Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Which units should I use in molecular dynamics simulation? I have written a simple molecular dynamics simulation program. The simulation runs fine but the physical properties (in particular, I have calculated temperature) are off by many scales. I understand that this might be due to not using the proper dimensionless ... | The possible choices of sets of units for your simulations is probably infinite, so the answer is ultimately going to be choose a set of units that fit what you need & run with it.
For instance, suppose you want to study the Argon interacting via the Lennard-Jones potential, an appropriate choice of units could be mass... | {
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"timestamp": "2023-03-29T00:00:00",
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Units of vector differential operator del ($\nabla$) My book says that $\left[\nabla \cdot (\vec E \times \vec H)\right] = \mathrm{W/m^3}$. I see that $\vec E$ is in $\mathrm{V/m}$ and $\vec H$ is $\mathrm{A/m}$, so these multiplied is $\mathrm{W/m^2}$, but how does dotting with $\nabla$ give another $\mathrm{m^{-1}}$?... | The $\nabla$ operator is a spatial derivative of the $\frac{\delta}{\delta x}$ etc kind. This has units of $1/m$
| {
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Total angular momentum of electron in a magnetic field In this question: Electron in the proximity of a magnetic monopole
It is stated that for an electron in the magnetic field of a monopole,
$
\vec{B}(\vec{r}) = \frac{g}{r^3}\vec{r}
$
, that the quantity
$
\vec{J} = \vec{r} \times \vec{p} + eg\frac{\vec{r}}{r}
$
is ... | After further examining the original question, and the source for the question, which was in the book "Electromagnetic Theory" by Ferraro on p.543, I was able to understand the conserved quantity $\vec{J}$ as thus.
Considering that with $\vec{B}(\vec{r}) = \frac{g\vec{r}}{r^3}$ the Lorentz force yields:
$\begin{align}
... | {
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How to determine whether a nuclear transition would be electric octupole, or hexadecapole? The transition from one nuclear state to another is classified as quadrupole/octupole, etc, depending on the units on angular momentum transferred. But depending on the angular momentum of the two states involved, the net J can t... | The short answer is that all transitions which are not forbidden by parity or angular momentum conservation happen, though not necessarily at the same rate. When several multipolarities are allowed, the one with the lowest multipolarity dominates.
| {
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$\hat{L}_{x}$ and $\hat{L}_{y}$ do not commute... or do they? So $\hat{L}_{x}$ and $\hat{L}_{y}$ do not commute:
$$ [ \hat{L}_{x}, \hat{L}_{y}] = i\hbar \hat{L}_{z}$$
But, what if we perform this operation on a state such that:
$$\hat{L}_{z} \phi_{l, m_{l}} = \hbar m_{l}\phi_{l, m_{l}},$$
where we require that $m_{l} ... | Elaborating on ACruiosMind's comment, assume that the matrices $A$ and $B$ are defined the following way:
$$A=\begin{pmatrix} 1 & 2 \\ 5 & 4 \end{pmatrix} \quad \text{and} \quad B = \begin{pmatrix} 1 & 1 \\ -1 & -1 \end{pmatrix}$$
Notice that the eigenvectors of $A$ are
$$\begin{pmatrix} 1 \\ 5/2 \end{pmatrix} \quad \t... | {
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Why specific heat at constant pressure is greater than specific heat at constant volume? I know the relation between specific heat at constant volume and pressure and I also know how to calculate it.
Thing is, I don't understand its concept
I want to know why at constant pressure, specific heat is always greater than ... | At constant volume, all the heat that goes into the system goes into raising the temperature of the system, and no external work is done.
At constant pressure, some of the heat goes into expanding the system, which does external work, and therefore leaves less energy available for raising the temperature.
| {
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direction of friction on an object rolling with constant speed Although there are many questions similar to this, but none of these specifically talk about the situation with constant speed.
A wheel is rolling on a horizontal plane (having some friction) with constant speed.
What will be the direction of force of ... | What Haliday describes is in an "Ideal" situation, where the wheel and surface are perfectly solid and there are no other forces like air resistance. Then the only force between the wheel and surface is an upward force equal to the weight of wheel (assuming we have gravity)
Actually if there is any friction, then energ... | {
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Smooth collar sliding down smooth shaft
For part (a), we find that the acceleration of the collar is $6.94~\mathrm{m/s^2}$. In part (b), we say that the acceleration of B with respect to A is $6.94~\mathrm{m/s^2}$, which makes sense.
However, in part C, the acceleration of C with respect to A is not $6.94$ anymore. F... | No.
A is accelerating away from C. Don't forget that C is not fixed to the smooth shaft, AB. The shaft is accelerating away from C, which has to catch up with A. So from the standpoint of A, C is accelerating slower.
| {
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Explanation of Michelson Interferometer Fringe Shift I have been working on an experiment where 2 glass microscope slides are pinched together at one end (so that there is a "wedge" of air between them) and placed in the path of a laser in one leg of a Michelson interferometer. When I move the glass slides (fractions o... | In the 2 glasses there are 4 surfaces, i.e interface air/glass, and 8 surface orientations (a..h) and plenty room for interference between reflections and the main beam.
LASER (air) a1b (glass) c2d (air) e3f (glass) g4h
At each interface the is reflection that will be reflected forward again (self-in... | {
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Physical Meaning of Cone used in Conic Section for Orbital Mechanics Does the polar angle (complement of $\theta$ below) of a cone which intersects a plane to yield a conic section have a physical meaning in orbital mechanics?
Note that the angle of incident planes, which form parabolas, ellipses, etc., is not the p... | Ellipses, parabolas and hyperbolas are both:
*
*Defined as the conic sections you speak of: work out the intersection between the cone $\vec{R}.(\cos\phi\,\hat{X} + \sin\phi\,\hat{Z}) = \sin\theta\,|\vec{R}|$ and the plane $z=const$ where $\theta$ is your polar angle and $\phi$ the angle between the cone's axis of s... | {
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General solution of a mass spring system This is the differential equation that describes small amplitude vertical oscillations of a mass $m$ that is hanging from a spring
$$\frac{d^2x}{d t^{2}} + \frac{b}{m}\frac{dx}{dt} + \frac{k}{m} x = 0$$
Where $x$ is defined to be the displacement of the mass from equilibrium pos... | Substitute $x$ by $A(e^{wt})$.
Thus your equation becomes:
$$
A(w^2)(e^{wt})+A(\frac{b}{m})(w)(e^{wt})+(\frac{k}{m})(A)(e^{wt})=0
$$
Simplifying:
$$
(w^2) + (\frac{b}{m})(w) + (\frac{k}{m})=0
$$
Find out the roots . Here you understand that $(b^2)<=4km$ for real values of $w$.
Let the roots be $w_1$ and $w_2$
Finally... | {
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Is this definition of orthohelium and parahelium incorrect?
