Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
How unique is the length scale picked out by intelligent life? Our human bodies pick out a length scale (let’s say 1m). How unique is this scale and why did it arise?
In other words, how much smaller could humans, or multicellular lifeforms in general, be while sticking with approximately the same architecture of life... | Physicist Don Page estimates
the height of the tallest running, breathing organism on a habitable planet as the Bohr radius multiplied by the three-tenths power of the ratio of the electrical to gravitational forces between two protons.
This gives 3.6 meters for The Height of a Giraffe, which is the title of his pape... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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Confusion about circular motion So today in class, I learnt that the angular quantities are related to the linear quantities by
$$s = r\theta \qquad \qquad v = r\omega \qquad \qquad a = r\alpha$$
where it is assumed that the object travels in a perfect circle.
My teacher then went on to derive the formula
$$a = \frac{v... | The problem is the distinction between the radial (or centripetal) acceleration and the tangential acceleration (it is key to know the difference between them).
The radial acceleration (I will call it $a_r$) is always there in circular motion. It is the thing that keeps circular motion, changing the direction of the t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/508510",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Are there any physics formulas with high/large exponents? Most physical laws seem to only have low integer exponents for their variables - in my experience I've never seen a physical law containing variables raised to a power greater than 3 or occasionally 4. Are there any physical laws containing variables raised to l... | The exponents of laws become arbitrarily large when you start getting in to Multipole expansions. For a $2^N$-pole potential, the potential will fall off, to leading order, like $r^{-1-N}$ as $r\rightarrow\infty$ (with the force falling off like $r^{-2-N}$). This falloff goes even faster when you consider induced multi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/508797",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Confusion about Ohm's law So does ohms law say if the resistance is increased the voltage will also increase but not the current? And in non ohmic conductors the current increases with the voltage even though the resistance is also increasing? (meaning it shouldn't but still is, defying the law thereby)
| So does ohms law say if the resistance is increased the voltage will also increase but not the current?
Well that is true (in a strange kind of way) but it would be better to say: if the resistance is increased, it will require an increase in voltage to keep the current the same.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/509154",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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"answer_id": 2
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Salt and electricity Recently, I did an experiment with salt and electric current. I set up an open electric current in a used battery holder where the missing part of the circuit is two metal plates. I then fill this open space with table salt. Then, I close the circuit by putting a 3V battery inside the battery holde... | It sounds like the electric field (perhaps added by the current flow) turned the salt crystals into electric dipoles, which were then attracted to each other and to the charged plates.
| {
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"url": "https://physics.stackexchange.com/questions/509352",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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What helped Einstein to provide a more accurate description of gravity than Newton? Newton's explanation of gravity as an attractive force seems to have been superseded by Einstein's explanation of gravity as warping of space-time. Was there any advances in math and science that was not known in Newton's time, that wou... | Riemannian geometry, the mathematical basis for General Relativity, was unknown in Newton’s day. The only geometry available to Newton was Euclidean geometry.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/509650",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "22",
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derive the density of water from its molecular structure? Is it possible to derive the density of water by looking at its molecular structure?
Is there a theoretical formula that describe the dependence with temperature?
Thanks for the help!
| I might have a qualitative picture which has some naive, quantitative implications. I'm not sure how accurate the results would be.
In the Bohr model of the atom, we basically have the electron orbiting the proton at a position where the kinetic energy matches the potential energy and the angular momentum of the electr... | {
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Mean Gravitational 'Potential' Energy in Space Imagine an arbitrary point in space. It is within the gravitational 'potential' of every mass (although billions of ly away) in the entire universe.
Since every mass adds a tiny fraction, what is the total gravitational 'potential' energy in this point?
Edit:
Let point ma... | It seems to me you are asking about gravitational potential, not gravitational potential energy, since gravitational potential energy is property of some object and not space.
First of all, potential must be specified against some reference point. The Universe as we understand it today is homogeneous and isotropic at l... | {
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Why does it seem everything I push moves at a constant velocity? I am aware that a constant force causes a constant acceleration but friction can counteract this. However, if I push something across a table, for example, it seems no matter how hard I push, the object travels at a constant velocity, even if I apply more... | It's very difficult to apply a constant force to a small object with your hand. Your hand will move at the speed your brain commands it, rather than applying a constant force.
Try pushing something very heavy, such as a boat, car, or a trolley stacked with drinks, stones or another person. Then you will have to push wi... | {
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Einstein's initial clue that spacetime is curved I did General Relatively years ago at Uni. I have revised a lot of the maths demo Dirac''s book. It is incredible the leap in thought to noting from the Bianchi identities that the curvature term's on the left might equal the stress tensor energy tensor on the right. But... | The field form of the Newton gravitational law: $\nabla^2\Phi = 4\pi G\rho$, where $\Phi$ is a scalar field and $\rho$ is the density of matter might have been a starting point.
But a relativistic equation should be a tensor equation.
If we replace the scalar field with a tensor field, the Ricci tensor can be thought a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/510275",
"timestamp": "2023-03-29T00:00:00",
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To lift an object, do we need a force equal to its weight, or greater than its weight? We have all heard people saying that to lift an object of mass $m$, you have to apply a force $F$ equal to its weight $mg$. But isn't it getting the force equal to its weight from the surface to which it is attached to (normal force)... | Yes we apply a slight greater amount of force at the beginning and then we lift it up in equilibrium condition.In fact in extremely small amount of time the object gains some velocity when we apply a force just greater than its weight.After that extremely small period of time we can lift the particle up in equilibrium.... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/510399",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What problems (other than crypto) can quantum computing solve? So my (limited) understanding of quantum computing lends its self very well to breaking public-private crypto; by being able to factor products of large primes.
However in some press releases (google quantum supremacy, october 2019) I saw vague press copy, ... | The quantum algorithm zoo gives a lot of examples, ranging from the theoretically interesting to the possibly practically useful.
Some examples of algorithms that may (if quantum computers get good and the algorithms don't have too much overhead) be useful: factoring numbers, decoding some error correcting codes, const... | {
"language": "en",
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Can a photon be split?
*
*A photon is pure energy, zero mass.
*Different photons have different wave length and carry a different amount of energy.
Now, it seems logical that a high energy photon can be split into 2 low energy photons.
I don't know if this could happen via some natural decay or under an external i... | Yes, you are right. Spontaneous parametric downconversion is one way that a high - energy photon can be converted into two low-energy photons.
| {
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Diode Diffusion Capacitance I'm confused on the topic of diffusion capacitance in a diode. In the book, Solid State Devices by Streetman and Banerjee, I see an equation for the diffusion capacitance which gives an exponential dependence on voltage. However, there is also this figure:
I do not understand why the diffus... | The diffusion capacitance is capacitance of a diode when small forward bias is applied ie.,$V_f (\text{forward voltage})<V_{\gamma} (\text{cut in voltage})$. So as the diode is forward biased increases the capacitance increases according to the formula up to cut in voltage, after that the diode barrier breaks and start... | {
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Why can't we define more Maxwell's relations? Let us define a new thermodynamic function $X$ such that,
$$dX = TdS + PdV$$
where $T$ is the temperature of the system, $S$ is the entropy, $P$ is the pressure and $V$ is the volume.
