Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Reason behind vector addition law What is the reason behind triangle law of vector addition, in other words, how is this really justified?
| A naïve answer...
If you go from A to B then from B to C, you can represent your displacement from A to B as an arrow and from B to C to another arrow. Clearly your displacement from A to C can be represented by an arrow going from A to C or by the two arrows already mentioned, placed with the tail of the second touchi... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Power generation by extracting heat from the environment? It is chilly outside now and I am kept warm by a heat pump with COP 5.5: eating only 0.6 kW, it steals 2.6 kW from the outside air (making it even colder) and delivers the resulting 3.2 kW into my house.
Which makes me wonder: why isn't it practicable to generat... | This is all about entropy and the difference between heat and work. Electrical power is a form of work. To get work output using heat transfer, the best one can do is such that there is no net change in entropy of the system and its surroundings. So you run a reversible heat engine (power stations in practice do their ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/489126",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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Coulomb's law experiment, why consider the distance between the body's centers? In $F_e=\frac{1}{4\pi\epsilon_0}\frac{q_1q_2}{r^2}$, why did Coulomb consider the distance between the center of the charges? Why not the distance between the immediate outer surface between the two bodies? Did he assume that this "electric... | Coulomb’s Law as you wrote it applies to point charges.
When you aren’t dealing with point charges, you can treat a continuous charge distribution as a collection of infinitesimal volume elements that can be treated as point charges, where $dq=\rho dV$, with $\rho$ being the charge density. You can then integrate the i... | {
"language": "en",
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How did Einstein know the speed of light was constant? I often hear the story of how Einstein came up to the conclusion that time would slow down the faster you move, because the speed of light has to remain the same.
My question is, how did Einstein know that measuring the speed of light wouldn't be affected by the s... | In 1887 the Michelson Morley experiment provided evidence that the speed of light was independent of the direction of travel of the observer (in their case, they used the movement of the Earth around the sun).
Morley conducted additional experiments with Dayton Miller from 1902 to 1904 which confirmed the results.
Eins... | {
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Why are massive particles clocks? Or are they not? I recently came across a public lecture "Dark matter decay?" by Sir Roger Penrose.
In his lecture he states that the two equations
$E=mc^2$ and $E=h\nu$ can be combined to form a formula for the frequency $$\nu=mc^2/h$$
He also states that "massive particles are clocks... | Suppose you annihilate an electron and an antielectron, producing two gamma rays. Your equation then gives the frequency of the gamma rays. This is a sort of universal time unit. If we get in contact with extraterrestrials through SETI, one way of correlating our time units would be this.
On the other hand, suppose we ... | {
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Irradiance Measurement of Incandescent Lamps I have two spectroradiometers that use the same detector from two different manufacturers an Oceaan Optics FX and a Gamma Scientific GS1220. They each have their own cal lamps.
After calibrating the FX I can measure the absolute irradiance of that lamp and it looks great, ... | It looks to me that the root of the problem lies in the different reflectance properties of the two lamps holders and interfaces to the integrating sphere.
| {
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Numerical calculation of skyrmion number I'm having trouble finding a numerical method to calculate the skyrmion number for a certain system. I want to calculate
$$ n = \frac{1}{4\pi}\int \textbf{M} \cdot \left( \frac{\partial \textbf{M}}{\partial x} \times \frac{\partial \textbf{M}}{\partial y} \right) dxdy$$
for a s... | You can compute the skyrmion number discretising the integrals using finite differences, and then using the midpoint rule for the numerical integration. It's a rough approximation but it gives reasonable results, specially if your FD mesh has a decent resolution.
I wrote a tool to compute the sk number from OOMMF files... | {
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Help me distinguish between an Amperian loop and a surface
This image is from the Resnick-Halliday-Krane textbook.
These images have been used to see that a correction was needed in Ampere's circuital law.
What I am confused about is, how are the two end surfaces of a 3D surface used as Amperian loops and how do the d... | By Stoke's theorem you are free to use any surface bounded by your Amperian loop. That surface does not need to be contained in a single plane.
The problem that then arises is that Ampere's law as just
$$\int\mathbf B\cdot\text d\mathbf l=\mu_0 I_{enc}$$
doesn't work here because the right hand side for each case is di... | {
"language": "en",
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2 dimensional massless scalar field propagator in position space I have been trying to calculate the massless scalar field propagator in position space by directly Fourier transforming the momentum space propagator. $$\int{d^2p\frac{1}{(p^0)^2-(p^1)^2}e^{-i(p^0t-p^1x)}}$$
Upon referring to multiple sources (linked belo... | The idea for this kind of computation is the following. Firstly, add a mass term to the propagator. This will yield
$$
\int \frac{d^2p}{(2\pi)^2}\frac{1}{p^2-m^2}e^{ip\cdot x}.
$$
This integral can be evaluated provided we make the rotation $p_0\rightarrow ip_0$ that yields
$$
i\int \frac{d^2p}{(2\pi)^2}\frac{1}{p^2+m^... | {
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Electromagnetic waves according to Maxwell If a variable Electric field creates a variable magnetic field and VICE VERSA (according to Maxwell's equations), then why don't we enter a loop where E vector and B vector keep creating one another until they reach infinite magnitudes?
| The fields are vectors with (signed) direction. In a wave, the $\mathbf{B}$ field "creates" $\mathbf{E}$ field components, but they are, at some times at least, opposite to the currently present $\mathbf{E}$ field and therefore reduce the total field. And vice versa. This manifests via the relative minus sign between... | {
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Newton's third law in magnetic fields Say I have a charged particle moving through a magnetic field perpendicular to it. It will experience a force, but according to Newton third law
Every force has an equal and opposite reaction.
So what is the opposite reaction/force of this magnetic force.
Which body experiences... | @Jon Custer is right if a magnet producing the magnetic field is present.
But there is more to learn of this question: As Hertz famously discovered, there are so called electro-magnetic waves.
These waves are made up of alternating electric and magnetic fields, that are unrelated to any physical object in the classical... | {
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How do the thermal conductivity and specific heat influence the amount of heat transferred between two objects Through research on the topic I found that the one with the higher thermal effusivity would be able to transfer more heat. I was wondering what the effect of one material being in liquid state vs solid state w... | One essential difference between a solid and a liquid is that the liquid is mobile, so it can transfer heat via convection in addition to thermal conductivity. How much of a difference that makes will depend on a number of factors, such as the viscosity of the liquid or initial speed at which the liquid is moving.
Anot... | {
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Is $X\otimes X$ not the simultaneous position operator? I had thought that $X\otimes X$ would be the operator on $H_1\otimes H_2$ to simultaneously measure the x-positions of two particles.
