Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Is Newton's third law always correct? Newton's third law states that every force has an equal and opposite reaction. But this doesn't seem like the case in the following scenario:
For example, a person punches a wall and the wall breaks. The wall wasn't able to withstand the force, nor provide equal force in opposite ... | Newton's third law is not always correct, contrary to what you may have heard. It is correct in the context of newtonian mechanics, because we assume then that point particles are described only by their mass, and symmetry and conservation of momentum of the system imply that the third law must apply for the case of a ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/114669",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "16",
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What happens to atoms in extremely strong electromagnetic fields? I know that strong gravitational fields on the order of neutron stars (at the crust) atoms get compressed so tightly, the empty space between them is significantly reduced and it becomes denser. (http://www.newscientist.com/article/dn16948-star-crust-is-... | Atoms are bound together by electrostatic forces. The energy is on the order of 10eV (e.g. 13.4eV for for an electron and proton in the ground state of a H atom), and the size is of the order of an Angstrom (Bohr radius is ~0.5 Å). Therefore when electric fields are greater than roughly
$$E\sim \frac{10\text{V}}{0.1\t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/114824",
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Why is the ratio of velocity to the speed of light squared in the Lorentz factor? Why is the ratio of velocity to the speed of light squared in the Lorentz factor?
$${\left( {{v \over c}} \right)^2}$$
My only guess is the value must be positive.
| I'll chime in with the hyperbolic geometry take:
The $\dfrac{v^2}{c^2}$ term in the Lorentz factor can be better understood if we look at the entire Lorentz factor:
$\gamma = \dfrac{1}{\sqrt{1-\dfrac{v^2}{c^2}}}$
Now we've got the term you asked about back into context. If we take a factor of $\frac{1}{c^2}$ out of th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/114913",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
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What is the generating functional for a scalar theory with two different (interacting and real) fields? My question is specifically about how to use sources? For an interacting theory with one field, one puts a $J(x)\phi(x)$ term in the exponential in the path integral for $W[J]$. I now have two different fields ($\phi... | Yes, what you want to do is to bring down $\psi_1(x)$ and/or $\psi_2(x)$ and you do that by multiplying them by independent currents and integrating over space-time, which then allows you to take the functional derivative w.r.t. either of the currents independently.
This is completely analogous to $\int J(x) \psi(x)... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/114976",
"timestamp": "2023-03-29T00:00:00",
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Why Shock wave propagation is faster From The Blast Wave
A fraction of a second after a nuclear explosion, the heat from the fireball causes a high-pressure wave to develop and move outward producing the blast effect. The front of the blast wave, i.e., the shock front, travels rapidly away from the fireball, a moving ... | As per my answer here. The air on the inside of the explosion is also moving "faster then the speed of sound" so relative to that air, the shock wave is traveling at subsonic speeds. Thus the shock wave travels at a weighted average of the velocity that sound would travel in the mediums on either side of it.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/115027",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Power fit to some experimental data I have to fit some data to a power law
$$ F=\alpha q^{\beta}$$
being $q$ and $F$ the experimental data points. What I usually do is taking logs so that
$$ \ln(F) = \beta \ln(q)+\ln(\alpha)$$
and apply least squares with uncertainties in both variables. How may I approach this in the ... | This sort of problem is reasonably straightforward to solve numerically using Gauss-Newton or similar algorithms and your favourite programming language. Matlab even has an entire curve fitting toolbox which does everything very nicely.
These non-linear least squares techniques should work for any (differentiable) func... | {
"language": "en",
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"source": "stackexchange",
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Oscillations in forces other than the Weak As I understand it neutrino oscillations arise due to the neutrino mass eigenstates being distinct from the neutrino flavour eigenstates.
Flavour eigenstates are the states in which neutrinos interact via the weak force, and so are the eigenstates in which they are created and... | Only weak interactions can change the flavor of quarks and, therefore, produce mixing (oscillation) effects in mesons. Mixing always involves the weak interaction because it requires to change the flavor of the constituent quarks (strong and electromagnetic interactions can not change flavor).
Also, electric charge is ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is it more efficient to stack two Peltier modules or to set them side by side? Is it more efficient to stack two Peltier modules or to set them side by side?
And why?
I have a small box that I want to cool down about 20 K below ambient -- cold, but not below freezing.
(I want to keep my camera cool, so I'm putting in t... | An efficiency of 10% does not mean you require 100W to produce 10W of cooling. This is complete nonsense. Efficiency is comparing the amount of heat shifted with the ideal Carnot cycle. In the ideal Carnot cycle 'coefficient of performance' (COP) values of over 5 are possible. That is why the efficiency of a TEM can ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/116271",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "20",
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Quick question on sketching wavefunction in well
Usually for an infinite well, the sketch for n=3 level is this:
Now I think if one side of the potential barrier is higher, the particle will be more likely to spend time on the left side than the right side, so the wavefunction should have higher amplitudes on the lef... | You are correct that for $n = 3$ there are $2$ non-boundary zero points.
Also, the modulus of $\psi(x)$ is lowest where $V(x)$ is lowest.
Where you are wrong is that $\psi(A)$ is not zero and $\psi(B)$ is not zero either, as you indicate in your schematic. For $x < A$ and $x > B$, $V(x)$ is not $\infty$ (your well is a... | {
"language": "en",
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Where does the term "boost" come from for rotation-free transformations? I had never seen rotation free transformations called "boosts" (I think I have it right) before reading some questions here. I'm too old perhaps. I have not found the etymology after some searching, though it sounds like something V.I. Arnold woul... | In Gravitation, Misner, Thorne and Wheeler first use the term boost in box 2.4 starting on page 67. They don't make a fuss of defining the term, so I assume it must have been in common use at the time of publication (1970).
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Normal reaction - force without acceleration When a body lies on the surface of the Earth it is under the influence of gravity. The force on the body due to gravity causes it to exert a force on the ground and the normal reaction acts in the opposite direction causing the resultant force on the body to be zero.
However... |
When a body lies on the surface of the Earth it is under the influence of gravity. The force on the body due to gravity causes it to exert a force on the ground and the normal reaction acts in the opposite direction causing the resultant force on the body to be zero.
Correct
However, how can the body exert a force o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/116632",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Dielectric boundary I am trying to determine why electric field may be confined to a certain region if there is a large difference in the permitivity for example if electric field flows through water and then reaches a water air boundary.
I have also been reading about EM waves, is it possible to model electric field ... | What you're saying is mostly correct, but your language is a bit imprecise, which makes me think your understanding is a bit incorrect.
To be clear: there are both static electric fields, as well as time varying electric fields, which occur together with magnetic fields electromagnetic (EM) waves. The equations you're ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/116702",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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What will happen after escaping earth's gravitational field? Suppose that I escaped the gravitational field of earth.
