Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Proving that force satisfies the laws of vector addition A vector quantity has both magnitude and direction. So, for any physical quantity to be a vector, it should have a direction and a magnitude. Though this is a necessary condition for any quantity to be a vector it is not sufficient. To qualify as a vector a quant... | I don't think that "satisfying the laws of vector addition" is necessary for something to be a vector, depending on what you mean by that.
Take velocities in special relativity. They are vectors; the vector sum of velocities is well defined. But it's rarely useful. More commonly, when you have two velocities and need t... | {
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Multiplicity Identity in Kittel's Thermal Physics On page 25 of Kittel's Thermal Physics, the author derives the multiplicity of $N$ harmonic oscillators with total quanta of energy $n$, $g(N,n)$.
He writes
\begin{align}
g(N,n) &= \lim_{t\rightarrow 0} \frac{1}{n!}\left( \frac{d}{dt}\right)^n \sum_{s=0}^{\infty}g(N,s)t... | I really like Kittel's philosophical approach to the subject in this book (counting multiplicity exactly in model systems, leveraging those systems to define entropy and temperature, ...). But here, and in many other places, his derivations/calculations seem to obfuscate rather than illuminate.
The multiplicity of $N$ ... | {
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Notation about basis of gamma matrices in $4d$ In Quantum Field theories, we encounter gamma matrices a lot.
Reading from various textbook, i encountered some textbook use different basis for their gamma matrices.
Gamma matrices are defined such that $\gamma^{a}\gamma^{b}+\gamma^{b}\gamma^{a}=2\eta^{ab}$. Multiplying ... | In 4D Minkowski space the $\Gamma^{a}$'s has standard form. As $\Gamma^{a}=\mathbf{1}_{4\times4},\gamma^{\mu},\sigma^{\mu\nu}=\frac{i}{2}[\gamma^{\mu},\gamma^{\nu}],\gamma^{5}\gamma^{\mu},\gamma^{5}$, altogether 16 matrices. Provided that $\gamma^{\mu}\gamma^{\nu}+\gamma^{\nu}\gamma^{\mu}=2\mathbf{1}_{4\times4}\eta^{\m... | {
"language": "en",
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Schrödinger's Equation with multi-part potential I have this potential
$$V(x) =
\left\{
\begin{array}{ll}
\infty & \mbox{if } x < -a \\
\frac{V_o}{a}x & \mbox{if } -a \leq x \leq a \\
V_o & \mbox{if } x \geq a \
\end{array}
\right.$$
And I want to know, qualitatively, how the wave function would look lik... | Qualitatively, the wave functions of the bound states in a triangular potential well like the one you described, look like this:
For $x<-a$, $\psi=0$ because of the infinite potential in that region.
Where the wave function crosses the potential line, quantum tunnelling occurs and $\psi \to 0$.
For particle energies a... | {
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Transforming Qubits Into Bits From what I understand, a qubit exists in a superposition of states and once it has been measured, it must fall into one of the two possible states. Now, I have been told that once a qubit is measured, it is no longer proper to call it a qubit but a bit since it no longer exists in a super... | The qubit can be in a superposition of states thanks to the superposition principle, when you measure the spin of your photon it collapse in the vertical or horizontal state (eigenstates of the spin operator) and during the measure you extract the "bit" intended as the information about the outcome of this measure. But... | {
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Distance between adjacent planes in a crystal This question has been asked before, but there doesn't seem to be a decent answer.
Many sources state that " For cubic crystals with lattice constant a, the spacing d between adjacent (ℓmn) lattice planes is:
$$ {\displaystyle d_{\ell mn}={\frac {a}{\sqrt {\ell ^{2}+m^{2}+... | In answer to the question: adjacent planes are planes that are closest to one another when distance is measured along the normal to the plane. It is important to understand that every lattice point has exactly one of the infinite set of planes described by the Miller indices $(h k \ell)$ passing through it. (I will use... | {
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Does the universe expand in every direction evenly? I've heard that the universe is expanding constantly and that galaxies are moving further and further away from each other because of this. However, does the universe expand in every direction evenly or does it expand in one direction more than another direction?
| We believe that the universe expand in every direction evenly. Even-if there's any unevenness, it's hard to see, and will only be clear at very very large scales. Some people have combed the CMB (cosmic microwave background) and argue that there's maybe some evidence that things aren't perfectly even, but it's not real... | {
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Velocity of satellite to crash into the earth I was reading through this post today and was very impressed by the response that was given. However, what would have to happen to the velocity in order to collide with the Earth?
Velocity of satellites greater than required velocity
I was think of setting up an equation... | All you need to do is calculate the perigee distance $r_p$ that is the distance of closest approach. Then if $r_p < R_A$ your satellite will crash and burn.
Once again we start from the vis-viva equation:
$$ v^2 = GM\left(\frac{2}{r} - \frac{1}{a} \right) \tag{1} $$
The parameter $a$ is the semi-major axis of the ellip... | {
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Reflectivity and transmissivity greater than 1 In plasmonics, it is often seen that reflection coefficient and transmission coefficient are greater than 1. How is energy conservation valid in such cases?
| In the book "Plasmonics and Plasmonic Metamaterials: Analysis and Applications" edited by G. Shvets, Igor Tsukerman, we read in section 2.1:
In other words - they clearly state that the enhanced reflectivity is a result of the presence of a inverted dye - that is, a dye with a population inversion, meaning that it ca... | {
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Spontaneous symmetry breaking of gauge symmetry in 1+1 dimensions? The Mermin-Wagner theorem states that continuous global symmetries cannot be broken in two or fewer spacetime dimensions; however, I have not seen this statement applied to gauge theories. Does it apply; ie, is there a Higgs mechanism for 1+1 QFTs?
| Gauge symmetry is actually not spontaneously broken in the Higgs mechanism; this is a common misconception. See What role does "spontaneously symmetry breaking" played in the "Higgs Mechanism"?. Therefore the Mermin-Wagner theorem does not apply to the Higgs mechanism, and the Higgs mechanism is possible in 1+1D.
| {
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How does gauge invariance protect the SM gauge boson masses in SUSY from divergent radiative corrections? The W and Z gauge bosons receive radiative corrections in loop from the heavy SUSY scalars. There is an argument using gauge invariance which explains how the masses remains protected. I am not able to understand h... | What I say below are very general facts and probably this is not the final answer you were looking for but maybe it helps.
A gauge theory (forget about SUSY for the moment) gives rise to a massless spectrum of gauge bosons and massless matter content. If you want to give mass to your gauge bosons you need spontaneous s... | {
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Scalar fields and general coordinate transformations In classical mechanics, a scalar field is characterised by the fact that its value at a particular point must be invariant under rotations and reflections of coordinates. That is, one requires that $\phi'(x')=\phi(x)$, where a point, $x'$ in the new coordinate system... | Yes, that is the definition of a scalar field in a theory with general covariance.
