Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Does the track do work? (second try) When a ball rolls without slipping down a track, it seems like static friction from the track does rotational work on the ball. As explained in this post:
Is work done in rolling friction?,
this work is exactly the same as the work done by gravity around the pivot point. But shouldn... | Yes, the track does work. You can verify that the final velocity of the ball is less than $\sqrt{2gh}$. This is because the friction force did negative work.
This is exactly what is the work-energy theorem says: The sum of the forces on an object times the displacement of the center of mass of the object is equal to th... | {
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What happens to Kinetic Energy in Perfectly Inelastic Collision? I’m going over a chapter on linear momentum in my physics course right now and am somewhat puzzled with what happens with some of the kinetic energy that is lost in a perfectly inelastic collision.
Imagine a world without sound, heat, or any non-mechanica... | Your question contains a contradiction. You imagine a world without any forms of non-mechanical energy- in such a world, inelastic collisions could not exist. The whole point of inelastic collisions is that mechanical KE is lost to non-mechanical forms of energy.
| {
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Time averages of complex quantities If an electric field $E$ oscillates as $E_0\sin(ωt)$ then the average value of $E^2$ over one period of oscillation will be
$$E_0^2\left< \sin^2(ωt)\right>=E_0^2/2$$ since the average value of $\sin^2(ωt)$ is well known to be $1/2$.
However if we write $E$ using complex numbers as $E... | The real part of the product of two complexes is not the product of the real parts. So it is mandatory to go back to real notation before calculating the average.
Another solution is to use the trick :
$$\langle x(t)y(t)\rangle=\frac{1}{2}\Re\{\underline{x}{\underline{y}}^*\},$$
with the exponent * which represents t... | {
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Wave Equation Simulation I've been recently trying to simulate a wave equation in P5.js.
My aproach is to plot a bunch of points with $(x, y)$ coordinates. I've used the wave equation for obtaining the movement of those particles.
This is my numerical integration method:
var pos = this.masses[i].pos
var nextPos = t... | I am not at all an expert in numerical methods but the stability condition for the algorithm "time stepping" is $c<∆x/∆t$.
This condition does not seem to be verified in your case, with $c=10$ ?
| {
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Why are there both antinodes at both ends of the tube? I learned stationary/standing waves the other day. For stationary waves in open tubes, the textbook says both ends must have an antinode. Can anyone tell me why? (shown as figure)
And also, when playing with the instruments like guitar, what's the number of harmon... | The air molecules are free to move at the open end of a tube, so there's an antinode. At a closed end, there must be a node as the air molecules don't move there.
That's similar to a wave in a string, at the fixed ends the string can't move and there are nodes there. The first harmonic for a string (the fundamental),... | {
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How is electromagnetic induction analogous to gravitational frame dragging? This wiki says: https://en.wikipedia.org/wiki/Frame-dragging
Qualitatively, frame-dragging can be viewed as the gravitational
analog of electromagnetic induction.
I was wondering what exactly this means, and the wiki for electromagnetic induc... | The easiest way to access the idea behind this analogy is to think in 4-vector, we know that the electric and magnetic fields can be represented in one being $A^{\mu}=(\phi/c, \vec{A})$ with $ \vec{B}=\vec{\nabla}\times\vec{A}\;\;,\vec{E}=-\vec{\nabla}\phi-\frac{\partial\vec{A}}{ \partial t} $
If we replace the electr... | {
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What formula is this and what does it signify? (Electric Field and Potential) I probably skipped the useful part of the lecture, but while we were being taught about electric potential energy, my professor mentioned an equation, which he said we will seldom use, but which is significant. The equation is for the potenti... |
So, I want more insight into this equation, what is the significance
of this and if possible a name of any of these two.
Perhaps showing you the connection between the formula and the potential energy stored in the volume containing the electric field between the plates of a parallel plate capacitor may give you some... | {
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Averaging over spin phase-space for a cross section In Peskin and Schroeder the Dirac equation is solved in the rest frame for solutions with positive frequency:
$$\psi(x) = u(p) e^{-ip\cdot x}$$
$$u(p_0) = \sqrt{m} \begin{pmatrix} \xi \\ \xi \end{pmatrix},$$
for any numerical two-component spinor $\xi.$ Boosting to an... | We can't solve it analytically, so the average is taken as a good approximation.We also make the assumption that each particle has finite spinors.
| {
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Why Do We Ever Get Interference in a Quantum Eraser? There are many questions on this site about the quantum eraser, but I think mine is not quite answered by any of the other answers on the topic.
Here's the setup:
My understanding of this experiment is the following. If a stream of photons is passed through a double... | At the heart of your question is the supposition that:
"basically the act of destroying a photon and making two new ones represents a measurement which collapses the wavefunction"
This is not necessarily the case, if we consider the photon process per Feynman/Dirac, we have excited electron, photon creation and path de... | {
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The change of mechanical into electromagnetic waves and vice versa I know that sound is a type of mechanical wave, so the human eardrum changes mechanical energy into electronic energy (impulses) so the information may be processed by the brain.
Question: As satellites transfer info by electromagnetic waves that are al... | Yes, a microphone is a device that takes mechanical vibrations from sound waves and turns them into electrical signals. A loudspeaker takes electrical signals and creates mechanical vibrations of a speaker and that causes pressure oscillations in the air that we hear as sound.
Any such device that has created sound on... | {
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Why do we need insulation material between two walls? Consider a slab made of two walls separated by air. Why do we need insulation material between the two walls. Air thermal conductivity is lower than most thermal conductivities of insulating material and convection cannot be an issue in the enclosed volume: hot air ... | You can think of thermal conductivity as a measure of how readily heat will flow through the material while it is stationary. The low thermal conductivity of air means that it takes a long time for heat to diffuse through an air pocket.
If the air is permitted to move, however, this intuition goes out the window. The ... | {
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Solving this problem using the Work-Energy Theorem
A block is tied to a string wound on a cylinder of mass $m$ and radius $r$, (Through a pulley) which can rotate about its axis on a massless mount placed on a smooth surface.
The system is released from rest, what will be the velocity $v_1$ of the block after it falls... | Thanks to BioPhysicist for the hint. I decided to complete my answer now,
As mentioned in the post, the work energy equation we get is:
$$mgh=\frac{1}{2}mv_1^2+\frac{1}{2}\omega ^2+\frac{1}{2}mv^2$$
Also, as mentioned in the post (Equation 5) we have:
$$g=a_1+a \space\space\space-(1)$$
Using Newton's speed equations, ... | {
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Can we measure the one-way speed of anything at all? I know the one-way speed of light question has been exhausted, and I'm sorry for the naive question, but I would like to understand one thing. Can we measure the one-way speed of anything at all? If we "truly" can, why can't we synchronize that thing and an emission ... | According to Derek Muller from Veritasium, no:
https://www.youtube.com/watch?v=pTn6Ewhb27k&ab_channel=Veritasium
At this point in time, we are measuring the 'average' speed of the roundtrip of light. This is due to the problem of needing two points in space to measure speed:
Speed = Distance/Time
So you would need to s... | {
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Can laser beam condense water vapour? Suppose you pump humidity (water vapour) in an enclosed tank fitted with lasers in all directions, will the water vapour turn to liquid due to collision of photons and $\text{H}_2\text{O}$ molecules?... My thought is that when the high speed water vapour molecules collide with phot... | Firstly, water vapour is made up of individual, isolated water molecules.