"One electron is presumed to be in the ground state, the 1s state. An electron in an upper state can have spin antiparallel to the ground state electron ($S=0$, singlet state, parahelium) or parallel to the ground state electron ($S=1$, triplet state, orthohe... | Yes you can do that; the space and spin parts just have to have opposite symmetry characteristics so that the total wavefunction is antisymmetric.
| {
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What would put a harddisk drive (HDD) under 350G's of force? I always see the label and it says 350G's withstandable. What would put this over 350G's? Is it even possible to hit 350Gs of force to a hard drive?
| Here's an application where an ability to withstand high shock is important.
Explosions. In the mid 1980s I did work for a mining company's research laboratory (BHP Research, now defunct like all Australian corporate research).
We would lower data-logging computers into boreholes to set up a grid of dataloggers, then d... | {
"language": "en",
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The notion of fixing a gauge I don't understand the notion of gauge fixing; can we choose any gauge or are there some restrictions?
For example why can we choose $\nabla\phi = 0$ here:
https://physics.stackexchange.com/q/188778/
| It's first important to note that in classical electromagnetism, the $\mathbf{A}$ and $\phi$ fields are not physical in the same way that the $\mathbf{E}$ and $\mathbf{B}$ are. We can't measure them and they aren't uniquely defined.
Gravitational potential energy is a good analogy. Suppose an object is on a table a hei... | {
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Power of several focused laser beams on a small surface After viewing this: My Homemade 40W Laser Shotgun
Will the initial 40W power of the diodes beams be roughly transferred to the targeted surface where the 8 beams are focused, or will there be a power loss due to some kind of interferences where the beams overlap?
| If energy is lost, it must go somewhere. So, there won't be any "interference" where the beams overlap which saps the power. Unless, and this does happen, the lasers are powerful enough to ionize the air, in which case the light is blocked at that point and converted to heat, which will never make it to the surface. Se... | {
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What happens if gravity of all objects in the universe disappears? I've been trying to find the answer to this question for a few days and I ended up in having different answers from different sources. A website says:
Everything on the universe would move in this exact direction it was moving at the instant gravity st... | The Earth is rotating at around 1000mph. There is also immense pressure inside the earth pushing the crust outwards. If gravity "stopped working" then the rotational velocity plus the internal pressure would rip the planet apart pretty quickly. However, if gravity "stopped" the sun would explode, as would all other sta... | {
"language": "en",
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Flaws of Broglie–Bohm pilot wave theory? I recently learned about an oil drop experiment that showed how a classical object can produce quantum like behavior because its assisted by a pilot wave. How has this not gained more attention? What flaws does Broglie–Bohm pilot wave theory have in explaining particle behavior?... | The Copenhagen interpretation refutes pilot wave theory because it's stand is that nothing has position until measured..... It has created a long history of discourse among physisist.
You have to buy in to the concept and I don't.
Einstein once asked a proponent of the Copenhagen interpretation if the moon was in pl... | {
"language": "en",
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Are wavelength and the distance same thing? Can you clarify for me the following question: are wavelength and distance same?
I know wavelength is measured in terms of distance but when we have a look at the two equations:
$$
c=f\,\lambda\\
v=d/t
$$
it actually explains the same thing where $v=c$=velocity and $1/t$ i... | The lambda is the distance between 2 points having the same phase like two successive crests the velocity is the wave can be conceived as how many crests for example passes through a reference in a given time you can use both equations but c=f*lambda is used if you have lambda , its proof is V = distance / time , if a ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/189121",
"timestamp": "2023-03-29T00:00:00",
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Could some astronomical objects have superconducting properties? The colder it is, the more efficient the superconductivity process works. And as we know, if there is no star nearby, space gets pretty cold.
I do appreciate that many condensed, burnt out, stars may take a long time to cool off, but are there any other ... | This is not a complete answer to the question, rather a explanation of Kyle Oman's answer.
When we (or at least me) think of superconductivity, we have in mind the pairing of electrons to form Cooper pairs. But this pairing is quite weak, and a moderate magentic field can destroy superconductivity.
But electrons are no... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/189192",
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Really how can an observable quantity be equal to an operator?
A wave-function can be written as $$\Psi = Ae^{-i(Et - px)/\hbar}$$ where $E$ & $p$ are the energy & momentum of the particle.
Now, differentiating $\Psi$ w.r.t. $x$ and $t$ respectively, we get
\begin{align}
\frac{\partial \Psi}{\partial x} &= \frac{i... | Not equal, but equivalent, in the sense that they have the same effect on the wavefunction in question.
More precisely, the book is using a slight abuse of terminology. Taking momentum as an example, it's not really the case that the dynamical quantity of momentum is equivalent to the operator $\frac{\hbar}{i}\frac{\pa... | {
"language": "en",
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Antenna direction I have a router with a wifi antenna that can be turned in any angle. I wonder what difference does the direction of the antenna make to the electromagnetic signals propagation? Where is the signal strength the biggest?
| Well a router antenna is simply a dipole. It will have maximum radiation in its broad side direction and it's radiation pattern looks like a donut.
Check the link below for the illustration of the dipoles far-field
https://www.cst.com/Academia/Examples/Wire-Dipole-Antenna
Of course the router itself and any metallic ob... | {
"language": "en",
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The speed of light/EM waves in vacuum; as if there was another one in non-vacuum? Q1: is there a speed of a photon other than in "vacuum"?
Q2: isn't "speed of light in vacuum" misleading?
If I understand, that light moves with speed of light until there is "something in between" (no matter what) (1)
What I ask for, is... | first the speed of light is related to the permittivity and permeability of the medium. changing either one of those values changes the speed of light.
copper has different values then free space. the speed of light through copper is 2/3rds that of free space. about 1 foot per nanosecond. slightly faster in aluminum, ... | {
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"url": "https://physics.stackexchange.com/questions/189684",
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Why do sea waves seem to be standing still when you look from the window of an airplane? Looking from the window of a passenger plane even at moderate altitude such that one can still recognize individual waves and even something like white foam, and small boats close to the cost line, it already looks like the water i... | Think of it this way: You are way up in the sky and the distance you see as a centimeter could be meters long since you see objects getting smaller as you go farther away. Assuming that an ordinary water wave travels with a velocity of 3 or 4 m/s at a maximum, it is not hard to imagine that you are seeing them as if th... | {
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Constructing differential equation from arbitrary Hamiltonian Suppose I begin with the time-independent Schrodinger equation
$$ \left(-\frac{1}{2m}\partial_x^2 + V(x)\right)\psi_n(x) = E_n\psi_n(x), $$
ordinarily we specify the function $V$ and then solve for a set of eigenfunctions and eigenvalues. And just to be slig... | After thinking about it, as long as the original eigenvalues are non-degenerate it should be possible to have the new Hamiltonian be represented by a differential equation of arbitrarily high order. The key is that the projection operators $P_n$ onto the eigenfunctions exist in the algebra generated by the original Ham... | {
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Quantum entanglement and the big bang Prior to the Big Bang all matter was compressed into a point of high density. Why isn't all matter already entangled?
| I actually happen to believe that they can be, and not only that but I think it would be very likely that all particles in the universe were entangled prior to, during and after the big bang. The problem would be verifying this entanglement in experiments as I can see no way of deducing which particle any given particl... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/190274",
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I don't understand black body radiation graphs
Let's look at the above graph.