$\phi^{\prime}(x^{\prime})=\phi(x)$
where $x^{\prime}$ is the coordinate in the new coordinate system corresponding to a given $x$ in the original coordinate system. i.e. $x$ and $x^{\prime}$ are, in general, different values representin... | {
"language": "en",
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Are Newton's laws invalid in real life? One of my friends and I had an argument over this topic. He stressed the fact that in real life many forces exist, whereas in physics we deal only with ideal situations. He put the following arguments:-
*
*Newton's First Law is invalid because friction exists in real life.
*N... | Newton's laws are valid for all situations where velocities are small (compared to the speed of light, ie relativity is not important) and where quantum effects are negligible (mostly where objects are much bigger than elementary particles). The problem with your argument is that you and your friend are using idealiz... | {
"language": "en",
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Does a "capacitor" for light exist, which could filter out flickering? If I have a light that is flickering at a frequency low enough to be perceived by the human eye, is there any type of material that exists that will smooth out the appearance of flickering? Similar to how a capacitor smooths the output of a rectifie... | You could argue that this is exactly what glow-in-the-dark materials do. Phosphorescent materials gather energy in the form of electrons moved to higher potentials. The result is a very lossy low-pass filter on the light received.
The real issue is the lossiness. Phosphorescent materials are substantially less effici... | {
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Is a light wave's amplitude stretched, along with the "red shift" stretch - making it brighter? When light waves are stretched and "red-shifted", is the amplitude of the light wave stretched as well, affecting the intensity/brightness of the light wave?
| The speed of light is constant in all reference frames. This is a principle of relativity derived from Maxwell's Equations.
The energy of a photon is given by $E = hf$ where $h$ is Planck's constant and $f$ is the frequency at which the photon propagates.
Now picture this: Kinetic energy is the energy of motion. When... | {
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Largest Mass Diffraction I have read "Matter-wave interference with particles selected from a molecular library with masses exceeding 10000 amu" which claims to observe diffraction patterns in objects of around 10'000 amu. What is the largest mass objects shown to have diffraction patterns and show wave-particle dualit... | According to http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/mossfe.html it takes 200,000 iron nuclei to preserve the natural line width of the 57Fe transition used in Moessbauer spectroscopy, so that gets you to approx. 11 million AU of coherently moving mass. I don't know if one can do better than this with phonon... | {
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How is a neutron produced in a hydrogen fusion? So during a fusion reaction, a hydrogen atom (which consists of only a electron and proton) fuses with another hydrogen atom to produce deuterium which contains a proton and neutron. My question how does the neutron come out of nowhere when we have only 2 protons as the r... | Most of the time, proton-proton fusion results in the brief creation of a very unstable di-proton, which immediately decays into a pair of protons.
But very occasionaly, during the brief moment they are together, one of the protons will undergo a weak force interaction, changing one of its quarks from up to down, hence... | {
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Is there a case (besides light speed in any given medium) where speed is experimentally measured rather than theoretically calculated? I studied physics throughout college, but I cannot recall a single time where I directly measured the velocity of an object or force. Every time I measured the components of velocity (d... | The term "direct measurement" is tricky. It's easy to take a philosophic position and say no measurement is a "direct" measurement. We're always interacting something with something else to do our measurements. Accordingly, I have to play a little loose with the "direct measurement" concept.
*
*A speedometer meas... | {
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Is this constraint holonomic or non-holonomic? $$f(q,q^\prime, t) = 0, ~\mathrm df = \frac{\partial f}{\partial q}~\mathrm dq + \frac{\partial f}{\partial q^\prime}~\mathrm dq^\prime+ \frac{\partial f}{\partial t}~\mathrm dt = 0$$
I really want to know whether this constraint is holonomic or non-holonomic.
(As far as I... | If $f$ is defined such that $f=0$ at all points, then it is a holonomic constraint. One example is this:
$f(x,y,z)=x^2+y^2+z^2-r^2=0$
which constrains motion to the surface of a sphere of radius $r$.
| {
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What is the relation between Work and Power? If I lift 40 kg 6 times 60 centimeters, is that 40*6*0,6*9,82 Joule? And then if I take the time into account, I will know the Watts? Or did I misunderstand?
The background is that I read that you can use the work from exercising to power energy, and I find that one set tha... | No you did not misunderstand, your calculation is correct. You have done 1414 J of work in lifting the weights. Assuming this took about 30 s your average rate of working was 50 W. If you were to keep this up and you convert the energy into electricity, you could probably keep a desk lamp glowing!
| {
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Why can any general motion of a rigid body be represented as translation + rotation about center of mass?
*
*Why can any general motion of a rigid body be represented as translation + rotation about center of mass?
*I am beginning to read rotational dynamics and my textbook states this fact without proof. I am wond... | The fact that the motion of a rigid body can be represented as a translation and a rotation about the center of mass is a consequence of a mathematical theorem that states that every function that goes from R^3 to R^3 such that, for all x, y, d(x,y) = d(f(x),f(y)) (where d(x,y) means distance between x and y) can be ex... | {
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Ground state of local parent Hamiltonians and invariance under local unitaries Assume that a finite-dimensional pure state $|\psi\rangle\in \mathcal{H}\simeq \mathbb{C}^m$, $m<\infty$, is the (unique) frustration-free ground state of a local parent Hamiltonian and suppose that the locality notion is given in terms of a... | Here's one idea:
Say $U|\psi\rangle = |\psi\rangle$ for $UU^\dagger = U^\dagger U = I$.
Then if we consider the exponential form $U = \exp(iG)$ with $G = G^\dagger$ as usual, $|\psi\rangle$ must necessarily be in the kernel of $G$, $G|\psi\rangle = 0$.
On the other hand, having $U$ of the product form $U = \prod_k{U... | {
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Negative number on weighing scale if I move my hand above it? So, I wondered if my electrical weighing scale could detect the air pressure exerted by something flat like a plastic plate or even my hand. I noticed that if I move my hand with my arm vertical to the scale, 2-3 grams are detected at most, as expected since... | There are 3 effects. First is the orientation of the balance. Moving around a floor that flexes or deforms, even slightly as you move your weight around, is a no-no. (similarly if the balance isn't isolated from you putting or removing weight from the table it is on). Second is that YOU carry an electric charge. So cou... | {
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Why aren't trigonometric functions dimensionless regardless of the argument? Consider this equation :-
$$y = a\sin kt$$
where $a$ is amplitude, $y$ is displacement, $t$ is time and $k$ is some dimensionless constant.
My instructor said this equation is dimensionally incorrect because the dimension of $[kt] = [\tex... | All maths functions can only be used with dimensionless arguments. The reason is quite boringly that these functions are only defined for real numbers, or perhaps integers, complex numbers, real vectors. But time is none of these.
The only exception you can make are homogeneous functions, especially linear functions. A... | {
"language": "en",
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Does an object float more or less with more or less gravity? This might be a stupid question, but I'm a newbie to physics.
An object less dense than water (or any other fluid, but I'm going to use water for this example) floats normally on Earth when placed in water. But if the object was placed in a hypothetical place... | The object would actually float exactly the same for both values of $g$. Let $V$ be the volume of the body, $d$ its relative density, and $V'$ be the volume inside water.