Over a wide electromagnetic spectrum water does absorb electromagnetic radiation, in particular IR/VIS/UV which you can see here.
But what makes you think that such absorptions can make the water molecules aggregate and condensation to occur?
AFA... | {
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Peskin and Schroeder equation 3.136 (book edition 1995) I'm studying Peskin and Schroeder's QFT and I'm confused by equation 3.136 on page 68:
$\textbf{Previously, on page 48, equation 3.62 says:}$
$\textbf{My question is: how do we deduce 3.136 from 3.62?}$ $\textbf{It doesn't seem to me that} \boldsymbol{\xi^s}\tex... | Try to use latest version! In the latest version book, equation (3.62) is the spinor solution belongs to negative energy electrons, and (3.136) is belongs to positive energy positron. If you still don't understand then try to interpret it with Dirac sea level (particle-hole transformation), then you will see (3.62) and... | {
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Can current flow in a simple circuit if I enclose the battery in a faraday cage? So suppose I have a regular circuit with a battery connected to a resistor and a lightbulb.
Suppose now somehow the battery is inside a metal box (faraday cage) but the rest of the circuit is outside of it so the wire is maybe poked throug... | Yes, it will. The Faraday cage won't stop the current flowing through the wire around the circuit.
| {
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Does anyone know of an adjustable focusing mirror? Does anyone know of an adjustable focus mirror? Allowing short sight and long sighted people to see clearly in a mirror with no specs on. Is it even possible?
| Most of the glass telescope mirrors currently being manufactured are adaptive: they are made thin enough that their shape can be easily changed by piezoelectric actuators mounted underneath them. This allows almost instantaneous adjustment of their focal length across the mirror area that nulls out the effects of atmos... | {
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Planck radiation law of a dielectric layer Suppose we have a rectangular slab of thickness $h$, width $a$ and length $b$. The upper surface of the slab is put at constant temperature $T$ while all the rest is at initial temperature $T_0$. Obviously the temperature of this slab will increase according to the heat equati... | If I understand your question, you’re asking about the flux of thermal radiation from a heated side of a dielectric slab (index $n$), through the slab, incident to the other side. Correct me if I’m wrong.
I would analyze this starting with the relation
$$A=E,$$
where $A$ is the absorptivity and $E$ is the emissivity of... | {
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Landau levels degeneracy in symmetric gauge I'm reading David Tong's lecture notes on the Quantum Hall Effect.
When symmetric gauge taken, a basis of the lowest landau level wave functions is
$$\psi_{LLL,m}\sim\left(\frac{z}{l_B}\right)^m e^{-|z|^2/4l_B^2},$$
where $z=x-iy$,
and we have
$$J_z\psi_{LLL,m}=\hbar m \psi_{... | why $r_{max}=\sqrt{2m}l_B$? You can square $\psi$ and take derivative w.r.t to z. And assume z is positive since radius r is positive. Then $|z|^2$ is just $z^2$. You solve this equation and then you can obtain $r_{max}$. This procedure is just finding the maximum value.
Other parts of your problem has already been ans... | {
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Is there any *global* timelike Killing vector in Schwarzschild geometry? I have been dealing with the following issue related to the Schwarzschild geometry recently. When expressed as:
$$
ds^{2}=-\left(1-\frac{2GM}{r}\right)dt^{2}+\frac{1}{1-\frac{2GM}{r}}dr^{2}+d\Omega_{2}^{2}$$
one can find a Killing vector $\xi=\par... | Suppose $\xi$ is a Killing field. Then its flow is a local isometry, so for any scalar $K$ we have that the derivative of $K$ in the direction of $\xi$ is zero i.e. $dK(\xi)=0$. Take the Kretschmann scalar for $K$, this implies that $dr(\xi)=0$. Therefore inside the horizon you have that $\xi^\mu\xi_\mu>0$, because all... | {
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Does capacitance between two point charges lead to a paradox? Is it possible to have a capacitance in a system of two point charges? Since there is a potential energy between them and they both have charges then we can divide the charge by the potential and get capacitance.
However, capacitance is supposed to depend on... | If we talk about capacitors that can be charged electron by electron, then these are an everyday reality in modern nanostructure physics (for the past few decades already): see Coulomb blockade.
Remark: there is some ambiguity in the question, since it attributes capacitance to charge itself, rather than a structure/co... | {
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Varying the Hamiltonians between two fixed states Let us have a Hamiltonian $H_0$ and 2 states which can time evolve into each other via this Hamiltonian. In this particular situation, say one of the states evolves into the other in time $t_0$ .
Now let us fix these two states ; then we may have infinite Hamiltonians (... | As RoderickLee has commented already, the answer to your question as stated is yes. The reason is that rescaling any Hamiltonian $H$ with a dimensionless constant $\alpha$ speeds up the dynamics by a factor of $\alpha$.
But you might be interested to learn that quantum speed limits are an active area of research. The s... | {
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Why do guitar strings behave so nicely? To explain the harmonics on a guitar string, we use 2D models of the string. For example we assume that the string can only go up and down. But the string is inherently a 3D object and it could vibrate in a combination of side to side and up and down motions. My question is:
Why ... | Given a very simplistic model of a string in space, fixed at both ends, you're right that the vibration can be in any direction, and furthermore that the vibration can be decomposed as a combination of vibrations in some basis (such as up/down and left/right).
However, due to the rotational symmetry of the setup, when ... | {
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Is the Newtonian gravitational potential $-\frac{GMm}{R}$ just an approximation? Is $-\frac{GMm}{R}$ just an approximation? I believe that it is since we assume that one of the mass is at rest when deriving it.
| So when we use this Potential we tend to use it in cases whereon mass is much larger than another so any movement from gravity is negligible, like with us on earth we are pulling back on the earth as the earth pulls on us so we give it a minuscule change in momentum so in our reference frame negligible movement so can ... | {
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If you were invisible, would you also be cold? If you were invisible, would you also be cold? (Since light passes through you, so should thermal radiation.)
Additionally, I'd like to know if you were wearing invisible clothes, would they keep you warm? In my understanding, the heat radiation from the body would pass th... | Two key points to remember:
*
*Radiation is not the only form of heat transfer. There's also conduction and convection.
*Being invisible doesn't only mean that you shouldn't absorb any light. It also means you shouldn't emit any.
From the perspective of heat transfer, making yourself invisible would be similar to w... | {
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What happens at $V=Nb$ in the Van der Waals equation (i.e. becomes divergent)? The VdW equation:
$$\left(P+a\left(\frac{N^2}{V^2}\right) \right)\left(V-Nb\right)=Nk_BT$$
when the intermolecular forces are zero $a=0$, so $P=\frac{Nk_BT}{V-Nb}$ which diverges at $V=Nb$ for fixed temperature.