*
*This black body graph is for the temperature of 5000K. Each temperature has a different black body graph?
*How am I supposed to read this graph? Do I start from the left, the right, or the peak?
*As wavelength is approaching zero, i... | The x-axis on the graph shows the wavelength, while the y-axis shows the corresponding intensity for that wavelength (all for a given temperature of the black body, in this case 5000K). Also note that this graph shows a distribution of the various wavelengths and their intensities at that temperature. It is a distrib... | {
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Can we find actual rest mass of things on Earth Earth moves around the Sun and the Sun moves around the galaxy and the galaxy moves with unknown speed and direction. We have speed so the mass of us all altered.
Can we know the real rest mass? If so, can we deduce our speed in the universe?
| When the object is an elementary particle or a charged ion we can use electromagnetic interactions to measure its rest mass, given the charge in an e/m experiment. One can get the charge with Milikan's oil drop experiment. Here is a setup for the lab.
| {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is the scalar magnetic potential continuous? If we have two current-free spaces and separated by a surface current, we can solve the magnetic problem by solving two magnetic scalar potentials and then using matching conditions. My question is, is the general scalar magnetic potential continuous? Why?
| A potential is essentially an integral of work to carry a particle (magnetic or electric one) from an infinite distance up to the point you need to know the potential value. If the force making the work is not a Dirac's Delta, then the integral (i.e. the potential) must be a continuous function.
| {
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Bottle stability optimization A few days ago some friends and I played a game called "flunkeyball" where you need to upset a bottle with a ball. Then a question occurred: "How much water do we need to put into the bottle that its stability is optimal?"
My first thoughts were that the centre of mass must be as low as po... |
simple force body diagram shows rotational motion of the force of weight on a pivot straight edge bottom
| {
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"question_score": "15",
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What does it mean to say that "remembering the future and not the past?" I encountered a rather stupid question which I don't quite understand. - "Why can we remember the past but not the future?" It sounds cool when I first read about it but I think about it more, about how to explain it to a person who doesn't know p... | In this case one could argue that 'remembering the past' would be a methaphorical expression to describe being able to predict the future. Experimental evidence says that people that have declared being able to predict the future are either scammers, delusional, self-fulfilled prophecies or just extremely intuitive. As... | {
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Why can microphone be much smaller than wavelength of sound? For sound from 20Hz to 20kHz, wavelength is 17m to 17mm, for sound at 2kHz, wavelength is 17cm.
And I saw tiny microphone which is much smaller than that. In electromagnetic, there is a smallest size for antenna of each wavelength (half wavelength???). And th... | Microphones transform the pressure wave of sound to an electric signal.
The wavelength of the sound wave tells us the distance over which the wave's shape repeats itself in space. The frequency measures the changes in the medium in time.
As the sound wave passes, the molecules of the microphone vibrate in place ,accor... | {
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Does isotropy imply homogeneity? This question comes from exercise 27.1 in Gravitation by Misner, Thorne and Wheeler. They required the following:
Use elementary thought experiments to show that isotropy of the universe implies homogeneity.
I know homogeneity as the universe is the same everywhere at a given time, a... | A few years late here, but I think a clear way of thinking about this is any two points in the universe, A and B, will be connected by a great circle drawn around C. If the universe is isotropic at point C then the points A and B must look the same. This logic can then be extended to any two points in the universe.
Thi... | {
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"timestamp": "2023-03-29T00:00:00",
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Is it possible for two events happen at the exact same time? Is it possible for any two events to occur at the exact same time?
As I see it, because time intervals can always be split up into smaller units (it is infinitely divisible), we can always be more and more exact with measuring the time at which something happ... | Events are points $(x,t)_S$ onto a chart $S$ on some space-time manifold and in this respect whenever two such points $P_1 = (x_1,t), P_2=(x_2,t)$ have the same $t$-coordinate in that reference frame then yes, they do occur at the same time for the observer described by the chart $S$. For another observer, represented ... | {
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Does paint affect the thermal conductivity of a metal? We noticed that in our experiment that painting a metal increases its thermal conductivity; is this true? If so, can you guys send me a link to a research paper to support this claim.
|
painting a metal increases its thermal conductivity; is this true?
No it is not true.
Thermal conductivity is a bulk property of the material. It expresses how well the metal conducts thermal energy through the bulk of an object made of that metal.
As CuriousOne commented, surface treatments do not affect how heat i... | {
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Probability flux I was reading a text on Quantum Mechanics in which it said that
$$\int{d^3 x \, j(x,t)} = \frac{\langle p\rangle}{m},$$
where $\langle p\rangle$ is the expectation value of the momentum operator at time $t$.
I tried using $$\langle p\rangle = \int d^3x \, \psi^* (-i\hbar \nabla) \psi.$$
Either I am u... | I was stuck on this same problem. ACuriousMind does give a good hint though. Using integration by parts on the second term for $j(x,t):$
\begin{align*}
\int d^3x ~ j(x,t)&=-\frac{i\hbar}{2m}\int d^3x~ \left(\psi^* \nabla\psi-(\nabla\psi^*)\psi\right)\\
&=-\frac{i\hbar}{2m}\left(-\left[\psi^*\psi\right]^{+\infty}_{-\inf... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/191849",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Velocity of Rocket Exhaust i recently learned a bit of rocket propulsion.It wasn't much complex but was explained in simple terms.The only problem i had understanding it was that in calculating the thrust of rocket the velocity of the exhaust was taken relative to the rocket.My problem is : Shouldn't the velocity of th... | To see why the exhaust speed is important, let's do a calculation.
*
*Let's start with a rocket of mass $m$ going at speed $u$. (We measure all speeds with respect to some inertial reference frame.)
*Now, suppose it exhausts a tiny amount of propellant of mass $\delta m$ and the propellant is traveling at speed $u... | {
"language": "en",
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How are determined experimentally the energy levels of the atoms ? How is the calibration done to several decimal points? I see discrepancy for the absorption edges for the atoms in the X-ray ?
For example K-absorption edge of carbon can be anywhere between 282 to 284eV according to different sources.
My question is h... | It is possible to measure wavelengths of light to many decimal places. When you see accurate determinations of atomic energy levels, they were done spectroscopically, looking at absorption or, more commonly, atomic fluorescence. Since $E=hc/\lambda$, one can accurately convert between wavelength and energy.