Then: am I going to be pulled by Sun's gravity?
| Yes, you will be pulled by the sun's gravity. However, that has nothing to do with whether you have "escaped" earth's gravitational field or not. That is a non-sensical concept because the gravitational fields of objects don't have a hard distance limit where they suddenly go to zero. Once you get far enough from a ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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A strange audio phenomenon, could there be a physical interpretation to it? https://mathoverflow.net/q/165038/14414
Motivation : Here is a motivation as to why this problem is so important.
Let $f(t)$ be an audio signal. We can safely asume it to be bandlimited to 0-20kHz as we cannot hear anything above that. Capture ... | To your Question:
*
*There is no quantum mechanics involved. This is essentially a signal processing question, which is rooted in calculus.
*Why does it sound the same?
The ear works essentially as a power spectrum analyzer, i.e. what you hear of a signal $f(t)$ is mainly determined by the powerspectrum $|{F(\omeg... | {
"language": "en",
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Why doesn't a block rotate due to friction? In a horizontal surface, a block (cube) is sliding due to a sudden push. When the block slides, there is frictional force which is acting on the block.
Frictional force will have a torque around the center of mass, so why does the block not rotate/roll around (a horizonta... | First consider the initial push. If the friction is high enough and the push is high enough on the block it will roll instead of slide. Generally static friction is greater than dynamic friction, so if it starts sliding it will continue.
If the friction gets great enough, the block can roll. Say you have a box sli... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Moment of inertia of a cylinder When I tried to calculate the moment of inertia ($I_C$) of a cylinder (mass M, height H, radius R) around the rotating axis going symmetrically through its middle, I came up with a different result than expected ($\frac{1}{2}MR^2$), but I do not spot my mistake, since my calculation make... | You made two mistakes:
*
*$dV = dr d\phi dh$ is wrong.
*
*$dV = r dr d\phi dh$.
*$V = 2πR H$ is wrong.
*
*$V = πR^2 H$.
$$
I_C := \int_V{ρr^2dV} = \int_0^H{\int_0^{2π}{\int_0^R{ρr^3 dr dφ dh}}} = ρ \int_0^H{\int_0^{2π}{\frac{R^4}{4} dφ dh}} = ρ \cdot 2πH \frac{R^4}{4} = Vρ\frac{R^2}{2} = \frac{1}{2}MR^2... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/117151",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why is the movement of electrons random in electric field? Suppose an uncharged conductor is present isolated and there is no net electric field applied. Then by assumption we have the motion of electrons random,i.e. isotropic.
But now suppose there is a closed conductor present. We apply a net electric field and the e... |
Is the motion of elections in a particular direction more probable or they have more velocity in that direction?
Both are actually true in the Drude model. In presence of a field, the probability for the electron to move in the direction opposite to the field is enhanced. As a result, their Brownian motion is drifted... | {
"language": "en",
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Moon's pull causes tides on far side of Earth: why? I have always wondered and once I even got it, but then completely forgot. I understand that gravity causes high and low tides in oceans, but why does it occur on the other side of Earth?
| The Earth is free falling towards the Moon. Because gravity decays with distance, the side near the moon wants to fall faster than the center of the Earth, while the other side tends to fall slower. So observed on the Earth, the other side "lags behind" and therefore we have high tide there.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/118460",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "80",
"answer_count": 8,
"answer_id": 2
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Placing two similarly charged particles in space Now, I will make a hypothetical situation. Assume that we place two similarly charged particles (lets take electrons) in space. Imagine that there is no other force acting on the particles except the repulsive force and the gravitational force of the particles. In other ... | The problem is not so simple. In fact I think the final kinetic energy of the electrons is not equal to the initial potential energy. But this not means the energy conservation is violated. A moving charge that accelerate emits electromagnetic waves. This waves transport energy so the electron slows down while moving t... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Irreversible heat engines strictly less efficient than reversible ones I understand how Carnot's theorem implies that irreversible heat engines must be no more efficient than reversible one's, but it is less clear why they need to be less efficient, as I have seen stated in some places.
If they could be equally efficie... |
I understand how Carnot's theorem implies that irreversible heat engines must be no more efficient than reversible one's, but it is less clear why they need to be less efficient, as I have seen stated in some places.
The answer is that it is always possible to construct an incredibly inefficient engine, which is to s... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/118591",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 2,
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Entropy was created after inflation? I'm puzzeled by a statement in Big Bang Cosmology-review about the reheating phase subsequent to the exponential expansion during inflation:
In this reheating process, entropy has been created and the final value of $RT$ is greater than the initial value of $RT$.
(Taken from sect... | There is nothing wrong with that statement (assuming that the meaning is: prior to inflation we have a total amount X of entropy, then after the inflation we have a lot more than X).
After the inflation, the scalar field (inflaton) is in the minimum of the potential well and is a super-cooled Bose-Einstein condensate ... | {
"language": "en",
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Universal central charge in higher dimensional AdS/CFT? In the $AdS_3/CFT_2$ correspondence, the central charge of the dual CFT2 is universally given by
$$
c = \frac{3\ell}{2G}
$$
This is independent of the matter in the bulk of AdS3. Is it also universal in the higher dimensional analogues $AdS_d/CFT_{d-1}$ or does it... | The expression you've written derives from a proposal, due to Ryu and Takayanagi (See: http://arxiv.org/abs/hep-th/0603001), to calculate entanglement entropy of a CFT by making use of a gravity dual.
Define a CFT in $D$ space-time dimensions. Take a spatial slice, a ball of radius $R$ for example, and calculate the en... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/118744",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Energy of an EM Wave and its temperature and amplitude I'm trying to understand why classical physics fails to explain black body radiation.
I'm confused.
According to Boltzmann, energy calculation for em wave is based on temperature.
According to Maxwell, energy calculation for em wave is based on amplitude.
Are thos... | M. Planck started to explain black-body radiation by the relation predicted with classical statistical mechanics (with continous energy equi-partition to every degree of freedom of the system). This was Wien's Law which indeed was accurate for high frequencies but divergent for low frequencies.
Then Planck decided to a... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why can the entropy of an isolated system increase? From the second law of thermodynamics:
The second law of thermodynamics states that the entropy of an
isolated system never decreases, because isolated systems always
evolve toward thermodynamic equilibrium, a state with maximum entropy.
Now I understand why t... | We know that $ds_{\rm (universe)}$is equal to $ds_{\rm(system)} + ds_{\rm (surroundings)}$,and for an isolated system $ds_{\rm (surroundings)} = 0$ because $dq_{\rm (reversible)} = 0$; therefore, for an isolated system, $ds_{\rm (universe)}$ is equal to $ds_{\rm (system)}$.
Now, we know that the spontaneity criteria f... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/119387",
"timestamp": "2023-03-29T00:00:00",
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Placing a lens in front of ultraviolet femtosecond laser with 10e38 J in pulse makes it a gun that fires microscopic black holes at speed of light? I calculated that in the focal spot of such a laser the critical energy density would be met.