I'm simulating some hard sphe... | By definition, $b$ is the volume of a molecule, and $Nb$ is the volume occupied by all the molecules in the gas. So $V\rightarrow Nb$ corresponds to squeezing the gas to a point where the molecules cannot move anymore. The fact that something diverges in this limit is a good indication that, perhaps, the underlying the... | {
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Can I conclude that acceleration happens a bit later after force is felt? We define forces like electric force, magnetic force and gravitational force etc, to be caused by field lines such as electric field, magnetic field and gravitation field respectively. Since these fields take time to reach the object on which the... | For a particle in a force field (like electric field, magnetic field, gravitational field etc. like you mention) the acceleration of the particle at time $t$ is determined by the value of the field at the particle's position at the same time $t$, in agreement with Newton's laws.
If you change the source of the field (c... | {
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Spacetime effects on human scale objects? For a human standing upright on the earth, gravity would have a different value at the feet than at the head, and gravity influences the flow of time. Does the difference in the flow of time cause any effects?
I was toying with the idea that gravitational acceleration is just n... | It's actually now possible to measure the difference in time flow across a millimetre of height.
In this report by Emily Conover at Science News, she details how:
physicist Jun Ye of JILA in Boulder, Colo., and colleagues used a clock made up of 100,000 ultracold strontium atoms ... after correcting for non-gravitatio... | {
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If $\mathbf{F}_{net} = m\mathbf{a}$ then how is $m\mathbf{a}$ not a force? The question is in the title: If Newton's second law says that the sum of the forces acting on a body in a given direction is the same as the mass of the object times its acceleration in that direction, then how is $m\mathbf{a}$ not a force? Eve... | Mathematical equality is not the same thing as physical equality. If you have a mass $m$ undergoing an acceleration $a$, then we know the net force acting on the mass is mathematically equal to $ma$, but an accelerating mass isn't a force itself. You can't take the "$ma$" and use that to accelerate something else.
Most... | {
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Where is quantum probability in macroscopic world? How can macroscopic objects in real world have always-true cause-effect relationships when underlying quantum world is probabilistic? How does it not ever produce results different than what is predicted by Newtonian physics, except for borderline cases?
| A simple way to understand this is to realize that a macroscopic object consists of trillions of individual quantum systems whose QM properties average out into Newtonian behavior as the number of particles in the system is increased.
The only exceptions to this rule are lasers, superconductors and condensates like liq... | {
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Does light have mass or not? We know light is made of photons and so it should not have mass, but light is a form of energy (light has energy) and has velocity ($c$), so according to $E=mc^2$, light should have mass... So what is correct?
|
Does light have mass or not
Light is the word we use for classical electromagnetic radiation at optical frequencies.
Electromagnetic radiation is emergent from a large number of photons. The figure in this experiment is a clear proof that the addition of photons, elementary particles of zero mass and energy equal to ... | {
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Energy of a photon I undestand that the energy of a photon is given by $E=h\nu$ where $\nu$ is the frequency of the light. Is this the total energy of the photon? Or its kinetic energy?
| It is the total energy of the photon and in some sense it is also the kinetic energy. The energy-momentum relation says that the energy of an object is given by
$$E=\sqrt{(mc^2)^2+(pc)^2}$$
Here $m$ is the rest mass of the particle. When a particle with mass is moving at non-relativistic speeds (it moves much slower th... | {
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Do the pupils of an eye emit blackbody radiation? A blackbody, by definition is an ideal system that absorbs all radiation incident on it.
If a good approximation of a black body is a small hole leading to the inside of a hollow object, then am I right in saying that the pupils of an eye are a good approximation of a b... | Any approximation has a region of applicability - that is the conditions where one can apply it or not:
*
*Human eye obviously absorbs the radiation only in a certain range - e.g., it si totally transparent for gamma rays, which are also a part of the Planck spectrum (sinc ethe latter includes all frequencies up to i... | {
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Sound wave travelling from high impedance to low impedance medium, what will be the reflection & transmission coeffiecient? Let us assume that a wave propagates in the direction perpendicular to the flat surface of discontinuity. When the characteristic impedance of the medium of medium 0 (where the incident and reflec... | Assuming that your media have characteristic acoustic impedances $r_0$ and $r_1$ you end up with the following reflection and transmission coefficients
\begin{align}
&R = \frac{r_1 - r_0}{r_1 + r_0}\, , \\
&T = \frac{2r_1}{r_1 + r_0}\, .
\end{align}
The intensity reflection and transmission coefficients are
\begin{alig... | {
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How come the number of wandering electrons is same as the number of the positive ions? My book mentions the following:
Cause of resistance : When an ion of a metal is formed , its atoms lose electrons from its outer orbit . A metal ( or conductor ) has a large number of wandering electrons and an equal number of fixed... | I think that paragraph is badly worded and, at face value, wrong.
Most probably the author meant something like:
A metal ( or conductor ) has a large number of wandering electrons and a number of fixed positive ions that amount to the same charge, but of opposite sign.
I guess in the process of making the sentence mo... | {
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What is the physical intuition behind this energy conservation theorem? I'm reading Quantum Theory for Mathematicians, by Brian C. Hall. Although the book is about Quantum Mechanics, it's chapter 2 is actually about Classical Mechanics, in which I encountered the following theorem:
Rephrasing in English, suppose a for... | Not sure if this helps, but...
If you start off with Newtonian mechanics, energy conservation has to be added in as an additional axiom. (As in "... and only forces which conserve energy are found in the wild").
If you start off with Lagrangian mechanics it is simply not possible to write a Lagrangian which does not l... | {
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Molecular explanation for pressure According to this post, viscous stress is the result of molecular diffusion. More specifically, it's a transfer of momentum in a direction perpendicular to the direction of a velocity gradient. This got me wondering: is pressure also due to molecular diffusion? Is pressure just the tr... | Statistical physics
In statistical physics one considers mainly the pressure of gas (liquid, solid) against the walls of the container. This indeed arises from the molecular collisions, in which the molecules are scattered from the walls of the container, transferring to the walls their momentum. Any basic statistical ... | {
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Factor $1/\sqrt{2\pi}$ in the normalization of wave function packet My book has started using the wave packet definition as follows (time independent form):
$$\Psi(x) = \frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty} A(k) \ e^{ikx}dx$$
I do not understand where the $1/\sqrt{2\pi}$ comes from in this definition. First, I ... | For normalization, you want to look at $\int\psi^*\psi\,\text dx=1$. Try this and the result will be much better.
| {
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Why in the first Friedmann equation quantity $ρ$ is directly proportional to Hubble's constant despite the fact that gravity counteracts expansion? Here is the first Friedmann equation:
$$H^2 = \left(\frac{\dot a}{a}\right)^2 = \frac{8\pi G}{3}\rho - \frac{kc^2}{a^2} + \frac{\Lambda c^2}{3}$$
We know that matter and en... | $\dot a$ is the rate of change of the scale factor i.e. it tells us how fast the universe is expanding. Shortly after the Big Bang the universe was very dense and expanding very rapidly so both $\rho$ and $\dot a$ were high. Then as time went by the universe became less dense as the matter was diluted by the expansion,... | {
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Calculating the speed of a train given its power and weight give nonsensical results Maybe I am missing something but whenever I calculate the maximum speed attainable by a train knowing only its power and mass I always get values that make no sense. If someone could explain my error that would be greatly appreciated. ... | The estimation for the coefficient of rolling friction of $C_{\rm friction} = 0.5$ sounds unrealistic. The whole point of a train is that it rolls with very little friction. The above value looks more like the coefficient of sliding friction.