When exci... | {
"language": "en",
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Is the Energy of an absorbed photon exactly the energy of the band gap? I was wondering, if the Energy of a Photon which is absorbed by an Electron, hast to be exactly the Energy of the bound gap.
So if i have two energy levels in an atom $E_2$ and $E_1$, does my Electron have to have exactly the Energy
$$h\nu = E_2 - ... | No, it is sufficient for the photon energy to exceed the band gap. Any excess energy is transformed into kinetic energy for the electron in the new band. You get exactly the same effect when ionizing an atom - the excess energy simply powers the electron into a faster continuum state.
You should also take into account ... | {
"language": "en",
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Do electrostatic fields really obey "action at a distance"? In an electromagnetic theory class, my professor introduced the concept of "action at a distance in physics".
He said that:
If two charges are at some very large distance, and if any one of the charge moves, then the force associated with the charges changes ... | The force does not change instantaneously, the correct way the electromagnetic field of (and thus the force exerted by) a moving electric charge is given by the Liénard-Wiechert potential, where one can see that the effect of the charge does not travel faster than light.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/192527",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
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current splitting in the presence of superconductors When you have two resistors in parallel, the current splits up based on the resistances. What will happen if we have two superconductors in place of the resistors? What will happen to the current?
| Current going through a superconductor (or otherwise) will form a magnetic field. The potential energy of the magnetic field depends on its size, and the permeability of its surrounding environment.
The current will be divided between the two superconductors such that the total magnetic field energy is minimal.
Actuall... | {
"language": "en",
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How does phonon scattering change the distribution function? For a one-dimensional structure, we know that the modified distribution function has the following energy dependency in equilibrium:
\begin{equation}
Z(\varepsilon)\,f(\varepsilon) = \dfrac{N_\text{1D}}{\sqrt{\varepsilon-E_\text{C}}}
\times \exp\left( -\dfrac... | First off, let's answer the question: what part of that equation would change?
$f\left(\epsilon\right)$ is always the same if you're in equilibrium. Scattering won't change that, because scattering alone won't move you out of equilibrium. If anything, scattering has the opposite effect.
What can change is $Z\left(\epsi... | {
"language": "en",
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Free fall into circular motion If I'm on a roller coaster free falling from height $h$ and then suddenly start going into horizontal motion with a radius $r$ of turn what is the $g$-force I experience?
I worked out the equation like this but am not sure if it is correct:
*
*(1) instant velocity of free-fall $v=\sqrt... | You asked two simple questions - I will give two simple answers.
I don't know if I can use uniform circular motion equation since v is not constant
At the very instant that the curve starts, the velocity is given by $\sqrt{2gh}$ - and for that first instance it is constant. So yes, you can use uniform circular motion... | {
"language": "en",
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What happens if the load on the electrical generator exceeds its generation power? And why? What happens if the load on the electrical generator exceeds its power generation? and why?
To be more precise, suppose we have a standard induction generator operating at frequency $\nu=50\:\mathrm{Hz}$ and voltage $V_0$, and r... | If the generator's power source exceeds the generator's capacity, and if a load is placed on the generator that also exceeds the generator's capacity, and if all safety devices are disabled; the generator would heated up to a point where the weakest link would burn out like a fuse and thus remove the electrical load.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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How do gauge boson interact with elementary particles? We know that gauge bosons are the force carriers of fundamental interactions, but how do the gauge bosons themselves interact with particles?
| Gauge bosons, such as the photon, are indeed the force carriers of fundamental interactions. The interactions are built upon local gauge symmetries of a Lagrangian. A Lagrangian is a list of interactions in our theory. A symmetry is an operation (such as a rotation) that leaves the Lagrangian invariant.
Local gauge sym... | {
"language": "en",
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Free energy of coupled classical harmonic oscillators I'm looking to find the thermodynamic (NVT) free energy of a classical coupled harmonic oscillator system such as the one below:
(image taken from http://openmetric.org/StatisticalPhysics/equilibrium/week3.html)
I would like a solution that allows an arbitrary $N$ ... | Make the change of variable to $\delta_i = x_{i+1} - x_i,\; i=0\dots N-1.$ Then the system is uncoupled and $Z = \prod_i z_i$ with
$$ z_i = \int e^{-\beta p^2/2m_i}dp \times \int e^{-\beta m_i\omega_i^2\delta^2}d\delta = \frac{\pi\sqrt{2}}{\beta\omega_i}.$$
| {
"language": "en",
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"source": "stackexchange",
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Why aren't the weights of the beads considered in this equation? I was solving this problem:
A ring of mass $M$ hangs from a thread and two beads of mass $m$ slide on it without friction.The beads are released simultaneously from the top of the ring and slides down in the opposite sides.
We are asked to find the cond... | Your confusion will be removed if you consider the FBD of the ring itself.
(Mg acts from center of mass of the ring.)
I think you can now see why the weight of the beads is inconsequential while determining equilibrium condition of the ring: regardless of the various forces felt by the beads, the ring itself feels onl... | {
"language": "en",
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A simple derivation of the Centripetal Acceleration Formula? Could someone show me a simple and intuitive derivation of the Centripetal Acceleration Formula $a=v^2/r$, preferably one that does not involve calculus or advanced trigonometry?
| In order to move through a concave path, an agent has to impart force to otherwise a linearly-moving object. The object , by virtue of its motion, under the absence of any external force, always travels or tends to travel in the direction of the velocity vector at the concerned instant.
So, when the object has to trans... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/193621",
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"source": "stackexchange",
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Why are angles dimensionless and quantities such as length not? So my friend asked me why angles are dimensionless, to which I replied that it's because they can be expressed as the ratio of two quantities -- lengths.
Ok so far, so good.
Then came the question: "In that sense even length is a ratio. Of length of given... | Meter refers to something quite physical. Two people should be able to measure something called a "meter" and agree they are the same. NIST says:
The meter is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.
Angles come in units e.g. degree or radian. $1^\circ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/193684",
"timestamp": "2023-03-29T00:00:00",
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Why are heavier nuclei unstable? If you have more neutrons than protons, then there will be more strong force present to counteract the repulsive forces between protons. Why is it that above bismuth, no nucleus is stable, regardless of its N:Z ratio?
| The reason is because the strong force isn't cumulative but the electromagnetic force is. Now, the strong force is a bit more complicated as it does change based on the number of protons and neutrons, but it doesn't build continuously as more protons or neutrons are bound to the nucleus, but the electromagnetic force... | {
"language": "en",
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Do you encounter more photons (per unit time) when moving forwards at a constant velocity? Let's say you have rain hitting you evenly on all sides (not very realistic, I know). If you were to move forwards at a constant speed, there would be more droplets of rain hitting you per second on your front, since the relative... | You are right in that the speed of light doesn't change. It is a completely different effect to the rain drop analogy. If you had only light hitting you directly from the front and directly form the back, you would observe the same intensity in the moving frame (only blue/red shifted). But for light coming at you from ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/193844",
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Kinetic Theory of Liquids I am familiar with the Kinetic Theory of a gas, where atoms or molecules are in relatively high-speed, random motion, and the bulk properties of the gas are determined by aggregations of these particles - eg. averaging the particle velocities to determine bulk velocity.