Then for equilibrium of the body,
$V \cdot d \cdot g=V' \cdot 1 \cdot g$
So, $V'/V$ is independent of acceleration due to gravity.
| {
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Why is the surface of a liquid slanted when it is accelerated? Consider a uniformly horizontally accelerated tube of water. I know that the fluid experiences a pseudo force in addition to its own weight, so that it reaches equilibrium in the below diagram.
But why can't the water also exert a force like this, so it ca... | For the sake of simplicity, let's assume it's a cubical container of water. The concept remains the same.
Look at the "free body diagram" of the water itself. As you noted, one side of the water is higher than the other. The surface is slanted.
The water is accelerating, so we know that there must be a net horizontal f... | {
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How radioactive is uranium? Look at this video:
People face uranium directly. Does this mean the radioactivity of uranium is very weak? Because its half-life is very long? Personally, I would never dare to touch any radioactive element.
I also remember seeing people holding a big chunk of uranium in hand. See here
| There are two sides to this question.
Naively, the answer would be "bah, not much" because it is not terribly active and neither alpha, nor beta radiation is really dangerous. The former (which occurs early in the decay chain) is absorbed even by a few centimeters of air, and the latter (which appears later in the deca... | {
"language": "en",
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Redshifting light in an expanding universe It's evident and well known that light traveling across an expanding FLRW universe is redshifted via an equation:
$$\frac{\lambda_{arriving}}{\lambda_{emitted}}=\frac{a_{now}}{a_{then}}$$
Where $a$ is the cosmological scale factor when the light is emitted and observed (denote... | The cosmological expansion can be seen only with very large structures. Its effective "force" is so weak that even galaxies are not affected, gravity keeps them bound and invariant .
Thus, the Andromeda galaxy, which is bound to the Milky Way galaxy, is actually falling towards us and is not expanding away. Within the... | {
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Are carbon nanotubes superconductive? I've heard all kinds of various properties ascribed to carbon nanotubes, from amazing (conventional) conductors that work in a different way to metals, to semiconductors with tunable properties and properties that very with mechanical manipulation.
How good of conductors are they, ... | As per Wikipedia
While there have been reports of intrinsic superconductivity in carbon nanotubes, many other experiments found no evidence of superconductivity, and the validity of these results remains a subject of debate.
From Sciecemag
Investigation of the magnetic and transport properties of single-walled small... | {
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What is optical density? I'm a zoology minor and we are doing protein estimation by colorimetric method. I have stumbled upon a term 'Optical density'. I don't understand the term well. Is it a measure of the extent of light that can pass through a particular object?
I've checked a related question of this community an... | You're a little confused probably because there are two usages of the words "optical density".
The first usage is as a synonym for refractive index, as described in the answers to the related question you cite. This is the commoner usage in physics.
The second usage is the total attenuation afforded by a protective s... | {
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Spring force on both sides of spring I am a little confused about springs. I just wanted to know that if I pull an ideal spring of spring constant $k$ such that the spring has been symmetrically pulled and its elongation (total) comes out to be $x$ then would the force on one side by $$F=kx$$ or $$F=kx/2$$ I am a litt... | The other answers simply quote Hookes law, the static relationship between displacement and force. But if you consider the question more deeply, the spring has distributed mass and distributed compliance, and so a spring all by itself is dynamic and therefore does not propagate force instantaneously as Hookes law impli... | {
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Metal temperature change I have a pipe that’s $70^{\circ}\text{F}$, in a constant room temperature of $80^{\circ}\text{F}$.
I would like an equation to solve for pipe temperature ($\text{F}$) after X amount of time.
Material: Iron
Height: $100~\mathrm{cm}$
Diameter: $3.81 ~\mathrm{cm}$
Based on this equation, using Ne... | In my thinking that you may use following equation
$\frac{dT}{dt}\propto-(T-T_0)$
$\frac{1}{T-T_0}dT=-kdt$
$T-T_0=Ce^{-kt}$
from graphical method you may estimate the value of k.
| {
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Does empty space have energy? My physics friend suggested that "the answer to why matter exists in the universe" is because all massive particles are just the fabric of space excited into little packets. To illustrate, imagine a blanket on the ground. Then, pinch a small bit of the blanket and twist it. This is a parti... | After looking at the other answers and comments, I understand the question little bit better now. So, will take a shot at it.
The question is about own energy of vacuum/space, not about the energy spread in space from big bang etc. There is a difference between the two.
Just like many other questions, this also needs l... | {
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What is the difference between these two ways to calculate average velocity? Average velocity:
$$v_{\rm avg,1}=\frac{v_{\rm final}+v_{\rm initial}}{2}$$
and average velocity:
$$v_{\rm avg,2} =\frac{\rm total\;displacement}{\rm time \;taken}=\frac{\Delta x}{\Delta t} $$
What is the difference between them and when do ... | The average velocity of a particle during some elapsed time $\Delta t$ is, in words, the constant velocity that gives the same displacement in the same elapsed time.
Mathematically, the average velocity is given by
$$\mathbf{v}_{avg} = \frac{\Delta \mathbf{r}}{\Delta t}$$
where $\Delta \mathbf{r} = \mathbf{r}_f - \math... | {
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What exactly is a "volt"? What exactly is a volt? So I Studied the chapter "electricity" in the month of April and got introduced to the concept of "volt".
The concept was too unclear for me so I tried to ask some questions to my teachers and to do some searches on google and watch some videos.
I observerd that noone i... | Let $\mathbf{E}(\mathbf{r})$ be the electric field: the work done by the field on a unitary charge $q$ along the path $\gamma$ is, by definition,
$$
W_{\gamma} = \int_{\gamma}\textrm{d}\mathbf{r}\cdot\mathbf{E}(\mathbf{r}).
$$
If the work done by the field happens not to depend on the path $\gamma$ but only on its boun... | {
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Can gravitational wave create anti-gravity, i.e. repulsive gravity? A very layman question as in title. Like every wave having a negative side, can a gravitational wave have anti-gravity.
To put it in different words, a gravitational wave passing through a complete vacuum, if in positive cycle, can create a denser spac... | Gravitational waves are not cycles of compression and rarefication like sound waves. They're transverse, and there is no such thing as compression or expansion of spacetime. There is curvature of spacetime. In a gravitational wave, the curvature is what oscillates.
In general relativity, the precise definition of what ... | {
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Is the speed of light dictated by Vacuum Permittivity, Vice Versa or Neither? Instinct, and my limited knowledge of Maxwell's Equations and the Wave Equation tell me that the first statement is true.
By my interpretation, the relationship between the frequencies and wavelengths of e.m. waves (and hence the speed of lig... | At first sight, I understand that it might be plausible that permeability and permittivity seem to be fundamental constants of spacetime which are together forming the constant of speed of light.
However, the speed of light is the more fundamental parameter. The speed of light c is not limited to electromagnetic waves,... | {
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Why doesn't Helium freeze at 0K? I have read that Helium does not freeze at absolute zero under normal pressures.
