\mathrm i\hbar (t'-t)} \right) . $$
Meaning that $\psi(x', t') = \int K(x'-x, t'-t)\, \psi(x, t) \, \mathrm dx$.
Here, $m$ is the particle mass.
In plain(er)... | {
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Lunar eclipse redness not visible through telescope? I watched the total lunar eclipse on January 20-21 in North America. Looking at it with my eyeballs it appeared red. This is due to Rayleigh Scattering. When I looked at the eclipse through binoculars and a telescope, the color was washed out, and it looked like its ... | This is strictly related to psychology, and the physiology of the eyes. Specifically, if our eyes have nothing to compare the hue of a scene too, we assume it is color balanced. Also, the retinal pigments are depleted the stronger the color energy.
| {
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Being Frictionless, surface of contact I frequently hear references to a smooth surface, or frictionless pulley.
Can being frictionless be obtained if only one of the 2 surfaces has 0 coefficient of friction?
Or is it for the contact of those 2 surfaces (in friction due to material roughness)?
What in the cause of fric... | Let's try to answer your question.
Can being frictionless be obtained if only one of the $2$ surfaces has $0$ coefficient of friction?
So if we consider two surfaces which are not adhesive in nature and do not deform, then yes, friction can be minimised by making only one of the surfaces smooth.
What in the case of ... | {
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Difference between $\bf J$ and time derivative of $\bf E$ in Maxwells equations? Maybe I am being confused. It was some years ago I did this. An electric current changes charge distribution which creates rotation in $\bf B$. So in Ampères / Biot-Savarts law what is the difference between $\bf J$ and the time derivative... | $\partial \mathbf E / \partial t$ represents the rate of change of the electric field $\mathbf E$ at that point. Electric fields do not need to change at a point due to movement of charges at that point. For example, consider the space between the plates of a charging capacitor (moving charges are nearby, but not at th... | {
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Derivation of the work-energy theorem We state the following version of work-energy theorem :
$$ K_2-K_1=Fd=W $$
Where acceleration is assumed to be constant, so is the force $F$.
Then the physicists proceed by writing
$K_2-K_1=F[x(t_2)-x(t_1)]$
$$=F(x_2-x_1)$$
Notice, $x(t)$ was a polynomial of time $t$ with highest... | Change in kinetic energy is the work done on the body (let us say by a force as a function of distance).
$K_2-K_1 = \int F(x)dx$ $=W$
And $\Delta U = - W$. Which implies $K_1+U_1=K_2+U_2=E$ where $E$ is the total energy.
If your concern is as to how $W$ is derived, then you must realise that it is a definition.
| {
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Stress in a rod clamped between two rigid walls when the temperature is increased The usual approach to calculate stress is to equate thermal expansion in the unclamped condition to the magnitude of contraction caused by strain produced due to the walls. I have some questions about this approach:
*
*Wouldn't Young's... | The original length of the rod is L (when the temperature is not raised), when the temperature is raised by ∆T the NATURAL TENDENCY of the rod is to stay in a length of L(1+α∆T), where α is the coefficient of linear expansion.Due to the fixed walls , the rod is being kept at a length of L , although at that temperature... | {
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"answer_id": 3
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Electric Flux of A Point Charge Derivation I am trying to understand the derivation of Gauss's Law and came across this line describing the electric flux through a small area of a sphere from a point charge: Source $$ E\cdot\Delta A_i = E_n\Delta A_i = E\Delta A_i$$
Where:
*
*E = electric field
*A = area on the i... | Because only the perpendicular component of the electric field contributes to the flux through an area. To simplify notation we define an infinitesimal 'area vector' as
$$
d\mathbf A \equiv \mathbf n \, dA
$$
where $\mathbf n$ is the local normal vector of the surface. So you can either write Gauss' law as
$$
\oint_S \... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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If mass can be converted to energy than how is it said that energy can't be created? From the mass-energy equivalence E=m(c*c), it can be seen that energy can be created and it is not converted from one form of energy.
