Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Why can you hear sound over a wall? I know it has to do with diffraction of sound, as it is a wave, but how exactly does this diffraction occur?
| It is not quite clear to me what you are asking, but I would refer to simulations like on PhET: Wave Interference.
There you can switch between sound waves, surface waves on water (ripple tank) or light waves.
There are two important things to realize:
*
*The wavelength of sound waves is of the order of 1 meter, com... | {
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When can I set $d=4$ in dimensional regularization? I am using dimensional regularization to extract the divergence of some complicated integral. I work in $d=2\omega$ dimensions, with $\omega\approx 2$. After I extract the divergence, I have an expression of the form
$$f(\omega)\Gamma(\omega-2)\int_{-\infty}^{\infty}d... | The important quantities in dimensional regularization are precisely the poles you will obtain in the limit $\omega \rightarrow 2$ and their associated residues. In other words, your bare correlation functions will involve integrals with some divergences,
$$
I = \sum_{n = 1}^m\frac{a_n}{(\omega - 2)^n} + \mathrm{finite... | {
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How does the Lorenz Gauge condition lead to four wave equations? The 1972 book by L. Eyges's, The Classical Electromagnetic Field, on p. 184, in $\S$11.7, Integral Forms of The Potential, the statement
"We now turn to the problem of finding $\mathbf{A}$ and $\mathbf{\Phi}$ in terms of $\mathbf{J}$ and $\rho$. For thi... | The Equation,
$$
\nabla^2 \mathbf{A}- \frac{1}{c^2} \frac{\partial^2 \mathbf{A}}{\partial t^2} = - \frac{4 \pi \mathbf{J}}{c} $$ ,
is actually three seperate equations in three dimensions. In Cartesian coordinates this Equation expands to,
$$\nabla^2 A_x- \frac{1}{c^2} \frac{\partial^2 A_x}{\partial t^2} = - \frac{... | {
"language": "en",
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Escape velocity and orbital velocity confusion If orbital velocity is reduced when we want to put a satellite in a higher orbit, and if to achieve a lower orbit we need to increase it's velocity, then how come by increasing the speed of the satellite we can escape the same satellite from earths gravity?
| This is an extension of Dale's answer. We need to introduce a bit of orbital mechanics. The specific energy of the satellite has the form
$$
E = \frac{v^2}{2} - \frac{k}{r}.\tag{1}
$$
In general, a bound orbit has the shape of an ellipse with semi-major axis $a$ and eccentricity $\varepsilon$. The distance of the satel... | {
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On work done by internal forces which is coming out to be not equal to zero 1) Let us consider a block which explodes due to some internal mechanism into two smaller fragments of equal masses.The system was initially at rest and now is having some finite kinetic energy(due to momentum conservation).We can hence comment... | Something to keep in mind is that "internal force" is a subjective term. It completely depends on what we say the system is, and therefore what we say is "internal" and "external". However, the work done by a force is not dependent on this distinction. Therefore, we should not expect that the label of "internal" or "ex... | {
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Can a "time dimension" be part of a spherical topology? I've heard it speculated that the spatial dimensions of the universe is a 3-sphere. Or a 3-torus. But usually, I guess, it's assumed that the "time" dimension just has its own geometry, like a line, in Cartesian product with the geometry of the spatial dimensions.... | No, Lorentzian manifolds can be spheres only in odd dimensions. This is because the Euler characteristic of compact Lorentzian manifolds must vanish, which it doesn't for $S^n$ for even $n$, cf. e.g. this MathOverflow question.
| {
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Why doesn't hot charcoal glow blue? I was learning about black body radiation and the explanations given by Max Planck and Albert Einstein when a thought crossed my mind.
When we heat an iron piece, its color changes gradually from red, orange, yellow to bluish white. Yet such a change is not visible in a glowing piec... | The glowing color of an object is based on its temperature. Wood Charcoal probably won't get hot enough to look blue. The sun is around 5500 degrees and emits all colors of em radiation. Wood charcoal will take a lot of help from the user (pumping air on the charcoal) to approach that required temperature and it will p... | {
"language": "en",
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Are there scattering targets other than nuclei, protons or electrons in experimental particle physics? I am not too familiar with particle physics, so maybe I missed something. Typical scattering targets seem to be nuclei, protons, electrons, i.e. stable targets, which of course makes some sense. Have there ever been s... | There are other forms of baryonic matter besides the ones you've listed, e.g., white dwarfs and neutron stars. There are cases where particle physicists have gotten useful bounds on certain observables from this. For example, Giddings and Mangano rule out certain scenarios involving large extra dimensions because micro... | {
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How can atmospheric $CO_2$ absorption of infrared be 100% when its atmospheric concentration is 0.04%? An absorption spectrum from high in the atmosphere of infrared radiation emitted from the earth, shows that for the 15µm wavelength there is almost complete absorption. This is attributed to absorption by CO2 in the... | Let's say a 15µm photon has a nonzero probability of interacting with any $CO_2$ molecule that it passes within a distance of 1 wavelength. How many $CO_2$ molecules are there in a cylinder with radius 15µm and extending from the earth's surface out to space? More than $10^{16}$.
I think what bothers you is the idea t... | {
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Can we detect a cyclic coordinate by just inspecting the Lagrangian? I'm reading through Susskind-Hrabovsky's Theoretical Minimum. On page 126, where they are talking about cyclic coordinates, an example is given:
Suppose two particles moving on a line with a potential energy that
depends on the distance between the... | *
*1 & 2. A bit oversimplified a strategy to find candidates for cyclic coordinates is to find coordinates that parametrizes equipotential surfaces of the potential $V$.
*
*In physics we often use the same notation for a function $V$ and its value $V(x)$ at a point $x$. If we transform the argument $x=f(y)$, we ofte... | {
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Physical reason for $T^2=a^3$ when $T$ is in years and $a$ is in AU Kepler's third law states $$T^2\propto a^3$$
When $T$ is in years and $a$ is in AU, the proportionality constant becomes $1$. This can't be a coincidence; I would like to know the physical reason for it.
| It is almost trivial! The law in SI units:
$$\tag{1}
T^2 = \frac{4 \pi^2}{G M} \, a^3.
$$
Now write this, for $T_0 = 1~\mathrm{year}$ and $a_0 = 1~\mathrm{AU}$:
$$\tag{2}
\frac{T^2}{T_0^2} = \frac{\displaystyle{\frac{4 \pi^2}{G M} \, a^3}}{\displaystyle{\frac{4 \pi^2}{G M} \, a_0^3}} \equiv \frac{a^3}{a_0^3}.
$$
Now, ... | {
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Complex number representation of a wave There are some aspects to waves I am confused, for instance in Chapter 11. Fraunhofer Diffraction.
The incoming electric fields can be partially expressed as $e^{i(kr-\omega t)}$. I have two questions regarding this:
*
*What does $\,(kr-\omega t)\,$ indicate, and how do we kno... | We write $kr$ to show how the wave changes through space. For example you can fix $t$=constant, so the part $e^{i\omega t}$=constant, so you can see changes through space just shifting the "$x$" - space component.