How could this be possible given that the absolute zero is the lowest attainable temperature and at that temperature, all random movements of the atom stop?
Shouldn't the atoms just stop vibrating and soli... | The key point here is the following: the contribution from the zero-point energy is seven times larger than the depth of the attractive potential between two He(4) atoms. Therefore, the zero-point energy is enough to destroy any crystalline structure of He(4) that the material would otherwise form.
A more rigorous answ... | {
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Microscopic interpretation of pressure in liquids Pressure can be explained at microscopic level for a gas with kinetic theory of gases. From that the pressure $p$ is linked to the velocity of molecules (and it is caused by the high amount of collisions in the gas).
$$p=\frac{m N_a}{V} \frac{\bar{v}^2}{3}$$
Where $m$ i... | Unlike a gas a liquid has a finite volume at zero pressure i.e. a liquid floating in vacuum would not expand beyond a certain volume. This volume is determined by the interatomic/intermolecular forces in the liquid.
If you look at the potential energy between two liquid molecules as a function of intermolecular distanc... | {
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Working of potentiometer
So can you simply explain why current increases in lower loop as we move towards A why it increases in upper loop as we move towards X and please give explanation based upon what changes occur voltage between A and X. Also why there is 1V and -4V potential at terminals.
| Presumably there is a resistive wire between A and X (implied by the question).
The two batteries have their positive terminals connected at point P - I am going to assume that part of the wire has no resistance.
This gives us the following picture:
As the contact point (let's call it C, not shown explicitly in the di... | {
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Variation of double slits experiment Setup goes something like this: the laser gun fires only 1 photon each time and the only way for the photon to appear on the hidden screen is for them to be reflected from the 2 narrow mirrors.(see image below)
I was watching a ping pong match and suddenly this pops into my mind.
W... | As an experimental physicist I would advice you to do the experiment.
What the theory predicts for single photons is what the boundary conditions the wavefunction of the photon has obeyed for the particular experiment. This wavefunction is complex and carries the phase information for building up the classical electrom... | {
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Is $\pi^2 \approx g$ a coincidence? In spite of their different dimensions, the numerical values of $\pi^2$ and $g$ in SI units are surprisingly similar,
$$\frac{\pi^2}{g}\approx 1.00642$$
After some searching, I thought that this fact isn't a coincidence, but an inevitable result of the definition of a metre, which w... | $g$ is a value with units, and $\pi$ is a dimensionless number. If you consider a unit system that uses miles, days, and grams as the units of length, time and mass, you can see that $g$ will be quite different.
| {
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Rewriting bosonic action in Altland and Simon Chapter 4 In page 179 of Altland and Simon, Condensed Matter Field Theory, the author obtained the action
\begin{equation}
S[\theta]=\frac{1}{2\pi}\int dx\,d\tau\,\left[(\partial_x\theta)^2+(\partial_\tau\theta)^2\right] \tag{4.48b}
\end{equation}
The author then obtained ... | TL;DR: The trick is not to Wick-rotate the momentum field
$$ \Pi_M~=~i\Pi_E, \tag{1}$$
because it would otherwise lead to a divergent Gaussian momentum integral in the Euclidean (E) path integral. So we will keep the Minkowski (M) momentum $\Pi_M\in\mathbb{R}$ even in the Euclidean formulation.
Further details: Standar... | {
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What's the difference between Quark Colors and Quark Flavours?
Each of the six "flavors" of quarks can have three different "colors". The quark forces are attractive only in "colorless" combinations of three quarks (baryons), quark-antiquark pairs (mesons) and possibly larger combinations such as the pentaquark that c... | The "flavor" is the type of quark, like up or down.
"Color" is a characteristic property, somehow similar to electric charge just that it can have three values and not just two.
Going back to a less deep level, an analogy may be particles that can be protons, neutrons, electrons, mesons, etc. These will be like "flavor... | {
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What exactly are "primordial fluctuations"? Are "primordial fluctuations" essentially the same as "virtual particles" and "quantum fluctuations" that created the universe from nothing like what is featured in the Lawrence Krauss book, A Universe from Nothing?
| It's well-known, that the large-scale structure is incredibly rich. Although on the largest cosmological scales the Universe looks boring (isotropic and homogeneous), at slightly smaller scales that are still very large (we're talking about considering clusters of galaxies as a single entity), we see incredibly rich st... | {
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Does a larger camber produce more lift? I'm doing an experiment using two airfoils of the same dimensions except for the camber. I am getting results in which more lift is produced using the smaller wing. Is this correct or are my results incorrect?
Thanks
| When you say smaller wing, I assume you mean less camber? Because you say they are the same dimensions, which I take to mean wing plan.
Here is one explanation, it all depends on the regime the wing is designed for.
I am sure you know most of it already though, sorry.
If an airplane is being designed to fly at low spe... | {
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How can we show the increase of number of microstates intuitively? After the thermal exchange of two bodies with different temperatures $T_1$ and $T_2$ reaching a equilibrium temperature $T_2$< $T_3$ < $T_1$, how can we prove the number of microstates is increased intuitively? Don't use the entropy explanation, since t... | To get an intuitive idea we start by assuming that no. of microstates$(N)$ are monotonically increasing(or simply linear) function of temperature. This is fairly intuitive since more temp usually allows the system to access more of its energy levels. Thus $N$ $\alpha$ $T$.
Now one of the bodies are at temperature $T_1$... | {
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Can someone please explain what happens on microscopic scale when an image becomes unfocused on a screen from a projector lens? My questions is basically asking when you move a projector back farther from a screen the image tends to blur unless you focus it. Logically I would think that every point(ray of light) of th... | Only the lens equation is relevant: $\frac{1}{f}=\frac{1}{g}+\frac{1}{b}$.
$g$ is the distance from the object inside the projector to the projector lens and $b$ is the distance from the lens to the image plane. If you change your $b$, but let $f$ of your lens system constant, you have to change $g$ by changing positi... | {
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Do we actully feel a change in acceleration? Let's say you were in a sports car with your foot to the floor racing at maximum acceleration then all of a sudden you completely stop accelerating and maintain the speed you are going.
Would you actully feel this "jerk" as it's called or do you only feel the actual acceler... | I have to record this comment by user Velut Luna for its pithy logic:
When we can feel something, we can feel the change of it. We can feel acceleration, therefore we can feel jerk.
which is certainly true, but there is another sense wherein jerk can directly affect our bodies in some cases. Those cases are when one'... | {
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What is the physical meaning of the Schwarzschild radius for objects that aren't black holes? Earth has a Schwarzschild radius of a little less than a centimeter. What does this mean for the matter of Earth's core that is within this radius?