Will these black holes really move at the speed of light, just as the the phot... | As Carl mentioned, such a contraption would be hard to build. However, I think it might work given a huge energy source and a HUGE lens.
The black hole would not move at light speed, though. Since you focused the light with a lens, the momenta of photons are not aligned. So the magnitude of the total momentum is small... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/119649",
"timestamp": "2023-03-29T00:00:00",
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What is the concept of cosmic strings? What is the concept of cosmic strings? Is it related to the strings in the string theory, and if it is, then how?
| In a paper by R. Gregory, Effective Action and Motion of a Cosmic String, the concept is explained well:
In high energy physics, a defect will generically occur during a symmetry breaking process where different parts of a medium choose different vacuum energy configurations, and the non-compatibility of these differ... | {
"language": "en",
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Why is the constant velocity model used in a projectile motion derivation? I was re-studying university physics last week, I'm now in the chapter about kinematics in 2 dimensions and specifically the one treating projectile motion. In page 86 of his book (Serway - Physics for scientists and engineers) he derives the eq... | "Why did he use the particle under constant velocity model to derive that formula, whereas here we deal with a projectile under constant acceleration?" You appear to have the classic confusion between the vertical component of the motion and the horizontal component. Vertically you have to include the acceleration du... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/119778",
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Why is the speed of light arbitrarily the limit? I know Einstein was great and all. Why is it that exactly at the speed of light is where infinite energy is required to accelerate any object with mass? Is it simply because the math of relativity checks out and explains most of everything? Are there any physicists who d... |
Why is it that exactly at the speed of light is where infinite energy
is required to accelerate any object with mass? Is it simply because
the math of relativity checks out and explains most of everything?
To say that the math checks out is the wrong way of putting what's going on because it separates the math an... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/120067",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
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Why is charge not taken as a fundamental unit? According to the definition of electric current, it appears to be a derived quantity. Charge on the other hand seems more fundamental than electric current. Then why is current taken as fundamental quantity instead of charge?
Is it arbitrary choice? Is it because we can ... | I think that the question is why the SI system of units considers one ampere, the unit of current, to be the elementary one, rather than the unit of the electric charge.
Recall that one ampere is defined in SI as
"the constant current that will produce an attractive force of $2\times 10^{–7}$ newton per metre of leng... | {
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Why would we need to ground an AC source I'm new to this field hence this weird question. Why would we need to ground an AC source? Why wouldn't it be enough to have just one pole to get an AC current going? I understand why it wouldn't work in DC case where current is flowing in one direction. However, in case of AC s... | You need a return wire to complete the circuit. Otherwise the electrons would all try to pile up at the end and the current doesn't flow. In $60$ Hz circuits, the current flows in one direction for $1/60$ second. That doesn't mean you need a ground wire-AC works fine isolated from ground.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/121197",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Bragg diffraction and lattice planes Crystalline substances show, for certain sharply defined wavelength and incident directions, very sharp peaks of scattered X-ray radiation.
From the illustration below we see that we get constructive interference when the path-length difference is a multiple of the wavelength $\lamb... | The d in that formula is the distance between lattice planes, not points. Basically, one ray (the top one) bounces off the top "plane". The other ray (the bottom one) passes the first plane and "bounces" off the second plane. It then comes out and meets the first ray at some far away point.
Question: Since they travell... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why doesn't time change in the non-relativistic limit of Lorentz transformations? A simple boost in the $x$ direction is given by:
$$ \Lambda = \begin{pmatrix}
\cosh(\rho) & \sinh(\rho) & 0 & 0 \\
\sinh(\rho) & \cosh(\rho) & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1 \\
\end{pmatrix} $$
Which get linearized to the followi... | The Lorentz boost has two different low-velocity limits: the Galilean transformation appropriate for transforming ultra-timelike four-vectors, which is usually what we're interested in if we want to recover low-velocity kinematics, and the whimsically named "Carroll transformation" appropriate for transforming ultra-sp... | {
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How much electricity could be generated by cloths made of thermocouples? Lets say that we made a glove, shirt, pants and a hat out of the most effective thermocouple material available today. How much electricity would be generated by each, by a healthy person, on a cool day (98 degrees F vrs 79 degrees F?)
| As a starting point, figure out what the limit is due to the Carnot efficiency. The Carnot efficiency is the maximum possible work that can be extracted from heat flow. It is Tdiff / Thot.
You have Thot = 98°F = 310°K, and Tcold = 79°F = 299°K, so Tdiff = 11°K.
11°K / 310°K = 3.5%
That's the maximum theoretical porti... | {
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How is sweating a pipe an example of capillary action? I learned how to sweat a pipe today from my father. If you're not familiar with the process, this might help.
One thing that jumps out at me is this line (from the above link, as well as my father's explanation)
Solder, which melts at low temperatures, wicks into... | Molten solder has a low contact angle on (clean) copper. So if you looked at a cross section of the pipe joint as the solder was flowing in you'd see something like:
The solder is drawn into the joint in exactly the same way as water rises in a capillary tube. Both are correctly described as capillary action.
| {
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"timestamp": "2023-03-29T00:00:00",
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How exactly to show that s-matrix elements diverges because time-ordering is not well determined? Let's have s-matrix:
$$
S_{\alpha \beta} = \langle \alpha | \hat {S} | \beta \rangle ,
$$
$$\hat{S} = \hat{T}e^{-i\int \hat{L}(x)d^{4}x}, \quad \hat{T} \left( \hat{\Psi}(t) \hat{\Psi}(t') \right) = \theta (t - t')\hat{\Psi... | Mathematically one way to see it is that the (combined) step functions become Dirac pulses i.e $\theta(t) \to \delta(t)$, which diverge. When $t \to t'$, the fields have nearly identical values, thus the time-ordered product involving step functions degenerates into dirac pulse (a dirac pulse is the derivative of the s... | {
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Why $e$ in the formula for air density? I am reading a book that says that the density of air is approximately $D = 1.25 e^{(-0.0001h)}$, where h is the height in meters. Why is Euler's number $e$ used here? Was a differential equation used in deriving this formula?
| It's actually a surprisingly straightforward differential equation. If you assume that the acceleration due to gravity $g$ doesn't change with altitude (a good approximation if the atmosphere is thin compared to the radius of the earth), Bernoulli's relation tells you the change in the pressure $P$ with height $h$:
$$ ... | {
"language": "en",
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Why is the outside run of high presure line on a ductless mini-split airconditioner insulated? On every ductless mini-split air conditioner I've ever seen, both the high and low pressure lines are insulated between the compressor and the building.