"$kx-\omega t$" express the whole phase, so you take a real part if this exponent, and after multiplying t... | {
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Is tension always the same as centripetal force? For example, if a ball is attached to a string and released from a vertical height and then pivots around a point to initiate circular motion, tension is equal to centripetal motion.
If, on the other hand, a ball hands from a string and it’s hit in such a way that it tra... | I think that part of the misunderstanding is due to the use of the term centripetal force in a context where more that force is involved.
Take the vertical circle motion as an example.
The circulating mass is under the action of two forces, the gravitational attraction due to the Earth and the tension in a string.
Th... | {
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Proof of continuity of voltage across a capacitor It is known that the voltage drop across a capacitor is a continuous function of time. This means that, for each instant t0, we may write:
V(t0-) = V(t0+)
This relationship is very used in the time domain analysis of RC circuits for instance, and it is due to the fact ... | Well, you wrote your answer yourself !
Since
$i=C dV/dt$
it means that for the current $i$ to be finite, $V$ may not have "jumps". A function that has jumps does not have a derivative at that point, in a rigorous mathematical point a view.
If one does "hand-waving" about that, one might (erroneously) speak of the "(s... | {
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Confusion regarding fermi-dirac distribution function The fermi dirac distribution function given in http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/disfd.html is different from what I learnt. What I learnt had the chemical potential $\mu$ in place of $E_F$ . Isn't $\mu$ only equal to $E_F$ when $T = 0$ ? Or am I mi... | In solid state physics, especially in the subfield of electronic devices, it is not uncommon to use Fermi energy as a synonym of chemical potential. Some texts explicitly disclose this possible source of confusion and misusage of the term Fermi energy, others do not.
| {
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How to disturb a particle distribution I have a set of N macroscopic particles, each representing a group of electrons. Each of these macroscopic particles has a different charge.
My system is one-dimensional so all particle´s positions are described by their position along the z-axis. I have an array positionsof lengt... | I am assuming that you want to keep the total charge constant. Let's assume that your array is of size $2m$. Then you can update the first $m$ entries of the array using the assignment $r[i] \leftarrow r[i] + A\cos(\pi i/m)$ and the last $m$ entries using the assignment $r[i] \leftarrow r[i] - A\cos(\pi i/m)$. I sugges... | {
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Can someone explain what is the force the ball will exert? If a ball is falling under free fall then the force exerted by the ball on the ground would be $mg$. But that's not the case in real life ball would hit with more force. But when i draw free body diagram there is only one force that is acting on it $mg$
Can som... | perhaps you also want to calculate the contact force between the ball and the ground.
your ball is falling from height $H$ with start velocity $v_0$ and then touch the ground. if we take a simple model of the ground with stiffness $k$ and damper $d$ you get this equation of motion.
$$m\ddot{x}+d\,\dot{x}+k\,x=m\,g... | {
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Newton's third law and Coulomb's law Coulomb's law states that if we have two charges $q_{1}$ and $q_{2}$, then $q_{1}$ will act on $q_{2}$ with a force $$ \textbf{f}_{12}=\frac{q_{1}q_{2}}{r_{12}^2} { \hat {\textbf {r}}_{12}},$$
and $q_{2}$ will similarly act on $q_{1}$ with a force $\textbf{f}_{21}$ such that
$$\,\te... | It is worth repeating that laws in physics are axioms, there is no proof or derivation other than that the law is necessary, so that a physical mathematical theory can choose those solutions that will fit existing data and, important, will be predictive in new situations. Laws in effect are a distillate of data.
Coul... | {
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Is there a limit of electrons a single hydrogen atom can have? Is there a limit of electrons a single hydrogen atom can have? If so what is it? why? Is the the answer to why scalable to helium?
| Your question is about the Hydrogen ion, when it gains electrons. Normally, the Hydrogen ion (we usually call the single proton without electron the Hydrogen ion) when it gains an electron, will have a negative charge.
Now these negative ions (with two or more extra electrons) are unstable. You are basically asking if... | {
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Representation of the $\rm SU(5)$ model in GUT In Srednicki's textbook Quantum Field Theory, section 97 discusses Grand Unification. On page 606, it states:
In terms of $\rm SU(5)$, we have
\begin{equation}
5 \otimes 5 = 15_{S} \oplus 10_{A} \tag{97.5}
\end{equation}
where the subscripts $S$ and $A... |
Am I right?
Only in a small way, but basically not. (97.5) denotes dimensionalities of the irreducible representations of SU(5) involved, so how the respective vectors are acted upon by the coproduct of SU(5) generators.
On the left hand side, you have two quintuplets (5-vectors), each acted upon by 5×5 matrices $T^... | {
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Interpretation of the photon scattering rate? The photon scattering rate $\Gamma$ describes the rate at which photons scatter off an atom$^1$. In a two-level system, the ansatz for the photon scattering rate often is given by
\begin{equation}
\Gamma = \rho_{22}\gamma
\end{equation}
where $\rho_{22}$ is the probability ... | Considering light as a stream of photons at energy hω, photon scattering is usually defined as cycles of absorption and subsequent spontaneous emission.
$$Γsc(r) = Pabs
/hω = 1
/he0c*Im(α) I(r).$$
http://cds.cern.ch/record/380296/files/9902072.pdf
The photon scattering rate is the radiated power divided by the photon e... | {
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Is the sound of hammering nails louder since it travels through the walls? The question might sound silly but hear me out.
When people are hammering nails into a wall in a nearby room, you can often hear it very loudly. It seems natural to suspect that this is because, on top of being loud to begin with, the sound is t... | hammering on a wall will transmit the sound vibrations much more strongly than playing a recording of hammering towards the wall, even at the same volume level in the room. This is because instead of the sound waves hitting the wall, the hammer itself is hitting the wall and so the displacement waves are being fed dire... | {
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Entanglement of initially unentangled state of two non-interacting systems Suppose we have two subsystems $A$ and $B$, and the hamilitonian $H$ for the system separates into a sum $H_A(t) + H_B(t)$ of two time dependent hamiltonians $H_A(t)$ and $H_B(t)$ that act only on subsystems $A$ and $B$ respectively.
Suppose th... | Define $|\alpha(t)\rangle$ and $|\beta(t)\rangle$ as the solutions of the IVPs
\begin{align}
i\hbar \frac{\mathrm d}{\mathrm dt}|\alpha(t)\rangle & = H_A(t) |\alpha(t)\rangle
\quad\text{under}\quad
|\alpha(0)\rangle = |a\rangle,
\\
i\hbar \frac{\mathrm d}{\mathrm dt}|\beta(t)\rangle & = H_B(t) |\beta(t)\rangle
\quad\te... | {
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Derivation of scaled Richardson number and speed of internal gravity waves for density stratified fluid My questions relate to page 29 of this document. In particular, on page 29, two expressions for the bulk Richardson number are given; one is said to be 'before scaling'. How is the first expression for the bulk Richa... | I am not sure but there might be a small error in this derivation that compensates itself. It has been quite some time since I have seen a linear stability analysis so take the following thoughts with a pinch of salt.