But there seems to be something wrong with this -- for a given eigenvalue $z$, there is an entire subspace $\mathrm{Span}\left(|x... | Let $\Omega$ denote any set of one or more mutually commuting self-adjoint operators, such as the observables corresponding to the $x$-coordinates of two particles. Let $\Omega'$ denote the commutant, which is the set of all oeprators that commute with everything in $\Omega$. Then let $\Omega''$ denote the double commu... | {
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Do objects besides strings, ropes, and rods have tension? Why do we define tension only in strings and ropes and rods and such? Shouldn't every object experience tension force? Like when you pull a paper from opposite sides, it gets taut, and experiences what seems like a state of tension. If every object does experien... | Pick up a brick. Try pulling it apart. What stops you from pulling it apart? It's the tension in the brick. Where does the tension in the brick come from? It comes from the inter-molecular forces inside the brick.
The same goes for strings. Here's a second example. If you look closely at a thick rope, it's made of many... | {
"language": "en",
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The specific heat changes based on the actual temperature. How do I calculate the thermodynamic equilibrium when this value changes? I have 2 substances with huge differences in temperature, with the specific heat of one starting at 0.6 J/kgC and ending at about 2.8 J/kgC. It goes from -200°C to 0°C. With this huge dif... | Instead of using $C(T_f-T_i)$ you use $$\int_{T_i}^{T_f}{C(T)dT}$$ To find the final temperature, this might then require you to solve a non-linear algebraic equation.
| {
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Trouble with Math in Physics I am a current high school student and I am very interested in physics, especially particle physics (that stuff is super cool!). Unfortunately, my school only teaches classical physics, so I have to continue my study at home. I've read several books and watched videos and online lectures on... | Ah I remember my high school days of yearning to learn complex physics (it was only 10 years ago lol). I’d start at one Wikipedia page and go from page to page trying to understand something but having to try to understand something else first. It was a lack of prerequisites as Allure said. If that happens, don’t let i... | {
"language": "en",
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How does alternating current provide energy? In my head, direct current makes complete sense; the electrons carry energy around the circuit to something being powered losing its potential and then return to the battery or whatnot to have their potential raised again.
This is probably wrong, so I would like an explanati... | Imagine a current going through a resistor and generating heat.
Does it matter which way the current goes? No, it doesn't; you get heat either way. So reversing the current many times a second, as AC, still generates heat.
Sometimes people get tangled up because they somehow think that electrons are "used up" in elec... | {
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Common potential in Capacitors If two isolated charged capacitors (of different capacitance) are connected in parallel to each other they acquire a common potential. But suppose if i connect positive plate of one capacitor to negative plate of another capacitor will they still acquire a common potential or will the cha... | If you are asking about connecting positive to negative and negative to positive in a closed circuit with two charged capacitors, and nothing else, then you are creating a direct short which will drain both, heat the entire circuit, and may damage capacitors, and, or wires.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/492614",
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Why is carrying a heavy object more taxing on the body than pushing the same object on wheels? Where is the "extra help" coming from when rolling the object on wheels?
| Carrying a heavy weight feels more strenuous and uses more energy because your muscles are resisting the force of gravity on the load, as well as supplying the forward momentum for it. When you put the load on wheels, as the Viet Cong did with their bicycles on the Hoe Chi Minh trail, then provided you have a smooth, f... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/492712",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is the difference between uniform velocity and constant velocity? I think that uniform velocity implies constant speed but not constant direction. while constant velocity implies constant speed without any changes in direction.
Both tell us that there's no acceleration (since magnitude of velocity is constant).
Th... | I don't believe the distinction between "uniform" and "constant" in this context is important: I would use them interchangeably. I certainly have not encountered any serious technical usage of these terms in this context that relied on an implicit knowledge of any such difference. In general, I would take both "uniform... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/492797",
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Momentum operator in QM - scalar or vector? The momentum operator for one spatial dimension is $-i \hbar\frac{\mathrm d}{\mathrm dx}$ (which isn't a vector operator) but for 3 spatial dimensions is $-i\hbar\nabla$ which is a vector operator. So is it a vector or a scalar operator?
| Momentum is a vector operator. Period.
When restricted to one-dimensional problems, momentum becomes a one-dimensional vector, which coincides with scalars in that space.
| {
"language": "en",
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K theory and Holography I have a general or overview question related to charges on D- Branes lies in the K theory of Spacetime. We normally think charges of D branes lies in the Cohomology like $D_0$ branes couple to RR-1 form and so on.
The whole idea behind AdS/CFT duality (Maldacena' paper) is based on the fact tha... | This is a good question which -- as far as I am aware -- has received little to no attention (but see below).
On the one hand it is clear why the question is outside the scope of traditional discussions:
AdS/CFT is commonly practiced in the large-$N$ limit of a huge (in fact humongous) number $N$ of branes. In this li... | {
"language": "en",
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Is the only absolute difference between types of light frequency? Probably a bad question but for some reason, it seems too simple in my head that anyone at home could theoretically create anything from radio waves to gamma waves by generating electrical signals at different frequencies.
Say I had a electronic frequen... | There are no different types of light in the elementary sense. Whys should we distinguish types of light based on frequency or spin, as we don't do this for any other particle.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/493394",
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In QFT, are forces made out of multiple fields? I’ve been reading about 1,5 books about quantum physics and I’ve also watched a few YouTube videos. In one book, I learnt that there are fields, such as the electromagnetic field, which carries forces between particles (vibrations in the field) via virtual particles. But ... | Short answer: forces are particles (except maybe gravity). But not all particles carry a force!
Look for the Standard Model. A particle carrying a force is simply a "special" type of particle called a "force carrier". The photon is the most common example of a particle being also a force carrier (the electromagnetic in... | {
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Applying Kirchhoff Rule to an LC circuit In a simple LC circuit (just one capacitor and one inductor), using the Kirchhoff rule has $$\frac{Q}{C} + L\frac{dI}{dt} = 0.$$ But isn't the voltage drop across an inductor $-L\frac{dI}{dt}$? What happened to the negative sign?
| You have to remember that, when a capacitor is discharging and the current on the inductor is increasing, then:
$$q=q_o-it$$
Therefore:
$$\frac{dq}{dt}=-i
\quad\Rightarrow\quad\frac{d^2q}{dt^2}=-\frac{di}{dt}$$
Upon doing the loop rule, you get:
$$-L\frac{di}{dt}+\frac{q}{C}=0
\quad\Rightarrow\quad
L\frac{d^2q}{dt^2}+\... | {
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How to find distance given candela values on a coordinate system? Consider this diagram:
Let's say that some lamp at 1.5D, 2R has a luminous intensity of 35,000 cd. I want to find the maximum distance at which this lamp can put 5 lux on the road.