It seems like the liquid refrigerant coming out of the condensing coil ... | Many AC units can be run in reverse as a heat pump. When that is the case, the high and low pressure sides are swapped.
| {
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Fermion as a mixture of particle and antiparticle The solution to the Dirac equation (in the Dirac basis) are 4 coupled fields. The first 2 of them represent a particle (spin up/down), the other 2 fields are the antiparticle (spin up/down). When the particle is observed from its rest reference frame, the antiparticle s... | Literally speaking the answer is negative. The charge of the state has to be always defined in view of the charge superselection rule. Thus for a particle described by Dirac equation, there are no things like coherent superpositions of electron states and positron states. A Dirac particle always stays in a quantum sta... | {
"language": "en",
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Is it ok to have two events $A$ and $B$ so that for one person $A$ occurs before $B$ but for another $B$ preceds $A$ Imagine two laser beams A and B are released at the same moment to bounce between two mirrors, A was moving and B was at rest, doing the calculations I found that for a person at rest B would reach the u... | If the two laser beams are emitted at the same moment in one frame, they will not be emitted at the same moment in another frame moving relative to the original frame. This is relativity of simultaneity. Since the light beams start at different times, it's not a problem for them to travel a different distances.
| {
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Moving wire relative to stationary charged particle "Now we turn our attention to what happens in $S'$, in which the particle is at rest and the wire is running past (toward the left in the figure) with the speed $v$. The positive charges moving with the wire will make some magnetic field $\ B'$ at the particle. But th... | The whole point of Feynman's paragraph is to show that what we might believe is not what must happen by physical law. The full electromagnetic force on a particle is the Lorentz force, which is
$$\vec{F} = q (\vec{E} + \vec{v} \times \vec{B})$$
Since the particle is stationary, the second summand is necessarily $0$ in... | {
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Why does the speed of the propellant limit the speed of a space ship in open space? Isn't speed a relative thing in space? If so, why would the speed of a propellant matter? Why can't a space ship accelerate infinitely?
| The maximum theoretical speed that a spaceship can reach isn't limited by anything (except the speed of light of course). However for a practical spaceship with a finite amount of fuel, the speed of the exhaust will set a practical maximum on the speed of the spaceship. This is because in order to accelerate to a hig... | {
"language": "en",
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How quickly should a fluid come to hydrostatic equilibrium? Let's say I'm holding a one-liter water bottle, full of water, which I then drop.
Before dropping the water bottle, the equilibrium is for there to be a pressure gradient in the water canceling the gravitational force on the water. While the bottle is in free... | My problem with the assumption is that sound is quite poorly absorbed in water. The $$30 cm = 1/4 \lambda$$ size means you'd look at waves of about 120 cm = 12 Hz. Absorption at those frequencies is measured in deciBels per kilometer. If we'd model the bottle as a cylinder, we might get a standing wave pattern that cou... | {
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Why are anti-de Sitter spaces so interesting when we believe the universe is expansionary? Perhaps this is a naive question, but in my recent (admittedly limited) readings about AdS spaces, I keep wondering why they seem to be such a hotbed for theoretical research (AdS/CFT correspondence, etc.). To my understanding, ... | An AdS universe can explain the cosmological observations. Our universe can be interpreted as an effective de Sitter brane in an Anti-de Sitter space. Therefore, you have to distinguish between a 5-dimensional cosmological constant from the bulk and the 4-dimensional constant from the brane (which is responsible for an... | {
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Why are the backs of airplanes curved? I get the front part, but why is the back curved too? I do not see a problem with the back being flat.
| The reason why the aft ends of airplanes are streamlined is to preserve a smooth flow of air. Just as the fore ends of airplanes are streamlined to smoothly cleave the air, so too the aft ends are streamlined to smoothly reintegrate the flows. Turbulence is bad, regardless of where on the aircraft it occurs.
(sourc... | {
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Uniformity in a solenoid I know the magnetic field strength increases as the number of turns in the solenoid increases.
However, I've learnt the field inside the solenoid is usually nearly uniform.
So, does the number of turns in the solenoid effect the uniformity of the field inside the solenoid? Does the field gets c... | The expression for the magnetic field due to a long solenoid can easily be derived using Ampere's Law. The expression is $$\vec{B}=\mu_onI\hat{z}$$
where $\hat{z}$ is a unit vector pointing along the axis of the solenoid, $n$ is the number of turns per unit length, and $I$ is the current running through the solenoid. T... | {
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Specific Internal Energy Decreases with Increasing Pressure? I was looking at "Properties of Compressed Liquid Water" (Table A-5) in Fundamentals of Engineering Thermodynamics by Moran. Table A-5 shows that the specific internal energy $u$ of compressed liquid water decreases as as the pressure increases at a fixed tem... | If dealing with a gas, the internal energy must be reduced with increasing pressure, as the temperature will be constant and the gas will be more compact.
Also see the P-T diagram of water, when changing pressure keeping the temperature constant, the vapor phase will change to liquid phase or solid phase which have les... | {
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Black and white matters. But why and how? I know black conducts heat while white reflects it.
But they are colors after all.
If a metal is painted black, it conducts more heat or at a rapid speed than it would do before it was coated.
But, as far as I know, colors don't have any special "substance" in them, which might... |
I know black conducts heat while white reflects it.
The correct term is "black absorbs light while white reflects it".
We have named colors of light we see in the visible spectrum .
White reflects most of the energy falling from the visible spectrum, black absorbs it. When the energy of light is absorbed it turns in... | {
"language": "en",
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How does AC current flow in an open circuit? In common house hold wiring we have the hot lead, neutral and ground.
If the hot lead in electrical wiring contacts earth ground (perhaps though a short circuit in the chassis of a device) then the current shorted to earth. This however doesn't appear to me to be a complete ... | There is a LOT of capacitive coupling between the neutral wire and ground even if a DC current cannot flow. And we are talking about AC here.
| {
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Fork and Sheet Lightning I've noticed that during British lightning storms, I have only ever seen sheet lightning
However, on holiday in other countries, I frequently see Forked Lightning
Q) Is this just caused by cloud, or is it two distinct forms of lightning?
Q) Is there a reason Britain only seems to get the she... | Sheet lightning is just lightning where you can't see the strike because there is cloud in the way - the phenomena is the same.
Lightning storms occur in Britain in regular rain storms, so along with lots of cloud which hide the strike. In places further inland the storms are associated with hot air rising over plains,... | {
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Why ONLY Maxwell's equations are the basic equations of electromagnetism? In electromagnetism we say that all the electromagnetic interactions are governed by the 4 golden rules of Maxwell. But I want to know: is this(to assume that there is no requirement of any other rule)only an assumption, a practical observation, ... | Depending on how "basic" you consider an equation to be to electromagnetism, you could consider other equations to be important enough to be thought of as basic, given the type of situation.