The Richardson number is defined as
$$ Ri := \frac{g}{\rho} \frac{\frac{\partial \rho}{\partial z}}{\l... | {
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Dimensional regularization of a divergent integral Suppose there is an integral in four dimension Euclidean space
\begin{equation}
I_{d=4}=\int_0^\infty d^4x\frac{1}{|x|^2},~
\end{equation}
which is divergent. $|x|$ is the length of the vector. Can one use dimensional regularization to compute this integral by using $d... | In dimensional regularisation this integral would normally be set to zero - the reason is that the integrand contains no dimensionful parameter upon which the result can depend. This is curious in qft because it removes ir and uv divergences at the same time
| {
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Should the ground state electron density of an atom go to zero at the origin? I have heard from my professor that the particle density of electrons (in the ground state) of an atom should vanish near the nucleus. Hydrogen is an obvious counter-example. So I am trying to work out what he could have meant? Which quantum ... | As per QM, there are three forces that balance out to keep an electron at a stable energy level:
*
*the electron's potential EM energy keeps it close to the nucleus
*the electron's kinetic energy (momentum) keeps it away from the nucleus
*the HUP keeps it away from the nucleus (in case it should get too close)
In... | {
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How can one tell they are accelerating? In Newtonian mechanics all inertial reference frames follow the same laws of physics. Why does this break down for acceleration. In a rocket you feel acceleration because the rocket is accelerating but everything inside is staying at the same speed so it looks like there is a for... | You're correct - if every single particle that you have access to experiences the exact same acceleration, then you have no way to do detect that you're accelerating, even in principle. In practice, gravitational fields are the only way to arrange for this to happen.
Every time you literally feel acceleration, it's bec... | {
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Problem Regarding Buoyancy
A spherical marble of radius $1\,$cm is stuck in a circular hole slightly smaller than its own radius (for calculation purposes , both are equal) at the bottom of a filled bucket of height $10\,$cm. Find the force on the marble due to the water.
I have always been troubled by problems like ... | For the first problem, you should know that buoyancy arises due to pressure difference which in turn arises due to mass of fluid above a certain level.
You are correct in saying that the ball will displace a volume of water, and that is equal to half the volume of the sphere.
So we can write that the force acting due t... | {
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Can frequency affect loudness? I don't think there is any relationship in frequency and loudness, and frequency only affects the pitch of the wave. But could a really high frequency somehow affect the amplitude of a transverse wave in real-life conditions?
| I first want to clarify a few terms as they are commonly used in acoustics:
*
*Frequency is the number of times per second that the sound pressure changes from low to high.
*Amplitude is an objective physical measure of the strength of the sound wave. For a sound wave with an amplitude of 1 Pa, the high sound press... | {
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In adiabatic expansion does the internal energy of an ideal gas decrease? By First Law of thermodynamic, for an ideal gas, if there isn’t heat transfer, work done by the gas is equal to decrease in internal energy of the gas.
Suppose that I have a perfectly-insulated syringe closed at one end and a frictionless piston... | Microscopically, gas molecules impacting on the outward-moving surface get reflected with a lower velocity. Of course, the average molecular velocity is orders of magnitude larger than the velocity of the piston and the difference in energy for each collision is very small. But it all adds up, and the gas is cooling.
| {
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Concept of Maximum Kinetic Energy What is the concept of maximum Kinetic energy of an electron when a photon is incident on a metal surface? Why the ejected electron can have a range of Kinetic Energy?
| When a light of certain frequency is incident on a metal then the photoelectrons may get emitted by the metal.If the light has just threshold energy then photo electrons will have zero kinetic energy.If the wavelength is greater than threshold wavelength then photoelectrons will come out from the surface with some kine... | {
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Question about description of Gibbs free energy When introduced to the gibbs free energy, it was derived as follows:
First law: $dU=dq+dw$
Second law: $dS>dq/T$ for a spontaneous change.
Note $dq$ and $dw$ are inexact differentials.
Subsituting $dq=dU-dw$, into the second law gives us:
$TdS>dU-dw$
using $dw=-P_{ext}dV$... | I'm going to call a thermodynamic transformation that's both isothermal and isobaric a $TP$ transformation for convenience.
Let's say we have an irreversible $TP$ transformation $A$ (with $T=T_0$ & $p=p_0$) that starts from state $1$ and ends at state $2$.
$$\text{State 1 : }p_1=p_0 \;|\;T_1=T_0 \;|\;V_1\;|\;S_1\; |\; ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/511775",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Does diffraction depend on refractive index of a medium? Does diffraction pattern depend on refractive index of a medium? Does the transmitting media influence on difraction the phenomenon or is it caused by light and the edge alone? Is a diffraction pattern will be identical in air an in water?
| Yes, diffraction does depend on the refractive index of a medium.
The invariant property of a light source is its frequency, and the wavelength this light takes in a given medium will change with the medium's refractive index. Diffraction is a spatial interference phenomenon, which means that the locations where the d... | {
"language": "en",
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How does adding a second magnet on the other side of a coil affect induced voltage? From what I understand, if you have a magnet moving with a relative velocity towards a coil, Lenz's law states that the current flow induced in the coil will create a magnetic field that opposes the change that induced it. So it will es... | What you are thinking is right. This is a perfect application of the famous superposition theorem. The individual effects of both the magnets are added together. In this case, since they are supporting each other, the induced EMFs are added together.
Consider what will happen when magnet 2 is going the other direction?... | {
"language": "en",
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If I kept a body in a groove on a frictionless circular table, and rotate the table with a constant angular velocity, what will happen to the block? I have read that it would slide off the table, because apparently in the frame of the table it experiences a centrifugal force outwards, but I can't seem to agree with tha... | The groove applies a normal reaction on the block, which is the reason that the block rotates along with the table with the same angular velocity as the table. Now since this normal force is tangential to the table it causes the tangential speed of the block to increase. Tangential velocity is equal to angular velocity... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How is many worlds different to basic probabilities? In the many worlds theory the universes branch according to the wave function. We find ourselves travelling down one path of an immense number of these branches of a tree. When we branch, we have no interaction with the other branches.
This sounds to me very similar ... |
In the many worlds theory the universes branch according to the wave function.
I would consider this to be not quite right.
Many-worlds is not a theory, it's an interpretation (MWI). For all practical purposes, in essentially every experiment ever done, its predictions are the same as those of, for example, the Copen... | {
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How do I experimentally measure the surface area of a rock? I hope this is the right place to ask this question.
Suppose I found a small irregular shaped rock, and I wish to find the surface area of the rock experimentally. Unlike for volume, where I can simply use Archimedes principle, I cannot think of a way to find ... | Difficult. Adsorb some chemical, heat it up, measure the amount that evaporates?
I would look at the literature, maybe start with a search for "experimental determination of the surface area" in geological contexts.