A related question comes up for what happens when an almost black hole accret... | The answers by tparker and Симон Тыран work well enough. There is though I think a bit more. Suppose you put a black cloak around a gravitating body so you could not probe beneath it. The body's gravitation would be the same if it were a star of some mass, or the same mass collapsed into a black hole. So from that pers... | {
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How is heat represented on a quantum level? Heat is just a form of kinetic energy for molecules, because as temperature rises, the heated molecules are "shake" and "vibrate" more and more. But how does that show up on a quantum scale? What element actually carries the kinetic energy: the heated molecule as a whole, its... | It is somehow an open subject of research. No way through just subdividing you end linking quantum world to classical one. At quantum level, different classical processes reading to a particular concept, always rely on just already determined positions and energy of a system. When one goes to systems with very low entr... | {
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Newtonian derivation of perturbation in density In Barbara Ryden's Introduction to Cosmology, chapter 12.3, she derives an equation describing the evolution of mass perturbations with time, for small perturbations $|\delta|\ll 1$. Before she starts the derivation, a disclaimer is added stating that
By performing Newt... | When you write out the gravitational acceleration as
$$
\ddot{R} = -\frac{GM}{R^2},
$$
you are approximating gravitation as Newtonian. Your source is telling you that this approximation implicitly demands that $R$ is much smaller than the Hubble length, and much greater than the Jeans length. I would wager the latter i... | {
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Why is a $5-60 mph$ time slower than a $0-60 mph$ time for some automobiles? This doesn't make a lot of sense to me, from a physics 101 point of view. I've read a few blog entries on why this is, but none of them explain it well or are convincing. "something-something launch control. something-something computers."... | This is not so much a question of physics as it is a question for mechanics.
The 0–60 mph benchmark is commonly quoted in publications for car enthusiasts. As with any benchmark, manufacturers will try to game the system. Fancy sports cars have launch control systems: if the car starts from standstill and the acceler... | {
"language": "en",
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Helmholtz Free Energy minimization during an irreversible process Consider the classical $(N,V,T)$ system, and its Helmholtz free energy (HFE) $A=U-TS_{system}$.
The system is placed in contact with an hotter heath bath.
It is said that, at equilibrium, the HFE of the system reaches a minimum, i.e. $dU - TdS_{system} =... | Your differential form is incomplete.
Actually: $$dF=dU -SdT-TdS =-SdT$$
Equilibrium is reached when $dF=0$, so when $-SdT=0$, meaning the temperature constant over time ($T_{system}=T_{bath}$).
That's why at constant temperature Helmoltz free energy is the minimum potential. In the same way regarding a constant pressu... | {
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How does curved spacetime affect gravitational waves? How differently will a LIGO detector detect a gravitational wave which came directly to it with a detector which happened to have a black hole between it and the source?
| I hope you get a proper answer from an expert, but just in case you don't, I don't think a black hole would have much effect on gravitational waves.
I say this because I asked a similar question previously and I think it was made clear to me regarding the small amount of scattering involved.
From Black Holes And Gravi... | {
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Gravitational Force - Newton Mechanics Why do we use gravitational force in earth by relating just the mass of an object with the acceleration produced by the gravitational field:
$$
F_{g} = m\cdot \vec{g}
$$And when we're dealing with planets, we use a relation defined by the masses of two planets, distance squared an... | The second equation is always correct, and you can derive the first equation from it.
Here on the surface of the Earth, $d$ is the radius of the Earth $r_e$ plus our height $h$.
$$
F = G \frac{M_e M_2}{(r_e + h)^2}
$$
The radius of the Earth (6,371 km) is huge compared to our height above the surface (at least, when ... | {
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Orange sky 3.7 billion years ago because there was little oxygen? PhysOrg quotes Martin VanKranendonk of the University of New South Wales and director of the Australian Center for Astrobiology:
Because the atmosphere had very little oxygen and oxygen is what makes the sky blue, its predominant color would have been o... | Nope! The blue sky comes from Rayleigh scattering through air, but pretty much any gas whose molecules are decently polarizable will work equally well - it doesn't have to be oxygen. I suspect the guy probably said that there was very little atmosphere and atmosphere is what makes the sky blue (although does it reall... | {
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Good resources for understanding inflationary cosmology I'm currently trying to self study inflationary cosmology and am finding it difficult to find good resources which explain the motivation behind such theories while providing all the mathematical details.
Does anyone know any good text or resource on inflationary... | I was trying to understand scalar field models of dark energy which are motivated by inflationary cosmology. The motivation is that we may also explain the late-time acceleration using scalar fields(e.g quintessence, k-essence etc.). Anyway the following textbook was useful for me.
Cosmological Inflation and Large-Scal... | {
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Has the Landauer Limit really been overturned? What was wrong with the original analysis? This news, summarizing results from
M. López-Suárez et al. Sub-$k_B T$ micro-electromechanical irreversible logic gate, Nature Commun. 7, 12068 (2016).
Makes the claim that
It clearly shows that there is no such minimum energy ... | Edit: my first answer was wrong.
What this paper appears to be doing is creating a reversible element which is being treated logically as an irreversable OR. Because the element itself is reversible, it can easily avoid Landauer's principle.
As best as I can tell, this has been known for a long time: you can have a co... | {
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What does thrust and thrust axis mean in particle physics? Would someone be kind enough to explain to me:
1) How thrust and thrust axis are calculated/determined
2) What is the significance/interest in these quantities for an event in particle physics?
Though I have seen the general formula, I haven't found a good ex... | Sphericity and thrust came into being when scattering experiments demonstrated that the parton model of particle physics could not explain the data, that there was a type of "hard core" giving tracks with high p_transverse. The need arose to be able to orient the individual events in a way that would demonstrate the e... | {
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Weight factor in Path Integral Formalism In Quantum Mechanics, transition amplitude between two states in given by (path integral approach):
$$
\left\langle q';t'|q;t\right\rangle= \int[\mathrm dq] \exp \left(i \int L(q,\dot{q})~\mathrm d\tau\right)
$$
This tells that contribution of the paths to the amplitude is given... | Although you are looking for a more intuitive explanation i think the best way to see it is to simply derive it mathematically which is done in every QFT book.
Since $H=i \frac{\partial}{\partial t}$ the time evolution transition amplitude between two infinitesimally close states would be $\langle q_i|1-iH\Delta t|q_{... | {
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Is there a geometric object analagous to a spinor that encodes projections onto bivectors? The most sensible geometric interpretation of spinors that I've come across is that they encode projections in the Clifford algebra. So if $\mathbf A$ is a vector with components $A_i$ and $\psi$ is a spinor, then $\psi^\dagger ... | The geometric object which corresponds to spinors is the external bundle, the bundle of differential forms. The natural equation on such a bundle is the Dirac-Kähler equation.
This bundle is essentially used in lattice computations under the name "staggered fermions".
A problem with this geometric interpretation is ... | {
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Centrifugal Pump Head What is pump head? and how is it different from the difference in elevation between the suction and delivery reservoir? Also why must the kinetic energy of the fluid leaving the pump must be least? I mean if it leaves with more velocity then it can go farther up to the delivery reservoir.