Now since $X$ is a state function (if it isn't, then explain why?), we can derive some rel... | The other answer is good, but it seems to stop short of actually explaining why:
$$dX = TdS + pdV$$
cannot be an exact differential. This is because $dU=TdS-pdV$ is exact and so if $dX$ were we would also have:
$$d(X-U)=2pdV$$
being exact. But you can check for yourself that it isn't.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Product rule of variations I am deriving the Einstein equation using the Einstein-Hilbert action:
It is obvious that the variation in the Riemann Tensor is calculated from a variational product rule. What is not obvious to me is why variations obey this rule, and I'll like an explanation.
| It's a fundamental property of infinitesimal variations $\delta$ that they are linear derivations, i.e. they obey Leibniz product rule. Short of a rigorous definition of infinitesimals, the proof is basically to consider variations as 1-parameter families of functions, and then differentiate wrt. the parameter, cf. abo... | {
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What does the magnitude of centripetal acceleration actually represents? A fan moving with an angular velocity of 5π rad/second has a centripetal acceleration of 175.185 m/s^2.The Centripetal acceleration doesnt express the change in velocity as it is constant. Then what does 175.185 m/s^2 actually represents?
| Suppose that there is an object moving at constant speed $v$ in a circle.
In a time $\Delta t$ the velocity of the object changes from $\vec v_{\rm old}$ to $\vec v_{\rm new}$ as shown in the diagram below.
A velocity vector triangle can be drawn showing that $\vec v_{\rm old}+ \Delta \vec v = \vec v_{\rm new}$. ... | {
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"timestamp": "2023-03-29T00:00:00",
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Why the emitted photon has exactly the same energy,phase and direction as the incident photon in stimulated emission? My textbook says:-
When an atom emits a photon due to its interaction with a photon incident on it,the process is called stimulated emission.the emitted photon has exactly the same energy,phase and dir... | You are basically asking about direction and frequency.
*
*Direction
You need a background photon field, and population inversion. Basically spontaneous emission happens in a random direction, and stimulated emission happens in the direction of the background photon field.
The background field creates extra photon... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/512269",
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What's the link between Eulerian/Lagrangian approaches and macroscopic/microscopic point of view? From what I know, in fluid dynamics, the Eulerian approach studies points that are fixed in space and time, while the Lagrangian approach studies individual particles and follows them.
Is it correct to say that the Lagrang... | The Lagrangian or Eulerian formulations make no specific distinction in size—they merely relate to whether you are tracking the properties at a point or volume of space (Eulerian), or the properties of a point or volume of “something” which moves along with whatever flow field that causes said “something” to move (Lagr... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/512359",
"timestamp": "2023-03-29T00:00:00",
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Double slit experiment with electron one at a time I understand how a wave create the interference pattern, but what is the mechanism for a single electron after it pass the slit and scatter and land at different location on the screen to produce the same interference pattern.
Does the electron pass through one slit or... | The electron doesn't really interfere with it self but it act as if it does so by avoiding regions with destructive interference and hitting the screen where it should when it would constructively interfere with its hypothetical self coming from the other slit, thus, there is a higher probability of it hitting the scre... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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What dictates the set of microcanonical ensembles of a system in the canonical ensemble? So in the canonical ensemble we have a system inside of a heat reservoir, which can exchange energy with the system. This means the energy of the system is not necessarily a constant value but determined effectively by the local en... |
So in the canonical ensemble we have a system inside of a heat reservoir, which can exchange energy with the system. This means the energy of the system is not necessarily a constant value but determined effectively by the local energy distribution of the reservoir.
I would say that "this means the energy of the syst... | {
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How friction force synchronize linear velocity and angular velocity? I am doing a simulation about moving balls on a surface. There are frictions between different balls and the surface. In the beginning, balls have a linear velocity and an angular velocity (which are independent from each other), then because of the f... | When there is friction $f$ acting on a ball of mass $M$ and radius $R$, the friction delivers both linear impulse and angular impulse to the ball. In a time step $\Delta t$, the change in linear velocity is
$$ \Delta v = \frac{1}{m}f\Delta t $$
whereas the change in angular velocity is
$$ \Delta \omega = \frac{1}{I}fR... | {
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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 ... |
I would prefer an accuracy to at least one hundredth of the stone size.
*
*Weigh the stone.
*Dip the stone in thin paint; let excess drip off.
*Weigh the stone.
*Repeat steps 1-3 with a square, 1 cm2 object.
Divide the weight of the stone's paint by the weight of the square's paint to get the surface area of ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/512834",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "140",
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Velocity in SHM
By book defines SHM as
Simple harmonic motion is defined as the projection on any diameter of a graph point moving in a circle with uniform speed.
but in the next line it says -
Moving back and forth along the line AB, the mass point is continually changing speed vx' Starting from rest at the end p... | This isn't the definition of SHM I would go with, but it is equivalent so we'll run with it for now.
The point is that the particle moving around the circle at uniform speed is purely fictitious, the real particle is its 'shadow' moving back and forth along the $x$ axis. If you visualise this for a bit, you should see ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/512900",
"timestamp": "2023-03-29T00:00:00",
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How does an traceless symmetric tensor of rank two $S_{ij}$ transform under $SO(3)$? The irreducible tensor representations of $SO(3)$ all have odd dimensionalities given by $2j+1$ with $j=0,1,2,3,...$ etc. The representations can be designated by their dimensionalities as ${\bf 1}, {\bf 3}, {\bf 5},...$ etc, and they ... | I think this was answered recently. The skew symmetric $A_{ij}$ transforms in the vector "$3$" repesentation in the same way as $V_i =\epsilon_{ijk}A_{jk}$. This is because $\epsilon_{ijk}$ is an invariant tensor under SO($3$). All such invariant tensors can be regarded as Clebsh-Gordan coefficients. For examble the v... | {
"language": "en",
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Why don't people just put a water sprinkler on their roof for cooling? Some air conditioners work with evaporative processes. So I'm not sure why people wouldn't just use a sprinkler that turns on for a minute every hour or half hour or whatever in order to wet the roof. The water will not only absorb the heat from the... | There are products sold that are intended to be connected to the outside water supply of the home and blow a fine mist towards an area where evaporative cooling is desired, such as an outdoor deck that gets very hot in summer. I have one. It works pretty well.
The product mimics the cooling one experiences under a sha... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/513189",
"timestamp": "2023-03-29T00:00:00",
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Wightman quantum field - Interpretation I have a question regarding the interpretation of the Wightman quantum field in mathematical quantum field theory.
A quantum field $\phi$ is a operator-valued distribution. This means that $\phi$ is a linear function
$$\phi:\mathcal{S}(\mathbb{R}^{n})\to L(D,\mathcal{H}),$$
wher... | These smearing functions are closely related to the single particle wave functions.