I understand that candela, lux, and distance are related as such:
$$ E_... | No. The base of this right triangle (you have labelled "road") will be the distance at which that point in the beam, 1.5D, intersects the road surface. With a more or less typical passenger car lamp mount height of 0.69m, your 35,000-candela hot spot at 1.5D will strike the road at 26.35 m, or just shy of 86.5 feet.
| {
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What is the difference between position, displacement, and distance traveled? Suppose the question is somewhat like this:
If $v=8-4t$ and the position at time $t= 0\ \rm s$ is $2\ \rm m$, find the distance traveled, displacement, and final position at $t=3\ \rm s$
Since $\text dx/\text dt=v=8-4t$, ... | If we go from point A to point B we undergo a displacement. This is the distance from A to B, together with its direction, and is the archetypal vector quantity.
We can give the position of a point as a displacement from some agreed datum point or origin, O.
In your question – which in my opinion is not nicely worded ... | {
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How to understand observables in quantum field theory I am reading a paper about quantum field theory, something that I am new to. I have some experience with quantum mechanics. In the paper, it explains how a field is a function from a spacetime manifold(M) to a vector space(V):
Φ:M→V
The paper then explains the for... | The following is a Schwartz function, for any $\epsilon > 0 $:
$$ f_\epsilon (x) = N \int e^{-(\|\vec{x}-\vec{y}\|^2 + (x^0 -y^0)^2)/\epsilon^2} \theta(\|\vec{y}\|-R) \theta(|y^0|-T/2) d^4 y $$
This is a smoothened version of the function which is $1$ in a ball of radius $R$ in space and for a time duration $T$, an... | {
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Does magnetic moment change under inversion symmetry? Since magnetic moment can be view as a small electric current circle. Pictorially, when apply inversion operation, the current direction is reversed, so I think the $\vec{m}\to -\vec{m}$ under inversion symmetry operation.
On the other hand, the formula for the mag... | Under a full parity inversion, the magnetic moment is unchanged. In your first paragraph, the current is reversed, but the location of the current is also changed.
| {
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Motion between two particles in a relative manner Suppose a particle A is travelling in east direction with velocity of x m/s and another particle B is travelling with velocity y m/s in the west direction. Why does the the particle B appears to move towards A with a velocity of x+y and not just y m/s?
| Suppose body $A$ is going to the right with a speed $x$ and another body $B$ is going to the left at a speed $y$.
The motion of the bodies can be represented as vector diagram 1.
To both motions add a velocity to the left of equal magnitude to that of the velocity of body $A$, ie stopping body $A$, as shown in vector ... | {
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Resistors are used to reduce current to prevent light bulbs from "exploding" but it's also said that "current remains same at all points in a circuit" Resistors are used to reduce current in order to prevent light bulbs and other electrical components from “exploding”, but it is also said that “current remains the same... | You seem to be proposing that all series circuits have the same current. That isn't true.
The equivalent resistance of a set of resistor in series is $$R_{eq}=\sum_iR_i$$
i.e. you just find the sum of all the resistances. If they are all ohmic then the current that flows through the circuit with voltage source $V$ is g... | {
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Lorentz boost in light-cone coordinates Consider a particle with momentum $p^{\mu}=(p^+,p^-,p_{\perp})$, where the momentum is written in light cone coordinates defined as,
\begin{align}
n^{\mu}&=(1,0,0,1)& \bar{n}^{\mu}=(1,0,0,-1)
\end{align}
and $p^+\equiv n.p$ and $p^-\equiv \bar{n}.p$. I am not able to understand ... | In the usual coordinate system where $p_t^2-(p_x^2+p_y^2+p_z^2)$ is Lorentz invariant, a boost in the $t$-$z$ plane is
\begin{gather}
p_t\to p_t\cosh\theta+p_z\sinh\theta
\\
p_z\to p_z\cosh\theta+p_t\sinh\theta
\end{gather}
with
$$
\cosh^2\theta-\sinh^2\theta = 1.
$$
In light-cone coordinates with $p_\pm = p_t\pm p_... | {
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Can the flow be irrotational if the viscous forces act on fluid? I tried to answer the question only using the definitions and the Navier-Stokes equation:
$$\rho \frac{Dv}{Dt} = -\nabla P +\rho g -\mu[\nabla \times(\nabla \times v)] $$
In my opinion if the vorticity is zero, then the fluid is irrotational, regardless ... | The answer to the title question is yes, it is possible for the flow to be irrotational if there are nonzero viscous forces acting on fluid.
As an example, let us consider a simple yet physically meaningful example of such flow: radial, spherically symmetric flow in a viscous incompressible fluid (without gravity). A ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/495738",
"timestamp": "2023-03-29T00:00:00",
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Equivalence of POVM and projective measurement Suppose I have a POVM whose elements are given by $\{M_i^\dagger M_i\}$ such that $\sum_i M_i^\dagger M_i = I_A$. Let it act on some state $\rho_A$. Everything here happens in the Hilbert space $A$.
By Neumark's theorem, it is known that one can write this POVM as a PVM b... | There is a mistake (or rather: inconsistency) in how you define the $M_i$ (which makes the condition you want to prove incorrect, so there cannot be a proof!).
To be consistent, given the Kraus representation $\rho\mapsto \sum M_i\rho M_i^\dagger$, you need to define
$$
M_i = \langle i_B| U |0_B\rangle
$$
(with $U$ th... | {
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Can force be applied without accelerating? When I push against a wall, I am applying force on the wall and the wall applies an equal force against mine therefore the wall doesn't move and neither does my hand. But isn't acceleration required to apply force? My hand is not accelerating when I am applyin the force. Still... |
But isn't acceleration required to apply force?
In fact, there's a branch of mechanics concerned with (static) applied forces that (vector) sum to zero so that there's no net force and, thus, no acceleration.
For example, consider the analysis of a truss in a steady state condition.
Image credit
Note that there are ... | {
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Meaning of time derivative of the Lorentz factor $\gamma$? This question about the Lorentz factor $\gamma$ in special relativity. I know what $\gamma$ means and how to drive. I'm wondering if I have time derivative of $\gamma$, what dose it mean conceptually?
| For a test particle, it's essentially the power being delivered to a test particle by a force, because $E=m\gamma$ (or $E=m\gamma c^2$ in units where $c\ne1$).
| {
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Normalization constant of a planar wave As we know for the plane waves ( $ae^{i k x}+b e^{-i k x}$), the normalization constant can be easily obtained from the integral $\int^{x_{2}}_{x_{1}}\psi^{*}\psi dx=1$ by the relation $|a|^{2}+|b|^{2}=1$. But what happens if the parameter $k$ is imaginary, i.e. $k=i \kappa$ wher... | Plane waves can't be normalised, because they don't represent physically realisable states. It doesn't make sense to normalise a function like $ \psi = ae^{ikx} + be^{-ikx} $ over the boundary $(x_1, x_2)$ unless the particle is bounded, in which case the wavefunction will have a different solution. Another way to thin... | {
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Are the electrons' orbitals the same for all atoms? Are the electronic orbitals of an atom always quantified in the same way (i.e. the same energy required to reach the next level), or does each atom have its own values for each level?