For example if you use a more realistic $C_{\rm friction} = 0.0018$ the resul... | {
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Thermodynamics (Pressure-Temperature) Graph Analysis I am studying the Graphs in Thermodynamics, and I have found one graph that had made me very curious to know the Real concept of that. Please see it (below here) -
So, here The Line with Negative Slope is the Main, which we have to analyze. So, here the Volume is co... | Most probably you are missing the core idea of Gay-Lussac's Law, which says: If $V=\text{constant}$, then $P\propto T$, and converse is also true. See the dotted lines here are called isochore lines or simply isochores. if we have to write equations of lines we do following substitution: $x \rightarrow T, y\rightarrow ... | {
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If diverging rays never meet, why do parallel rays meet at infinity? I've seen that in the case of concave mirrors if the object is between focus and the pole - the reflected rays diverge and never meet.
But if the object is at the focus, it's defined to be meeting at infinity. Why is it so?
| Infinity is not a real distance or an actual number. It's used in mathematics when describing limits as a parameter increases without bound.
Parallel lines, by definition, never actually meet in a flat plane (there are non-Euclidean geometries where they do meet, and these are relevant when General Relativity is taken ... | {
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Is energy really Conserved in rolling motion? Energy is conserved in pure rolling motion. Then why does the ball stops its motion after some time. I think it's not the case of air drag only. Does all work gets Transferred to surrounding in the form of heat?
| Rolling resistance is an interesting topic. It is clear from experience that a rolling wheel does eventually slow down and stop. So clearly there is some dissipative process that removes the energy from the wheel and transfers it to the environment. However, it is more than that, momentum and angular momentum are also ... | {
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What mechanism will force mechanical watch to tick slower when go fast, due to relativistic effects? To make mechanical watch tick slower, watch tick rate must be changed, oscialtion of balance wheel must be SOMEHOW changed, how would speed change oscialtion of balance wheel, due to relativistic effects?
I dont unders... | As a supplement to Marco Ocram's excellent answer: we are all moving not only in space, but also in time. We have no choice about that: even if we think we are "at rest" in space, we'll be moving forward through time. But different observers may be moving in different directions in spacetime. If we assign $(x, t)$ coor... | {
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Wave Equation energy time independence I'm a bit confused about how the energy of the solution of the wave equation is constant. For a general solution of $\phi_+(x,t)$, the energy in the Hamiltonian formulation is given to be
$$H=\int[\partial_x\phi_+(x-vt)]^2dx=\int[\partial_x\phi_+(x)]^2dx$$
I'm quite confused about... | The spatial derivative has nothing to do with the independence of time. Any integral
$$H(t)=\int_{-\infty}^{\infty}dx\,f(x-vt)$$
is going to be independent of time, by a simple $u$-subsitution. Let $u=x-vt$, so that $du=dx$; then $H$ can be rewritten as
$$H(t)=\int_{u\,=\,-\infty}^{\infty}du\,f(u),$$
which is just th... | {
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"The resultant of two forces of equal size, that form an angle, is lowered by 20% when one of the forces is turned in the opposite direction."
"The resultant of two forces of equal size, that form an angle, is lowered by 20% when one of the forces is turned in the opposite direction."
Does anyone know how one would g... | I think this problem can be solved the easiest without introducing coordinates.
Say we have two forces $\mathbf{f}$ and $\mathbf{g}$, then the question statement can be written as
$$
\alpha\sqrt{(\mathbf{f} + \mathbf{g})^2} = \sqrt{(\mathbf{f} - \mathbf{g})^2} \, ,
$$
with $\alpha = 0.8$.
Squaring and using $\cos \thet... | {
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Source of randomness Is the random nature of all macroscopic phenomena like for example, turbulence or chemical kinetics ultimately traceable to quantum randomness?
| You are effectively asking "What is the relationship between quantum mechanics and classical chaos?" This is an open question and an intense area of study, known as quantum chaos. Stack exchange questions on quantum chaos have already been asked here (in a general context), here (in the context of predicting the weathe... | {
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What causes this frost pattern on my windshield? I was walking back to my car yesterday when I noticed the frost on the back windshield formed these long "straight" lines:
The temperature was about -10C and I was wondering what the mechanism behind these lines was (the horizontal lines I can guess have to do with the ... | Additional information:
Just got into my car Dec 23 in Michigan and saw this frost pattern on my windshield. It is 6°F
Wind chill -14 and the frost pattern is on the inside of the glass.
My hypothesis is that the extremely cold temperatures freeze the water vapor at random points on the windshield along the major stres... | {
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How to draw the phase plane of this equation? Using various computational tools, it's possible to draw a phase plane from two first-order ODEs or a single second-order ODE. However, when there is a parameter in the equation and we don't know the value of the parameter, is there any way to draw the phase plane and see t... | The authors seem to consider a simple (analytic) stability analysis of the obvious equilibrium solutions (from the OP's last equation they are $x=y$ and $\gamma=\pm1$) and then to obtain the phase space not numerically, but to draw it schematically.
| {
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Under what condition is an electrostatic field both solenoidal and irrotational? I'm trying to figure out
under what condition is an electrostatic field both solenoidal and irrotational?
A solenoidal field satisfies $\nabla \cdot \mathbf{F}=0$. An irrotational field satisfies $\nabla \times \mathbf{F}=\mathbf{0}$.
Fr... | You've identified that E-field can be both solenoidal and lamellar when the charge density is zero, but it is actually possible that the E-field is not solenoidal at points in space without charge densities. Likewise, it is possible for the E-field to be solenoidal even when there is charge density.
According to Maxw... | {
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Understanding ergodicity and what an ergodic system is I am trying to understand the concept of ergodicity/ergodic system in physics, but because my understanding of phase space, its elements is a bit unclear,I have trouble understanding the former. Regarding ergodicity (in physics), in Wikipedia I read this:
A physic... | The wikipedia article is talking about ergodicity in classical physics. This is where concepts like phase space are most relevant. Allow me to quote the first paragraph of the section you're reading:
The case of classical mechanics is discussed in the next section, on ergodicity in geometry. As to quantum mechanics, a... | {
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Terminology referring to the term "quantization" in Schrödinger and Dirac equation When people write "Quantization of Dirac equation" is the word "Quantization" the same as "second quantization"?