I am curious of if, an... | Max Born and Herbert S. Green developed a kinetic theory of liquids in the late 1940s. However, as they say in the introduction to their first paper on the topic, the kinetic theory of liquids cannot use the simplifying conditions of the kinetic theory of gases (low density) or solids (spatial order). As a result, thei... | {
"language": "en",
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Does center of mass affect how an object falls? Suppose you drop an object which has two ends, of which one is heavy and the other is pretty light. Will the object fall with its heavier end downward or with the lighter one? Why does it happen?
| Drop a piece of paper and it glides sideways as well as flips. So aerodynamics (and hence the shape) affect the way things fall.
Specifically aerodynamic forces have a center of pressure, which when ahead of the center of mass the body would rotate and flip, but if behind it will swing and stabilize at this orientatio... | {
"language": "en",
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Can anyone explain the unit for rate of expansion of universe? If you google for 'what is rate of expansion of universe' you get
Space itself is pulling apart at the seams, expanding at a rate of 74.3 plus or minus 2.1 kilometers (46.2 plus or minus 1.3 miles) per second per megaparsec (a megaparsec is roughly 3 milli... | The hubble relation is:
$$v = H d$$
where $v$ is the velocity of the galaxy relative to the Milky way, and $d$ is the distance of the galaxy relative to the milky way. The velocity is measured using redshift. The distance is measured through a complicated series of standard candles, along with the relationship $I = \... | {
"language": "en",
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Where does the $(\ell + x)^2\dot\theta^2$ term come from in the Lagrangian of a spring pendulum? I am reading some notes about Lagrangian mechanics. I don't understand equation 6.9, which gives the Lagrangian for a spring pendulum (a massive particle on one end a spring).
$$T = \frac{1}{2}m\Bigl(\dot{x}^2 + (\ell + x)^... | In general you can write the kinetic energy of a free particle as:
\begin{equation}
T = \frac{1}{2} m \,\vec{v}\cdot\vec{v}
\end{equation}
which holds whatever coordinate system you choose (could a physical quantity such the trajectory of a particle depend on the coordinate system that you choose?).
We can rewrite thi... | {
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What is the most efficient way to use a blow torch? Let's start with a torch and a piece of titanium. What is the fastest way to get the titanium up to red hot? I am not going for getting the Titanium malleable, just red hot.
Whenever I ask my science-y friends they like to point out that the bright blue tip is the ... | That's not an easy one...
First of all you must know the final temperature you are trying to achieve, then you need to choose a heat source and a way to trap heat where you need it
I'd sugest you build a "soup-can forge" or something like that and use a MAP-gas torch.
A J23 ceramic hoven brick might also be a good choi... | {
"language": "en",
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Why are tidal forces pointing away from the Moon?
I am currently reading The Science of Insterstellar, which explains most things very well, but some things leave me confuzzled, which I hope to get answers to here. I am no physicist, but highly interested and eager to learn.
I get tidal forces in principle, but one t... | This link explains it:
The Earth experiences two high tides per day because of the difference in the Moon's gravitational field at the Earth's surface and at its center. You could say that there is a high tide on the side nearest the Moon because the Moon pulls the water away from the Earth, and a high tide on the opp... | {
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Can all the theorems of classical mechanics be deduced from Newton's laws? As above, is the whole edifice of Newtonian mechanics built upon Newton's three laws of motion? Can I deduce all the theorems without referring to further assumptions?
| If "for every action there is an equal and opposite reaction" (F12=-F21) allows friction as a legitimate reaction, then no. Non-conservative forces like friction are not fundamental and would allow non-conserved energy and momentum if additional constraints are not included (like "heat" from thermo). They are not time-... | {
"language": "en",
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Does anti-matter increase or decrease in entropy over time? Antimatter is matter going backwards through time. From the perspective of a matter-based observer does antimatter:
*
*Increase in entropy (and therefore decrease in entropy in its own time)
OR
*
*Decrease in entropy (and therefore increase in entropy ... | The answers given are speculative, as the answer to your question is unknown. The thermodynamics of antimatter is an open question in physics, and future experimentation will be required to reach a definitive answer. If CPT (charge, parity, time) symmetry is true, then antimatter would be expected to behave has though ... | {
"language": "en",
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Noether's theorem: meaning of transformation of coordinates I have a question regarding Noether's theorem. In our introductory QFT class (which is based on the book by Michele Maggiore) we have derived the Noether currents in the same form as displayed in this post: Question about Noether theorem
In this formula, there... | Classical Lagrangian field theory deals with fields $\phi: M \to N$, where $M$ is spacetime and $N$ is the target-space of the fields. We shall for convenience call $M$ and $N$ the horizontal and the vertical space, respectively. OP is in this terminology essentially asking
Q: What is the meaning of horizontal transfo... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Does a gas in a container lose kinetic energy? When a gas is in a container, it frequently collides with the container wall, exerting pressure. However, with a collision, kinetic energy ought to be transferred from the gas molecule to the container wall. Does that mean a gas isolated in a container will lose kinetic en... | The temperature of the gas will eventually reach equilibrium with the walls of the container, and since a perfect insulator is not possible, the gas, walls and outside environment will, given enough time, be at the same temperature.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/195569",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Current constraints on lightest neutrino mass? This paper from 2005 claims that the mass of the lightest neutrino is unconstrained. (see p9)
Oscillations are only able to constrain the differences in squares as far as I know, but perhaps constraints could come from cosmology or beta decay experiments.
Is there still no... | there are many experiments that put different contraints on the neutrino masses. Here is a good collection from the particle data group.
To summarize: There are lots of experiments that put upper bounds on the neutron mass. The PDG groups estimate is that $\nu_e < 2eV$, $\nu_{\mu} < 0.19eV$, $\nu_{\tau} < 18MeV$. All w... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/195624",
"timestamp": "2023-03-29T00:00:00",
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What would happen if we tried to run a motor in space when it is not attached to anything to provide support to it? I know that a when a motor runs it generates torque and that torque can be used to do useful work. On the other hand, the motor needs strong support that absorbs the reaction torque. In our case let us a... | The astronauts working on the Hubble space telescope had to bring special low torque wrenches to counteract the effect of the torque of the motor spinning them around, due to conservation of angular momentum, although this meant far more use of muscular power to hold them in place. And also to avoid damaging the equipm... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Is Gauss' law valid for time-dependent electric fields? The Maxwell's equation $\boldsymbol{\nabla}\cdot \textbf{E}(\textbf{r})=\frac{\rho(\textbf{r})}{\epsilon_0}$ is derived from the Gauss law in electrostatics (which is in turn derived from Coulomb's law). Therefore, $\textbf{E}$ must be an electrostatic field i.e.,... | Maxwell derived his equations from 1) charge conservation law; 2) Coulomb's law; 3) Bio--Savart--Laplace law; 4) Faraday's law of induction. The equation $\boldsymbol{\nabla}\cdot \textbf{E}(\textbf{r})=\frac{\rho(\textbf{r})}{\epsilon_0}$ was indeed derived from Coulomb's law and in its differential form is written us... | {
"language": "en",
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Polarization of the Sky? I was hiking and noticed as I tilted my sunglasses (which are probably polarized), right at the horizon where the sky was against a mountain, it would change from lighter to darker blue.