Or am I wrong ?
Can you explain?
|
From the mass-energy equivalence E=m(c*c), it can be seen that energy can be created and it is not converted from one form of energy.
Have you checked what this m is in the famous equation? m is the relativistic mass, and is not an invariant.
It depends on velocity, and kinetic energy depends on velocity too,it is ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/457526",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What goes wrong, theoretically, when we reverse time? (Please bear with me if this is a stupid question; I'm not a physicist, just a curious student.)
I know that Noether's Theorem links symmetries to conserved quantities: the fact that the laws of physics work anywhere in space, for example, is linked to conservation ... | The Weak Nuclear Force throws off a lot of symmetries. Time reversal among them T-Reversal.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Torque due to friction on a series of disks Recently I was looking at two situations involving friction and torque.
The first situation seemed pretty straightforward at first. A disk of mass $m$ and radius $r$, with a coefficient of static friction $\mu _s$ with the ground, is given a force $F$ originating at its cente... |
Assuming that the coefficient of static friction is high enough such that $μ_sN=F...$, we can pretty trivially show that $Σ_xF=0$ and $Σ_yF=0$.
Actually, I'm not sure you can. $\mu _sN$ gives you the maximum possible force of static friction, not necessarily the actual force. To find the actual force you'd need to... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/457716",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Why is information indestructible in quantum mechanics? Why is information indestructible in quantum mechanics?
| We can paraphrase the question to a statement like this: "Entropy of any isolated quantum system with density operator remains constant with time".
$$S(ρ) = −\mathrm{Tr}(ρ \log_2 ρ)$$
This is because ρ is not time-dependent and the eigenvalues ρ does not change with time (preserves spectrum of ρ). Here there is no con... | {
"language": "en",
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"source": "stackexchange",
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Gravitational lensing redshift around a Kerr black hole Light from a source passes by a Kerr black hole on two sides at the equator and converges at the observer. The axis of rotation of the black hole is perpendicular to the direction of light. Two rays of light pass through the spacetime regions of a significant fram... | Kerr metric is stationary and has a Killing vector field $\xi_t=\partial _t $, time-like outside of the black hole, representing stationarity. This means that the quantity:
$$ E = g_{\mu\nu }\xi^\mu_t p ^\nu ,$$
where $p^\mu$ is 4-momentum (of, say, a photon), is conserved along the geodesics.
So, if both the source of... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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Temperature of items from a freezer I've read that all items in a freezer are at the temperature at which the freezer are set to (obviously items have to be in the freezer long enough). So, if I put normal tap water in a freezer which is set to -26C (which is what mine is set to) and it freezes, and I leave that ice lo... | Adding salt to water lowers its freezing temperature (and elevates its boiling temperature). It's called Freezing Point Depression (FPD). So liquid salt water near its freezing temperature will feel colder than the liquid fresh water near its freezing temperature.
But I can see be no reason for the frozen salt water at... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What happens to the spin when photon is absorbed by an electron? Photon is spin 1 and electron is spin 1/2, so when a photon is absorbed by an electron it is destroyed and the electron becomes excited by that amount of energy. The next moment the electron will go back to it's ground state and emits a photon with the sa... | If not coupled into otbital angular momentum, electron can flip its spin to compensate the spin of a photon. In the case require electron to flip spin, at the moment electron and photon interact they must have opposite spin to begin. So they can engage into quantum entanglement to allow the process happen.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Friction acting as an internal force I was solving this problem in my assignment:
Assuming a frictional force F acts on the block of mass m, a force -F will act on plank of mass M. Hence, the net work done by frictional force should be zero, as friction is an internal force , but option D is given incorrect. What's t... | Work is given by $$W=\int\mathbf F \cdot \text d \mathbf x$$ which, in the case of constant forces in 1D reduces to $$W=F\Delta x$$This definition depends on the path over which the force is applied, so having equal forces is not a sufficient condition to have the total work done on both blocks by friction be $0$.