As I understand it, both Schrödinger and Dirac equations describe one particle (or many specific number of particles using t... | Yes, the two equations describe quantum particles, i.e., the "first quantization" is already done, and the only further quantization possible is second. (Note how it is different for photons, which are classically already described by a wave equation, see this discussion.)
| {
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Why does the shape of Maxwell-Boltzmann distribution depends on temperature, but not mass and number of particles? My physics textbook provided the following probability density function for speed of particle in an ideal gas under a certain temperature.
$$f(v)=4\pi N\left(\frac{m}{2\pi k T}\right)^{3/2} v^{2} e^{-mv^{2... | As one can see from the expression in the OP, the shape is independent on the number of particles - increasing $N$ only increases the height of the distribution, i.e., it only changes the scale on the $y$ axis.
However, unlike it is suggested by the title, the distribution is dependent on the particle mass - the curves... | {
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What is the gravitational constant in 5D? I am trying to find the energy density for a given spacetime using Einstein's Equation $G_{\mu\nu}=\kappa T_{\mu\nu}$. I am trying to do this in 5D and with restored SI units, but I am having trouble finding what the constant $\kappa$ should be.
I know that the Einstein tensor... | For the case of a compactified 5th dimension, you can find your answer from Kaluza-Klein dimensional reduction:
The D-dimensional gravitational constant is related to the (D+1)-dimensional one by the volume of the compact space $$\kappa^2_{D+1}=2\pi R_z\kappa^2_D$$
where $2\pi R_z$ is the volume of the compact dimens... | {
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How would Newton explain mirages? Suppose we think of light as photon packets with tiny momentum, then with this picture in mind, go and see the refraction of light in mirages:
We see that the packets of light photons must be continuously under a nature of force since it must change natural path direction. How would N... | Newton literally wrote the book on Optics and knew perfectly well how to predict refraction.
He did posit a speculation on the reasons for refraction - that is, light was composed of tiny, very subtle pieces which were subject to kinematic laws and had the tendency to accelerate towards regions of higher density, an in... | {
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Particle density vs. Probability Density in Quantum Mechanics I am currently reading trough "Bose-Einstein Condensation and Superfluidity" by Pitaevksii and Stringari and noticed some inconsistencies in my reasoning.
In Chapter 5 (Non-uniform Bose gases at zero temperature) the authors introduce the condensate wave fun... | The wave function describing a BEC is in nature quite different to that of a single quantum particle.
Usually in quantum mechanics you have that $|\psi(t,x)|^2$ is the probability density of the particle being around $x$ at time $t$.
However in BECs the description is different, since quantum phenomena are now apparent... | {
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Thermodynamic Process in a Thermally Insulated Container Suppose we have a specific amount of gas in a thermally insulated container having a frictionless-massless piston. The piston initially is in the middle, dividing the container into equal two chambers, one of which has the gas while the other is vacuum. Now the p... | The first process you describe is irreversible. Why? Because there is no process you can devise for returning the system to its original state without resulting a change in the surroundings.
The second process you describe is not isothermal. So, in this process, the internal energy decreases as a result of the work ... | {
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Why displacement is not used to calculate average potential energy in SHM? We know that the average potential energy of a body executing simple harmonic motion (SHM) is
$$\frac{1}{4}KA^2$$
where $K$ is the spring force constant and $A$ is oscillation amplitude. This was derived using potential energy as a function of t... | The two integrals do not evaluate to the same value because the velocity is not constant. In a hypothetical situation, if velocity were constant the two averages would evaluate to the same value.
Let the displacement and velocity of the spring be defined as:
$$x(t) = A \sin(\omega t) \quad \text{and} \quad \dot{x}(t) =... | {
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Given a formula in Minkowski spacetime, how can we transform it so it works in curved spacetime? To bring a concrete example, let's say I know that the stress-energy tensor related to the electromagnetic field in flat spacetime is
$$T_{\mu\nu}=F_{\mu\lambda}F_{\nu}^{\;\lambda} - \frac{1}{4}\eta_{\mu\nu}F_{\rho\sigma}F^... | Better yet, you can derive this by starting with the Lagrangian:
$$L = \sqrt{|g|}\left(\frac{1}{16\pi}R + \frac{1}{4}F^{ab}F_{ab}\right)$$
And just finding the equations of motion (I recommend cheating and just "remembering" that the variation of $\sqrt{|g|}R$ with respect to $g_{ab}$ is the Einstein tensor, though).
| {
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Is a single photon a wave plane or a wave packet? According to the definition a photon is monochromatic, so it has a unique frequency $\omega$ and thus it can be expressed as
$\psi(x,t)=\exp i(kx-\omega t)$.
This suggests that a photon is a plane wave which occupies the whole space at the same time.
But why we can say ... | All you need is some mode with a definite freqency so that in that mode the EM field dynamics is that of a harmonic oscillator having that frequency. In a conducting cavity there are many such modes and a photon can occupy any of them. Similarly there are many confined modes in an optical fibre or waveguide and... | {
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Uncertainty notation: I am unsure of how the parentheses notation works If I have a value of $5.868709...×10^{−7}$, and an uncertainty of $7.88431...×10^{−12}$, is it correct to write this as $5.86871(8)×10^{−7}$ or $5.8687(8)×10^{−7}$?
A problem I have with the first is the values used to calculate the $5.868709...×10... | In the first place, I would write
$$ 5.868\,709\cdots×10^{−7} \pm 7.884\,31\cdots×10^{−12} $$
instead as
$$ (5.868\,709 \pm 0.000\,078\,8431 )×10^{−7} $$
with (a) grouped digits, (b) a common exponent, and (c) no ellipses. Next I would start removing “insignificant” digits.
The parenthesis notation gets rid of the lea... | {
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Possibility of combining photovoltaics and solar thermal energy In a private setting, photovoltaics and solar thermal energy are often harvested on the home's roof and roof area is limited. So, I thought about combining both, i.e. mounting solar collectors underneath solar cells. The rationale behind this is that the s... | From this site comparing solar panels,
solar panels are usually able to process 15% to 22% of solar energy into usable energy, depending on factors like placement, orientation, weather conditions, and similar.
As all the energy has to be absorbed, the photovoltaic if in contact would be loosing only ~20 percent of t... | {
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Is there a limit of size for superpositions? Can objects be always in superposition if there were no environment for decoherence to occur.
| According to the laws of quantum mechanics, certainly. However, this assumes the system is still completely isolated - even the presence of a gravitational source can lead to decoherence, as per this article, because the objects might be in superpositions of two different gravitational potentials. As well, it assumes t... | {
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Gravitational forces of a building In trying to understand the gravitational forces of a building, I have devised a thought experiment:
A building is floating in space. The building's mass is asymmetrically distributed. Inside it also has a large concentrated mass, not aligned to the center of gravity of the building a... | A is not correct. Gravitational forces inside the building will not cancel out, except in a few specific locations - and even those locations will not be stable equilibrium points.