Fix a decomposition of spacetime into space times time. Fourier transform the space coordinate. In the special case $f(t,p) = \delta_0(t) \psi(p)$, which can be reached by taking a family of gaussian approximations, the operator $\p... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/513330",
"timestamp": "2023-03-29T00:00:00",
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Role of friction during Collisions Normally, in questions of collisions, we tend to apply conservation of momentum (and in cases of elastic collisions, conservation of energy as well) and we usually ignore the frictional force acting. But what actually happens, when friction is to be accounted for, theoretically, and m... | With friction operating in the system between the two bodies while impact(elastic),mechanical energy conservation law still holds good because in elastic impact friction doesn't do work as it is instantaneous(somewhat impulsive).
Linear momentum may be conserved if there is no external force on two bodies but as fricti... | {
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"url": "https://physics.stackexchange.com/questions/513421",
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How and why Liquid helium climbs the walls of the container it is kept in? Liquid helium (He-II) shows a strange phenomenon, where it flows on its own, forming films across the surfaces of the container it is kept in. How and why this happens and how is it possible?
| After doing a quick research, on physics.stackexchange is no answer to your question. So I share my own thoughts with you.
At very low temperatures the energy exchange between the atoms respectively molecules in the helium is reduced to a minimum and the chaotic movement of the particles is negligibly low.
Electrons ... | {
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"url": "https://physics.stackexchange.com/questions/513527",
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Question about quantum fields, elementary particles, and quantum numbers, and fundamental forces As I understand it the allowable spin states of elementary particles is tied to the number of space and time dimensions, so for any two universes with the same number of space and time dimensions the allowable spin states w... | I think this question is too broad to be answered in any specific way.
We suspect that there could be different interactions in addition to electroweak, strong, and gravitational, but they could act on an energy scales that are not currently possibly to achieve in the lab or on LHC. Even if a different universe has exa... | {
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"url": "https://physics.stackexchange.com/questions/514093",
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A problem on thermal stress Here's the question:
There are 2 rods placed between rigid supports. Where $Y_{i}, \alpha_{i}$ and $A_{i}$ are the Young's Modulus, Coefficient of linear expansion and Cross sectional area of the rods. When the system is heated to temperature $\theta_{2} $ from $\theta_1$, find the relation... | The confusion is in part the difference between making a theoretical force balance and determining in practice force from stress. A theoretical free-body force balance is made at a point. Stress $\sigma$ is converted in practice to force $F$ using area $F = \sigma A$. To convert the latter (area) reference frame to the... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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On the distribution of sugar on water How could I get a function (at least a good approximation of it)that describes the density of the sugared water in relation with time and the dimensions of the container that holds the water? Consider that the sugar is sprinkled on the surface of the water. Fell free to use powdere... | Due to the second law of thermodynamics and diffusion, entropy of this system will increase and, when time approaches infinity, the sugar distribution should be uniform, if dimensions of the container are finite.
| {
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"url": "https://physics.stackexchange.com/questions/514288",
"timestamp": "2023-03-29T00:00:00",
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Creating Em waves Is it necessary for creation of em waves be from same source.
If a positive charge particle and negative charge particle is accelerating with same acceleration will the em waves created be identical in all aspects?
| You can think of an EM wave as a transverse disturbance introduced into a preexisting radial electric field (accompanied by a magnetic field). If you had identical positive and negative charges oscillating side by side, the two waves would be out of phase. They cancel each other and you have no wave from a net zero c... | {
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"url": "https://physics.stackexchange.com/questions/514429",
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How to mathematically find principal axes frame for a random distribution of mass $\rho(r)$? How to mathematically find principal axes frame for a random distribution of mass with density $\rho(r)$? That was, how to find the origin and orthonormal basis such that the moment of inertial matrix was diagonalized?
| Use any Cartesian coordinate system to compute the moment of inertia tensor. It will be symmetric.
Find its eigenvectors and eigenvalues, considering it as a matrix. The eigenvectors give the directions of the principal axes in the original coordinate system. Because the matrix is symmetric, they will be orthogonal; yo... | {
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What's 'force per second'? For example, if a force of 10 N per second (10 N/s) is applied to an object, does this have a name or a definition? I'm not referring to impulse - which is Ns.
An airplane's engine thrust is simply given as a force, but this must be a force applied by the engines each second (N/s)?
Thanks! ... | A force is an "instant" phenomenon so to speak. It might depend on time and be applied for a certain period of time. It may do work, such as your airplane thrust, and you can find the energy it transfers as $$W(t_0,t_1)=\int_{t_0}^{t_1} \vec F(t) \cdot \vec v(t) \;dt$$
At each instant, an infinitesimal amount of work $... | {
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What vector field property means “is the curl of another vector field?” I'm an undergraduate mathematics educator and I teach a lot of multivariable calculus. I posed this question on MSE over four years ago and I haven't gotten any definitive answers (despite 12 upvotes and a bounty posted). It could be there's no a... | I think it’s just called a solenoidal field (incompressible field), because by definition, if we have $\mathbf{\nabla}\times \mathbf{A}= \mathbf{V}$, $$\mathbf{\nabla}\cdot(\mathbf{\nabla}\times\mathbf{A})= \mathbf{\nabla}\cdot \mathbf{V }=0$$
because the divergence of the curl is 0. Because of this, any field that can... | {
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Is there some truth to the often told story that the running of couplings is the result of screening through virtual particles? It's a well established fact that coupling parameters changes with the energy scale at which we probe a given process:
A popular way to explain this phenomenon goes as follows. Particles are... | Basically I think that your explanation works. I would add the following intuition about the RG - following Wilson (his Nobel lecture is a wonderful read), I think it is useful to think of the RG as averaging over length-scales. For long wave-lengths (corresponding to low-energy), we average over large distances, meani... | {
"language": "en",
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Can we diagonalize optomechanical hamiltonian? The optomechanical hamiltonian is given as
$$\hat{H}=\hbar\Delta_{a}a^{\dagger}a+\hbar\omega_{m}b^{\dagger}b+\hbar g_{a}a^{\dagger}a(b^{\dagger}+b)$$
$a$ and $b$ are photonic and phononic operators and others are numbers.
Can a Bogoliubov transformation be made to such a... | Since the Hamiltonian in the question is not atmost a quadratic in bosonic creation and annihilation operators, it is not possible to reduce it to uncoupled form by just a combination of Bogoliubov and displacement transformations.
However it can be simplified by a generalized displacement transformation aka the Pola... | {
"language": "en",
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How does an AC circuit get anything done? if alternating current switches directions back and forth periodically it seems like to me that current would go forward a bit and then almost immediately back track the exact same distance, if this is the case then how does AC ever get to where we want it to? Could I be miscon... | Alternating current transmits powered by varying electric fields which makes the electron oscillate this oscillating energy transmitted through the wire in the form of electric fields and the energy is transmitted where it needs to be transmitted.