I wo... | {
"language": "en",
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Calculation of Gravitational Potential at the centre of the cube
I came across this problem in a test and have been able to come up with a solution however I am unsure if it is correct.
I started by building a cube of twice the initial dimensions to bring point P to the centre of a larger cube. This was to bring an el... | The Gravitational Potential at the corner of a cube of given density should be proportional to $L^2$ where $L$ is the length of an edge. The potential is the potential due to the cube minus the potential due to the removed cube, $1-{(\frac{1}{2}})^2 = \frac{3}{4}$ of the original cube, in agreement with your method. So... | {
"language": "en",
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Horizontal component of Coriolis force in an aircraft: compensating force with its wings angle I have the following problem:
"An aircraft is flying at 800 km/h in latitude 55◦ N. Find the angle through which it must tilt its wings to compensate for the horizontal component of the Coriolis force."
What I understand is t... | On a level flight, you know that all the vertical forces must sum to zero (or you'd be accelerating upward or downward).
By banking the airplane, you can change the direction of the force from the wings. When flying straight, all force is vertical. When banking, a component of the force is vertical and a component i... | {
"language": "en",
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Why doesn't observing a photon collapse it's wave function into a B or W3 boson? According to electroweak theory, the photon ($\gamma^0$) and weak bosons ($W^+, W^-, Z^0$) are all linear combinations or superpositions of the weak hypercharge boson ($B$) and the weak isospin bosons ($W_1, W_2, W_3$):
\begin{align}
W^+&=... | We are presently living in the world where the symmetry you describe has been broken, i.e. the particles instead of being massless have acquired through the Higgs mechanism a mass, a huge one for the W and Z , and zero for the photon.
Energy conservation is an absolute law , and masses are part of the energy budget of ... | {
"language": "en",
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Does the resistance of the voltmeter affect the behavior of this circuit? I have this setup.
It consists of a battery of no internal resistance with voltage $V$ and a resistor with resistance $R$. It also consists of a voltmeter of some (not so large) resistance as good ones should have.
Now my question is, will th... | Having an extremely high resistance in a voltmeter is crucial to measuring the voltage drop across a component.
The formula for finding the equivalent resistance of 2 resistors in parallel is $\frac{R_{1}R_{2}}{R_{1}+R_{2}}$.
Now, $$\lim_{R_{2}\to\infty} \frac{R_{1}R_{2}}{R_{1}+R_{2}} = R_1$$ if you go through some alg... | {
"language": "en",
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When can you simplify the $W$ boson propagator? I have seen in several sources that the propagator of the $W$ boson is:
$$\frac{- i \left( g^{\mu\nu} - \frac{P^\mu P^\nu}{m_W^2} \right)}{p^2 - m_W^2} . $$
But then in some calculations (usually approximations) I have seen that only $$ \frac{-i}{p^2 - m_W^2} .$$
is us... | You have to be careful, there are many subtleties on the quantization of a spontaneously broken gauge theory like the Standard Model (SM) electroweak sector. I recommend you to learn about the quantization of a gauge theory via path integral methods. To quantize a gauge theory, you need to introduce a gauge fixing ter... | {
"language": "en",
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Comparison of two proper times in Special Relativity using an in-between frame I would like to compare two proper times of two inertial observers in Special Relativity.
Let's consider three inertial observers A, O and B freely moving on a line in a flat space-time, with B moving with a constant velocity $v$ with respec... |
Please let me know what is wrong, thank you!
Nothing is wrong. $\gamma$ is an even function, as you have shown
It seems like there is an inconsistency.
The inconsistency in your edit is the pairs of events that you are choosing to compare.
When you use simultaneity in the middle frame to select the events on the... | {
"language": "en",
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Magnetic flux linkage of a solenoid is equal to BAN, but what is A representing? I have been taught that magnetic flux is equal to BA, where B is the magnetic flux density and A is the area. When calculating magnetic flux linkage you simply multiply by the number of coils in the solenoid.
I understand what the area A r... | For me the diagram needed to answer the question was difficult to draw and I did not make a video which would have illustrated the answer better because the soap film would have been easier to see.