The ene... | The head of a pump is a measure of how big of a pressure difference that pump can generate. I am not sure what the historical or practical reason for it is, but head is expressed as the height of a water column. The pressure $p$ required for such column with head $h$ can be calculated with,
$$
p=\rho\,g\,h,
$$
where $\... | {
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Quantification of entropy mathematically when $T$ and $V$ both change
$$ln\frac{W_f}{W_i}=N ln\frac{V_f}{V_i}=n N_a ln\frac{V_f}{V_i}$$
$$\Delta S=nRln\frac{V_f}{V_i}$$
$$ln\frac{V_f}{V_i}=\frac{1}{n N_a}ln\frac{W_f}{W_i}$$
$$\Delta S=\frac{R}{N_a}ln\frac{W_f}{W_i}=kln\frac{W_f}{W_i}=klnW_f-klnW_i$$
hence $$S=klnW$$... | For stable pressure it is ΔS= nCplnTf/Ti= nCplnVf/Vi (Cp=molecular specific heat)
To quantify,we set initial values Ti=1=Vi and derive: S= nCplnT = nCplnV
| {
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Definition of a calorie? My copy of "Resnick and Halliday" states the following:
"Before scientists realized that heat is transferred energy, heat was measured in terms of its ability to raise the temperature of water. Thus, the calorie(cal) was defined as the amount of heat that would raise the temperature of 1g wat... | You are right, heat really is energy, and the calorie is a unit of energy. However, the definition you gave is not up to current standards of defining units. As far as I know, there are two reasons: First is that the definition is not unambiguous, and the other is that nowadays SI units are the way to go when it comes ... | {
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Electric flux model for two different media Some books define (although some do not) the electric field flux as the number of electric field lines passing through a given area.
Suppose that there is a electric field created by a charge plate and the field lines emerging from the plate are passing through two adjacen... | The electric field can be considered to start and end on total charges represented by the sum of free and bound charges in the material. At the interface of two different dielectrics with different polarizations P a net bound charge appears which is the source and sink of the electric field lines in addition to free ch... | {
"language": "en",
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Do fluorescent white materials exist? From my understanding of fluorescence, a "fluorescent yellow material" (like in highlighters) is a material that contains yellow dyes and fluorescent dyes absorbing green to give yellow. Then, the material appears "more yellow" than usual objects because it has two sources of yello... | The phosphor on ordinary fluorescent tubes and also in white leds would seem to qualify; they take ultraviolet light and convert it to white(ish) light, using a blend of substances to get the color balance right.
| {
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Charging Up a Capacitor Well what I read that in the process of charging a Capacitor, charges are transferred from one plate to another. The work done to move a charge from one plate to another stores as electrical potential energy in it and the capacitor is charged up.
Before this I read that when a Capacitor is place... | There are no charges traversing between the plates because between the plates there is a strong insulating dielectric material. Charges on both plates are supplied by the battery. Through the electric field that crosses the dielectric they feel the presence of the charges on the other plate.
| {
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Differentiating D'Alembert operator It has been a while since I did field theory.
Euler-Lagrange equation
$$\partial_\mu \frac{\partial L}{\partial (\partial _\mu \phi)} - \frac{\partial L}{\partial \phi} = 0$$
If I have
$$L = \phi \Box \phi - m^2 \phi^2,$$
do we just get
$$\Box \phi - 2 m^2 \phi = 0$$
Because we d... | Since the Lagrangian contains second derivative, you will need to use
$$ \frac{\partial L}{\partial \phi}-\partial_\mu \frac{\partial L}{\partial (\partial _\mu \phi)} +\partial_{\mu}\partial_\nu \frac{\partial L}{\partial (\partial _\mu\partial_\nu \phi)} = 0$$
which yields equation of motion
$$\square\phi-m^2\phi=0$... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is speed of Hot air rising gravity dependent? Would say a heated air rise twice as fast in 2G than in the environment with standard Earth gravity?
| Yes.
The hot air rises due to the force of buoyancy as the hot air expands and becomes less dense. So, yes it rises due to gravity. The force of buoyancy is = (weight of air at regular density) - (weight of air at heated density). The weight involves g. So, yes your statement is true if we exclude complications like re... | {
"language": "en",
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Determine the maximum ratio $h/b$ for which the homogenous block will slide without toppling under the action of force F
Determine the maximum ratio $h/b$ for which the homogenous block will
slide without toppling under the action of force F.The coefficient of
static friction between the block and the incline is ... | You can apply it to either location, but there are some considerations:
*
*If you consider rotation about COM, then you need to understand the torque from the normal force. As you push the box, the normal force will move toward the front to counteract. At the tipping point, all the normal force will be there. See... | {
"language": "en",
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Degenerate modes in cylindrical wavguide The $H_z$ field (TE mode) in the case of the cylindrical weveguide is given by:
$H_z(\rho, \varphi, z) = H_0 J_m (k_t\rho)e^{i k_z z} e^{\pm i m \varphi} $, where the part that gives the azimuthal modal dependence is given by: $e^{\pm i m \phi} $ and corresponds to the two deg... | Do you mean $\cos(m\phi)$ and $\sin(m\phi)$ in the last sentence? Due to Euler's formula
$$e^{\pm i m \phi}=\cos(m\phi)\pm i \sin(m\phi)$$
you can represent the two degenerate modes written in exponential form in terms of the ones with $\sin$ and $\cos$. You can write
$$H_z^{\pm}(\rho, \phi, z) = H_0 J_m (k_t\rho)e^{... | {
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Heisenberg uncertainty and Lorentz contraction Consider a particle in a frame moving with speed $v$ relative to the lab frame. By Lorentz contraction, the width of the wavefunction will be smaller in the lab frame, resulting in smaller $\Delta x$. If $v$ is high enough, then the uncertainty principle $\Delta x \Delta p... | With apologies for the many typos (and worse) in the first version of this answer:
Write the wave function as $f(x)$ in the comoving frame. Then in the lab frame, the wave function is $g(x)=\sqrt{a}f(ax)$ where $a$ is some positive constant.
Write $\hat{f}(x)$ for the Fourier transform of $f$. Then $\hat{g}(x)=\hat{f}... | {
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Why was an 8 TeV collider needed to find a 125 GeV Higgs? This might be very naive, but why wouldn't a (say) 209 GeV LEP do the job?
| LHC is a hadron (proton) collider. But it's being used mainly as a gluon collider. Protons are composite particles, and at high energies they become a complete mess of quarks and gluons. While protons have a huge energy, the gluons that produce Higgs bosons only carry a small proportion of that energy. The rest of the ... | {
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Why is depletion region formed when electrons are so mobile? A depletion region is formed by electron hole combination at the junction and it creates positive ions on the $N$ side and negative ions on the $P$ side.
Can someone let me know why wouldn't the electron just beside the $(+)$ move towards it and neutralize ev... | Why am I missing the Coulomb's forces of a charge particle here? As far as I understand, the negative ions collect at the junction until there's enough force to repel the free electrons on the N side by Coulomb's force (both have like charges), this is the equilibrium (balanced) state.