For instance, when dealing with electromagnetism in media (typically linear media), the Constitutive Relations also apply and are... | {
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Analytical problems with Green's function I have a question about the right definition of the Green's function in physics. Why do we introduce (or not) an infinitesimal, positive number $\eta$ to the following definition:
$$\left[ i\hbar\frac{\partial}{\partial t} - \hat{H}(\mathbf{r}) \pm i\eta\right]G(\mathbf{r},t;\m... | A Green's function is nothing but the (generally distributional) integral kernel of the inverse of a given operator. The point is that the operator $$A:= \left[ i\hbar\frac{\partial}{\partial t} - \hat{H}(\mathbf{r})\right]$$
does not admit a unique inverse. Conversely,
$$A_{\pm\eta}:=\left[ i\hbar\frac{\partial}{\par... | {
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Electrostatics - Inserting a brass plate between two charges The question is: if I were to insert a brass plate between two charges, what will happen to the force between the charges? Would it increase, decrease or stay the same?
Does the brass plate increase the value of permittivity of the medium and therefore the f... | When you take a brass plate of considerable thickness and place it in between two charges, say positive and negative, induction takes place in the brass plate since it is a conductor: the electrons shift to the end near the positive charge while the cations stay near the negative charge. Now, induction occurs in order ... | {
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Why does intramolecular hydrogen bonding cause molecules to separate? Today I learned about intramolecular hydrogen bonding, which occurs in molecules such as ortho-nitro-phenol.
What I was told is that, in case of intramolecular bonding, the molecules separate from each other, opposite of what happens during intermole... | Hydrogen bonding arises when a chemical bond is polarised to one end of it has a slight positive charge and the other has a slight negative charge. In the case of o-nitrophenol it's mainly the OH bond that is polarised - the H atom has a slight positive charge and the O atom has a slight negative charge. The charge sep... | {
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The meaning of "heralded photon" I am not a native English speaker, and I have just started to study physics in English. However, I came across the term heralded photon while I was reading a review article about optical quantum memory. I don't understand what it means. A dictionary explains herald as, "to be a sign tha... | Spontaneous parametric down-conversion converts a single incoming photon to two outgoing photons. I think the article is saying that that if you measure one photon coming out there must be a second photon as well. The author is referring to the second as a heralded photon in the sense that measurement of the first phot... | {
"language": "en",
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How could the multiverse theory be disproven? Theorists (physicists) suggest that there is the term/entity, the Multiverse that contains a huge number of universes not necessarily like our own.
I personally find this theory very elegant because its explains the probabilistic outcomes of the experiments with fixed condi... | I agree with you that the mathematical multiverse theory of Max Tegmark is the triumph of Occam's razor in simplicity (Although I disagree in restricting it only to Godel computable, mathematical structures). Not only it gets rid of explaining the physical universe itself (why there exist a physical universe?) but has ... | {
"language": "en",
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Trying to combine red, green and blue to produce white I tried to mimic the mechanism of typical screens to produce white color out of red, green and blue.
What I did is displayed the attached image on the screen, and moved far away as to let the diffraction effects take place, so that the three colors appear as if the... | What you are seeing at a distance is not black. It is a darkish shade of gray, RGB gray 85,85,85. The reason you aren't seeing "white" is because each of those three rectangles has an HSV value of only 33% and you are seeing that merged square against a white background.
That merged square will appear to be whitish if ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/126536",
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Two air bubbles inside a liquid I know that if two air bubbles which are formed inside a liquid are somehow joined using something (say a small tube), then, as the bubble with the larger radius has less pressure and the one with the smaller radius has more air pressure, air will flow to the larger bubble from the small... | It is possible to write a relationship between flow and pressure drop in a tube. If the flow is laminar, this will be given by the Hagen–Poiseuille equation (http://en.wikipedia.org/wiki/Hagen%E2%80%93Poiseuille_equation). For turbulent flow, phenomenological correlations can be used (http://en.wikipedia.org/wiki/Darcy... | {
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Gradient is covariant or contravariant? I read somewhere people write gradient in covariant form because of their proposes.
I think gradient expanded in covariant basis $i$, $j$, $k$, so by invariance nature of vectors, component of gradient must be in contravariant form. However we know by transformation properties an... | Allow me to try to provide the simplest explanation of why the gradient is a covariant vector.
By definitions, the components of a covariant vector transform obey the law :
$$ \overline A_i = \sum_{j=1}^n \frac {\partial x^j} {\partial \overline x^i} A_j \qquad \qquad (1) $$
and the the components of a contravariant v... | {
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Why does a wine glass with less water resonate at a higher frequency? In this video https://www.youtube.com/watch?v=hWwM7F-zaHs, Professor Lewin showed that for the tube, the less water there is, the longer the effective length of the tube and therefore, the lower the frequency.
He then demonstrates an opposite effect ... | The qualitative reason is in the case of the pipe, the walls can be assumed for practical purposes to be rigid (i.e. they don't vibrate), and the resonant frequency of the vibrations in the air inside is determined by the boundary conditions. In other words, the shorter the air column in the pipe (more water), the sho... | {
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Is there a difference between "average acceleration" and centripetal acceleration? Question adapted from Examkrackers MCAT prep book:
A particle moves along a half circle (diameter=$10\text{ m}$) at a constant speed of $1\text{ m/s}$. What is the average acceleration of the particle as it moves from one side of the ha... | The problem with centripetal acceleration is that it is not a vector, and cannot possible have a negative sign. It should remain "constant" in this case, but its direction is changing. But actually, it's not remaining constant, just the magnitude is remaining constant while the direction is changing. Centripetal accele... | {
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Wrong calculation of work done on a spring, how is it wrong? So I would have thought that this would be how you derive the work on a spring: basically the same way you do with gravity and other contexts, use $$W=\vec{F}\cdot \vec{x}.$$ If you displace a spring by $x$, then it exerts a force $-k x$, so $F=-kx$, since th... | In school, generally you would do an experiment where you load a spring with weights one at a time. Then you use the weight times the change in height as the work done on the spring. You can use this because it is a closed system and the weight has lost potential energy of $mgh$. It doesn't matter that the force was al... | {
"language": "en",
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What determines whether a pool ball will bouce backwards after colliding with another pool ball? I'm no knowledgeable pool player, but I've noticed that sometimes when the cue ball hits another pool ball, they roll together; and sometimes the cue ball bounces back. And I have a very, very rough sense that a hard, shar... | The direction the ball will take depends on the angular momentum. The velocity with which the ball moves or bounces backwards but the chief determinant is the spinning effect of the incoming ball.
| {
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Ampere's law and Biot-Savart law gives different terms for magnetic field in middle of a current running in a loop
I would like if someone could clarify this issue for me:
When dealing with a current $I$ running in a loop with radius $R$ and looking for the magnetic field in the middle of the loop.
By using Ampere's l... | You probably misapplied Ampere's law. This law is usually used to find magnetic field only in special cases when the contour integral can be found as a function of single field value based on symmetry.
Magnetic field of a circular current loop is not so simple and Ampere's law cannot be easily used to find it. In such ... | {
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Why did nuclear testing not result in nuclear winter? According to Wikipedia over 2000 nuclear tests have been performed since the Manhattan Project. If nuclear war would bring about a nuclear winter, why didn't testing do? Were they too much spread out in time to cause any real climate damage?
| A nuclear winter would be a result of large amounts of smoke blocking light from the Sun. The smoke would be from the fires started by nuclear bombs on cities, not directly from the bombs.