If the quantification is universal, then the creation of photons (due to the deexci... | To add to @john-rennie 's answer: things get even worse as the environment of the atom makes additional modifications to the energy levels (ranging in the meV). For example, a carbon atom bound to an oxygen will have a slight energy shift compared with a free carbon atom, or a carbon atom bound in a diamond structure. ... | {
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Why are you doing no work when carrying a body through a horizontal distance? Work done on an object is equal to $$FD\cos(\mathrm{angle}).$$
So, naturally, if you lift a book from the floor on top of the table you do work on it since you are applying a force through a distance.
However, I often see the example of carr... | You do work on the book. To carry the book in the horizontal direction you move with a force equal to Mass of the person plus mass of book times acceleration. F = Ma where M is the total mass. Hence work done is the force times the distance traveled. You have to keep applying a force to overcome atmospheric resistance ... | {
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What happens if a traveling sound wave encounters vacuum? Suppose a sound wave is emitted by an object in a medium like a gas so it travels in some direction. If the wave meets a rigid object, for example a wall, it reflects back as one should expect; and if it encounters another medium, like a denser one, it will be t... | It would get reflected due to the impedance transition from free air to vacuum. The exact nature of reflection will depend on the exact way how the air is separated from the vacuum. Whatever means this may be, it would have to prevent air molecules to enter the vacuum, i.e the normal velocity component at the boundary... | {
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Is kinetic energy always conserved in an elastic collision/impact? While working out through some problems I encountered this problem :
A ball moving with a velocity $v$ hits a massive wall moving towards the ball with a velocity $u$. An elastic impact lasts for a time $\Delta t$
Now I have to answer whether the Kin... |
In the theory books which I read, it is mentioned that Kinetic energy is conserved before and after in an elastic collision.
Yes, but keep in mind this is the total kinetic energy. i.e. it's the sum of kinetic energy of both the ball and the wall.
So my question is how is it possible for Kinetic energy to increase a... | {
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How to figure out the distribution of Normal Force on a body? I was solving a problem and came across some confusion regarding the point of application of Normal Force.
In Classical Mechanics 101, we had always treated the Normal Force as acting on a point (which can be called as the "centre" of the Normal Force), and ... | The distribution of a force over the surface of a body (as opposed to a "point") is called stress. If the force is normal (perpendicular) to the body, it is called normal stress and is given as
$$σ=\frac{F}{A}$$
When you deal with forces on deformable bodies (and all bodies are deformable) the force is never applied to... | {
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Total force on upper block in two block system If a block $m$ is placed on another block $M$ and a force $F$ is applied on bolck $M$. Then how many forces are acting on block $m$.(Friction is non zero)
The image is taken from this site.
Is pseudo force acting on block $m$ or not?
| Pseudo-forces only appear if you work in a non-inertial frame of reference.
In this case, you could work in a frame of reference in which the lower block is stationary. Because we know that the lower block is actually being accelerated by the force $F$, this must be a non-inertial frame of reference, so pseudo-forces w... | {
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Schwarzschild Radius of a Galaxy If an ultra compact/dense Galaxy has a Schwarzschild radius same as it is own radius, how can it be observed from the outside of the Galaxy?
| Such Galaxy would probably look more like one single mass-body, no empty spaces left in between, would you still call it a galaxy?
Gravitational effects as usual can be detected,so its presence would still be inferred indirectly. If you are speaking about detecting it through light, then light bending such as the lens... | {
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Symmetry reason why magnetic dipole transitions are suppressed In the theory of light-matter interaction, electric dipole transitions between two atomic states of same parity are forbidden. This is because the Hamiltonian conserves parity. Is there a symmetry reason why magnetic dipole transitions happen but their ampl... | No. As a counterexample, magnetic dipole transitions in nuclei are often quite strong, competing against E1 and E2 transitions on fairly even terms. Since nuclei and the relevant forces (strong and electromagnetic) don't break any symmetry that is unbroken for atoms, any relative weakness of magnetic dipole transitions... | {
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Why do all fields in a QFT transform like *irreducible* representations of some group? Emphasis is on the irreducible. I get what's special about them. But is there some principle that I'm missing, that says it can only be irreducible representations? Or is it just 'more beautiful' and usually the first thing people tr... | Irreducible representations are always determined by some numbers, labeling the representation, which correspond to the eigenvalues of some observables which are invariant under the (unitary) action of the Lie group.
If the group represents physical transformations connecting different reference frames (Lorentz, Poinc... | {
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Complex rabi frequency I am learning quantum optics.
In the book written by Scully includes complex rabi frequency, when dealing with $\Delta$ level configuration, the Hamiltonian including laser-atom interacting concludes complex rabi frequency.
However, from the course I took as undergraduate, where rabi frequency ar... | The Rabi frequency is defined as
$$ \Omega_{i,j} = \frac{\vec d_{i,j}\cdot \vec E_0}{\hbar} $$
where $\vec d_{i,j}$ is the transition dipole moment for the $i\to j$ transition and $\vec E_{0}={\hat {\epsilon }}E_{0}$ is the vector electric field amplitude. $\hat\epsilon$ is the polarization of the light, which can be ... | {
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If an earthquake can destroy buildings why it cant kill us according to physics? Most earthquakes with magnitude 5.5 and higher can damage or destroy buildings. However, according to my knowledge and experience, I have never seen someone dying from an earthquake itself. Rather, they die from an associated tsunami, dama... | As an addendum to other answers, pressure and volumetric energy density may be more useful in explaining the total effect on a small body vs large structure.