C is not correct. The concept of centre of mass is only relevant for calculating gravitational forces on objects outside of the building - ... | {
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Measurement on mixed states I have a conflict between my lecture notes on quantum mechanics, where it is stated that the probability of measuring an eigenvalue $a_i$ on a mixed state with desnsity matrix $\rho$ is
$$
\operatorname{Tr}(P_i \rho P_i)\ ,
$$
where $P_i$ is the projector for the subspace corresponding to $a... | As mentioned by the OP both versions are the same. For an observable $A$ of the form
$$A = \sum\limits_k a_k \, P_k \quad , $$
with the projections $P_k^2 =P_k = P_k^\dagger$ on the eigenspace corresponding to the eigenvalue $a_k$, the probability to measure $a_k$ in the state $\rho$ is given by
$$p_\rho(a_k)=\mathrm{T... | {
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What is the order of the transition for a 2D Ising model? I have been running around the block trying to find answers for this question, and I keep running into caveats. So, I just want to write down the list of things I want to know:
Given that the order parameter is magnetization,
Consider the simple two-spin-state I... | For your 1, suppose we are on a 2D square lattice and $J<0$ (so ferromagnetic interaction), then yes there is a continuous transition at a critical temperature between ferromagnetic and paramagnetic phases. In fact the model was solved exactly by Onsager, whose main motivation was to prove the existence of a phase tran... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/690796",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Is thermal conductivity additive? Suppose I have water in a beaker. I measured, its thermal conductivity by some means to be $\kappa_0$. Next, I added some salt to it so that it dissociate from it. Say,
$$AB\rightarrow A^++B^-$$
Now, I again measured the thermal conductivity and found $\kappa$. Can I say that the therm... | In general, no.
First, it would not be expected to be the sum, but rather some kind of average. Otherwise, you could add fifty different materials to your mix and get a huge conductivity. So a weighted average of some kind might apply to some mixtures.
The factors affecting thermal condutivity will change in a mixture ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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What exactly is mass? I was looking for a definition of mass and most of the time what I got was that "it is the amount of matter". Now that is very vague. And the way we define matter is "anything that has "mass" and occupies space". so... what exactly is mass?
Can you please answer it to the level where a highschool ... |
«I was looking for a definition of mass and most of the time what I got was that "it is the amount of matter". Now that is very vague.»
No, that is wrong.
Chemists and physicists agree the «amount of matter» is not mass $m$ (e.g., in the unit of kg), but about a counting number n (in the unit of mol). The mole is ti... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/691147",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "20",
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Finding relation between matrix $S$ and matrix $M$ for wave propagation we have the same Scattering matrix concept in RF as in quantum physics however, I couldnt derive an expression for the $S$ matrix using the $M$ matrix elements and vice-versa. How can I derive eq 1.13 from eq 1.10 and eq 1.12
| $$\begin{bmatrix}b_1 \\b_2 \end{bmatrix} =
\begin{bmatrix}
S_{11} & S_{12} \\
S_{21} & S_{22} \\
\end{bmatrix}
\begin{bmatrix}
a_1 \\a_2
\end{bmatrix} \tag{1}\label{1}$$
$$b_1= S_{11}a_1 + S_{12}a_2 \\
b_2= S_{21}a_1 + S_{22}a_2 \tag{2}\label{2}$$
$$\begin{bmatrix}b_2 \\a_2 \end{bmatrix} =
\begin{bmatrix}
M_{11} & M... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/691429",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is exactly mean by wavelength in De Broglie equation? I'm wondering what exactly is meant by the wavelength in De Broglie formula $p=\frac{h}{\lambda}$, where $p$ is the momentum of a particle and $\lambda$ is the wavelength. I know that a wave function might very well be messy without a defined wavelength.
Can so... | De Broglie wavelength of a particle is the associated wavelength of the particle when the particle behaves as a wave. Simply put, in wave-particle duality, De Broglie wavelength of a particle is the wavelength that the particle would have if it were a wave exhibiting the particle's wave-like properties.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/691948",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Is kinetic energy relative or absolute? I only can think of kinetic energy as absolute. I know velocity is relative but I can't see kinetic energy as being relative because that would violate energy conservation. For example, if in some reference frame, the loss of kinetic energy is $60\mathrm{\ J}$, how can, in anothe... | There is a fundamental point in the interpretation of the concept of energy: even the kinetic energy (KE) exists in relation to other kinds of energy, whose exchange is realized through work. In this way, the existence of an absolute quantity, the KE does not make sense. On the other hand, differences that come from en... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/692210",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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"answer_id": 5
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A planet with a square orbit? To understand how gravity influence objects, time and space, I have been thinking of how a planets shape would change the orbits of its moons.
More specifically: can I design a planet whose moon move in a square orbit?
Below is a diagram of my first intuitive try. For simplicity I imagine ... | You can definitely have a system with any shape orbit. Try designing your square orbit solar system as a planet orbiting a binary star. Who cares about stability for now. Most non elliptical orbits probably become unstable by now, but that does not mean all sorts of orbits do not have there day. All things are possible... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/692338",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "55",
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Is the time interval between two events at different points in the same rest frame the proper time? For example, if an observer in the rest frame of a room measures an explosion on one side of the room and then at a time $\Delta t$ later observes another explosion on the opposite side of the room, is this time interval... | Three observers standing in a room will have their clocks synchronised, they will see that their private clocks run at the same rate as the other two. If two of them snap their fingers simultaneously then all three will agree that the snaps were simultaneous, after allowing for the speed of light (they don't hear but s... | {
"language": "en",
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Double slit formula derivation. Why not $I_{\theta} = 4 I_m (\cos \beta)^2 \left( \frac{\sin{\alpha}}\alpha \right)^2$? The intensity of the double slits is given by
$$I_{\theta} = I_m (\cos \beta)^2 \left( \frac{\sin{\alpha}}\alpha \right)^2$$
where
$$\alpha = \frac{\pi a}{\lambda}\sin \theta$$
$$\beta = \frac{\pi d}{... | You are correct that when you go from one slit to two slits, the center maximum is 4x greater in intensity.
I don't know which book you are going off of, but I am willing to bet that it is mainly concerned with the relative intensity rather than the absolute intensity. In other words, we aren't interested in calculatin... | {
"language": "en",
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What does Griffith mean by adding a prime on integration variables? In the book "Introduction to Electrodynamics" by Griffith, the author mentions electric potential as a point function writes the equation for electric potential as
Then in a side note he write "To avoid any possible ambiguity, I should perhaps put a p... | The primed coordinate is what you are integrating over, whereas the unprimed coordinate is the point in space you are computing the potential for. If $r$ was left unprimed in $E(r)$ it could be seen as ambiguous whether we are talking about the variable of integration or not.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Original BPS state paper by Bogomol'nyi I've been searching for the original paper by E.B. Bogomol'nyi titled "The Stability of Classical Solutions" online, and have yet to find a resource which holds it. So far, the closest I've come is a random website which seems to have part of it at least, but it is quite a low-re... | This answer was initially just a comment, since the resource I mention is not available for free. (At least not in a chivalrous way ;) But as it was pointed out to me it could still be useful, since it is maybe more likely that your local institute library holds the book rather than the original journal article.