Here's a good link: PN Junction
| {
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Lagrangian and finding equations of motion I am given the following lagrangian:
$L=-\frac{1}{2}\phi\Box\phi\color{red}{ +} \frac{1}{2}m^2\phi^2-\frac{\lambda}{4!}\phi^4$
and the questions asks:
*
*How many constants c can you find for which $\phi(x)=c$ is a solution to the equations of motion? Which solution has the... | is just want to add to this discussion that book has no type error according to page 30 kinetic terms are billinear meaning that they have exactly two fields so kinetic terms in this case are:
T=−1/2(ϕ□ϕ)+1/2(m2ϕ2)
| {
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Does the Dirac equation ever get used in Physical Chemistry? I'm just curious as to know if there are any examples in physical chemistry or condensed matter physics where the Dirac equation is preferable to the Shrodinger equation for making predictions on the material at hand?
| Graphene is a material that needs the Dirac equation for example. The electron band structure of this material has a closed gap some electrons have "mass=0", that can only we treated with the dirac equation. I dont know if this affects the chemical properties but it sure effects the electric ones.
| {
"language": "en",
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"source": "stackexchange",
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What IS the precise angle of repose of Cadbury Creme Eggs, anyways? So, in What If, made by xkcd guy Randall Munroe, an off-handed joke about his famous love of Cadbury Creme Eggs was made.
In the image's mouseover text, Randall jokes his life's dream is to own enough Cadbury Eggs to determine their precise angle of ... | Packaging engineer here who legitimately needed the answer to this question. The answer is roughly 25 degrees. Note the angle of repose is defined from the ground plane, opposite to your diagram.
I suppose this makes me the sad engineer stuck in a Cadbury factory.
| {
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Understanding tension based on assumptions of pulley system If we consider a simple pulley system with two masses hanging on each end of a MASSLESS and INEXTENSIBLE string around a MASSLESS and FRICTIONLESS pulley, how then can one reason that the tension at each end of the string must be the same?
My own reasoning:
MA... | Since the rope is massless, and since two identical masses are attached to rope-ends, then as far as forces on rope are concerned, the problem has left-right symmetry. This symmetry itself assures you that tension in both sides of the rope must be equal. This is true whether or not the pulley is frictionless.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Why is $p_y$ conserved in the Landau gauge when we know the electron moves in circles? Considering the cyclotron in $xy$-plane where the magnetic field is $\vec{B}=(0,0,B)^{T}$. In the Landau gauge, we have
$\vec{A}=(0,Bx,0)^T$ and we obtain the Hamiltonian
$$H=\frac{\hat{p}_x^2}{2m}+\frac{1}{2m}\left(\hat{p}_y-\frac{... | The short answer is that one must distinguish between the canonical/conjugate momentum $\hat{p}_{\mu}$ and the kinetic/mechanical momentum $m\hat{v}_{\mu} ~=~ \hat{p}_{\mu} - qA_{\mu}(\hat{x})$, cf. e.g. this post.
| {
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"source": "stackexchange",
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Self propelling vacuum container in water If I understand correctly: a pressurized container can propel itself if you would take off the "lit" because there is now an open end that can no longer apply a normal force for the pushing gas, resulting in a net force at the other end of the container.
I would say the concept... | It would move in opposite direction. This is because the pressure on the outside of the can and the force exerted on the can by the pressure is greater than the force exerted on the inside of the can because there is lower pressure. The net force is the opposite direction of the pressurized can, so it moves in the oppo... | {
"language": "en",
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Why do we feel cool when we turn our fans on? It is a question that came to me, but evaporation doesn't seem a nice answer. Please help.
| Two main mechanisms help cool your body when a fan blows on it:
1. Forced convection:
Newton's cooling law tells us that an object at temperature $T$ surrounded by a cooling medium at $T_{amb}$ will lose heat at a rate of:
$$\dot{q}=hA(T-T_{amb})$$
Where $h$ is the heat transfer coefficient and $A$ the surface area bet... | {
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Mix of oil and water under pressure I'm not a physicist so please ignore my ignorance. I'm wondering what would happen if:
Imagine a mug with hollow handle. Now, one half of that mug is filled with water, another half with oil (of some kind). If i seal that mug and apply a lot of pressure on top (where the opening is),... | I worked with a wide range of drilling fluids in the past and at the time they were water mud with oil in them and lessor times oil mud with water in it. Daily, multiple times a battery of tests were run and analyzed by sometimes multiple people. Pressures and heat were all part of the testing usually to do the oppos... | {
"language": "en",
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"source": "stackexchange",
"question_score": "3",
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Schwarzschild metric in expanding Universe In Schwarzschild coordinates the line element of the Schwarzschild metric is given by:
$$ds^2=\Big(1-\frac{r_s}{r}\Big)\ c^2dt^2-\Big(1-\frac{r_s}{r}\Big)^{-1}dr^2-r^2(d\theta^2+\sin^2\theta\ d\phi^2).$$
In the asymptotic limit where $r>>r_s$ the Schwartzschild metric becomes:... |
real astronomical objects are embedded in an expanding spatially flat FRW metric
Not really. If you think of the cosmos as clumps of matter on top of a FRW background, you're counting the same matter twice: once in a perfectly uniform distribution and then again in its actual clumped location.
You can start with FRW ... | {
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Why ket and bra notation? So, I've been trying to teach myself about quantum computing, and I found a great YouTube series called Quantum Computing for the Determined. However. Why do we use ket/bra notation? Normal vector notation is much clearer (okay, clearer because I've spent a couple of weeks versus two days with... | I think there is a practical reason for ket notation in quantum computing, which is just that it minimises the use of subscripts, which can make things more readable sometimes.
If I have a single qubit, I can write its canonical basis vectors as $\mid 0 \rangle$ and $\mid 1 \rangle$ or as $\mathbf{e}_0$ and $\mathbf{e}... | {
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How would you include gravity in a momentum problem?
Say you have a big ball of mass $m_1$ and a little ball on top of that of mass $m_2$ (assume they are a small distance apart, like $1~\mathrm{mm}$). Now lets drop these from a height of $h$ so that the big ball will bounce off the ground and collide into the little ... | Since the collision is elastic, you have 2 equations right off the bat. First, we have the conservation of kinetic energy at the moment where the bigger ball colliding with the lighter ball as the heavier ball moves up (dropped factor of 1/2): $$m u_{1}^{2} + M u_{2}^{2} = m v_{1}^{2} + M v_{2}^{2}$$
where $u$ is veloc... | {
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Equations of motion for a free particle on a sphere I derived the equations of motion for a particle constrained on the surface of a sphere Parametrizing the trajectory as a function of time through the usual $\theta$ and $\phi$ angles, these equations read:
$$ \ddot{\theta} = \dot{\phi}^2 \sin \theta \cos \theta $$
$$... | Considering you are aware of conservation of total angular momentum in a sphere (if not, I will prove it below), from the lagrangian I think you are using you get:
$$\mathcal{L}=\dfrac{1}{2}R^2\left(\dot\theta^2+\sin^2\theta\,\dot\phi^2\right)$$
$$l_\theta=\dfrac{\partial\mathcal{L}}{\partial\dot\theta}=\dot\theta$$
$$... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why do superconductors conduct electricity without resistance? Many authors have suggested that persistent currents in superconducting rings arise from the energy gap in the single-particle spectrum. Indeed, the argument has been put forward many times on this site! It is usually suggested that because there is an ener... | A superconductor is characterized by two main properties:
*
*zero resistivity, and
*the Meissner effect.