I have made a complete circuit out of bare copper wire and within the circuit formed a soap film which represents a plan... | {
"language": "en",
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Why magnetic field starts from north pole and ends in south pole? In magnets such as bar magnets the magnetic field lines are starting from North pole and ends in south pole..but I don't know what is the reason for it..why this happens.
| Your question is like asking "why pi is the ratio of circumference to the diameter of the circle.
It is the very definition of pi.
It has been experimentally concluded that magnetic field lines surround a magnet, which are closed figures. They just named it that way. They could've used cat or dog too, but that would b... | {
"language": "en",
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How can there will be current in purely inductive circuit? In a purely inductive circiut there are two emf's one is applied and other is induced
applied emf and induced emf are equal and opposite, then how can there will be current in a purely inductive circuit.
induced emf is not a potential drop and it produce curre... | For an inductor $\mathcal E_{\rm back} = - L \frac {dI}{dt}$ ie the current must be changing if the inductor is producing a back emf.
The back emf is in opposition to whatever is causing the change in the current though the inductor.
This means that the total emf in the circuit consisting of a cell with emf $\mathcal... | {
"language": "en",
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Rotational analogue of Newton's 2nd law If we are writing torque equation about general point what points must be taken into account for getting the correct result.
Also If that general point is accelerated then how do we deal with this.
Like the first one that should be taken into account is to have moment of inertia ... |
We first write the EOM's for the center mass $C_m$
Translation
$$m\,\vec{a}=\vec{F}\tag 1$$
and
Rotation
$$I_{cm}\,\vec{\alpha}_{cm}+\vec{\omega}_{cm} \times (I_{cm}\,\vec{\omega}_{cm})=\vec{\tau}\tag 2$$
Where :
$\vec{a}$ translation acceleration
$\vec{\alpha}_{cm}$ angular acceleration
$\vec{\omega}_{cm}$ angular... | {
"language": "en",
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When is the order of magnitude not equal to the exponent of scientific notation? Explain why the order of magnitude is sometimes not the same as the exponent in scientific notation. It is because of the units?
| The reason is the exact definition of order of magnitude.
It is defined as the logarithm (base 10) rounded to the nearest whole number (see wikipedia page). Thus, all numbers between $\sqrt{10}\cdot 10^{m-1}$ and $\sqrt{10}\cdot 10^{m}$ have $m$ as order of magnitude, even though, for example, $4\cdot 10^{m-1}$ has $m... | {
"language": "en",
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How does natural unit make sense? Both the fundamental constants $\hbar$ and $c$ have dimensions. In particular, $[\hbar]=ML^2T^{-1}$ and $[c]=LT^{-1}$. But in natural units, we make them dimensionless constants of equal magnitude. How is this possible? This means length is measured in the same units as time which is m... |
But in natural units, we make them dimensionless constants of equal magnitude. How is this possible?
It is not widely known or appreciated, but both the magnitude and the dimensionality of the units we use are a matter of convention. We are free to use different unit systems with different conventions, as long as we ... | {
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Resolve The Envelope Detector Circuit I was working on a little project and I was wondering if the envelope detector circuit could be resolved analytically. Let me explain.
The circuit is the one shown above, I know the values of $C$, $R$ and $V(t)$ which is the input signal. My $V(t)$ is a smooth function and I know ... | The differential equation can be written in the form :
$\frac{d{{V}_{s}}}{dt}=-\frac{{{V}_{s}}(t)}{RC}+\frac{Is}{C}\left( {{e}^{(V(t)-Vs(t))/{{V}_{d}}}}-1 \right)$
I can be wrong but I do not think she admits an exact analytical solution.
But this differential equation can be solved numerically very easily (with Python... | {
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Variational Navier-Stokes: where to find study material "for dummies"? I have worked with the Navier Stokes equations before but I'm a physicist. I was talking to a mathematician and they use a complete different notation and I am very lost.