Edit: a molecular probe should give something close to the maximum value. There is an end to the length ... | {
"language": "en",
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When the direction of a movement changes, is the object at rest at some time? The question I asked was disputed amongst XVIIe century physicists (at least before the invention of calculus).
Reference: Spinoza, Principles of Descartes' philosophy ( Part II: Descartes' Physics, Proposition XIX). Here, Spinoza, following... | It boils down to the direction of the force applied.
if the force works perfectly against the movement -><- then indeed the object comes to rest - but it would only remain at said rest, if the forces now are in equilibrium. Usually when throwing a ball upward - the gravity doesn't stop working magically ... so the net-... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/512902",
"timestamp": "2023-03-29T00:00:00",
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Why coupled oscillators tend to seek integer frequency ratios? In this document, the author writes (page 225)
Coupled oscillators have a tendency to seek frequency ratios which can be expressed
as rational numbers with small numerators and denominators. For example,
Mercury rotates on its axis exactly three times ... | The motion of two coupled harmonic oscillators is the sum of two "beat" frequency oscillations. The frequencies are functions of the masses and spring constants and can take any value, not necessarily "rational numbers with small numerators and denominators". I don't think this is a correct analogy to orbital resonance... | {
"language": "en",
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Which approach to take with a vertical spring? Lets say we have a spring hanging vertically with spring constant $k$ attached to a block of mass $m$. The system is at rest.
Then, you pull the mass downwards, extending the spring by distance $x$, then let go.
The spring will, of course, bounce back to its original sp... | Both approaches are actually the same, if you do them correctly.
I will address your second case first. You are correct to use conservation of energy and say that the potential energy stored in the spring at the lowest point is equal to the sum of the kinetic energy and the potential energy due to gravity at the equili... | {
"language": "en",
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Are the boundary conditions purely a consequence of Maxwell's equations? The boundary conditions, namely
were all these, realized only by looking at Maxwell's equations? Or is there a physical reasoning behind them? For example, Why does the component of the electric field parallel to the surface of interface remain u... | Consider an electrically polarized continuous medium. In its volume it is neutral but at its boundary a charge appears. For a magnetically polarised medium a current appears. This is why there is a jump in the fields.
| {
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Where does $\pi$ come from in the Heisenberg equation? In class today we were taught about Heisenberg’s equation, $$\Delta x\Delta p\ge\frac{h}{4\pi}. $$
Experience tells me that any time an equation involves pi, circles aren’t far behind. Obviously this is true in geometry, but even pure number theory equations, such ... | Very sketchy, but $\Delta x \Delta p$ has a unit of angular momentum. Angular momentum is quantized (Bohr's condition) which can be interpreted as standing wave condition on "circular" orbit of electron $$n \lambda = 2 \pi r,$$
for which the $\pi$ come from.
| {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Mean free path equation derivation I was reading about mean free path equation derivation online and stumbled upon this:
We will derive the equation using the following assumptions: let’s assume that the molecule is spherical, and the collision occurs when one molecule hits another, and only the molecule we are going ... | In fact there are two analogous formulas for calculating the collision mean free path by investigating the so called collision cylinder or tube. They differ about the diameter of the collision cylinder $D$ that can be either $d$ or $2d$ (where $d$ is the molecular diameter ) and still are correct. The delusion arise b... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/513777",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is running a gas stove more efficient than turning on an in-building radiator? It's cold in your studio apartment and you have two options:
*
*Turn on the four burners and the oven on your gas stove; or,
*Crank open the two small radiators.
Both deliver heat directly to the space of your apartment and we can igno... | Assuming you have a gas stove that is not externally vented, and a gas central heat system, the stove will probably be more thermally efficient. I would not recommend using your stove, as it releases dangerous carbon monoxide and other waste gasses into your room, and is not intended for extended use without ventilatio... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/514102",
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Can the work by kinetic friction on an object be zero? We know that friction is of two types - static and kinetic. Static friction acts when there is no relative motion between the surfaces in contact. Kinetic friction takes place when surfaces rub against each other. I was wondering whether the work done by the kineti... | Yes work done by kinetic friction may be zero for example:- consider a block slipping on ground work done by kinetic friction will be negative in ground frame but now observe the block w.r.t block itself now work done by each and every force will be zero as displacement of block w.r.t itself is zero.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How does the speed of light affect our cosmic observations/detections? -I learned that if you look at a star 10 million lightyears away, the light that you are looking at is 10 million years old since the photons have been traveling at the speed of light for 10 million years to reach you.
-I also learned that all EM ra... | Yes the speed of light is slow and everything you see happened in the past.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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The boundary conditions of an electromagnetic wave hitting a surface When I try to solve the Fresnel equations, I don't understand the condition:
E(i)+E(r)=E(t)
where E(i) is the incident wave, E(r) is the reflected wave and E(t) is the transmitted wave.
So the question is how it can be that the E(t) equal both fields... | The boundary condition here is derived from the Faraday-Maxwell law, and says that the component of the electric field parallel to the boundary is continuous. That is, the electric field parallel to the boundary is the same either side of the boundary.
Since solutions of Maxwell's equations can superpose, that means if... | {
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Will August be always summer in the northern hemisphere? Is the Earth orbit precessing, or are there other effects which will create a shift between our calendar (day counting), and the Earth's orbit?
I imagine these effects to be small, but I'm asking for long timescales.
[Edit] To formulate my question better, let me... | The Gregorian calendar, the calendar used most, adds a leap year every 4 years, and skips 3 leap days every 400 years. This gives it an average year of 365.2425 days. It has been proposed to omit another leap day every 4000 years to keep the Gregorian calendar even closer to an astronomers mean tropical year, currently... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/514567",
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"source": "stackexchange",
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What happens to the accretion disk when two black holes merge? I'm aware that accretion disks around black holes are formed from the swirling mass of matter that is slowly being stripped of its atoms, but what happens to it when two black holes merge? I was thinking maybe it gets eject or sucked in completely. Not sure... | If there are two BH moving around, there's a big chance that there's no accretion disk from the start or that it is far away from the binary.
Once both BHs merged, the far away accretion disk would still be there, without much changes.
Or depending on the initial conditions (accretion disk around each BH, for example),... | {
"language": "en",
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Ground → ship Wi-Fi bandwidth in my fast moving spaceship I have a hypothetical question that hopefully makes sense considering only the rudimentary amount of knowledge I have on relativity.
Assume I am in a spaceship orbiting around a spherical satellite, at a certain fixed radius. The satellite sends data to the shi... | Basically your question is the same as what Michaelson and Morley asked. Their experiment used the earth traveling around the sun instead of a spaceship. Their results did not show a difference in the speed of light either way.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Status of Space-Time Many physicists conjecture that space-time is not fundamental.
Is this the orthodox view in physics these days?
Follow ups - If a philosopher argues that space-time is reducible, are any physicists likely to argue? Are there many or any theories (for instance versions of string theory) that actua... | Since I am unaware of the level of physics you are familiar with, I shall try and give an answer for the general audience.