This only occured right above the horizon, and I didn't see a noticeable change when looking directly up at... | Where was the Sun at the time?
The sky is viewed through Rayleigh scattered light. Unpolarised light (or rather, the electric field in the electromagnetic radiation) from the Sun can be imagined to cause oscillations in the bound electrons of atoms and molecules in the atmosphere. These electrons then remit light as os... | {
"language": "en",
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Why does humidity cause a feeling of hotness? Imagine there are two rooms kept at the same temperature but with different humidity levels. A person is asked to stay in each room for 5 minutes. At the end of experiment if we ask them which room was hotter, they will point to the room with the higher humidity. Correct ri... | It because the higher humidity makes it more difficult to cool the body. Even though the room temperature is below body temperature, you generate more heat than needed to maintain your body temperature. To help cool you down, you sweat, and the water evaporates from your skin. The evaporation of the water cools you dow... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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In general, why do smaller guns have more felt recoil? Why is recoil easier to control on a more massive gun compared to a smaller gun with the same bullet. Presumably the bullet leaves both guns with the same momentum, but the larger gun seems easier to control. Since the momentum you have to control is the same in bo... | The larger firearm has more mass, and therefore more inertia for the recoil momentum of the bullet to overcome.
Also, small firearms may be more difficult to secure a good grip on.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/196312",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How and why the phrase "quark force increases with distance"? I have seen that phrase "force between quarks increases with distance" at many resources, some even relatively credible (albeit written for general audience).
What is the reason behind that, when the area law for the confining phase clearly gives the potent... | This is the strong interaction which sometimes called strong 'force'. It is one of four forces which
100 times stronger than electromagnetism, a million times stronger than the weak force interaction and $10^{38}$ times at a distance of femtometer.
This strong force actually explains how nucleus of atom stick toget... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/196527",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 2,
"answer_id": 1
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Conical train wheels I've been reading about how the conical shape of train wheels helps trains round turns without a differential. For those who are unfamiliar with the idea, the conical shape allows the wheels to shift and slide across the tracks, thus effectively varying their radii and allowing them to cover differ... | In both diagrams in the question, the left wheel has a smaller radius at the contact point than the right wheel. Because they're fixed to a common axle, in any given amount of time, the right wheel will travel a greater distance than the left, so the axle as a whole will rotate anti-clockwise (when viewed from above) a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/196726",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "24",
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Obtaining central force from the potential of an off-orgin object I was trying to go through a simple exercise and was getting tripped up on the mathematical intuition of my elementary physics. I thought I should be able to get any old central force from the central potential by noting the curl of the force is zero thu... | ( I turned my comment into an answer to signal that this is question is answered)
if in doubt (and unexperienced) work using Cartesian coordinates. That being said: You simply miscalculate the gradient. $F_c$ is not directed in the direction $r$ but $r−x$. If you want to compute the Gradient in spherical coordinates yo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/196809",
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What determines the probability of creating a particular particle in a collision? When discussing events at the quantum level, we deal in probabilities and not absolutes. Articles I've read on particle physics state that a particle has a probability of being created in a collision. What determines this probability?
Ass... | This is actually an open question.
So far what we are able to state from theoretical considerations are restrictions in terms of the conservation laws that we have observed. These tells you for example that the whole momentum in a reaction is conserved, an the mass-energy, or some quantum numbers. And this already con... | {
"language": "en",
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Can a magnet damage a compass? I've heard the claim before that a magnet can ruin a compass, and was about to repeat it to my son when I realized it sounds like complete nonsense. Googling turned up such unsubstantiated and illogical answers as this one and unanswered questions as this one but nothing that sounded rea... | A magnet is made by aligning the magnetic poles of all the molecules in a magnetic material so they all point the same way.
If you have a look at how a magnet is made, traditionally
http://www.princeton.edu/ssp/joseph-henry-project/permanent-magnet/
or commercially
http://www.arnoldmagnetics.com/Magnet_Manufacturing... | {
"language": "en",
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Wavelength vs Wavenumber etiquette When am I supposed to use the terminology of EM "wavenumber", instead of "wavelength" (or frequency)?
The concepts of wavelength and frequency are no problem for me, but wavenumber (number of wavelengths per unit length) seems redundant to me as a student engineer and proto-physicist.... | I don't think there's much to say beyond the obvious: You should use whatever terminology is most helpful in communicating the information that you want to communicate.
*
*That has to do with the audience you're talking to. Just like how you use °F when talking to Americans and °C when talking to non-Americans ... s... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Do we regularly measure and update our physical constants (By using the LHC)? This question is motivated by sheer curiosity. I certainly do not expect that the free parameters we use in the standard model have changed in value since we started measuring them with a "modern" degree of accuracy.
It would seem to me howe... | Every few year the Committee on Data for Science and Technology (CODATA) publishes recommended values of the fundamental constants, see http://www.codata.org/. They use the most accurate experimental results available, so yes, the values of the fundamental constants can -- in principle -- change. But what is more likel... | {
"language": "en",
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How light splits up into different colours when passed through prism using QED? I want to know how light gets splits up into different colours when it is passed through prism? How light interacts with atoms and electrons of the prism? Can someone explain this to me using Quantum Electrodynamics?
| As you know white light is made of many different wavelengths. Each wavelength of light takes a slightly different path through the prism. In QED we have a spinning clock which turns at different rates for different wavelengths of light. We calculate the probability of a certain path the light can take using these cloc... | {
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How do I know what variable to use for the chain rule? In my textbook the tangential acceleration is given like this:
$$a_t=\frac{dv}{dt}=r\frac{dw}{dt}$$
$$a_t=rα$$
I understand that the chain rule is applied here like this:
$$a_t=\frac{dv}{dt}=\frac{dv}{dw}\frac{dw}{dt}=rα$$
What I don't understand is why we have to ... | In the case of a circular motion, the tangential velocity $v$ can be expressed in terms of $\omega$ and $r$, i.e. $ v= \omega r$.
The formula in your textbook $$a=r\frac{d\omega}{dt} $$is obtained by taking the derivative of the previous equation, while taking into account that $r$ is constant.