The pa... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Speed of heat through an object According to the Heat equation (the PDE), heat can travel infinitely fast, which doesn't seem right to me. So I was wondering, at what speed does heat actually propogate through an object?
For example, if I have a really long iron rod at a constant temperature (say 0 Celsius), and one en... | If instead of one metal rod, we have $2$ of them, from different metals joined at one end, a voltage is produced between the other ends, when the join is heated. In this case, the velocity of the propagation is the velocity of the electric current, close to the speed of light.
If we have only one metal rod, the heating... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/693112",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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$I$ proportional to $V$ or vice versa? I am confused whether Voltage depends on current or the vice versa. I always thought that the vice versa was correct. I tried to find the answers of some of my other conceptual doubts on the web but I was not able to understand the answers as people were saying things beyond schoo... |
I am confused whether Voltage depends on current or the vice versa. I
always thought that the vice versa was correct.
Both are true, but you have to know where the voltage and current are being measured to determine the dependence.
Also, please tell me why it is officially stated that $H = I^2Rt$ not
$VIt$.
Heat is... | {
"language": "en",
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"source": "stackexchange",
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Finding deflection of an electron through 2 charged plates when given initial velocity I've been trying to relate the initial velocity of an electron to the deflection created based on the electric field between 1 pair of plates. The 2nd half of page 3 of this pdf is what I'm concerned with. Now, I was trying to derive... | You have found yourself the cause of your misunderstanding,
($\sin{\theta}$ is equal to $\frac{\Delta y_1}{L}$ and probably equal to $\frac{v_y}{v}$ in the diagram, this could be part of the misunderstanding).
So let me clarify it for you so you really understand.
The only meaningful $\sin{\theta}$ is in fact $\frac{... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/693502",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Are there any slow neutrinos? Since we now know that neutrinos have a rest-mass, we ought to be able to observe relatively slow-moving neutrinos. Have we seen any?
| They haven't been seen and I doubt they will ever be. Since they were created they have traveled almost undisturbed. I find it difficult to believe most neutrinos from the Sun travel through the Earth. But it seems to be the case.
Because they have mass and interact (though weak), they should be stoppable. Maybe in be... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/693767",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Is there a physically meaningful example of a spacetime scalar potential? From Misner, Thorne and Wheeler, page 115.
0-Form or Scalar, $f$
An example in the context of 3-space and Newtonian physics is temperature $T\left(x,y,z\right),$ and in the context of spacetime, a scalar potential, $\phi\left(t,x,y,z\right).$
I... | Within the Standard Model, the simplest model of the Higgs field is a multiplet of Lorentz scalar fields. This multiplet does have a non-trivial transformation under an underlying gauge group of the Standard Model; but under Lorentz transformations, the Higgs field is invariant, as all good Lorentz scalars should be... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/693884",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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What would happen if you left Earth and then it was destroyed? (Potential energy and thermodynamics) So I did some research on magnetic generators and what kind of energy magnets loose when they move something. Turns out magnets loose potential energy (you need to expend energy to get the object moved closer to or furt... | If you could delete the Earth, that would cause the concept of gravitational potential energy to be quite problematic, which is one the reasons why the conservation of mass is considered to be a solid law (there's also other issues such as Noether's Theorem).
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/694021",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 2
} |
Can two waves be considered in phase if the phase angle is a multiple of 2$\pi$? Question is essentially what the title states. Wavefront is defined as the locus of points that are in phase. So I wanted to know if the locus would be the points of only a single circle or multiple circles whose points all have the same d... | Yes. Two waves are in phase when phase difference is two pi. Out of phase when phase difference is one pi.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/694127",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 1
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Non-dimensionalizing laser system of diffeqs, Strogatz Nonlinear Dynamics and chaos 3.3.1 D The system of equations in question is
$$ \dot{n} = GnN - kn$$
$$\dot{N} = GnN - fN + p$$
Where ${N(t)}$ is the number of excited atoms, ${n(t)}$ is the number of photons, ${G}$ is the gain coefficient, ${f}$ is the rate of deca... | As march already commented, the variables described as "numbers", $n$ and $N$, can safely be taken to be dimensionless (though, of course, we do use pseudo-units "dozen", "mole", etc. — see this question), and thus $\dot{n}=dn/dt$ will have the inverse unit of time, and so on for the other quantities.
| {
"language": "en",
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"source": "stackexchange",
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How to make the Moon spiral into Earth? I recently watched a video of what would happen if the Moon spiraled into Earth. But the video is pretty sketchy on the physics of just what would have to happen for that to occur. At first I thought I understood (just slow the Moon down enough), but my rudimentary orbital mechan... |
wouldn't the Moon just settle into a lower orbit?
Yes. To make the moon spiral into the earth requires continuous application of some drag or retarding force, not just some singular event.
What forces would have to be applied to the Moon to get it to spiral into the Earth, at what times?
If the only (significant) ... | {
"language": "en",
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"source": "stackexchange",
"question_score": "1",
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If force depends only on mass and acceleration, how come faster objects deal more damage? As we know from Newton's law, we have that $\mathbf{F} = m\cdot\mathbf{a}$. This means that as long as the mass stays constant, force depends solely on acceleration. But how does this agree with what we can observe in our day-to-d... | Force on the victims head is rate of change of momentum. i.e. Force=rate of change of momentum. If the time is tiny then the rate of change is huge. This is why crumple zones in cars work, they increase the time over which the passengers' momentum changes.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/694736",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "13",
"answer_count": 14,
"answer_id": 11
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Time constant versus half-life — when to use which? In some systems we use half-life (like in radioactivity) which gives us time until a quantity changes by 50% — while in other instances (like in RC circuits) we use time constants. In both cases the rate of change of a variable over time is proportional to the instan... | Wrong but slightly useful heuristic is to use time constant for events that are repetitive and half life for events that are one-off
More useful is to use whatever is used by others in that particular field. Half life for radioactivity, time constant for electronic filters, time till failure for reliability calculation... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/694850",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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Acceleration as a function of displacement I am given a question such that a 0.280kg object has a displacement (in meters) of $x=5t^3-8t^2-30t$. I need to find the average net power input from the interval of $t=2.0s$ to $t=4.0s$.
I know the formula for average net power is $\frac{\int^{x_2}_{x_1}F \ dx}{t_2-t_1}$ as t... | You can use the fact that $\frac{dx}{dt} = 15t^{2} -16t -30$ first of all. Then, you can make a substitution into your work done integral, for $dt$, and change the limits so that instead of the displacement $x_{i}$, you have whatever initial and final times $t_{i}$. That should then work! If not, let me know and I can ... | {
"language": "en",
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How to understand the notion of critical temperature in thermodynamics? I just want to verify my understanding of the notion of critical temperature of fluids, because the more I read about it in the literature I become more and more confused.