Earlier, when Einstein presented the idea of space-time, it was assumed as well as critical to his theory of general relativity, that space-time is a continuous background, on which every event in ... | {
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Finding potential using spherical harmonics I have been trying to solve the following question:
The potential on the surface of a sphere is given by
$\mathbf {V = V_{0} \sin^2\theta \sin2\phi,\;}$
find the potential outside the sphere
I am trying to solve it by separation of variable in spherical coordinates by using ... | You already noticed $\sin 2\phi$ is the imaginary part of $e^{2i\phi}$.
Another way to say this is
$$\sin 2\phi=\frac{i}{2}\left(-e^{2i\phi}+e^{-2i\phi}\right)$$
From the table of spherical harmonics you have:
$$Y_2^{+2}(\theta,\phi)=\frac{1}{4}\sqrt{\frac{15}{2\pi}}\sin^2\theta \ e^{2i\phi}$$
$$Y_2^{-2}(\theta,\phi)=\... | {
"language": "en",
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Why does a photon have spin 1? Are we taking the photon spin to be one to describe electromagnetic force or there is any equation (is it relativistic Schrodinger or Dirac equation?) with a solution that tells us that its value is one?
| The question $\textit{why it has spin 1}$ is inappropriate. Particles, by definition, are embedded into irreducible representations of the Poincaré group, i.e., a field. Fields with distinct Lorentz representations have distinct phenomenology and so we must $\textbf{choose}$ the representation of the field in order to ... | {
"language": "en",
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How can the mechanism of electrons in an atom be explained? I am a high school student who takes both Physics and Chemistry.
Recently I learnt about the quantum mechanical point of view of looking at electrons or nuclei. I also learnt that the wave functions can be obtained by solving the Schrodinger's equation with va... | Chemistry and classical mechanics work well because they deal with statistical behavior involving many atoms and molecules, rather than individual particles. Due to the Law of Large Numbers, the overall behavior corresponds very closely to the probabilities calculated using quantum mechanics. So in many cases quantum b... | {
"language": "en",
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Is the Casimir energy in CFT an observable? We know that if we transform a 2d conformal field theory from a plane to a cylinder with perimeter $L$, the ground state energy will be shifted by $$E = -\frac{c}{24L}$$ due to the Schwarzian derivative term in the transformation of stress energy tensor.
This energy is the d... | Of course, the free energy on the cylinder is not a measurable observable if you're given the theory on the infinite plane. But one can measure other observables which are proportional to the central charge, such as the two-point function of the stress-energy tensor.
There are situations where that expression is an obs... | {
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Minimum time to cover distance with variable acceleration I have a problem to solve and I got stack. The question is: Having a vehicle that weighs $m$ that can move at variable speed but with maximum acceleration of $a_1$ and minimum deceleration of $a_2$ calculate the minimum time to cover distance $\ell$. The startin... | We accelerate and then when there is no choice anymore, we decelerate. Indeed, if your minimal deceleration decelaration was infinite, you would have been able to decelerate completely brutaly at the end and that would have been the best. Now you have to tend to that limit. The idea to prove it is to look at how to opt... | {
"language": "en",
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Why is torque a cross product? If I'm not wrong, torque is perpendicular to both the radius and force i. e. It is along the axis of rotation. Questions that arise are- why do we consider the length between the axis/point of rotation while calculating torque? More importantly why is torque a cross product?
| Torque is defined as $\quad\vec{\tau}=\frac{d\vec{J}}{dt}$ where $\vec{J}$ is the angular momentum of the object. The angular momentum is defined as $\vec{J}=\vec{r}\times \vec{P}$. Then
$$
\vec{\tau}=\frac{d\vec{J}}{dt}=\frac{d(\vec{r}\times \vec{P})}{dt}=\frac{d\vec{r}}{dt}\times\vec{P}+\vec{r}\times\frac{d\vec{P}... | {
"language": "en",
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Why 2 electrons can't be in the same quantum state when they are distant apart? I understand that when 2 electrons are confined into a very small volume of space slightly bigger than their debroglie wavelength, one of the pair must jiggle with increase momentum due to pauli exclusion principle.
But looking at G. Smith'... | Electrons, in general, don't necessarily have well-defined positions, so the idea that they are "separated with a vast distance of space" is nebulous, at best. I'm going to assume that when you say
2 electrons separated with a vast distance of space
you mean
2 electrons whose wavefunctions are well-localized (i.e... | {
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Is my visualization of a photon correct? When trying to visualize a photon, I imagine it as an electromagnetic wave of very short length. Is this accurate?
| The visualization of a photon is not really part of physics, because physics is a science and as such it only make statements about things that can be tested by observations. The existence of photons are inferred from the interactions of light with matter. We can therefore say that photons are involved when such intera... | {
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Work Done by a time-variable Force My problem gives a time-dependent force as follows:
lets say that the force is fairly simple, $F=6t$
lets say that we want to find the work done in the 1st second.
Here's my approach:
$W=F(t).v$
So, for a small interval where force can be considered constant,
$dW=F.dv$
using the kine... | You are confusing work and power.
Because of the pioneering work (no pun intended !!!) of James Watt, the unit of power is called the Watt and denoted by $W$. This should not be considered as the first letter of "work" in the physical meaning of the word. I think this may be the cause of your confusion.
You are suppos... | {
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Phase transition on magnetic materials Is ferromagnetic to paramagnetic phase transition a reversible process?
If I start with a ferromagnetic material with a spontaneous magnetization below the Curie temperature, and then I start to heat it, it will become paramagnetic above the critical temperature. If I then start t... | Let me rephrase your question slightly to make it clearer what (I think) you are asking.
Suppose we start with a ferromagnetic material above the Curie point and we cool it through the Curie point in the absence of any external influence e.g. no externally applied magnetic field. And suppose we repeat this experiment m... | {
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Why is the divergence of the field zero in Maxwell's equations? I read in a book called Vector Analysis by Murray R. Spiegel by Schaums Series, and I found that there is somewhere printed that the divergence of the electric field is zero.
Since my teacher told that divergence means something which originates from a poi... | When ${\bf \nabla} \cdot {\bf E}$ is introduced in Vector Analysis by Murray R. Spiegel, it is stated explicitly that it is proportional to the charge density and therefore it is zero only if the charge density is zero.
I guess that you may have been mislead by the solved problem n. 19 of Chapter 4, where it is shown t... | {
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What happens when a weapon breaks on impact? Here is the situation:
You are attacking someone with a wooden pole (such as a pole arm or tree branch). You either (1) hit as hard as you can and the pole breaks into two pieces on impact OR (2) hit quite hard but the pole remains in tact. Assume that you are hitting the sa... | You don't want to break the weapon you want to break another object with the weapon. It's a game theoretic thing to not lose your weapon in a fight :D.