For example in a electric heater the alternating current oscillates ele... | {
"language": "en",
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Because things smell, is everything evaporating? Everything, in theory, can have a smell, but that is not the whole point of this question.
My main query is, since things do smell, does that mean that everything is slowly evaporating (or, sublimating, I suppose)?
For example, if we perceive metal to have a scent, this ... | Well. "Everything smells" breaks just at consideration of methane. Simple molecule $CH_4$ does not smell. Water $H_2O$ does not smell either. Most gases, in fact, do not smell. "Smelling" tends to be achievable only when reactivity of molecule is high enough. Consider ozone $O_3$, it smells because it is unstable $2O_3... | {
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Why do we slip while trying to run on a wet floor but we don't slip when we walk slow and steady? When we try to walk( or run) on a wet surface we tend to slip but on the same wet surface when we walk slowly, it is likely that we won't slip ?
Why is it so? What is the role of friction here ?
|
When we try to walk( or run) on a wet surface we tend to slip but on
the same wet surface when we walk slowly, it is likely that we won't
slip ? Why is it so? What is the role of friction here ?
When we walk or run our foot applies a pushing force backwards against the ground. Per Newton's third law, the ground a... | {
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Suppose you have airflow through a narrow glass tube. Does the air slip at glass surface? I was just pondering a silly physics problem where air is made to flow though a narrow tube. For a viscous fluid and laminar flow through a pipe you have the
Hagen–Poiseuille equation.
$\Delta P=\frac{8\mu L Q}{\pi R^{4}}$
I beli... | ‘Viscous’ doesn’t mean ‘sticky’. It means “the fluid exerts force against adjacent slip”.
The viscosity of air or water is less than treacle, but it’s still non-zero. Air next to a non-moving surface will feel a force that’ll tend to make it stop. Smaller viscosity means less force, but that just means a less massive ... | {
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Heisenberg uncertainty principle in single slit diffraction I have a question about the vertical uncertainty (z direction in the diagram below) for an electron in a single slit diffraction experiment.
Would it be correct to take the uncertainty to be $3\mu m$, half of the slit width?
Thanks
| You need to have some info on the momentum of the electrons $p$. Using the uncertainty principle we can write
$$
\Delta z=L\Delta \theta=L\frac{\Delta p_z}{p}\approx L\frac{\hbar}{2d\cdot p}
$$
So if we know $p$ we can calculate $\Delta z$
| {
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Problem observing secondary flow in the Tea Leaf Paradox I read about the Tea Leaf Paradox on Wikipedia, but didn't understand enough, so I wanted to see the secondary flow with an experiment. I set it up and filmed this. It's water and some tea from different tea bags. I stir it for a minute and then see what happens ... | It is necessary to take a photo from above, then you can see the toroidal vortex as in the first frames in Fig. 1
In the numerical model, it is possible to determine the velocity field in a liquid and the particle trajectory as in Fig. 2
| {
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Is there SSB in IQHE? The Wikipedia page on FQHE mentions that the discovery of FQH states is significant partly because it shows the limits of Landau's symmetry breaking theory, since different FQH states all have the same symmetries. But isn't it true that IQHE, which was discovered two years earlier, also doesn't fi... | IQHE is a topological phase transition, but it’s non-interacting. FQHE is also a topological phase transition, and it involves interactions.
IQHE is therefore a special (“boring”) case of FQHE.
The Ginzburg-Landau theory of phase transitions relies on interactions. The potential energy usually looks like:
$$ V \propto ... | {
"language": "en",
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Parallel transport on the earth's surface, for a vector initially pointing down I am new to general relativity, and trying to understand parallel transport.
I want to transport a vector along a line of longitude, on a sphere, starting at the equator, and ending (just shy) of the North Pole. I want the vector to point ... | Locally the pendulum is always swinging relative to the local direction of gravity, in other words "down". That's true when you start at the equator and when you get to the pole. The real issue is if you take a closed path back to where you started. Start at (0,0) with pendulum swinging north-south and go north to t... | {
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Infinite number of microstates? I am having trouble in understanding the value of the number of microstates of a system, compatible with a given macrostate. I know the definitions and can perform the calculations. However when I start thinking about the problem of counting microstates in a intuitive way, I run into tro... | In a classical setting, (E, V, N) has a continuous energy spectrum, while the microstate picture makes logical sense only if there is a discrete energy spectrum; for the continuous spectrum its equivalent is the density of states.
To see how this makes sense, try to derive Boltzmann's equation from the second law (hint... | {
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Why do we need 3 variables to parametrize $\scr{I}^\pm$ in a Penrose diagram? In the figure we can see the Penrose diagram for Minkowski space
If I understand correctly, $i^-$ and $\scr{I}^-$ have coordinates $r=\infty$ and $t=-\infty$ while $i^+$ and $\scr{I}^+$ have coordinates $r=\infty$ and $t=+\infty$. I would th... | Here's another way to think about it. It's true that both $r$ and $t$ go to infinity, but the surface is still three dimensional for the following reason. If $u = t - r$, and $r \to \infty$ while $u$ remains fixed, then $t = u + r$ should be thought of as $t$ "shifted by an infinite constant." While $r$ is "set" to inf... | {
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Can the forces change with frame of reference? Consider a ball kept on man's head (mass $M$) on the Earth. Now supposing I throw the ball from height $h$ of tall building then why does he gets more hurt? Isn't the force still mg?
I would like to know what happens in ideal case (no air resistance)
and then in real case ... | The force is no longer $mg$. In the second scenarion the ball has a speed $v(h)$ just before it hits the person's head. If the speed of the ball is slowed down from $v(h)$ to $0$ by the head in time $\tau$, then the total force felt by the head is:
$$F_{head}= M\frac{v(h)}{\tau}.$$
In the first scenario there is no suc... | {
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Modelling a particle under the influence of an electric field with a restoring force Suppose I have a particle under the influence of an electric field. The particle is also attached to a spring. The particle should therefore feel the influence of two forces such that the total force is then:
\begin{align}
F_T &= F_E +... | The general trick is to convert the one second-order differential into two first-order ones. This is done by introducing an extra variable to carry around:
\begin{align}
\frac{\mathrm dv}{\mathrm dt}&=f(x,\,t)\\
\frac{\mathrm dx}{\mathrm dt}&=v
\end{align}
for whatever function $f(\cdot)$ you need.
This can easily be a... | {
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Tension in a massless string being pulled at its ends with unequal forces There is a question in my textbook. If a massless inextensible string is pulled on with a force of $10 N$, at both ends, what is the tension in the string?