Of course, you could con... | {
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Why the optical gap is not identical to the charge gap? The optical gap is the photon energy required to create an exciton (in a solar cell for example). The charge gap (aka electrical gap) is the energy (voltage) required to create a photon (in an LED for example). Why are these two gaps not identical?
Ref:
Undoped (... | The difference between the fundamental gap (following IUPAC definitions - and your diagram ) (this is what you refer to as your electronic gap in your question) exists because the optical gap corresponds to the energy of the lowest electronic transition accessible via absorption of a single photon. The optical gap is g... | {
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Will a gas rotate as fast as the spherical container it is contained within? Let's say I have a sealed spherical glass container 30 cm in diameter which contains plain air.
The glass container is rotated about its axis at 1 revolution per minute.
My question is, would the gas also rotate at 1 revolution per minute with... | Given viscous effects, that is indeed the case if:
*
*We are looking at a steady state system
*It is not a rarefied gas (i.e. at pressures much lower than atmospheric)
*The walls of the container are rough enough such that the gas molecules don't 'slip' over the surface but can be assumed at the same angular velo... | {
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How to estimate if an image is in focus I am building a test measurement (optics) to look a rectangular slit opening (1mm x 15 microns). The slit opening is illuminated by a white LED and using a microscope objective to magnify it to 10X on an image sensor.
What would be the possible method to estimate if the image is... | You could try using contrast. The contrast in the image is highest when the image is in best focus. You can analyze the contrast information and move the object, lens, or sensor into a position that gives the maximum contrast value.
The downside to this is that you will need to typically adjust your opto-mechanics thr... | {
"language": "en",
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Is heat conduction impeded at interfaces between dissimilar materials? Sound in air essentially echoes off concrete walls, rather than penetrating them, because of the difference in the material properties of air and concrete.
By analogy, are there pairs of solid materials where their interface would be very inefficien... | Conduction across the interface between two materials mostly depends on how well they are in contact. If you want to make a very good insulator you try and ensure the surfaces aren't in good contact. The ideal is no contact at all - hence the thermos flask.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/199357",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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"answer_id": 2
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Infinite dimensional manifolds in general relativity In GR the concept of a manifold is very useful. However, all of these manifolds are of finite dimension. Is it possible to define a manifold with infinite dimension (ie much like Hilbert space in QM) such that we can still define terms such as curvature, tensor field... | Technically speaking, manifolds are by definition topological spaces, which resemble locally an inner-product space. Since there are vector spaces (with a dot product) of infinite dimension, then there shall be infinately-dimensional manifolds as well. The infinity of the dimension is not a problem for the tensors as w... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/199422",
"timestamp": "2023-03-29T00:00:00",
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Why is it easier for the ocean to push someone over by exerting force on their front side than by exerting force on their left or right side? If I put two clones of normal weight on a beach in the ocean, with one standing perpendicular to the waves, and the other standing parallel to them, the one standing perpendicula... | The main reason for this difference in stability is the orientation of the feet of the clones. If you were to do this experiment on dry land by simply putting sandbags on someone's feet (the water makes it hard to move your legs fast enough to catch yourself, and so do the sandbags) and pushing on them from different ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/199655",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Can there be eternal stars? the question is quite straightforward:
*
*Can there be stars that shine forever without ever collapsing nor growing?
*Do we know some really, really old stars? (whatever age that might be)
I hope to get answers from physicists, as for the nuclear reaction constraints involved; but I'm al... | The word thing you are looking for is "Black Dwarf" stars. Which are White Dwarf stars which have cooled to match the temperature of the cosmic background. Since this is likely to take more than the current age of the universe, there aren't any. These will exist forever, unless hypothetical proton decay finishes them o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/199742",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Adding fluctuations to a hydrodynamic simulation to trigger instabilities I'm doing a 2D combustion hydrodynamic simulation and there's a hydrodynamic instability that should be triggered because of the particular physical properties of my system. The key to the instability are temperature gradients perpendicular to th... | I think the answer would have to depend on the nature of the simulation. I'm guessing it is some sort of flow simulation in which fluid "enters the system" at some point and exits at some other point. If so, there must be parameters to do with the fluid at the intake which you have control over. Is $\rho(\mathbf{x})... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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What is really a light ray? I've been studying geometric optics and I'm still a little confused with this idea of light ray. In the book I'm studying everything is being done starting from Fermat's principle which states that the ray path is the one which extremizes the optical length.
Now, I thought that because of th... | In a wave picture we can put an arrow at each point of the wave that points in the direction of propagation which is (normally) at right angles to the wavefront. If we string a bunch of these arrows together into a line, we get a ray.
I tend to think of this as being analogous to field lines in electromagnetism. In fa... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Definition of a Supercluster A group of astronomers in September 2014 redefined what classifies a supercluster. Before this, the supercluster where the Milky Way resides was the Virgo Supercluster. Now, the Virgo Supercluster & three other previously defined superclusters are simply 4 lobes of the newly-defined Laniake... | According to here, there was no precise definition before this group redefined what it meant for a group of galaxies to constitute a supercluster--before their redefinition, it seems it was just loosely defined as "extended regions with a high concentration of galaxies." They now define a supercluster to be a volume in... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/200238",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Collision of Inelastic ball above the ground
An inelastic ball of mass $m$ is dropped from a height $h$ above the ground and at the same time a second ball of mass $m_1$ projected vertically upwards to meet the former. Show that in order that immediately after collision, the balls may be at rest, the 2nd ball must be ... | Let $t$ be the time from the dropping the fist ball until the collision of the balls. Then, $v_1=gt$ and $v_2=u-gt$. Moreover, $d=ut-\frac{1}{2}gt^2$ and $h-d=\frac{1}{2}gt^2$, so that $ut=d+(h-d)$, which gives $t=\frac{h}{u}$. Because $mv_1=m_1v_2$, we must have $m\left(\frac{gh}{u}\right)=m_1\left(u-\frac{gh}{u}\r... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/200525",
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Poincaré Recurrence and Immortality If, as Luboš Motl says, Poincaré recurrence is relevant for our universe, does this mean (1) that, after I die, I'll one day live through my life again after the same physical pattern that is currently me reconfigures and (2) that I'm thus immortal because this reconfiguration of my ... | This is more a philosophical answer, but it is also more a philosophical question since it is actually the question how you define Immortality.
If you were really reborn after $10^{10^{10^{120}}}$ years, would it still be you? Of course, it will be an identical version of you, but is it really the same you as it was $1... | {
"language": "en",
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Car Crash Scenario Two vehicles travelling at 80mph in the same direction.
Vehicles are directly behind each other.
12 meter distance between them.
Front door of car in front rips of and hits the front window of the car behind.
At what speed did the door make contact with the car?