Physically it is harder on the enemy than if the weapon had not broken. Though :]
| {
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Confusing definition of proper time – which is correct? I have googled for „definition of proper time“
This source https://www.collinsdictionary.com/dictionary/english/proper-time gives the following definition:
*
*proper time ... measured by a clock that has the same motion as the observer. Any clock in motion rel... | The definitions are both trying to say the same thing, but they are not quite managing to avoid all scope for misunderstanding. For a non-technical appreciation of the meaning of proper time you should start with the principle that proper time is the time experienced at any point in one's own reference frame. As you si... | {
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Near-field energy transfer If you absorb energy in the near field of the antenna, it will produce a loading effect on the source. Whereas in the far field it will not.
Is there an intuitive explanation why this is true for one type of the field and not the other?
Can the common electrical transformer be thought of as t... | You can think of two antennas in each other's near field as two halves of an air-core transformer. As such, they will load each other in ways that don't happen in the far field.
This principle can be used to couple RF power to an antenna in a manner that prevents induced currents from other nearby antennas from propag... | {
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Lagrangian for a forced system Suppose that for a non-forced system Lagrange's equations are
\begin{equation*}
\left\{
\begin{array}{l}
m\ddot{x}+\left( k_{1}+k_{2}\right) x-k_{2}y+2c_{1}\dot{x}=0 \\
m\ddot{y}-k_{2}x+\left( k_{2}+k_{3}\right) y+2c_{2}\dot{y}=0.%
\end{array}%
\right.
\end{equation*}
But if the system is... | The short answer is yes: when the system is not conservative because of dissipation or driving, one must include generalized forces on the right hand side of the usual EL equation:
\begin{align}
\frac{d}{dt}\frac{\partial L}{\partial \dot q_k}-\frac{\partial L}{\partial q_k}={\cal F}_k\, ,
\end{align}
where ${\cal F}_k... | {
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Observed speed of a receding light source Let’s say there’s a planet 4 light years away from Earth and we send a rocket ship towards that planet at 99.9% light speed. We stay behind on Earth and watch the rocket ship travel towards the other planet.
Eventually we should be able to see our rocket ship reach it’s destina... | It all depends on what the meaning of the word "appear" is.
In about eight years, you'll see the ship land, and you'll say "Ah. I see the ship landing at a place four light years away, so it must have landed four years ago".
Does "appear" refer to what you see, or to the meaning you attribute to what you see after you... | {
"language": "en",
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What are real world applications of the Duistermaat–Heckman formula? In the famous 1984 paper "The Moment Map and Equivariant Cohomology" by Atiyah and Bott, an equivariant de Rham theory was presented in relation to the Duistermaat–Heckman formula
$$ \int_M e^{-itf} \frac{\omega^n}{n!} = \sum_p \frac{e^{-itf(p)}}{(it)... | Here are some applications that might qualify for your criterion of 'real world':
Yasui, Y., & Ogura, W. (1996). Vortex filament in a three-manifold and the Duistermaat-Heckman formula. Physics Letters A, 210(4-5), 258-266.
Karki, T., & Niemi, A. J. (1994). On the Duistermaat-Heckman Integration Formula and Integrable ... | {
"language": "en",
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Do colors differ in terms of speed? Here is a very simple question about light. As far as I remember from the school program, each color is merely one of the frequencies of light. I also remember that each color's wave length is different. On the other hand, when talking about the speed of light, I've always heard only... | No, they are related by the formula
$$c_0 = f \cdot \lambda$$
with speed of light in vacuum $c_0$, frequency $f$ and wavelength $\lambda$.
A change in frequency demands an anti proportional change in wavelength and vice versa, since the speed is constant. It is not possible to change the frequency and leave the wavelen... | {
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Light beam vs sound beam Why is it that it's very common to have beams of light but not beams of sound? Laser beams are widely available, and I am aware that it is also possible to direct sound, however, we rarely see examples of it.
Is it more difficult to direct due to longer wavelength or is it more dispersive in a... | Wave beams require to have a transversal section of lenght of the same the order of magnitude than the wavelength. Whereas for light, we can get very tiny and focused beams (of $\mu m$ order), for sound the wavenlength (of centimeter or meter order), you cannot get beams s focused.
Hence the utility of such beams to e... | {
"language": "en",
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Moving charge in different frames of reference Imagine we have a uniform magnetic field, $\mathbf{B}$, and a single electron is moving normal to it, the electron will produce a magnetic field of its own which interacts with $\mathbf{B}$ and so electron experiences a force.
This is perfectly fine, but what troubles me i... | Electric and magnetic fields are in effect different views of a single electromagnetic field. That is, if we have an electromagnetic field then different observers moving at different velocities will see the electromagnetic field as different combinations of an electric field and a magnetic field.
And it is this that a... | {
"language": "en",
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Pressure needed to compress iron to double the density? What is the pressure needed to compress iron to twice its density? (with "its density" meaning solid iron at room temperature and atmospheric pressure, reference 7.874 g/cm³ from Google. )
| It is difficult to calculate such properties accurately. The standard technique is density functional theory, which is as much an art of approximation as science. I am not qualified to speak to experimental techniques involving sudden compression, but they are of obvious interest to designers of nuclear weapons.
Geop... | {
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Physical interpretation for wave function in infinite square well If you look at the wave function of a particle in infinite square problem for some specific energy level, say for n =1, then the probability of particle to be found in middle of the well is higher than at any other point. Similarly for higher energy lev... | I will not go any deep into the nature of reality but instead I will try to convince you why it has to look like from a logical point of view:
-The potential is infinite at the edges of the well. Therefore, we have to agree that the probability to find the particle there is zero. These are the nodes of the wavefunction... | {
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How often do positrons appear in a typical Wilson cloud chamber? I would like to know a rough estimate of how often positrons appear per meter cubed per second in a typical Wilson cloud chamber based off of your experience. I'm interested in the same quantity for the other typically observed particles as well. Also on ... | A Wilson chamber is an interesting way of seeing the cosmic rays which continually bombard the earth, as well as any radioactive material placed close to it, but it is not good in getting data in an organized method so that one can answer your question:
But in general I'm just wondering how often positrons end up run... | {
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Distance between laser diode and photodetector I have a laser diode with a wide divergent elliptical beam (angles: 57°-13°).
If I want to use a light detector with 50mm diameter, how can I estimate the distance at which I can put the LD from the detector to have all the LD beam inside the detector?
I do not know the ... |
I do not know the beam waist.
The beam waist is almost certainly not important.
The reason the divergence is at such a high angle is that the waist diameter is very small. Likely less than a micron in the "out-of-plane" direction, leading to the 57° divergence in this direction.
If you just assume the waist is a poin... | {
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Justification for Loop de Loop minimum speed I was trying to figure out the minimum speed an object would have to travel on a loop not to lose contact with the loop. Setting the centripetal force equal to gravity $m\frac{v^2}{r} = mg$ gives $v = \sqrt{gr}$ that explanation is valid and makes sense to me but I was wonde... | What you have done is, you have taken the initial kinetic energy as $\frac{1}{2}mv^2$, then you have taken the change in potential energy to be $2mgR$ at the topmost point not$mgR$, that was your first mistake. Even then you are having zero velocity at the topmost point, which means the body has no velocity, and hence ... | {
"language": "en",
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Why are 8 images formed for a object kept symmetrically between two mirrors kept at angle 50°? Let us consider two mirrors $M_1$ and $M_2$ kept at $50^\circ$ with each other.