Equivalently, these can be stated more succinctly as
*
*$E = 0$ (remember that resistivity is defined as $\frac{E}{j}$), and
*$B = 0$.
So even more succinctly: superconductors are characterized by no int... | {
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Proof of equality of chemical potentials and temperature for diphasic system My question is the following :
I have a system at (T,V,N) which is composed of two phases : (T1,V1,N1) and (T2,V2,N2).
Initially I wanted to proove that $ \mu_1 = \mu_2 $, but I had troubles.
To proove it i use the fact that $F=F_1+F_2$ must b... | Since in your case temperature does not remain constant, there is no point in trying to minimize $F$. If the reaction occurs in an isolated container, then total internal energy of the combined system, $U=U_1+U_2$, remains constant. If this is the case then it proper to maximize entropy, $S$, which is a function of $U,... | {
"language": "en",
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Problem in understanding the derivation of Bernoulli's principle I am trying to understand the derivation of Bernoulli's principle by using the conservation of energy. This is the sketch I will be referring to. I am stuck in understanding a seemingly basic step in finding the total work done by the fluid without gravit... | Ideal fluids are, by definitions, continuous bodies which support only compressive stresses. It means that a portion of fluid, say, a volume with regular boundary, is such that every small area of its boundary receives a surface force (proportional to the area) from the external part of fluid, and this force is always ... | {
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Intensity of light after it passes through a convex lens When a parallel beam of light falls on a convex lens and get converge to its focus, does the intensity of light change?
| Yes, the intensity changes, because intensity is just energy per area per second. You might be thinking of the related concept of "specific intensity", which is also called "brightness", which is the energy per second per area per incident solid angle (and can also be per frequency bin, but that's not of importance he... | {
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Does the unit hypercube in Minkowski space always have the 4-volume of 1? Suppose we have a unit hypercube in Minkowski space defined by the column vectors in the identity matrix $$ \mathbf I = \begin{bmatrix}
1 & 0 & 0 & 0 \\[0.3em]
0 & 1 & 0 & 0 \\[0.3em]
0 & 0 & 1 &... | In terms of matrix components, Lorentz transformations have matrices that satisfy
$$\eta = \Lambda^T \eta \Lambda$$
where $\eta$ is the Minkowski metric. Taking determinants of each side, we have
$$|\eta| = |\Lambda^T| |\eta| |\Lambda| = |\Lambda|^2 |\eta|$$
which implies that $|\Lambda| = \pm 1$. Since a transformatio... | {
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Are there any additional fundamentals of physics in addition to space-time, energy, mass, and charge? What do you consider the fundamental quantities in physics to be? By fundamentals, I mean quantities that cannot be described by a combination of other quantities. Fundamentals are things that just are.
| With fundamental quantities, I could imagine that you mean properties that differentiate various particles.
In particle physics, there are multiple charges:
*
*electric charge
*color charge
*weak isospin
*mass (“Higgs charge” so to speak)
Then also discrete symmetries like parity and charge conjugation that giv... | {
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If you hold a compass needle vertical does it point down or up differently on which hemisphere you are? Usually our compass is hold horizontally, and in the northern hemisphere it will point in the direction of to the north of the earth (actually to the South pole of the Earth's 'magnet').
But looking closer at some po... | The north end of the compass needle is pulled down towards Earth when you hold it in the normal horizontal position in the northern hemisphere. So much so, in fact, that the south end needs to be slightly heavier to balance it. If you bring that same compass to Australia, the south end, already weighted, will be pul... | {
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Help with this geometrical approach to deriving the lens equation for weak lensing All images and quotations are from Schneider, Kochanek and Wambsganss.
Here is an image of a typical weak lensing setup. Since $D_{ds}$ and $D_s$ are much larger than the extent of the lens and source plane, we can model the curvature o... | Took me a while, but i think I figured it out.
Lets use a distance $\Gamma$. In first order approx $\Gamma=\theta*D_s$ and $\eta=\Gamma-\alpha*D_{ds}$. So that:
$\Gamma=\theta*D_s=\eta+\alpha*D_{ds}$
And as $\theta=\xi/D_s$
$\eta=\theta*D_s-\alpha*D_{ds}=\frac{\xi}{D_d}D_s+\alpha D_{ds}$
Giving the previous relation. I... | {
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How electron get deflected in magnetic field while moving? I don't understand why electron moves this way... e.g. A light object (crampled paper) going down until gets hit by the wind will go parallel (at least a few seconds) to the wind direction ... why not with electron?
| Some basics at the beginning:
*
*an electron, moving parallel to a magnetic field won't be deflected
*a positron as well as a proton will be deflected in the opposite direction to the direction of an electron or a antiproton
*during deflection these particles emit photons
*loosing energy these particles slowing d... | {
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What is the location of an object in expanding and finite space? I was thinking that does it mean the same thing when we say that we are trying to find a stationary object in expanding space or trying to find a moving object in a finite region of space?
| You need to be clear about what you mean by "stationary" and "moving".
If an object in expanding space(time) is stationary with respect to the expansion, it will appear to other such "stationary" observers to be moving away at the expansion rate. If that object is the only thing you have experimental access to you woul... | {
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If energy is quantized, does that mean that there is a largest-possible wavelength? Given Planck's energy-frequency relation $E=hf$, since energy is quantized, presumably there exists some quantum of energy that is the smallest possible. Is there truly such a universally-minimum quantum of $E$, and does that also mean ... |
since energy is quantized
You have a misunderstanding here on what quantization means. At present in our theoretical models of particle interactions all the variables are continuous, both space-time and energy momentum. This means they can take any value from the field of real numbers. It is the specific solution of ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/284444",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "26",
"answer_count": 3,
"answer_id": 1
} |
Tangential speed and Tangential velocity A slight confusion on terminology.
Tangential speed refers to the linear speed when travelling across a circular path, it refers to the distance covered across the circular path for a given time. I have seen the word Tangential velocity used with tangential speed in various web... | In a 2D radial coordinate system, there are two orthogonal directions: radial and tangential. You could call these $\hat{r}$ and $\hat{\theta}$. Tangential velocity is the component of velocity in $\hat{\theta}$. It is still directional because it can be positive or negative. Tangential speed is the magnitude of this v... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/284566",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 5,
"answer_id": 0
} |
Connecting Ammeter and Voltmeter in the circuit I am unable to comprehend why ammeter is connected in series and voltmeter in parallel in a circuit. My book doesn't give any explanation about it nor am I able to understand it from the internet. Can someone please explain this to me (a beginner).
| An easy way to see it might be this:
Voltmeter: needs to measure a potential difference, so you need to hook its ends to the two points which voltage you want to measure. This means you need to put it in parallel.
Ammeter: needs to measure a current, so you need to put it somewhere where all the current you want to mea... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/284642",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 0
} |
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