Since reasonably-sized buildings and people on the surface will be a small fraction of the overall earth mass being moved in a quake, the effective pressure $$P=F... | {
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Why would entropy of a system be fixed if it can exchange energy with its environment? Entropy maximization and energy minimization are equivalent statements of the same thing, as I understand it. If the internal energy is fixed, entropy is maximized because of statiatical reasons. If the entropy is fixed, and the syst... | The energy maximisation or equivalently entropy maximisation is a property of an equilibrium state. So in the case of when there is energy exchange with the surrounding, clearly the system isn’t in equilibrium. Once all the exchange is complete, the energy/entropy is maximised.
| {
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Heisenberg's uncertainty principle: what is the correct interpretation? In this video: https://www.youtube.com/watch?v=xsnTrAEiyHg
Prof. Walter Lewin showed when a laser beam passes through a very narrow slit the projection of it becomes wider. He claims it is because of the uncertainty principle in action: as we know... | I'm not an expert here but having watched the video (very good) I would guess the change in momentum is due to direction change only. Likely the momentum imparted is from the slit itself. So total momentum is conserved but the light has spread. Likely the momentum spread is larger in slit but after the slit it is con... | {
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Conservation of linear momentum with mass defect Suppose we have an insulating container, like a perfect black body, which absorbs all the radiation coming from a radioactive element placed in the center (or some equivalent process like matter annihilation). Assuming a spherically symmetric emission. It will transform ... | From the spherical symmetry it is clear that the body cannot accelerate. (Which direction would it go, everything is symmetric). However, let’s look in a little more detail.
As you say, the center radiates and therefore loses mass. The mass lost is equal to the energy of the radiation. By the problem setup the contain... | {
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Is the statement that $U(x)$ is quadratic for simple harmonic motion equally strong as the statement that $F(x)$ is linear? Is the statement
"If the potential energy of a particle under oscillatory motion is directly
proportional to the second power of displacement from the mean
position, the particle performs a ... | Both of your statements are true for SHM and can be seen as true for approximations as well. Each statement is essentially saying the same thing, because $F=-\text dU/\text dx$, and we can choose $U(0)=0$. Whether or not you use approximations to make these statements applicable to your system doesn't change that.
In o... | {
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From volume density to surface density Let us say we have a volume $V$ having a volumetric mass(charge) density $\rho(x,y,z)$.
Suppose we have a smooth surface $S$ within the volume with a surface mass(charge) density $\sigma(x,y,z)$, if possible, how can one obtain $\sigma (x,y,z)$ from $\rho (x,y,z)$?
If it is an in... | Modelling a true volumetric distribution of charge by a surfacic distribution usually only makes sense if one of the dimensions of the distribution is small (yet finite) compared to the others. It would be the case for a shell with a small thickness (difference between outer and inner radii) compared to the surface of ... | {
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Show that $\partial_i A_j - \partial_j A_i = \epsilon_{ijk}B_k$ Let us start from $\textbf{B}=\nabla \times \textbf{A}$ and write its components $B_k=\epsilon_{ijk}\partial_i A_j$.
I want to show that $\partial_i A_j - \partial_j A_i = \epsilon_{ijk}B_k$. I can sense that it works, but I want to see it directly. How sh... | Using the identity $\epsilon_{kij}\epsilon_{klm}=\delta_{il}\delta_{jm}-\delta_{im}\delta_{jl}$,$$\epsilon_{ijk}B_k=\epsilon_{ijk}\epsilon_{klm}\partial_lA_m=(\delta_{il}\delta_{jm}-\delta_{im}\delta_{jl})\partial_lA_m=\partial_iA_j-\partial_jA_i=F_{ij}.$$
| {
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Some digital watches display digits in black on a white background and in the dark the backlight is reversed. How is this possible? Some digital watches display digits in black on a white background and in the dark the backlight is reversed, blue on a black background. How is this possible?
Here is an example:
https://... | In a typical LCD panel with two linear polarizers, rotating either linear polarizer by 90 degrees will invert the colors. For instance, if the linear polarizers are originally cross-oriented (as in the Wikipedia article) so that applying a bias across the liquid crystal prevents the system from transmitting light, rota... | {
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Why are the left- and right-hand sides of a differential equation with two separated variables equal to a constant? While deriving the Time Independent Schrodinger Equation, my book mentioned this line.
So time and position of a particle are two independent variables. If they are equal to one another for all values of... | There are two logical options when you vary $t$: either the value of the left-hand side changes, or it doesn't. If it changes, then the right side must change as well, since they are equal. But the right-hand side can't change when you vary $t$, since it is not a function of $t$! Therefore, since varying $t$ produces n... | {
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Differences between charge quantity and electric charge As a senior middle school from China mainland, I am teaching physics about electric field. I work with my workmates, and we got a problem now. We cannot get an agreement. There are three viewpoints.
The first is that: electric charge is physical attribute and a ph... | If you look up the NIST website for the SI units
https://physics.nist.gov/cuu/Units/units.html
you will see that they use both expressions when it comes to charge:"electric charge, quantity of electricity". They are both measured in coulombs so both can be used to designate a physical quantity. At least in the US.
Of c... | {
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The answer to this question is not close to the age of the universe, then why do we say it is? I saw this question in our textbook
A great physicist of the century (P.A.M. Dirac) loved playing with numerical values of Fundamental constants of nature. This led him to an interesting observation. Dirac found that from t... | From the table of fundamental constants, Dirac derived the following:
\begin{aligned}
&\left(\frac{1}{4 \pi \varepsilon_{0}}\right)^{2} \times \frac{e^{4}}{m_{e}^{2} m_{p} c^{3} G} \\
=& \frac{\left(9 \times 10^{9}\right)^{2} \times\left(1.6 \times 10^{-19}\right)^{4}}{\left(9.1 \times 10^{-31}\right)^{2} \times 1.67 \... | {
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Why are some mistakes counted as "experimental error"? I have always thought (and been told) that experimental errors and uncertainties do not include mistakes which can be fixed by just conducting the experiment more carefully. Yet we still include parallax error and zero error when talking about experimental error. C... | Zero error can be usually fixed by re-calibrating measurement device or changing it into a newer not damaged device. It's one-time fix. However story is far more complex about parallax error - you can't be sure that you are looking at device readings at a right angle. Besides usually parallax error will be lost in othe... | {
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Is the equivalence of mass and energy a direct consequence of SR or not? Special relativity gives us the invariance of four-vectors. Consistency with Newtonian physics implies the conservation of four-momentum.
The spatial part of four-momentum is
$P^0=m\gamma(v)$
which can be expanded to second order
$P^0 =\frac{1... | It is a direct consequence of Special Relativity. The equation
$$E^2-(\mathbf{p}c)^2=(mc^2)^2,$$
which expresses the invariance of the length of the energy-momentum four-vector, makes the relationship between mass and energy when $\mathbf{p}=0$ transparently obvious.