First of all, I use the Control Volume method for discretization and they use ... | I found two books which look interesting but still feel it is not "for dummies" enough.
*
*The Finite Element Method: Theory, Implementation, and Applications,
Texts in Computational Science and Engineering, by M. G. Larson and
F. Bengzon
*A Mathematical Introduction to Fluid Mechanics by Chorin and Marsden
But sti... | {
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Why is blowing so different than sucking? Why is it so easy to blow out a candle from a significant distance, but nearly impossible to suck enough air to do the same?
Even without focusing the airflow through a nozzle or something, this affect seems to be present. For example, it's easy to feel the air coming out of a ... | A coherent stream of air can be said to be comprised of air particles with a similar velocity magnitude and direction. For both sucking and blowing, there is a relatively coherent stream of air in your mouth.
Sucking is pulling air almost equally from all directions, into your mouth, where it becomes coherent. See illu... | {
"language": "en",
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"source": "stackexchange",
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Energy formula for finite potential well The energy formula for infinite potential well is $$E=\frac{n^2h^2}{8ma^2},$$where $m$ is the mass of the particle, $a$ is the width of the well but in the case of finite potential well, I actually went to search online for the energy formula but to no avail. Does anybody here k... | There is no clean analytical formula for the eigen-energies of the finite potential well. As Wikipedia explains, the quantization condition for that problem reduces to a transcendental equation of the form
$$
\sqrt{u_0^2 - v^2} = v\tan(v),
$$
where $u_0$ is a fixed number and $v=kL/2$, a proxy for the energy $E=\hbar^2... | {
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Why didn't Lorentz conclude that no object can go faster than light? Based on Lorentz factor $\gamma = \frac{1}{\sqrt {1-\frac{v^2}{c^2}}}$ it is easy to see $v < c$ since otherwise $\gamma$ would be either undefined or a complex number, which is non-physical. Also, as far as I understand this equation was known before... | Because typically if you find an expression that seems to break down at some value of $v$, you would conclude that the expression simply loses its validity for that value of $v$, not that the value isn't attainable. Presumably this was the conclusion of Lorentz and others.
The reason Einstein concluded otherwise is tha... | {
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"source": "stackexchange",
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Kac-Moody algebra from WZW model via Poisson brackets In 'Non-abelian Bosonization in Two Dimensions', Witten shows that the Poisson brackets of the currents that generate the $G\times G$ symmetry of the WZW model give rise to a Kac-Moody algebra upon canonical quantization.
The Poisson brackets are calculated on page... | I think he may be using the distributional identity
$$
f(x)\delta'(x-a)=f(a)\delta'(x-a) -f'(a)\delta(x-a)
$$
which comes from differentiating
$$
f(x)\delta(x-a)=f(a)\delta(x-a)
$$
with respect to $x$.
| {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why can all solutions to the simple harmonic motion equation be written in terms of sines and cosines? The defining property of SHM (simple harmonic motion) is that the force experienced at any value of displacement from the mean position is directly proportional to it and is directed towards the mean position, i.e. $F... |
How can we assume so plainly that it should be sin or cosine only
It's literally just a guess. Those're obvious solutions which can be verified easily, and when they're such straightforward functions, you'll soon just be able to notice them. It's the like when you have an equation like $f'(x)=K\times f(x)$, you just ... | {
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Thickness of a target bombarded with deuterium I need to calculate de thickness of a sheet of Zinc that is being bombarded by deuterium nuclei. I'm given that the fraction of nuclei dispersed below $\theta=90º$ with $T=8MeV$ is $0.9999$ and the density of the sheet $\rho=7.14 g/cm^3$.
From this pdf (page 7)
(http://www... | I found out that I had to integrate the function $dN=N_i \frac{\rho L}{m} \frac{d\sigma}{d\Omega}d\Omega $.