How would one go about calculating thi... | Once the door is detached from the front car, it will start decelerating, because of air drag, friction with the floor, etc. You can start assuming that this decelaration is constant, it is not perfectly accurate, as the door will likely be rotating, and being an irregular form, the drag will vary chaotically. Also the... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is the time period of an oscillator with varying spring constant? It is well known that the time period of a harmonic oscillator when mass $m$ and spring constant $k$ are constant is $T=2\pi\sqrt{m/k}$.
However, I would be interested to know what the time period is if $k$ is not constant. I have searched hours af... | Alright, according to my knowledge there are some cases with a time dependent spring constant where a closed form solution is known. One of my favorites is the following where the spring constant is a power function. Assume that $k/m = \omega^2/t^\beta$ where $\omega \in {\mathbb R}$ and $\beta \ge 0$. Then the ODE in ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/201078",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Ligth clock with spaceships side-by-side In the reference frame of an observer, two spaceships travel in a straight direction (e.g. x axis) at a very high velocity and side-by-side; the distance between them is always d (km) = c (km/s) x 0.1 (s).
At its time zero, spaceship one begins the emission of one photon each 0.... | To answer question 2:
If it fires a photon orthogonal to its heading, it will travel orthogonal to the source's heading from the POV of the source. From the POV of an outside observer, it will travel not orthogonal to the motion of the source, but slightly along its direction of motion.
This can be easily intuited beca... | {
"language": "en",
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How to calculate the work of the electrostatic forces in a parallel-plate capacitor? The expression of the energy stored in a parallel-plate capacitor is:
$$U = \frac{e_0\cdot A \cdot V^2}{2d}$$
with $e_0$ the vacuum permittivity, $A$ the surface of the capacitor, $V$ the applied voltage and $d$ the distance between th... | I think your approach isn't wrong; however in your calculations you're making the assumption that the potential difference between plates, $V$, is constant: What remains constant is the charge on each plate. So the equation becomes:
$$W=\int_0^d {{q^2} \over {2\epsilon_0A}} \;\mathrm{dx}={{q^2d} \over {2\epsilon_0A}}$$... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/201261",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Is stress a property only relevant on surfaces? I saw that,
$$dF=\sigma \cdot dS$$
Where $dF$ is the differential force, $\sigma$ is the stress tensor, and $dS$ is the differential surface. This equation confuses me a bit. I'm under the impression that stress acts over a volume rather than a surface, so rather than $dS... | Both.
You can have the standard
$$\sigma_{ij} = C_{ijkl} \epsilon_{kl}$$
in the bulk, but you can also have a reduced tensor, a surface stress. This surface stress is the projection of the regular stress
$$\sigma_{\alpha \beta}^s = {\boldsymbol P} \sigma {\boldsymbol P}$$
where ${\boldsymbol P} = 1 - {\boldsymbol n}({\... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/201348",
"timestamp": "2023-03-29T00:00:00",
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"question_score": "2",
"answer_count": 1,
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Why does a moving fan seem transparent? We all know when fan starts moving faster, we cannot see its blades. Why is this?
First I assumed persistence of vision may be the reason. But that can happen with blade also right? Image of blade can remain in our memory and moving fan can appears as a circular plane with blade... | Because human eyes and brains are slow, they cannot resolve the motion of the blades, but only see the average of the moving blades and the image in the background (this is actually primarily really due to the slow reaction time of the cones, which is slow, as is demonstrated by the fact that a 24 frames per second vid... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/201504",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "39",
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Double slit experiment experiment with convex lens? In one version of the double slit experiment, the experimenters placed a convex lens far away from the two slits. After the individual photons passed through the two slits they then travel to the the lens, then after that they hit the back wall. However the detector ... | The interference pattern is not destroyed by the lens or the focal point, because in this case it never existed. The moment the lens is placed between the slits and the detector, all particles traveling through the slits will only behave like particles passing through a slit then a mirror and then hitting one of 2 poin... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
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What is the ratio of the acceleration in the two cases (a) and (b) What is the ratio of the acceleration in the two cases (a) and (b)?
I thought that the ratio would be 1:1 but it my textbook says its 1:3, so can someone explain to me how that's possible.
| $1)$ Let's make all the forces that would be acting on the blocks, in the first case.
Now we apply newtons' laws of motion assuming that block of mass 2m accelerates downward with $a_1$ acceleration and the block of mass m accelerates upward with same magnitude of $a_1$ acceleration( because they are ... | {
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"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
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How do we know that the CMBR is the oldest light? How do we know that the CMBR is the oldest light which we can see? Is it based just on the facts 1.that waves redshift with expanding space, and 2.predictions of the big bang theory;
Or is there a way to know which light is older/younger?
How can You tell the difference... | Distance is equivalent to time. The time at which the cosmic microwave background was emittied was the time when the universe made a phase transition from being a plasma to being atomic matter. During this time, the universe finally became transparent. Before this time, the universe was so hot that all matter was op... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/201791",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 1
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The pressure in a container of water is based on depth. So what happens if I remove the bottom of the container? So I understand that if we have a system that involves a container of water the pressure will equal atmospheric pressure at the top and as we go further down the container the pressure will increase with dep... | If you remove the bottom you no longer have a container. The pressure is atmospheric and you just have gravity at work.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/201896",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
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Why complexify in order to construct Dirac representation? Suppose we have a theory is covariant under the Spin group Spin(2n-1; 1). We consider the real vector space $V = R^{2n-1,1}$, which naturally comes with a Lorentzian inner product. On this vector space we introduce an orthonormal basis $e_0; e_1; ... ; e_{2n-1}... | We assume that OP asks apart from the facts that:
*
*Dirac representations by definition are complex;
*It is much easier to work with an algebraically closed field;
*Any real representation can be extended to a (possibly reducible) complex representation, so one is not missing anything by going complex.
In other ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/201989",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 1,
"answer_id": 0
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Does sound show wave-particle duality? We know that light and electrons both show wave-particle duality. Or in other words we can say that they can be both seen as a wave and a particle. Can a similar theory be applicable for sound? Can sound also be explained as a particle as well as a wave?
| To plainly put what WetSavannaAnimal have said. Yes, sound waves can behave like a particle. When sound wave have enough energy to excite the particles that is use for traveling to their excited state, the sound wave becomes a Phonon.
Phonons act like particles that oscillates relative to each other and no longer funct... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/202058",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 1
} |
How do we see? Where do the photons disappear? I know that the light is reflected from a object to my eyes, but I don't understand exactly how. The photons appear from the light source and disappear in my eye! Can someone explain the phenomenon of where the photons go and do to allow us to see?
| From the wiki article on color vision as an illustration of how photons are absorbed:
Perception of color begins with specialized retinal cells containing pigments with different spectral sensitivities, known as cone cells. In humans, there are three types of cones sensitive to three different spectra, resulting in tr... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/202284",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "27",
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"answer_id": 1
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