It’s a very common question. The answer is $10 N$, cf. e.g. this & this Phys.SE posts. It... | Consider a variation on the Atwood machine where instead of hanging straight down, the two masses $m_1$ and $m_2$ each sit on a separate frictionless plane at an angle of $\theta_1$ and $\theta_2$ to the vertical. The planes are joined along a ridge and the string connecting the two masses runs over the ridge, again wi... | {
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Does the J/$\Psi$ primarily decay into real gluons? so apparently the this cool looking decay of the $J/\Psi$ particle is OZI suppressed, which was confusing to me, because the Particle Data Group (link) says that 64% of its decays are into 3 gluons (as does wikipedia). So my question is, do I misunderstand what the PD... | Hot tip: read the PDG listing mindful that the partial widths given, $\Gamma_1-\Gamma_6$ are not mutually exclusive! (Your $\Gamma_{80}$ is in $\Gamma_{3}$ and $\Gamma_{1}$.)
That is, the BRs must sum to 100%.
So, roughly, you either look at real particles in your detector,
$$
\Gamma_1 + \Gamma_5 + \Gamma _6 \sim \G... | {
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Generalised measurements and collapse My reference is Nielsen and Chuang's "Quantum Computation and Quantum Information". When introducing qubits, $|\psi\rangle=\alpha|0\rangle+\beta|1\rangle$ the authors state that
(*)When we measure a qubit we get either the result $0$ with probability $|\alpha|^2$, or the result $1... | Whether a state is in superposition depends entirely on what your measurement basis is. Changing your measurement basis will change what states are in superposition with respect to that basis.
For example, let $|0\rangle$ and $|1\rangle$ be the states with definite spin in the $z$-direction, and let $|+\rangle$ and $|-... | {
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Is there a Lagrangian action that leads to gradient descent? It is well-known that Hamilton's equations $$\dot{x}^\mu=\Omega^{\mu\nu} \frac{\partial H(x)}{\partial x^\mu}\tag{1}$$ where $\Omega$ is the symplectic form and $x^\mu=(q,p)$ follow from a Lagrangian, namely $$L(x)=\dot{q}p-H(x).\tag{2}$$
Gradient descent is ... | Ok, I think I figured out the argument: For gradient descent, all solutions around a global minimum will converge to this minimum. As (time-independent) Lagrangian dynamics is equivalent to Hamiltonian dynamics, it is clear the energy (value of Hamiltonian) is preserved under time evolution. By continuity, the value of... | {
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Why does atmospheric pressure act on us? I have a bit of misconception about weight which I want to clarify.
The air pressure is explained as the weight of the air column above our head acting per unit area. But since air is not continuous how can the weight of all the air molecules (above our head) be acting on our h... | The very top air molecule of our atmosphere is attracted by gravity. So it has a weight.
*
*The second-top-most molecule thus must carry the weight of the top-most molecule.
*The third-top-most molecule must hold back against both the force on the second-top-most molecule as well as the weight of it - so it must c... | {
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Should damping ratio increase or decrease with increase in mass? I'm currently doing a small project in college for structures being damped. We're adding weights to a structure and measuring the damping affect. We've calculated the damping ratio and coeffecients, however, we currently have damping ratio increasing with... | I assume that your structure is a simple single spring mass damper system?
For such a system the assumption of decreasing dampingratio $\zeta$ for increasing mass $m$ is correct. You need more dampingforce to stop a heavier system, therefore resulting in a smaller $\zeta$.
In reality though it could be that the additio... | {
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Where does the power delivered to car's wheels go? Okay, so power is work/time. Most cases, when power is provided to something, energy is gained as kinetic energy or lost to friction.
But in a car, the engine puts power ( torque x rpm/5252) to wheels, but very little ends up in the wheels, assuming friction keeps them... | When the engine applies a torque on the wheels via the gear mechanism, the wheels want to spin around, but the mass of the car and the friction between the road and the tires constrains it. So the only way is to move the vehicle forward. The friction between the tires and the road provides the necessary traction to do ... | {
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Why is frequency a fundamental property of waves? We are taught that although wavelength can change from one medium to other, frequency of a wave doesn't whenever Velocity varies in different media.
But why at a deep level, is frequency so fundamental? Why can't both frequency and wavelength change? Or why isn't wavel... | When modeling waves, we require that the amplitude of the wave is continuous across the boundary between media - in other words, we require that there is no infinitely-sharp change in amplitude at the boundary. This means that in a sufficiently small region around the boundary, the amplitude of all of the points must b... | {
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I can't understand one of deduction in Simple Harnomic Motion, can anyone help? source:http://farside.ph.utexas.edu/teaching/336k/lectures/node18.html#e4.8
in order $x=0$ to be a stable equilibrium point we require both
$$f(0)=0$$
and
$$\frac {df(0)}{dx}<0$$
Now, our particle obeys Newton's second law of motion,
$$m \f... | On a previous web page the author notes that the force and the potential energy are linked via the relationship $f(x) = - \frac {dU}{dx}$.
The condition $f(0)=0$ is there a statement that the potential energy needs to be a turning point at $x=0$ and $\frac{df(0)}{dx}<0$ that the potential energy needs to be a minimum... | {
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Force produced by muscles proportional to area or volume? I've heard it said that the force a muscle can exert is proportional to its cross-sectional area. It seems to me it should be proportional to length also. If you have someone pulling on a large block, you could increase the force by getting another person to pul... |
you could increase the force [...] by attaching a rope to the block and having both of them pull in series on that one rope
No, this doesn't work. In the series arrangement, their forces don't add. However, the work they do does add.
This is all exactly in analogy to the way muscles work. The force a muscle can do is... | {
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Why do the $L_z$ and $L^2$ operators share eigenfunctions, but the $L_x$ and $L_y$ operators don't? In my lecture notes the following was written:
I would understand in the case of an applied field if there was some symmetry breaking feature which would allow for a preferred axis or something which could explain why ... | It is possible to have a simultaneous eignfunction of ${\hat L}^2$ and one other component of the angular momentum. Typically this is taken to be ${\hat L}_z$, but it could just as well be the $x$ or $y$ component - there is nothing special about $z$. This is known as "choosing a quantization axis".
| {
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What's the projection operator for topological insulator with three band crossings For weyl semimetal whose Hamiltonian is $\hat H= v_f \ \vec k \cdot \vec\sigma $ [1,2], its eigen value is $\epsilon_ {\pm}=\pm v_f k $, thus the hamiltonian can be written as $\hat H= \frac{1}{2}\epsilon_+(I+\hat k\cdot \sigma)+\frac{... | If you know the eigenvalues, you know equation obeyed by $H$ is
$$
0=(H-E_1)(H-E_2)(H-E_3).
$$
Then the algebraic identity
$$
1= \frac{(H-E_2)(H-E_3)}{(E_1-E_2)(E_1-E_3)}+ \frac{(H-E_1)(H-E_3)}{(E_2-E_1)(E_2-E_3)}+ \frac{(H-E_1)(H-E_2)}{(E_3-E_1)(E_3-E_2)}
$$
becomes the orthogonal projector resolution of the identity... | {
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Radiation of a distant point source In class, starting from the Maxwell equations, we showed that :
\begin{equation}
\mu_0 \vec{J} = (\frac{1}{c^2} \frac{\partial^2{}}{\partial{t^2}} - \vec{\nabla^2})\vec{A}
\end{equation}
Until there, no problem.