By doing this I got:
$$L=\frac{N}{N_i} \frac{m}{4\pi D \rho}$$
where $D=(\frac{Z_1 Z_2 e^2}{4\pi \epsilon_0 4 T})^2$
And thats it, I got a thickness of $L=66.9cm$, which is a bit too long to hold with this approx... | {
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Behaviour of quantum spins I am reading the Jordan-Wigner transformation in the book "Introduction to many-body physics" by Piers Coleman. When I read the introduction of this chapter, it is stated that:
Quantum spins are notoriously difficult objects to deal with in many-body physics, because they do not behave as can... | If I understand your question correctly, there seems to be a misunderstanding in your statement
As far as I understand, in quantum mechanics, you can identify any spin half particle to be fermion and any spin one particle to be boson. Even if we have many of them, why do they not behave just like one of this (fermion... | {
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Reason why dot notation isn't used for time derivatives in Maxwell's equations Maxwell's equations seem to be usually written:
\begin{align}
\nabla \cdot \mathbf{E} &= \rho/\epsilon_0,\\
\nabla \cdot \mathbf{B} &= 0,\\
\nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t},\\
\nabla \times \mathbf{B} &= \m... | The dot notation typically refers to a total time derivative. In field theory partial & total time derivatives of the field are often the same, and the dot notation can sometimes be seen in the field theory literature as a convenient short-hand.
An important exception is the material derivative in fluid dynamics.
Simil... | {
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Physical meaning of electric field flux I need to test my understanding regarding the physical meaning of the electric field flux. First of all, the electric flux is found by the surface integral of the field dot product a differential surface. So what I understand is by doing this dot product we are capturing the norm... | Yes, what you are understanding is correct. I should point out that it is the nature of electrostatics that makes flux a physically important quantity. In particular, the flux, as defined in the way you defined (i.e., the surface integral of the vector inner-product of the field at a point and the area element of the c... | {
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How does current flow in a short circuit? In a short circuit, the potential difference across the terminals of a battery (consider a single cell with internal resistance)is 0 according to the equation
$$V=E-Ir,$$
where $r$ is internal resistance of the cell,$E$ is the emf of the cell and $V$ is a potential difference ... | Think about a conventional (idealized) circuit with an ideal voltage source driving current through a resistor. I am sure you agree that current
$$ I = \frac{U}{R}$$
will flow.
Now take any two points between resistor and voltage source. The voltage drop between them is zero (in practice), but still a current flows!
Th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/463247",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
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Do Chern Insulators (QAHE) have topological order (long-range quantum entanglement)? I know IQHE is a example having "invertible" topological order from Professor Wen's definition. And Topological Insulators is SRE because of necessary of underlying symmetry protection. After that, the Chern Insulator (QAHE) needs a un... | Chern Insulator = QAHE = IQHE. Chern Insulator has "invertible" topological order and long-range entanglement as defined in https://arxiv.org/abs/1004.3835 .
Chern Insulator does not need any symmetry, although one usually assume Chern Insulator has an U(1) symmetry.
Q: what topological order does IQHE have? | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/463466",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 0
} |
How can we use Newtons 1st and 2nd Laws on Earth when gravity makes all frames non-inertial? As Newtons laws of motion only hold in inertial reference frames, how come we use them freely to describe motion of particles under the influence of gravity?
Isn't the only frame where we can apply Newtons laws in a frame acc... | Inertial reference frames are frames where bodies with zero net force move at constant velocity. It follows from this definition that inertial reference frames have constant velocity with respect to one another. Measurements in one inertial frame can be converted to measurements in another by a Galilean transformation.... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/463554",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 2,
"answer_id": 1
} |
Why is oil called more viscous than water when we slip on oil more than we do on water If we were to throw some water on the floor then walk over it we may or may not slip but it wouldn't that be difficult to walk. If we repeat the same thing with oil we it would be harder to walk as me spread our legs and apply a forc... | Firstly, friction is a resistive force which acts between two surfaces in contact. Viscosity is fluid friction; the frictional force that acts between the layers of fluid particles or between an object immersed in the fluid and the fluid particles. Scientifically, the frictional force that acts between the layers of oi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/463636",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 2,
"answer_id": 1
} |
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