Most bomb tests have been underground, and the above ground tests were mainly done where there wasn't much to burn, for example in ... | {
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How would an X-ray scanner identify a mirror? A mirror is under normal circumstance used to reflect Electromagnetic radiation also known as photons (light) and in airport security or medical facilities, they use X-rays to detect anomalies inside objects or bodies to detect narcotics or injuries. However, I always wonde... | The thing that makes a mirror a mirror is a that it has a high reflectivity (and is very smooth of course, but that doesn't enter into this issue), but all optical properties including reflectivity are functions of wavelength.
The mirror is not reflective in the x-ray band, so it looks like a layer of glass (moderately... | {
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What is the advantage of AdS/CFT in studying strong coupled system comparing with the lattice method I often heard AdS/CFT correspondence provides a powerful framework to study strong coupled system, which perturbation is not applicable. However, lattice method still works in non-perturbative domain. My question is, wh... | In general, lattice calculations are quite cumbersome and require advanced numerical techniques and computational power. In the AdS/CFT correspondence, the involved concepts surpass those of lattice QCD greatly in complexity, as they involve string theory and general relativity in geometric backgrounds that are far fro... | {
"language": "en",
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Why do some hand dryers blow hot air? I am not sure why some hand dryers are blowing hot air and not just air at room temperature.
To me, hair dryers are just a way to dry one's hands using the same principle as when we shake our hands in the air, or when we blow some air over a hot drink.
Given that the blown air temp... | To take an extreme case, suppose your hand dryer is located in a room without climate control, such as in an isolated restroom in the middle of a park. Occasionally the temperature in the room will fall to the dew point. In that case a room-temperature hand dryer would blow saturated air and have zero drying effect. Ho... | {
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Radiation emission and absorption Any object can emit and absorb radiation and the power of emission can be represented by the Stefan-Boltzmann law:
$$P=A\epsilon\sigma T^4$$
In many texts the net power radiated is the difference between the power emitted and the power absorbed:
$$P_{net}=A\epsilon\sigma (T^4-T_s^4)$$... | I think the key to the paradox is that you can't ignore the reflection coefficent. Lets say you have a lump of coal inside a shphere of polished steel. Yes, the coal emits much more heat than the steel; but that doesn't mean there is a net transfer of heat from the coal to the steel. Because the steel reflects back the... | {
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Proof of Liouville's theorem: Relation between phase space volume and probability distribution function I understand the proof of Liouville's theorem to the point where we conclude that Hamiltonian flow in phase-space is volume preserving as we flow in the phase space. Meaning the total derivative of any initial volume... | To obtain the result $\frac{\text d \rho }{\text d t}=0$ you need two facts: the first is that the hamiltonian flow preserves the volume of phase space. The second fact is the conservation of probability, that is, the probability that the system is found in a volume $U$ at time $t=0$ equals the probability of finding i... | {
"language": "en",
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Why is the pressure inside a soap bubble higher than outside? Apparently, the air inside a soap bubble is under higher pressure than the surrounding air. This is for instance apparent in the sound bubbles make when they burst. Why is the pressure inside the bubble higher in the first place?
| It is like a balloon. The pressures of the inner and outer air tend to equilibrate, creating a force over the balloon surface from the higher pressure to the lower one, trying to make them equal (the force goes from inside to outside, when you inflate it, from outside to inside when you deflate it). That's why it chang... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Pool in a submarine A common theme in aquatic science fiction is the submarine pool/access to the ocean. That terrible TV show Seaquest had it, The Deep & Deep Blue Sea (Samuel L Jackson is standing in front of it when the shark chomps him). My question is how this could possibly work? From what little knowledge I have... | You can do it without raising the internal pressure. First you have your pool, at 1 atm or ambient inside the vessel. Then you have a wet chamber which can be sealed at both ends. Enter the pool, then only the inner door of the wet lock opens, enter this area, and close the door to the moon pool behind you. When the... | {
"language": "en",
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"source": "stackexchange",
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Which ball touches the ground first? This is a very well known problem, but I can't find an answer in the specific case I'm looking for.
Let's consider two balls :
*
*Ball 1 weighs 10 kg
*Ball 2 weighs 1 kg
*Balls have identical volumes (so Ball 1 is much more dense)
*Balls have identical shapes (perfect spheres)... | Since air creates a force that is approximately proportional to the square of the velocity, the acceleration for each sphere is $a_r = kv^2/m (where \text{ } k = \frac{1}{2} C_x\rho\ S) $ The net acceleration on each sphere is $ a_n = g - a_r$. As the velocity increases, the $a_r $ increases until the net acceleration... | {
"language": "en",
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Calculate water flow rate through orifice I'm not very good with fluid physics, and need some help. Imagine the following setup with water contained in-front of a wall with an opening on the bottom:
How do I calculate the water flow $Q$?. I have made some re-search and found I need to (partially) calculate the pressur... | From a Wolfram article we get the simplified Bernoulli equation:
$$Q = a c \sqrt{2 g h}$$
Where
*
*$Q$: the flow rate ($\mathrm{m^3/s}$)
*$a$: the area of the hole ($\mathrm{m^2}$)
*$c$: flow coefficient (dimensionless)
*$g$: the gravity acceleration ($\mathrm{m/s^2}$)
*$h$: the depth of the hole ($\mathrm{m}$)
... | {
"language": "en",
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"source": "stackexchange",
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AM Receiver and sideband frequencies How sorry for "dummy" question. I have difficulty to understand how the AM receiver.
Being a child I was taught that AM receiver resonates only with the radio frequencies it is tuned to, and "passes" only this frequencies to "other" circuits.
Recently I have read in articles that s... | There is no realizable filter that blocks all frequencies except one.
The fact is that frequencies above and below the tuned frequency are passed but with greater and greater attenuation the farther away from the carrier frequency.
More importantly, the actual information is in the side bands, not the carrier. If the... | {
"language": "en",
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How would an X-ray mirror work? I was wondering if light can be reflected how can someone reflect X-ray of what material does it need to be made of and is its design completely different to that of our original mirrors? Does this mean during long-space voyages in which radiation is an problem why can scientists not dev... | Yes it is possible but as BarsMonster points out it isn't like an optical mirror. X-ray reflectors are used in the construction of nuclear weapons and are critical to increasing the yield. How they work is the initial fusion reaction releases high energy radiation, this is then reflected back into the reaction mass i... | {
"language": "en",
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Critical size and Radioactive Nuclei Nuclear fission requires the mass of the fissile material above the critical mass. So that the explosion takes place at least in the case of a nuclear bomb. But once a single nucleus got involved in the reaction, the reaction can't be stopped easily if I'm right.