An object $O$ is kept symmetrically between the mirrors making angles $25^\circ$ with each.
Now the number of images is given by the formula:
$$n... | The formula
$n = \frac{360}{\theta}$
has on one side an integer and on the other a continuous variable. This should give you pause. For correctness, we may either restrict $\theta$ to precisely those values which give integral $360/\theta$ or modify the formula.
So, for $50^\circ$, the formula doesn't hold. Truncati... | {
"language": "en",
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Applications and limitations of the Hamilton-Jacobi formalism It was my understanding that the Hamiltonian formalism was inadequate to describe systems that are invariant under time reparametrization or that have gauge symmetries.
However, I see in Classical Dynamics by Jorge V. José and Eugene J. Saletan, that both a... | *
*Hamiltonian formalism also works for gauge systems, although one has to introduce constraints (and possibly the corresponding Lagrange multipliers), see e.g. Ref. 1. For the relativistic point particle, see e.g. this Phys.SE post.
*In fact the Hamilton-Jacobi equation is derived from the Hamiltonian formalism, not... | {
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Quantum operator calculations
We define the quantum operator
$$
P^\mu=\int{\frac{d^3p}{(2\pi)^3}}p^\mu a_p^\dagger a_p
$$
Now how can I calculate
$$
\langle p_2|P^\mu|p_1\rangle~?
$$
My attempt:
$$
\langle p_2|P^\mu|p_1\rangle =\int{\frac{d^3p}{(2\pi)^3}}\langle 0|a_{p_2} p^\mu a_p^\dagger a_p a_{p_1}^\dagger|... | Use the canonical commutation relation $[a_p, a^{\dagger}_q] = (2\pi)^3\delta^3(p-q)$:
We have that $a_{p_2}p^{\mu}a^{\dagger}_pa_pa^{\dagger}_{p_1} =p^{\mu}a_{p_2}a^{\dagger}_pa^{\dagger}_{p_1}a_p + p^{\mu}a_{p_2}a^{\dagger}_p[a_p, a^{\dagger}_{p_1}]$
The first term is ignored, because when considering
$<0|p^{\mu}a_{... | {
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"timestamp": "2023-03-29T00:00:00",
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How to justify symmetry in a torus for the calculation of $\mathbf H$? The typical texbook example of finding $\mathbf H$ in a torus filled with a material with magnetic permitivity $\mu_0$ (of course we don't need this, that's to find $\mathbf B$ later) always starts like this:
"The symmetry of the problem suggests t... | The Biot-Savart law $$ \vec H = \frac{1}{4 \pi}\int_C \frac {d\vec l \wedge \vec r'}{\vert \vec r' \vert^3} $$ tells us that the contribution to $\vec H$ of a current element $d \vec l$ is perpendicular to $d \vec l$ and the vector linking the point of measurement of $\vec H$ to the current element $d\vec l$. A toroi... | {
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Time period of a simple pendulum in an accelerated frame
Suppose I have a simple pendulum oscillating in an accelerated frame then my textbook says that the time period of the pendulum is no longer given by:
$$ T = 2\pi\sqrt{\frac{L}{g}} $$
but by:
$$ T = 2\pi\sqrt{\frac{L}{a_{eff}}} $$
where $a_{eff}$ is the magnitud... | In the frame of the cart a pseudo force acts towards the left. Notice that this is the new equilibrium position of the bob:
Now, let us turn the axis of the drawing so as to make it easier for us to understand.
Here $g_{eff} = \sqrt{a^2+g^2}$
Now, we take a small angular displacement of $\theta$ and analyse the motio... | {
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A doubt in trigonometric approximation used in the derivation of mirror formula The following text is from Concepts of Physics by Dr. H.C.Verma, from chapter "Geometrical Optics", page 387, topic "Relation between $u$,$v$ and $R$ for Spherical Mirrors":
If the point $A$ is close to $P$, the angles $\alpha$,$\beta$ an... | I believe the author is assuming that you recognize that AP is an arc by the context of the image. The main point here then is that C is the center of curvature of the mirror while O and I are not. As C is the center, AC = PC, and the usual arc length formula can be applied exactly with angle $\beta$ even if $\beta$ is... | {
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Why does light spread out? So we know the light that's emitted from a torch (flashlight) must be moving in straight lines, so why does it spread out when moving? Why does it cover larger area?
|
So we know the light that's emitted from a torch (flashlight) must be
moving in straight lines, so why does it spread out when moving? Why
does it cover larger area?
The reason for such spreading out lies in the idea of "Diffraction". You can read more on diffraction at this resource.
The following are some usefu... | {
"language": "en",
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Energy conservation in motional emf If a rod enters a region of uniform electric field, a potential difference arises between the ends of the rod. The work required to create this potential difference comes from the magnetic field. If the work done by the magnetic field increases the potential energy of the rod then w... | The electric potential energy due to the separation of charges along the rod comes either from the work done by an external force acting on the rod to keep the rod moving at constant velocity or from a decrease in the kinetic energy of the rod as negative work is done on the rod by the force on the rod due to the inter... | {
"language": "en",
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What are $a$ and $a^*$ called in the context of a classical harmonic oscillator? Consider a harmonic oscillator defined by the coupled differential equations
\begin{align}
\begin{split}
\dot{X} &= \omega Y \\
\dot{Y} &= - \omega X \, .
\end{split} \tag{1}
\end{align}
Defining new variables $a = X + i Y$ and $a^* = X - ... | I would call them normal modes, which are by definition the degrees of freedom of a system that oscillate at a single frequency.
Beyond terminology there is a whole body of classical theory behind this term making it useful, for example for more complex oscillators or continuous oscillating fields.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Internal force disintegrating a solid body? Let $M$ be a block on a frictionless surface. Now let us mentally divide (not physically) the block into 2:1 ration (i.e $1/3$ of the left be called $M_1$ and $2/3$ right be called $M_2$). So $M_1$ applies force $F_1$ on $M_2$ and $M_2$ applies force $F_2$ on $M_1$ and by 3rd... | I believe you are making a mistake in the way you are imagining force is being applied on the masses. The scenario where $M_1$ and $M_2$ move with acceleration $2a$ and $a$ respectively is when $F$ is applied on both the bodies separately, imagining both are rigid bodies.
The idea of deformation in your mind, what I pe... | {
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Gravitational potential energy defined as the work done on a mass Our physics sir made us write that gravitational potential energy is the work done in bringing a mass from infinity to a point without acceleration, but I am confused because if acceleration is $0$ it means that the external force is 0, and hence net wor... |
...if acceleration is $0$ it means that the external force is $0$...
No. If acceleration is $0$ then net force is $0$.
...and hence net work done should always be zero.