Then the teacher said that :
\begin{equation}
\vec{A}(\vec{r}, t) =... | One way of deriving it is by looking at the solution for Poisson's equation
$$ \nabla^2 \phi = \frac{\rho}{\epsilon_0} \implies \phi(\mathbf{r}) = -\iiint \frac{1}{4\pi\epsilon_0} \frac{\rho(\mathbf{r'})}{|\mathbf{r}-\mathbf{r'}|} d\mathbf{r'}, $$
and introducing a time dependency in the most obvious way, evaluating t... | {
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Is it possible to conserve the total kinetic energy of a system, but not its momentum? It is possible to conserve momentum without conserving kinetic energy, as in inelastic
collisions. Is it possible to conserve the total kinetic energy of a system, but not its momentum? How?
To clarify, I am not necessarily talking a... |
Is there any scenario which we could devise in which momentum is not conserved but kinetic energy is?
When a ball bounces off the ground or a wall. The momentum is flipped but the kinetic energy stays about the same.
| {
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Does Birkhoff's theorem still apply to an ultra-dense spherical shell of matter falling into a black hole? In previous posts I discovered that the effects on space-time geometry of an ultra-dense stationary spherical shell yielded pretty simple equations but I imagine some sort of secondary non-linear effects start hap... | The Brinkhoff theorem was recently challenged in this 2017 paper:
Does Birkhoff’s theorem really hold?
The author claims that:
Birkhoff’s theorem is inconsistent with the post-Newtonian solution to Einstein feld equations for a dynamic spherically-symmetric system in the weak-feld limit. The time-spatial component of ... | {
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Work done by battery on a capacitor Work done by battery on a capacitor is QV/2, where V is the final potential across the capacitor plates an Q is the charge. I know that the Q charge which gets stored on the capacitor comes from the connecting wires. However, since
Positive charge on one plate is reducing (Assuming c... | Energy is transferred from the battery to the capacitor. Work is defined as a transfer of energy. Therefore, the battery does work on the capacitor.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/520606",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Reference request for a mathematical motivation for the Born rule I was reading the popular science book The Hidden Reality by Brian Greene. My question is about a part in the notes at the end of the book. It is chapter 8, note 9. Brian Greene describes a mathematical motivation for the probabilistic interpretation (i.... | Googling on the list of names in the footnote turned up the paper https://arxiv.org/abs/1405.6755, which led to Deutsch and the other references below.
Edward Farhi, Jeffrey Goldstone, and Sam Gutmann, "How Probability Arises in Quantum Mechanics," Annals of Physics, 192 (1989) 368, June 1989. http://www.sciencedirect.... | {
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Possible analogy to help students understand the Kelvin–Planck statement of second law of thermodynamics Let us consider a person has to transfer four bags upstairs to the top floor of a building.He Carries them one by one.Once he reaches the top floor, he has to return back to the ground floor to get the next bag. Wit... | The Kelvin-Plank Statement of the Second Law is "No heat engine can operated in a cycle while transferring heat with a single heat reservoir". What this means is no heat engine can take heat from a single reservoir and convert it entirely into work (100% efficiency) in a cycle. Some heat must always be rejected to a l... | {
"language": "en",
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Why is the normal contact force horizontal on an inclined ladder?
There is only one force acting on the ladder which is its weight and it acts vertically downwards. Then why does the normal contact force from the vertical wall act horizontally on the ladder? There must be a horizontal force acting on the wall to exert... | Normal forces are always perpendicular to the direction of possible slipping since they do no work. Zero work means they must be perpendicular to any displacement or motion.
Since the ladder can slip downwards at the top, the only possible direction for the normal force is horizontally.
You can think of normal forces a... | {
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Correct way of viewing a (1,1)-tensor returning a vector I am currently watching this excellent video series building up to general relativity. We have finally started looking at tensors and a question came up from the audience which (to my understanding) was asking why tensors are defined as multi-linear maps from set... | This kind of trick is common when thinking about tensors.
Let $v$ be a vector, $\alpha$ a one-form, and $c$ a number. A vector gives a map from one-forms to numbers,
$$\alpha \mapsto v(\alpha)$$
but it also gives a map from numbers to vectors,
$$c \mapsto c v.$$
Similarly, a $(1, 1)$ tensor $T$ gives a map from a vect... | {
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Why don't we define potential due to a magnetic field? We define electric potential and gravitational potential and use them quite often to solve problems and explain stuff. But I have never encountered magnetic potential, neither during my study (I am a high-schooler), nor during any discussion on physics.
So, does ma... | A charged particle in a magnetic field maintains its kinetic energy. You can see this from the fact that $\vec{F}_B \propto \vec{v} \times \vec{B}$ which means that $\vec{v}\cdot\vec{F}_B=0$ and therefore the force by the magnetic field cannot preform any work on the particle
$$ W_B = \int \vec{F}_B \cdot \vec{dx} = \i... | {
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"timestamp": "2023-03-29T00:00:00",
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Why is there a "blue hour" after the "golden hour"? There's a great story about why the sky is blue during the day, and turns golden during sunsets:
Rayleigh scattering affects blue light more. During the day, blue light from the Sun is scattered towards us from all directions, causing a blue sky. During the sunset, t... |
The Chappuis absorption bands occur at wavelengths between 400 and 650 nm. Within this range are two absorption maxima of similar height at 575 and 603 nm wavelengths
As seen here in the optical wavelengths , most of the visible light on the left of 500nm is absorbed, due to the large absorption lines leaving domina... | {
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Doubt regarding derivation of escape velocity In my text book the derivation goes like this:
The minimum speed required to project a body from the surface of the Earth so that it never returns to the surface of the Earth is called escape speed. If a velocity greater than the escape velocity is imparted, the body will ... | Here, the force is the force you are applying to the body, and not the force the Earth applies to it. As $F|_{by\,Earth} = -\frac{GMm}{r^2}\hat r$, and $F|_{by\,you} = - F|_{by\,Earth}$, $F|_{by\,you} = \frac{GMm}{r^2}\hat r$.
Thus, the force and displacement are in the same direction.
| {
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Driving a nail with a light object? I was wondering if it is possible to drive a nail through, for example, concrete by dropping a light object on the head of the nail over many iterations.
I.e. is there a certain threshold of force that must be reached for the nail to make even the slightest progress into the concrete... | My initial answer to that is no. This is because there is some maximum normal force $\vec{F_n}$ that the material can exert back on an object before it is deformed. Unless the object can exceed this $\vec{F_n}$, then it will not deform, and therefore not be driven through the material.