A single nucle... | There's spontaneous fission, a rare decay mode for some superheavy nuclei like uranium and plutonium. There's also induced fission, where some interaction with the environment (typically neutron capture) causes a nucleus to split. Both fissions typically produce a couple of free neutrons, which may be captured on other... | {
"language": "en",
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Who proposed the bulk-edge correspondence principle? Who proposed the bulk-edge correspondence principle?
The principle is often quoted in counting the number of zero energy states localized on the interface between two insulators with distinct band topology. However, I could not retrieve who was the first to say that.... | I believe it was Xiao-Gang Wen in 1989, see also this 1994 paper by him and his collaborators
http://dao.mit.edu/~wen/pub/ednab.pdf
He's at MIT. I was once hosting a seminar by him, he is one of the most creative and playful folks in this segment of condensed matter physics. The paper above contains some other releva... | {
"language": "en",
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Where does wave frequency come from? I am trying to wrap my head around where do oscillations in electromagnetic waves come from. As an example if I would take a string of guitar and ring it, it would produce a certain sound based on the amount of vibrations per second. That amount of vibrations would be the sum of mov... | For low-frequency radiation, it's quite simple: there's some electronic circuit that works (simple case) analogous to a tuning fork, but instead of building up mechanical tension it charges a capacitor and instead of the inertia in the fork's arms it has a magnetic field in a solenoid. You can measure the voltage again... | {
"language": "en",
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How to calculate the drag coefficient using terminal velocity? I was wondering if it were possible to calculate the drag coefficient by allowing an object to reach terminal velocity. Can you rearrange the terminal velocity formula to give the drag coefficient?
| Yes you could. Since the force on an object from drag is given by
$$F_D = \frac{1}{2}\rho v^2 A C_D$$
where $C_D$ is the drag coefficient, then all you would need to know are your velocity ($v$), your fluid density $\rho$, your cross sectional area ($A$) and the force of gravity on the body, which would then be equiva... | {
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Does Free Will Theorem imply that quantum mechanics plays crucial role in our brain’s functioning (consciousness)?
*
*Does Free Will Theorem imply that quantum mechanics plays crucial role in our brain’s functioning (consciousness)?
*Is opposite statement of Free Will Theorem right: If elementary particles have a ce... | Penrose is saying things much more subtle in his book "The Emperor's New Mind". I wouldn't attempt to describe it.
Another view is by Minsky in "Society of Mind".
Again, I think he does a far better job of explaining it than I could, though in that video he's talking more about consciousness. Free will is just another ... | {
"language": "en",
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"source": "stackexchange",
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Airplane on a treadmill I've heard conflicting answers, and would like to see the record set straight:
An jet/propeller airplane is traveling on a giant treadmill at takeoff speed. Will the plane takeoff, or will it remain on the runway, and why?
|
An jet/propeller airplane is traveling on a giant treadmill at takeoff
speed.
With respect to what does the plane have takeoff speed?
I believe the following two statements are uncontroversial:
(1) if the plane has takeoff airspeed (or greater), the plane can takeoff.
(2) if the plane does not have takeoff airspeed... | {
"language": "en",
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Determine the acceleration in a double Atwood machine Trying to solve the following double Atwood machine:
Suppose there is a mass of 12kg hanging on an ideal rope that wraps around an ideal pulley, and that the other end of the rope is attached to another ideal pulley's axis. This second pulley has a rope around i... | Let
\begin{align}
m_1 = 12\,\mathrm{kg}, \qquad m_2 = 4\,\mathrm{kg}, \qquad m_3 = 8\,\mathrm{kg}
\end{align}
If you solve this problem symbolically, then you'll find that the tension $T$ applied to mass $m_1$ satisfies
\begin{align}
T = \left(\frac{8m_1m_2m_3}{m_1m_2+m_1m_3+4m_2m_3}\right)g.
\end{align}
If you plu... | {
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"source": "stackexchange",
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Is this "cloaking in time" serious and what is really meant? I just found this news article: http://www.nature.com/nature/journal/v481/n7379/full/nature10695.html
What did those researchers actually do? The article itself doesn't sound to me like it can be taken seriously, so... what was the experiment and what was obs... | I do not understand all the nitty details, but the gist goes as follows:
You have a constant probe beam, which is cast on a sample and analysed later.
Suppose the sample has a very predictable behaviour, with an event every $24\mu \text{s}$. Then the analysis of the beam will show exactly that. This is the blue line in... | {
"language": "en",
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Kinetic Energy of a Particle Consider a particle of mass $m$ in $6$ dimension. Its coordinate w.r.t. origin $\left(0,0,0,0,0,0\right)$ is given as $\left(x,y,z,\dot{x},\dot{y},\dot{z}\right)$. If we denote $r = \sqrt{x^2+y^2+z^2}$, then which of the following two is the kinetic energy of this particle:
*
*$T = \frac... | Hard for me to say what you're asking. If you have a particle of mass $M$ in three dimensions such that its positions is described by coordinates $\vec x(t)=(x(t),y(t),z(t))$, then the velocity vector $\vec v=\frac{d\vec x}{dt}=(\dot x(t),\dot y(t),\dot z(t))$
The kinetic energy is then defined as,
$$T=\frac{1}{2}M\vec... | {
"language": "en",
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Diffusion and Drift currents in a PN junction In a forward-biased PN junction, the potential barrier decreases, allowing more majority carriers from one side to diffuse to the other side where they are minority carriers. After they cross the potential barrier, they form a diffusion current, the drift current of minorit... | The unbiased PN junction is in an equilibrium where the diffusion current is cancelled by the drift current.
The applied electric field in a forward biased PN junction "cancels" the electric field in the depletion region, eliminating the potential barrier and allowing diffusion current to flow.
| {
"language": "en",
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What if an asteroid the size of the moon hits earth? Would we all perish due to excessive heat? Or would that be limited to the area near the impact while the people on the rest of the earth would die from other phenomena such as mega earthquakes, volcanic activities, tsunamis etc.? Does it matter where the impact is -... | The University of Arizona had a neat website that addressed precisely such questions. It's moved here now.
You can choose all kinds of parameters - kind of projectile (ice / rock), impact angle, velocity, landing site and get a prognostication, expected damage etc. Really cool stuff.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is it possible to 3D print a mirror to create a high quality telescope? Is it possible to 3D print a mirror with todays available materials?
If so, would there be a reduction in image quality?
| The answer is "Yes" but not the way you might expect. It is possible to construct a telescope mirror from rotating liquid metal.Mercury used to be used but something like Gallium is safer and better.
So print a cradle for it, put in the Gallium, raise the equipment past the melting point (about 30 degC), spin gently to... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/129384",
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"source": "stackexchange",
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Differences between probability density and expectation value of position The expression $\int | \Psi\left(x\right)|^2dx$ gives the probability of finding a particle at a given position.
If wave function gives the probabilities of positions, why do we calculate "expectation value of position"?