I wouldn’t call that relationship “equivalence”. Mas... | {
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How to relate the Schwarzschild time $t$ to the status of the wormhole featured in the Kruskal diagram? The maximally extended Schwarzschild spacetime as described by a Kruskal diagram features a wormhole which is dynamical. As Kruskal time $T$ elapses, a spacelike hypersurface hits the past singularity, then the wormh... | In the Kruskal diagram, this "wormhole" consists of a single point in the diagram (i.e. a sphere in the spacetime). Hence it exists for only a single moment in Kruskal time. In the Krusal diagram, lines of constant Scharzschild time $t$ are straight lines passing through this point. So the "wormhole" exists for all val... | {
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Why is a piezoelectric material a capacitor? I am reading about piezoelectric elements and I am not sure why a piezoelectric material is like a capacitor. So a mechanical stres on the material will displace the electric charge distribution creating a potential difference. But current cant flow through ? So why is it a ... | Because that is exactly the effect a capacitor gives: It causes current to flow in other parts of the circuit around it due to attraction/repulsion of charges on either side of it - but no current can actually flow through it.
*
*In essence, in the piezoelectric element you have an atomic structure of the unit cell ... | {
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Does light have mass? Why? I've been wondering whether light has mass. Yet given the wave-particle duality of light, the statement seems to be affirmative. With that, how to calculate it?
| In quantum field theory, a photon's rest mass is proven to be zero. But relativistically, the photon's energy leads to the relativistic mass $m=\frac{h\nu}{c^2}$.
Related link: http://www.desy.de/user/projects/Physics/Relativity/SR/light_mass.html
| {
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Ward identity prohibits mass of photon On wikipedia one can read the following statement:
The photon and gluon do not get a mass through renormalization because gauge symmetry protects them from getting a mass. This is a consequence of the Ward identity.
Can someone briefly outline why the forbidden mass is a conseq... | Without gauge invariance, the masses of vector bosons would be affected by contributions from higher order Feynman diagrams. As a result, even if the bosons have zero mass in the fundamental theory, their masses can become nonzero due to these contributions.
In the presence of gauge invariance, those diagrams that woul... | {
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Why do things cool down? What I've heard from books and other materials is that heat is nothing but the sum of the movement of molecules. So, as you all know, one common myth breaker was "Unlike in movies, you don't get frozen right away when you get thrown into space".
But the thing that bugs me is that things in the ... | In the present epoch the universe is a long way from thermal equilibrium. It consists of a large number of isolated hot spots (a.k.a. stars) in a sea of background radiation which has an average temperature of just $2.7$ K.
But stars have finite lifetimes (although this can be a very long time for white dwarf start) so... | {
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Is the Earth a gyro? Due to rotation and low friction, can the Earth be considered a gyroscope? If so, any interesting implications to this? Thanks
| A spinning celestial body can indeed be considered to be a gyroscope.
Part of the motion pattern of the Earth is that it is subject to a gyroscopic precession with a period of about 26.000 years. The common name for this gyroscopic precession is 'precession of the equinoxes'. The precession of the equinoxes was noticed... | {
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Why does gradually increasing refractive index coating reduce reflection? Why does gradually increasing refractive index coating reduce reflection?
EDIT:
As @Michael Seifert nicely describes in his answer, reflection only occurs if there is an abrupt change in refractive index. Since for a gradually increasing refract... | The question itself isn't entirely clear, but I believe this can be understood in terms of the Fresnel equations. Whenever a light wave hits an interface, some of the wave is reflected and some is transmitted. If the media are very similar to each other, then very little of the wave is reflected; in the limit that t... | {
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In de Sitter space, does the cosmic horizon change its shape for fast-moving observer? If an observer moves at a speed close to the speed of light, will the horizon deviate from spherical shape?
If no, will it be the same horizon as for stationary observer (at the same position)?
| De Sitter space is a maximally symmetric space, which means that all its points and all 4-velocities at each point are equivalent and could be related via an isometry. This means that any inertial observer will experience de Sitter space in the same way, in particular cosmological horizon for each observer would have t... | {
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Spring mass damper system: Distance from equilibrium after applying velocity to mass I have a spring fixed to a wall on one end and a mass object on the other end in its natural resting position. The question is how far does the spring stretch when a velocity $v_0$ is applied to it, assuming there is no friction.
My id... | With the spring attached to a wall (and not the ceiling) one might assume that the mass is sliding on a friction-less horizontal surface. Then the starting kinetic energy = the final potential energy: (½) m vo^2 = (½) k x^2 where k is the spring constant and x is the stretch. If the spring is hanging vertically, th... | {
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Seeming violation-wave travelling faster than speed of light Consider the basic relation $$E=\sqrt{(pc)^2+(mc^2)^2}.$$
Every particle possesses a wave nature and it depends on the situation in which one among the two is perceptible...
Consider a particle with rest mass $m$. If we consider the speed of De-Broglie Waves,... | What you have calculated is the phase velocity, $v_p$, of the de Broglie wave associated with the particle. The phase velocity can be greater than $c$, and indeed it is always greater than $c$.
The velocity of the particle is the group velocity, $v_g$, and as you have demonstrated the two are linked by:
$$ v_p v_g = c^... | {
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Motivation for introducing quantum field theory in particle physics Why is it so that because particles can be destroyed and recreated we introduce QFT? I read at the begining of some textbook that this is so. My main problem is not the rest of the book but the first motivation for introducing QFT for modeling.
My thin... | To give a short answer, hoping it will be of some use to some other poor soul roaming the physics land. Lets look at it this way: In reinterpreting electrodynamics as a quantum theory we arrive at real relativistic quantum theory of fields. This is done from the obvious reason to explain the fact that EM radiation com... | {
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Climate Change Review paper Could anybody recommend me some review paper on climate change or tell me some major names in that field? I work in a completely different area but I would like to learn about the current state of our knowledge regarding this subject. In particular I am interested in currently accepted forec... | Of course the most authoritative review paper is the IPCC report.
You may find the latest report, the fifth revision, AR5, at the webpage: https://www.ipcc.ch/reports/
Depending on your background / time, you may like to first read the Synthesis Report and even Summary for Policy Makers. In the main report, consistin... | {
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Standard Model Lagrangian and Euler-Lagrange Equations First off, note that I only know physics through quantum mechanics, so forgive me if this is a foolish question. I've seen the Standard Model's Lagrangian density written out in full. My question is, could one send this through the Euler-Lagrange equations to get a... | There are several formalisms in which you can work out quantum field theory, and one of them does indeed involve using the Euler-Lagrange equation in some capacity. This is the Schwinger–Dyson equation.