There are of course so further qu... | {
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Is the energy of an electromagnetic radiation the sum of the energy of each photon? In A.P. French's Special relativity the author said,
We suppose that an amount
$E$ of radiant energy (a burst of photons) is emitted from one end
of a box of mass $M$ and length $L$ that is isolated from its surroundings
and is i... | The answer is yes. The total energy is the sum of the individual photon energies.
| {
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Can you please explain me phenomenon of reflection at subatomic level? When we see atoms under an electron microscope, what exactly are we seeing? I mean, these spheres that we know as atoms are electron clouds and that is what we are seeing, am I right?
https://www.youtube.com/watch?v=pGWSX6pStd0
Can you please expla... | The linked video shows a TEM image. In transmission electron microscopy, you have a parallel beam of electrons incident on the material, which gets scattered by the atoms in the material. Note that, it is not just the electron cloud, but the potential formed by the atomic core (nucleus+ core electrons) and the valence ... | {
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How do we know that light travels slower in denser medium? What experiment can we do to verify it? How do we know that light travels slower in denser medium? What experiment can we do to verify it?
How did Fermat knew that light travels with different speed in different medium?
| The usual method of making precision measurements of the index of refraction of gasses is to put a tube on one leg of a two-leg interferometer (Michelson, Mach-Zender or similar), and rig it so that you can control the gas pressure inside the tube all the way down to vacuum. Then you observe the fringe shifts as you ru... | {
"language": "en",
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Can we determine the probability of finding an electron without a potential well? Can we determine the probability of finding electron in a region of space if there is no boundary condition?
For example, if the wall of a one-dimensional potential well is infinitely far away then is there a way that we can find the prob... | Yes. A good example is a wave packet for the free particle. The ordinary free particle solution is not normalisable, but you can construct another solution which is, the wave packet.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Energy power relation If we have an energy equation like
$E=A\sin(wt-kx)$
If we differentiate it w.r.t. time, we will get power.
If we again differentiate the last equation, it will be termed as power per unit time.
But what it will represent and what is it's significance?
|
But what it will represent and what is it's significance?
It will represent how quickly your power is changing. A positive value indicates that the power is increasing and a negative value indicates that the power is decreasing. As far as I know it has no particular physical significance.
| {
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Confusion regarding Faraday's law Suppose we have a rectangular coil placed in a uniform magnetic field and the coil is rotated at a uniform speed. Now, we know that due to the change in the magnetic flux linked with the coil that an induced current flows. What is the force responsible for this? Is it the magnetic forc... | The rotating coil with a changing magnetic flux linked with it has an electric field induced in it - Faraday’s law.
If there is a complete electrical circuit an induced current flows in the coil because of the induced electric field.
The direction of the induced current and the resulting magnetic field produced by ... | {
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Conservation of Angular Momentum for Rigid Bodies I have question about Conservation of Angular Momentum of Rigid Bodies. I've been doing some examples from Hibbeler's book, and noticed that in this chapter about Conservation of Angular Momentum of Rigid Bodies, there are some examples where we sum all the angular mome... | You can do it both ways, as the torque equation or conservation of angular momentum is valid for the center of mass of the system, or an inertial point. Here they did not use the moment of inertia directly about the point $A$ as to do that, you would have to find the distance of the center of mass of the system from th... | {
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Bekenstein–Hawking entropy: the proportionality constant and the 2D black hole The Bekenstein–Hawking entropy is defined by the relation
$$S=\frac{k_BA}{4l_p^2},$$
where $k_B$ is the Boltzmann constant and $A$ is the area of the black hole's event horizon in units of the Planck area $l^2_p$.
I am not familiar with bla... | *
*While there are proofs of $S= A/ 4$ (in natural units $\ell_p=1$, $k_B=1$), I think a good interpretation of the $\frac14$ is an open nonproblem (a good interpretation being subjective of course). The proofs are unenlightening as to the $\frac14$.
*If the black hole horizon has the topology of a $d$-sphere $S^d$ ... | {
"language": "en",
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Why the Real Scalar Field lagrangian has this form? The lagrangian of the Real Scalar Field $\phi$ is given by
\begin{equation}
\mathcal{L} = \frac{1}{2}\eta^{\mu \nu} \partial _\mu \phi \partial _{\nu} \phi - \frac{1}{2} m^2 \phi^2
\end{equation}
\begin{equation}
\eta^{\mu \nu} = diag(+1,-1,-1,-1)
\end{equation}
But w... | The Euler-Lagrange equation following from this lagrangian is the Klein-Gordon equation, which is the field theoretical equivalent of the special relativistic energy-mass-momentum equation.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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After what time, the configuration will repeat? A ball rotates at a rate $r$ rotations per second and simultaneously revolves around a stationary point $O$ at a rate $R$ revolutions per second $(R<r)$.The rotation and revolution are in the same sense.A certain point on the ball is in the line of the centre of the ball... | I will give this a try. Shift to the reference frame of the center of the ball. The point on the ball (call it A) now rotates wrt the center at an angular velocity $\omega_{1} = 2\pi r$ whereas the point O rotates around it at an angular velocity $\omega_{2} = 2\pi R$ in the opposite direction. [Since rotation and revo... | {
"language": "en",
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Do gravitational mass equalling inertial mass when object is at rest just a coincidence? Rest mass can be thought of as the measure of energy that object posses. This mass that appears in Newton law of motion measures inertia and hence called inertial mass. Gravitational mass is like charge in coloumb law and tells us ... | No one knows for sure. The equivalence of gravitational mass and inertial mass is one of the two primary assumptions of general relativity from which the theory was later developed. The other is that the laws of physics are isotropically invariant. While general relativity has proven very successful in regions of low s... | {
"language": "en",
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Effect of collector plate potential on photoelectric current with varying frequencies?
The above graph is from my physics book which shows the effect of collector plate potential on photoelectric current for different frequencies.
Inference from above graph:
*
*Since all the three frequency curve have same saturati... | Yes higher frequencies emit more electrons, and yes there will be less photons at the same intensity.
"The saturation current increases with the increase of the light intensity. It also increases with greater frequencies due to a greater probability of electron emission when collisions happen with higher energy photon... | {
"language": "en",
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How gravity time dilation affect radio wave communication? I'm not in any way an expert so sorry if my question is silly.
So i was wondering about a hypothetical situation. I'm orbiting a black hole and I'm trying to contact via radio with someone outside the gravitational effect of that black hole. As far I understand... | Simply put, if you are outside the event horizon, transmitting data by radio to someone farther from the black hole, there would be two main obstacles. While the transmission would move at the same speed as light, the frequency would be received more stretched out, redshifted, than what you sent. So the receiver would ... | {
"language": "en",
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Which physical quantity is represented by the surface integral of magnetic field? The answer is given as magnetic flux in one place and Gauss law of magnetism in another. So which one is correct and why?
| Magnetic field always circulate (in steady current situations) like this
So, if you take any closed volume containing the magnetic field you will find that field lines enter from one side and leaves from the other side, therefore, for any closed volume
$$ \oint_A \mathbf{B} \cdot d\mathbf{A} = 0$$ By divergence th... | {
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What happens to matter when it is converted into energy? According to Einstein’s equation
$$E=mc^2$$
Matter can be converted into Energy. An example of this is a nuclear reaction. What happens to the matter in the process? Do the atoms/subatomic particles just vanish? Any insights into this process are appreciated.
| Einstein, in his famous but rarely-read paper "Does inertia of a body depend upon its energy content?", didn't write that matter (or, better, mass) can be converted into energy. The way he stated its result was:
$$
\Delta E = \Delta m \cdot c^2,
$$
i.e. in the rest frame of any system, variations of mass and variations... | {
"language": "en",
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Maximum speed in a spring-mass system I am studying energy right now and I can use only gravitational potential energy, elastic energy and kinetic energy to solve some problems. My doubt is how can I prove that the maximum speed in a mass hanging on a spring is reached at the middle of the elongation of the spring.