My main clue for understanding this notion is the statement that latent heat... | The surface energy of condensed matter generally decreases with increasing temperature because the increasing molecular vibration combats cohesion. The critical temperature is the temperature where the surface energy has dropped to zero. At this and higher temperatures, there's no driving force to form a condensed phas... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/695121",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Commutators as contour integrals in 2D CFT, and classical limits In a 2D CFT, the commutator of two operators
$$A_i=\oint a_i(z)dz$$
can be given by
$$[A_1,A_2]=\oint_0dw\oint_wdza_1(z)a_2(w)$$
where the $z$ integral is taken over a contour around $w$ and the $w$ integral is taken over a contour around the origin, and ... | If $$\hat{a}(z)~=~\sum_n z^{-n-h_a}\hat{a}_n
\quad\text{and}\quad
\hat{b}(w)~=~\sum_m w^{-m-h_b}\hat{b}_m,\tag{1}$$
or conversely,
$$ \hat{a}_n~=~\oint_0 \frac{\mathrm{d}z}{2\pi i}z^{n+h_a-1}\hat{a}(z)
\quad\text{and}\quad
\hat{b}_m~=~\oint_0 \frac{\mathrm{d}w}{2\pi i}w^{m+h_b-1}\hat{b}(w),\tag{2}
$$
then OP is essenti... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/695343",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Simplification of nested time-ordered products I'm trying to progress towards understanding, and perhaps finding a proof for, the "nested" Wick's theorem for time-ordered products $T\{ \ldots \}$ alluded to in part (II) of this answer.
Assuming bosonic operators for now, I've noticed that
$$T\{ T\{ A(t_1)B(t_2) \} T\{ ... | *
*Let us first define a $n$-ary Heaviside step function:
$$\begin{align} \theta&(t_1\geq t_2\geq\ldots \geq t_n)\cr
~:=~&\left\{\begin{array}{rl} 0&\text{if ineq. is violated}, \cr
\frac{1}{m_1!\ldots m_r!}&\text{if ineq. holds and there are $r$ sets of equal} \cr
&\text{times with multiplicities } m_1, \ldots, m_r. ... | {
"language": "en",
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Microwave inside-out cooking true/false The wikipedia article on microwave ovens says
Another misconception is that microwave ovens cook food "from the inside out", meaning from the center of the entire mass of food outwards.
It further says that
with uniformly structured or reasonably homogenous food item, microwav... | The whole reason why microwave ovens have turntables is that they always heat food unevenly because standing waves form inside them:
If a wave's antinode (where most energy is released) happens to be in the middle of your butter stick, the butter will melt in that place first, and may even explode if the temperature i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/695681",
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"source": "stackexchange",
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Time dependence of generalized coordinates and virtual displacement The Cartesian coordinates of particles are related to the generalized coordinates via a transformation (for the $x$ component of the $j$-th particle) as:
$$x_j = x_j(q_1, q_2, \ldots, q_N, t)$$
What I can't understand is why in the virtual displacement... | If you want to think of a virtual displacement as a curve $s\mapsto q(s)$, since time $t$ is frozen, you cannot pick time $t$ as a curve parameter, you have to pick something else, say $s$. Hence $\delta q=\frac{dq}{ds}\delta s$. See also e.g. this, this & this Phys.SE posts and links therein.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/695823",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Why should the electron's energy knocked out be dependent on the intensity of the light? I know according to the photelectric effect this is not true , but the belief that it should be according to classical physics ? , could someone explain the approach of what classical physics 's hypothesis was ?
| Exposure of a metallic surface by light knocks electrons out of the surface at an electric potential difference. The surprising thing was that the intensity of the photoelectric current periodically increased and decreased depending on the wavelength of the light. This was described as early as 1887 by Hertz and Hallwa... | {
"language": "en",
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Does 2D circular wave reduces amplitude as it spreads out in lossless medium? When we throw a pebble into water, a 2D circular wave is generated. Suppose the water here is completely lossless, will the wave amplitude still reduce as the wave front spreads out?
In the case of a 1D lossless and infinitely long string, th... | Yes, the amplitude will decrease due to spreading. Energy must be conserved, and as the radius of the circular wavefront increases the energy at any single point must decrease proportionately. Usually the square of a wave's amplitude is proportional to the energy density, and for circular waves the length of the wave... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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How can I calculate the intercept direction of a constant accelerating missile? I'm simulating missiles in 3d space and want the missiles to intercept a target which has constant velocity.
Given the targets velocity is "u" a vector and the missiles acceleration rate is "a" a constant scalar
what is the formula to calcu... | From your question
Given the targets velocity is "u" and the missiles acceleration rate is "a" what is the formula to calculate the direction the missile should be facing to intercept the target.
I infer that you are analyzing a simple problem of straight-line motion for both target and missile. This problem would be... | {
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Are one-dimensional tensors of arbitrary rank just scalars? Consider a tensor of arbitrary rank (2 for this case) $A_{ij}$, and dimension one. Granted there are two indices to specify a component, but since each index can only take one value, there is only one component in this entire tensor: $A_{11}$. So, are all one ... | Perhaps an example is in order. Consider e.g. a 1D charge density $\rho$ in a 1D world. It transforms as a covariant (0,1) tensor $\rho^{\prime}=\frac{\partial x}{\partial x^{\prime}}\rho,$ so it is not a scalar.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Could we estimate the total energy of the universe? So I know that we do not know the sum of all energy in the universe, but why can we not just estimate with the following logic? (That I assume has some fatal flaw preventing anyone from guessing the total energy of the universe with it)
Since the universe is considere... | This has been done. This energy density is called the critical density and is about 5 GeV/$c^2$ per cubic meter (i.e. 5 proton masses per cubic meter or or $10^{-26}$kg/m$^3$). So, I do not understand why you write that we did not know the sum of all energy in the universe.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/696863",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
What is the physical interpretation of the two tree-level Feynman diagrams for $e^-e^- \to e^-e^-$ scattering? In the tree level, the $e^-e^- \to e^-e^-$ scattering has two Feynman diagrams, the first one is indicative that one electron emitted a photon which was later absorbed by the other electron:
However, I have ... | It is precisely what you said. When you do a scattering experiment, you're throwing in two electrons with momenta $p_1$ and $p_2$ and see two electrons coming out with momenta $q_1$ and $q_2$. However, electrons are indistinguishable, so you can't know whether the electron with momentum $p_1$ is the one with momentum $... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/696979",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 1,
"answer_id": 0
} |
Euler-Lagrangian equation of motion of quantum fields in QFT A canonical way of doing quantum field theory is by starting with some Lagrangian, for example, that of free scalar field
$$L=\frac{1}{2}\partial_{\mu}\phi \partial^{\mu}\phi-\frac{1}{2}m\phi^2$$
Then by employing the Euler-Lagrangian equation, i.e. $\delta L... | The Heisenberg field operators $\hat\phi(\mathbf{x},t)$ do in fact obey the E-L equations, however expectation values of these operators don't and require corrections. For example, an expectation value containing two field operators obeys
$$(\partial_x^2-m^2)\langle0|T\phi(x)\phi(y)|\rangle = -i\delta^3(x-y)$$
the term... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/697049",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 3,
"answer_id": 2
} |
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