As all quantum formalisms should be roughly equivalent, you can probably prove this quite generally, but it is simple... | {
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Electron cloud and Quantum Physics Is it possible to detect the Electron Cloud? Also, it it possible for the Electron Cloud itself to contain any mass?
| The electron cloud is just a simplified and somewhat inaccurate way to describe electron orbitals around the atom. The electron cloud is not a physical thing, it's just something to convey the idea that the electrons do not exist at any point in space at some point in time. Rather, there is a probability of detecting a... | {
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Arnold's holonomic constraints being limits of potential energy The following quote comes from Arnold's "Mathematical methods in mechanics" book:
"We consider potential energy $U_N = Nq_2^2 + U_0(q_1, q_2) $, depending
on parameter $N$ (which we will tend to infinity). We consider the initial conditions on $\gamma$ ... | *
*The 2nd particle $q_2$ is effectively attached to a spring with coupling constant $2N$. From mechanical energy conservation, $|q_2|\leq\sqrt{E/N}$. In the stiff spring limit $N\to\infty$, the 2nd particle $q_2$ becomes confined to stay in the origin, thereby enforcing the holonomic constraint $q_2= 0$.
*Meanwhile... | {
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About the pressure of a confined gas According to fluid mechanics, we have Pascal's principle $P_2 = P_1 + \rho gh$. So, the pressure of a confined gas is different depending on the depth.
However, in thermodynamics, we have another formula $PV = nRT$. They use a confined gas to use this formula. Here, what is the $P$... | The atmospheric pressure drops about 11.3 pascals per meter the first 1000 meters above sea level. The pressure at sea level is 101,325 pascals. The fractional difference between the bottom and top of a cubic meter of air is therefore only 0.00011152
Hope this helps
| {
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On diagonal terms in the Coulomb matrix I have seen many machine learning algorithms for prediction of quantum chemistry properties that use Coulomb matrix as their input. Coulomb matrix is defined as
$$\boldsymbol{M}_{i j}^{\mathrm{Coulomb}}=\left\{\begin{array}{cc}{0.5 Z_{i}^{2.4}} & {\text { for } i=j} \\ {\frac{Z_{... | I know nothing about machine learning algorithms for quantum chemistry, however it is easy to guess what that $0.5 Z^{2.4}$ term means: it is an approximation to the total energy of atoms.
Consider, for example, the following ground-state energies of neutral atoms computed at the Dirac-Hartree-Fock level:
L. Visscher ... | {
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Notion of Present Can't I sync all watches in spacetime and call this time slice the present? In Carlo Rovelli's book he tried to explain that the notion of the present is local only, which I could not follow.
| In special relativity, you can pick an inertial reference frame, and then in that frame you can do essentially what you describe: place clocks all over space (not spacetime) and synchronize them all. The synchronization can be done by various equivalent methods, such as transporting clocks slowly or Einstein synchroniz... | {
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Is there a way to inspect thin metal weld (2 mm - 3mm) by ultrasonic testing? I am working with an ultrasonic device to inspect welds. So far, I have learned that the minimum thickness of the metal sheet for this inspection is 6mm - 8mm. But the product of mine has 3mm thick welds:
I have basic knowledge working with ... | The following is just a speculation, but maybe you can place a thicker plate under your thin plate and use reflections from the bottom of the thicker plate. Reflections from the bottom of the thin plate will be a problem, so maybe some oil should be placed between the thin and thick plates to make sure more ultrasonic ... | {
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Differentiability of wave function at boundary in infinite square well I was told in class that a wave function should have the following properties:
*
*Finite and single-valued
*Continuous
*Differentiable
*Square integrable
But if we consider the wave function in an infinite square well, the wave function isn'... | Like with a plane wave, the wave function you are giving is only a "limiting case".
In reality you should start with finitely high walls and impose all four requirements that you list.
Then, as you take the limit of higher and higher walls, you will obtain your wave function. However, think of it only as a limiting ca... | {
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Two-coupled oscillator: Doubt in finding normal modes and natural frequency I want to find the natural frequency of a two coupled oscillator system like this-
My book does it this way but I don't really get it.
The equations of motion for the pendula are-
$$I\frac{d^2\theta_1}{dt^2}=−M_\text{eff}\ gL\sin \theta_1− \k... | *
*Suppose $\alpha = \theta_{1} +\theta_{2}$ and $\beta = \theta_{1}-\theta_{2}$ then the first equation only depends on single variable $\alpha$ and the second on $\beta$, thus the equations are uncoupled.
*Stating that the equations are uncoupled, or that the matrix of the system is diagonal, or that the equations ... | {
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Work done by friction in a complicated path
A block of mass $M$ is taken from point $A$ to point $B$ in a complex path by a force $F$ which is always tangential to the path. We also have coefficient of friction as $K$. What will be the work done by force $F$ when it reaches point $B$ from point $A$? Given that the ve... | Friction is not a force from a scalar potential. As such the work done is path dependent so there is not enough information to answer the question.
| {
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Deriving the speed of light from Maxwell's equations? Relationship between speed of light and EM force?
Can it be said that Maxwell used measurements of the "strength of electric force and strength of magnetic force", to derive the value for the speed of light?
Explicitly, is Maxwells work fundamentally based upon mea... | It is true that Maxwell was able to derive an extra equation from his four equations of electromagnetism which allowed him to calculate the speed of electromagnetic waves, which turned out to be equal to the known speed of light.
That equation contained two physical constants (which had previously been measured in the... | {
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What does convergence to equilibrium for the Fokker-Planck equation mean? I am a math major who recently started to study thermodynamics seriously. I have some confusing points while studying it, so I'd appreciate it if you'd correct me and give me some answers.
(1) As far as I know, a small particle immersed in a flu... | The stationary solution of your Fokker-Planck equation is an equilibrium distribution.
Here, assuming that $v$ is the variable for the velocity, that mean a Maxwell-Boltzmann distribution.
So if your initial condition for the distribution $W(v,t)$ is not an equilibrium distribution, your system will not be at equilibr... | {
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The potential at a point According to my book, 'The potential at a point is said to be 1 volt when 1 joule of work is done in bringing 1 coulomb charge from infinity to that point.' But I wonder how it is possible. As the charge is being brought from infinity, the work done = force * infinity, thus, the work done would... | The force between two point charges is an example of an inverse square law where the force is proportional to the reciprocal of the separation squared, $F\propto \frac {1}{r^2}$, as illustrated below.
As the separation increases so does the force decrease.
The area under a force against separation graph is the wo... | {
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How can I prove Clebsch-Gordan coefficients are real? I know it is convention to taken Clebsch-Gordan $\color{blue}{<j_1,j_2;m_1,m_2|j_1,j_2;j,m>}$coefficients are real.If I want to make proof it's reality from any physical defination in backward then how can I do that?
| Mmmm... I don't think there is a proof as such, since it's simply a choice of phase for the individual highest weight states $|j,j\rangle$ states in the decomposition . It would be like asking for a proof that the coefficients $\sqrt{j(j+1)-m(m-1)}$ in the action of the ladder operator $J_-$ are real. This latter re... | {
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Understanding simple LC circuits I'm trying understand the physics of simple inductor-capacitor circuits such that there is just an inductor L and a cacpacitor C and a switch.