The... | The total energy you have is Kinetic + Potential. And for a spring system, the potential energy is minimum when the spring is not stretched or compressed. But since energy is conserved, when potential energy is zero, all the energy in the system is present as kinetic energy. So kinetic energy is maximum when the displa... | {
"language": "en",
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Time in Lorentz transformation While doing Lorentz transformation for position
$$x'=\gamma(x-ut)$$
Here I understand that instead of just length contraction we also use the term
$$ut$$
To include the distances between the frames of reference.
But while doing Lorentz transformation for time that is
$$t'=\... | Let's consider two S clocks sitting at x1 and x2. These are synchronized to an observer in S and read the same time but they will not be synchronized to an observer in S'. The ux/c2 term has units of time and accounts for the phase difference, as observed in S', between the two clocks. I don't know if that is a suffi... | {
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If quarks change colours constantly how are proton and neutron stable relatively? Say for example a proton is composed of Up, Up and Down (valance) quarks and suppose the Down quark absorbs a gluon, Down quark must change colour in order to conserve colour charges but so must the other 2 Up quarks? Unless at any given ... | Yes, all the quarks & gluons in the proton are continuously exchanging gluons with their neighbouring quarks & gluons, and the total color charge must always add up to white, due to color confinement.
However, as the anim below (from Wikipedia, courtesy of manishearth) shows, the color changes of 2 valence quarks don't... | {
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Longest wireless transmission I've recently been asked (by a flat earther no less) how Exalt have managed to achieve a world record data/communications microwave link if the earth is indeed spherical (which it obviously is).
I pointed out that radio waves can travel via line of sight (his argument) or groundwave, skywa... | Some basic geometry reveals the following formula where $R$ is the radius of earth, $h$ is the height of the tower above sea level and $d$ is the distance traversed-
$$(R+h)^2=R^2+d^2$$ The coast of Lebanon is pretty mountainous with an average altitude of $2500{\text m}$. Considering they built a tower with a decent h... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/525540",
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Why is the spin connection for spinors? (Bundles) I'm trying to learn about spin bundles and find myself very confused by the construction and motivation of the spin connection.
The places where I've seen the spin connection formulated, it seems to be explained by the need to account for the change in the vierbeins - i... | I explain how to obtain the spin connection from the ordinary Levi-Civita connection in this answer of mine.
As for why we need the "spin connection" to express spinors, note that spinors by definition transform in a particular representation of the Lorentz algebra $\mathfrak{so}(1,3)$ (or its generalizations). But thi... | {
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Does work expend a permanent magnet? My understanding of a permanent magnet is that it has the potential to do work. This would seem to me to imply it has a kind of magnetic charge similar to how a battery is charged with energy. Does this imply that that using the magnet to do work will expend this charge causing th... | The reason one does not use permanent magnets alone for electromechanical devises, is because permanent magnets would rapidly lose their magnetization if energy is taken from them. The law of conservation of energy is always at work, and the potential energy turning into kinetic energy will deplete the magnetization o... | {
"language": "en",
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What is the Eigenvalue of $T^2$ ($SU(3)$ Casimir)? For example, in $SU(2)$, $\hat{S}^2|s,m_s>=\bar{h}^2 s(s+1)|s,m_s>$.
What about in $SU(3)$, $\hat{T}^2|T,m_3,m_8>=?|T,m_3,m_8>$ where $\hat{T}^2=\sum_i^8 T_iT_i $, $T_i = \frac{\lambda_i}{2} $, $\lambda_i$ is $SU(3)$ generator.
| The finite dimensional unitary representations of $\mathfrak{su}(3)$ have highest weights (eigenvalues of $\hat \lambda_3$ and $\hat \lambda_8$) that are non-negative integer linear combinations ${p \omega}_1+q {\omega}_2$ of the fundamental weights
$$
{ \omega}_1 =\left(1, \frac{1}{\sqrt 3}\right),\quad {\omega}_2... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Quantum mechanics position/momentum state operator proof Is there any way to prove
$$
e^{-i\beta p}|q\rangle = |q+\beta\rangle
$$
just by using these identities $$
[q,\mathcal{F}(p)]=i\hbar \mathcal{F}'(p) \;\;\;\;[q,p]=i\hbar
$$
in quantum mechanics?
| Yes, you just have to check that $e^{-i\beta P/\hbar}|q\rangle$ is an eigenket of $Q$ (uppercase represents operators) with eigenvalue $q+\beta$. We evaluate
$$
Q \big ( e^{-i\beta P/\hbar}|q\rangle \big )
$$
by using the first identity (which is actually a consequence of the canonical commutation relation):
$$
Q e^{-... | {
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"url": "https://physics.stackexchange.com/questions/526197",
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Why is work defined as $W=Fd$? I am trying to understand what work really means in physics. I seem to be missing the conceptual link. Every resource says that $W=Fd$ but that does not make sense to me.
If, say, an elastic object suspended in space where there is no drag or resisting force of any kind is pushed by a for... | The concepts of work and the associated conservation of energy were found to be useful (and hence formalized) for solving certain types of problems in mechanics. Over time it was discovered that they also gave consistent results in a wide variety of situations. So much so that many of us have come to think of energy a... | {
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Why does orbital overlap cause attraction? I have been taught that when orbitals overlap as in $\sigma$ and $π$ bonds, the formation of a bond (which is basically an attraction) takes place. Why does this cause attraction, shouldn't they repel? I get that electrons get paired up because they have opposite spins which c... | You are asking why the formation of covalent bonds between two (or more) atoms causes attraction (bonding) between them.
Now it is very important to understand that the more correct expression is the sharing of electron orbitals that causes this attraction (overlap is not even needed, when there is only one electron be... | {
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"url": "https://physics.stackexchange.com/questions/526545",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 4,
"answer_id": 2
} |
Does $Δs^2 = - Δ\tau^2$ imply two distinct metrics for spacelike and timelike displacements? Reading Misner-Thorne-Wheeler concerning the metric for spacelike and timelike displacements it seems to me that two different metrics must be distinguished, one metric for spacelike and one for timelike displacements - is this... | $g_{\mu\nu}$ is a matrix used to calculate "intervals". The sign of a given interval depends on what it is about: either it is a distance in space or it is a duration of particle motion.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/526683",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 2
} |
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