I don't understand the c... | Expectation value is a different concept from probability. In fact, you can have an expectation value of energy, angular momentum, etc., not just for position.
An expectation value of an observable for a given state $\Psi$ is the average value of a large number of measurements of that observable, assuming each measurem... | {
"language": "en",
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Why do liquids boil when their vapor pressure equals the ambient pressure? Given that the boiling point of a liquid is the temperature at which the vapor pressure is equal to the ambient (surrounding) pressure, what significance does a liquid's vapor pressure have in the formation of bubbles that happens at and above t... | Once boiling starts, there is an equilibrium between the liquid and vapor phase. The pressure, temperature and partial molar Gibbs energy are equal for each phase so that water molecules have no preference for one phase or the other. That's for intensive variables. However, the total enthalpy of the liquid and vapor is... | {
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What is $c + (-c)$? If object A is moving at velocity $v$ (normalized so that $c=1$) relative to a ground observer emits object B at velocity $w$ relative to A, the velocity of B relative to the ground observer is
$$ v \oplus w = \frac{v+w}{1+vw} $$
As expected, $v \oplus 1 = 1$, as "nothing can go faster than light"... | Recalling that the relativistic velocity addition formula in 1+1 dimensions in terms of rapidity
$$\beta~:=~\tanh^{-1}\frac{v}{c}$$
is just ordinary addition of rapidities
$$\beta_1+ \beta_2,$$
then it becomes clear that OP is essentially asking
What is $\infty+(-\infty)$ ?
which is not defined mathematically.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How to approximate acceleration from a trajectory's coordinates? If I only know $x$- and $y$- coordinates of every point on a trajectory without knowledge of time information, is there any way to approximate Cartesian acceleration angle at each point? Time interval between every two points is very small, ~0.03 second. ... | In your case, lets $\Delta t = 0.03s $
By the method alemi explained,
$$a_{x}(t)=\frac{x(t-\Delta t)-2x(t)+x(t+\Delta t)}{(\Delta t)^{2}}$$
and
$$a_{y}(t)=\frac{y(t-\Delta t)-2y(t)+y(t+\Delta t)}{(\Delta t)^{2}}$$
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Conserved current for a constant translation of a free massless scalar field In Zinn-Justin's Quantum Field Theory and Critical Phenomena they start with an action for a free massless scalar field:
$$S(\varphi) = \frac{1}{2}\int d^{2}x\left[\partial_{\mu}\varphi(x)\right]^{2}$$
And say that the action is invariant unde... | For each continuous symmetry, infinitesimal transformations may be expressed, by a bracket involving the conserved charge operator associated to the symmetry :
$$\delta_\epsilon \phi(x) = i\epsilon [Q, \phi(x)] \tag{1}$$
In our case, we must have :
$$\epsilon \theta = i\epsilon [Q_\theta, \phi(x)] \tag{2}$$
A solutio... | {
"language": "en",
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The Gluon - Does It Exhibit Wave Properties? Do Gluons have frequencies and wavelengths? I assume that they do, but have been unable to find anything on point in SE or Wikipedia. Just beginning to study university-level physics here.
| They do, just as all quantum objects do. They have momenta, and since they are massless, their frequency/wavelength/energy/momentum relations are the same as for photons.
But since you will never detect a free gluon, as they are color-charged and thus confined, this is not a sensible thing to say. Quantum objects are n... | {
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How to determine the sign of the s-wave scattering length? I guess it is relatively easy to determine the magnitude of the scattering length $a$.
We just need to measure the scattering cross section. In this way, we can determine the value of $a^2$.
But how to determine its sign?
| I think the appropriate method will depend on what system you're studying. I don't know about a general method, but since you also asked about experiments which determined the sign of $a$, I can offer a specific example:
In ultracold atomic physics experiments there is the case of Feshbach resonance, where you have a ... | {
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Can an electron make a transition between sub energy states of the same energy level? Electrons make transition between different energy levels - say, $n =3$ to $n=2$ or $n =1$, as per the applicable selection rules.
My question is: can an electron make transitions between sub energy states of the same energy level?
F... | It depends on whether you're considering only hydrogen, or whether you're considering multi-electron atoms.
In hydrogen the states with different $\ell$ are (very nearly) degenerate in energy, so a transition like $2s^1 \rightarrow 2p^1$ is in principle allowed but in practice unobservable. However in Helium the $2s$ a... | {
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How to write QM operator if I know all of it's eigenfunctions? Suppose I have selected enough orthogonal functions in representation of operator A and I want to derive operator B which has these functions as it's eigenfunctions.
How to do that?
| It's difficult to answer your question because a collection of eigenvectors $\{ v_i\}$ does not uniquely specify an operator. For example, any two operators that are simultaneously diagonalizable are, by definition, operators that share the same set of eigenvectors. Moreover, an operator (and its matrix representation)... | {
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Complex semi-definite programming I'm doing some calculations and I want to simulate them in python or matlab (or whatever). However I use hermitian matrices and I don't really manage to find a library which enables me to calculate primal problems in complex form.
Do you know of any obvious extension to the real probl... | You may use PICOS for Python: "PICOS is a user friendly interface to several conic and integer programming solvers, very much like YALMIP under MATLAB."
Since the version 1.0.1, it is possible to do complex semidefinite programming with Picos:
http://picos.zib.de/v101dev/complex.html
| {
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Which way does the scale tip? I found the problem described in the attached picture on the internet. In the comment sections there were two opposing solutions. So it made me wonder which of those would be the actual solution.
So basically the question would be the following. Assume we would have two identical beakers, ... | The weight on the left bowl would be the weight of the water plus vase plus ping-pong ball (plus thread, ignored).
The weight on the right bowl would be the weight of the water plus vase plus the buoyancy of the steel ball (plus the buoyancy of the submerged thread, ignored). That buoyancy is the weight of an equivalen... | {
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"source": "stackexchange",
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Is our universe an emulation? I was watching one of Neil Degrasse Tyson talks and there was a scientist (can't recall his name sorry) who was talking about a recent discovery:
"Doubly-even self-dual linear binary error-correcting block code" has been discovered embedded within the equations of superstring theory.
Is... | As Count Iblis pointed out, The Church–Turing–Deutsch principle makes this impossible to decide using the structure of the laws of physics as it will always be compatible with the universe being simulated by a quantum computer.
Nevertheless, in this well-known paper the author argues that if we accept some very reasona... | {
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How does a fixed amount of transmitted radio energy supply an unknown number of destinations? I did some maths and physics up to the age of 18, and hold an amateur radio licence. This thing has puzzled me for a while - does reception of an electromagnetic wave imply an interaction with the transmitter? Does it drain so... | A wavefront (your signal) has a fixed amount of energy given to it by the transmitter. Whatever happens to the wave once it leaves the transmitter is independent of the transmitter, thus receiving a signal does not drain any additional energy from the transmitter (though it can drain energy from the wavefront itself).... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/130877",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 2,
"answer_id": 0
} |
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