Imagine first that the capacitor is fully charged and the switch is then closed.
I do not understand why the current increases from an initial l... | The instant the switch is closed the current in the circuit $I$ is zero because the changing current in the circuit $\frac{dI}{dt}$ induces an emf in the inductor $L\frac {dI}{dt}$ which opposes the exactly "opposes" the voltage across the capacitor $V = \frac QC$.
As time progress the voltage across the capacitor de... | {
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Do the oil and mercury in this manometer affect the pressure in A and B? One of my friends came to me with this homework question:
We've worked out that the height difference between A and B is 50 mm. That makes the difference in pressure between them
$$
\Delta P = \rho g h
=1000 \times 9.81 \times 0.05
=490.5 \mathr... | Yes the oil and mercury do make a difference, and have to be taken into account.
When you go up in a fluid there is a drop in pressure. When you go down there is an increase in pressure. The change in pressure depends on the density of the fluid as well as the distance.
Working from A round the manometer to B, there i... | {
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Do photons generate gravitational waves? I guess I’m trying to understand the difference between a rock orbiting earth, that would radiate gravitational waves. And say a photon orbiting a black hole that is just following a straight line path. Why does one radiate and the other doesn’t? Best Regards, Andy
| Questions of quantum gravity aside, viewed as moving blob of energy-momentum, a photon moving around a black hole should produce gravitational waves just like a massive particle would. In practice, this is a negligible amount. The fraction of the photon's (wavepacket's) energy that gets converted to gravitational waves... | {
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Why violet light bends the most? I have read about refraction through a triangular prism,rainbow formation and other natural phenomena.They all told about the strong bending of violet light .
I know that it has a shorter wavelength and high frequency.From the sources I searched I get to a conclusion that it is because ... | when light travels through a medium, it interacts with atoms or molecules in the medium. It brings temporary deformation of electron clouds near atoms or molecules and the energy retained is re-emitted without energy loss unless being absorbed by atoms or molecules in the medium. This interaction takes a little time an... | {
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Why does water boil harder when you push a ladle to the bottom of the pot? I noticed this today while cooking. When I push a ladle to the bottom of my pot on my stove top, the boiling sound gets louder, and the bubbles rise to the top more aggressively. Can someone explain?
| There’s either one or two factors at play, depending on what, “… push my ladle to the bottom of my pot…” means.
If you were pushing the ladle hard on a wonky old electric coil stove, then it could be what someone else eluded to: the force pushing down on the pot can effect how much of the pot is in direct contact with ... | {
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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... | The ground must do work on the falling ball to bring it to a stop. From the work energy theorem the net work done on the ball equals its change in kinetic energy or
$$F_{Ave}d=\frac{mv^2}{2}=mgh$$
$$F_{Ave}=\frac{mgh}{d}$$
Where $F_{Ave}$ = average impact force, $d$ = stopping distance after impacting the ground due t... | {
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Is dark matter inside galaxies different from dark matter in intergalactic space? I just read a text about astronomy and when talking about dark matter the author says:
[...], the dark matter responsible for the orbits of the stars in the Milky Way is probably different from the dark matter responsible for the orbit o... | Nobody knows what dark matter is, or even whether it exists (see for instance this link). So asking how many kinds of dark matter there are is like asking how many angels can dance on the head of a pin.
| {
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Justification for excluding gravitational energy from the stress-energy tensor I did general relativity years ago at Uni and was just revising with the aid of Dirac''s brilliant book; the beauty of this book is that it is so thin and concise. On reading this book I find that I have a few questions regarding energy.
One... | The simplest way to see this is that by the equivalence principle, we can always let the gravitational field at any point have any value we like, including zero. Therefore there is no possibility of defining an energy density of the gravitational field at one point.
| {
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Cold fusion with ionized hydrogen and neutron radiation Would bombarding ionized hydrogen gas with neutron radiation cause cold fusion as the neutrons have no electrostatic repulsion to overcome therefore making it much easier to get within range of the strong force?
| You don't have to ionize the hydrogen, because the neutrons (to excellent approximation) do not see the electrons. Low-energy neutrons in hydrogen are captured to form deuterium. Because deuterium doesn't have any bound excited states, each capture releases a single 2.2 MeV photon.
In building a practical apparatus... | {
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Why do the expressions for an object rolling down an incline not depend on the coefficient of static friction? In my physics course, we are doing an experiment rolling disks and spheres down an incline (assuming there is no slipping). In doing the derivations (assuming a moment of inertia of $\frac25mR^2$ for sphere an... | For rolling without slipping the force of friction does no work. The force of friction provides the constraint that keeps the point of contact of the rolling object at rest with respect to the surface the object is rolling on. The magnitude of the frictional force while rolling without slipping can be determined by a... | {
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Momentum conservation in spontaneous pair creation and annihilation I know that in free space, photon cannot decay into an electron and a positron since momentum is frame dependent for massive particles while invariant for a photon.
Given this, how is spontaneous pair creation and annihilation possible? Can someone she... | Pair creation
You are right: In free space a photon cannot
decay into an electron-positron pair
(because it would violate energy/momentum conservation).
However, near an atomic nucleus a photon can decay
into an electron-positron pair.
In this process the atomic nucleus receives some recoil.
See also Wikipedia: Pair pr... | {
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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 ... | Why do you imagine the photon scattering rate to the be absorption rate? The scattering rate is the rate at which an atom absorbs AND re-emits incident photons. $\rho_{22}$ captures how excited an atom becomes for a particular incident field and $\gamma$ captures how quickly the atom decays and re-emits the excitation.... | {
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How do you pick the wavenumber at which the group velocitiy is evaluated? The equation for group velocity is
$
v_g(k) = \frac{d\omega}{dk}.$ This is obviously a function of $k$ but typically the word is used as if there is a single group velocity and not a whole function. How do you assign a group velocity to a "group... | It depends a bit on context. For transmission of signals in optical cables, the bandwidth is very small compared to the frequencies of the laser modes. So the meaning of group velocity is unambiguous. (But over a long distance, there will be noticeable dispersion, which limits the data rate.)
In a case like water waves... | {
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Is there a black hole information paradox in string theory? In string theory there is, for several black hole-like objects, a precise way to account for the microstates which make up the macroscopic Bekenstein-Hawking entropy. For instance for the black brane made of a bound state of $Q_1$ D1- and $Q_5$ D5-branes wrapp... | No. There is no information paradox in string theory.
The example you cite (the D1-D5 system) is a stable BPS configuration, so no evaporation is taking place and all the black hole microstates (correctly computed by string theory) are evolving unitarily because string theory does not modify the rules of quantum mechan... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 1,
"answer_id": 0
} |
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