Yes, in this scenario the net work is in fact $0$, since the net force is $0$. However, this means that there are (at least) two forces acting on ... | {
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running on the outside of a moving train Seen a few films lately where the hero runs on top of a moving train, for example "Under Siege 2". It gives the impression that the train is moving quite fast (presumably its normal operating speed on a straight section, of order 100 km/hr $\approx$ 30 m/s). Is it realistic that... | If the train is moving at constant velocity, in order for the the man to walk on top of it in the direction of travel he would need to exert a force overcome the force of air resistance. On the other hand, he could easily walk opposite the direction of travel of the train since the force of the air at his back will cau... | {
"language": "en",
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Why does the second law of thermodynamics prevent 100% efficiency? So far in my thermodynamics lecture course, my understanding of the laws of thermodynamics is that the first law is about the conservation of energy, the second law says entropy must always increase or stay the same which apparently results in the fact ... | In any irreversible process, heat is lost. in almost every case by the friction of whatever kind (resistance in a circuit, friction between gasses, friction between plates moving on top of each other, magnetic and electrical friction, or friction in waves e.g.).
This is wasted energy, so you can never be able to get 10... | {
"language": "en",
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Why are the masses of $W^{\pm}$ and $Z^0$ different? We know that through the Higgs phenomenon, the weak bosons become massive. In our Lagrangian the $W^\pm$ boson is usually defined as $\frac{1}{\sqrt{2}}(W^1_\mu\mp iW^2_\mu)$ and $Z^o$ is usually defined as $(-B_\mu+W^3_\mu)$ ignoring pre factors and couplings. Becau... | You could ignore over-all factors, but definitely not couplings.
The (not quite purely) theoretical mass term in the generic Weinberg-Salam model is, instead, proportional to
$$
(W_\mu^1)^2+ (W_\mu^2)^2+\left (W_\mu^3-\frac{g'}{g} B_\mu\right ) ^2,
$$
(not quite purely, as the form was all but suggested by a skein of ... | {
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What is the cross-section size of a photon?
How "wide" is a photon, if any, of its electromagnetic fields? Is there any physical length measurement of these two orthogonal fields, $E$ and $M$, from the axis of travel? When a photon hits a surface, and is absorbed by an electron orbital, this width comes into play, as ... | This is a puzzle. I hear that you can slowly build up an interference pattern using an ultra low intensity beam. This suggests that the EM wave associated with each photon can interfere with other parts of itself to determine the probability that the photon will be absorbed at a particular point. When I was at MIT th... | {
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Gauss law when dealing with materials with conductivy Suppose we have a parallel plate capacitor filled with two dielectrics materials, one with conductivity $\sigma_1$ and permittivity $\epsilon_1$ and the other one with conductivity $\sigma_2$ and permittivity $\epsilon_2$. Each dielectric has thickness equal to half... | Your technique is not wrong... if $\sigma_1=\sigma_2=0$. See, if the materials you are working with can conduct current, the parts of the system with free charges will not just be the plates, but any part of the (partially) conducting media can also have free charges brought by the current that flow in these materials.... | {
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I dont understand the work equation I don't understand how work = force * displacement as if a force of say 1 Newton was to be applied to two objects of different mass until the object reached a displacement of say 1 meter, surely the object of less mass would displace 1 meter in less time (due to faster acceleration) ... | You are confusing the concept of "power" (that the user is giving to the system) with the concept of "energy" (that is something more inherent to the system).
Power is defined as $P=\frac{dW}{dt}=\mathbf{F}\mathbf{v}$ with $\mathbf{v}$ the velocity, $\mathbf{F}$ the force, and $P$ the power and $W$ the work done. Inde... | {
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Ways to derive black-body radiation in Unruh effect I know two ways to derive black-body radiation in Unruh effect and they are:
*
*Using Bogoliubov coefficients (N. D. Birrell and Paul Davies)
*Using Page approximation (David J. Toms and Leonard Parker)
Are there other ways to derive this effect (for example usi... | Unruh effect can be considered as a special case of Hawking radiation (See the beautiful answer of Motl to this question). Then finding ways to discover the Hawking effect gives you ways to infer the Unruh radiation existence.
Three lovely and strongly physical derivations of the Hawking effect:
1) Cancelling gravitati... | {
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What properties a medium must have to allow waves to travel? There are many types of waves - sound waves, water waves, light 'waves' etc.
What are the common properties of the media in which these various types of wave travel? And how these properties enable the wave propagation?
I'm especially interested in a mathemat... | Light does not need a medium.
Mechanical waves need a medium with inertia and a restoring force.
For longer waves on a water surface it is gravity that provides the driving force to a flat surface. The motion of water below the surface is not so easy to describe mathematically.
Sound waves in air or water are pressure... | {
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Does deep inelastic scattering produce photon? I know that DIS produces hadron jets, which are formed from the intense energy of the interaction. But I wonder, are photons also produced? And if so, what are the processes that create these photons?
| Photons are seen in the final state in many cases.
The "final" products of any process include only stable particles (or at least those long-lived enough to not matter in the context of the detector you are using): electrons, protons, neutrons, neutrinos, and photons (plus possibly muons depending on the size of your d... | {
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Is the car braking time formula $ T = v / (\mu_s \, g) $ valid only for uniformly accelerated motion? I'm wondering if the car braking time formula is valid only for uniformly accelerated motion.
$$ T = \frac{v} {\mu_s \, g} $$
with $ v $ average speed, $ \mu_s $ static friction coefficient between the wheel and the gr... | Yes, your equation is only valid for uniformly accelerated motion. This is because you substituted $a$ as $\frac vT$ in your derivation and that is only valid during constant acceleration.
| {
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"answer_id": 1
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Why is ampere still a base unit? The ampere is still a base unit, according to the SI brochure. However, in my perception the recent redefinition of units effectively defines the Coulomb as e/(1.602 176 634 × 10^−19), and the ampere is derived as 1 A = 1 C/s. Why did they not make the coulomb a base unit, instead of th... | It appears that they have deemphasized the concept of "base units". They did not remove the term, but mention that all units are now defined in terms of constants. As wikipedia puts it:
With the 2019 redefinition, the SI is constructed around seven defining constants, allowing all units to be constructed directly fr... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/524788",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "17",
"answer_count": 3,
"answer_id": 0
} |
Clarification in the difference between metastable states and excited states The answer of this question What is the difference between metastable states and excited states?
is that the difference lie in the the time that the systems lie in a given state.
So for example take the hydrogen atom and the state $2s$.
Whic... | Long lifetime of an excited state is just an indication of metastable state. The physical mechanism making a long lifetime is the presence of some dynamical obstruction of the direct mechanism for decaying to a lower state.
It is quite a widespread mechanism encompassing nuclear physics, electronic states in atoms and... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/524853",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Can particle with fractional charge exist in isolation? Since quarks are ruled out I wonder if it is possible for free fractional charge to exist not counting virtual particles?
| All the data gathered over the last 200 years or so show only integer multiples of charges, and the models that classify the behavior of particles are successful in predicting new data. Fractional charges arouse in the models to describe the symmetries of hadrons which were experimentally found to be composite.
The mod... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/525063",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
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