Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Why work is obtained from ordered molecular motion? I am trying to understand how entropy is actually a measure of randomness. The definition for Entropy is --> Entropy, the measure of a system's thermal energy per unit temperature that is unavailable for doing useful work. Because work is obtained from ordered molecu... | Heat is the transfer of energy that makes use of random motion (thermal motion). It is due to collision between molecules of bodies with different temperatures. It is random because linear momenta of the molecules are oriented at random, there's no preferred direction.
Work in thermodynamics is defined as in classical ... | {
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"timestamp": "2023-03-29T00:00:00",
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If I pull a metal bar for long enough with a constant small force, will it eventually break? Let's say I have a strong metal bar. I pull it apart with a very small constant force -- obviously it doesn't break. However, this would disturb the internal configuration. If I let go, then eventually the internal configuratio... | If in time no changes occur (whatever they are) in the elemental structure of the bar, then the bar will not break. If changes do occur, then there is a chance that the bar will break, so it eventually will break. How the breaking proceeds (breaking is a non-instantaneous process) is another story.
Taking quantum mecha... | {
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Is there an intuitive way to view the concept of momentum? Ideas like distance, velocity and force are very intuitive to understand because you can "see" their real-world applications and so one can come to understand them without having any knowledge of their mathematical formulas.
Momentum as it is defined is the pro... | If an object collides with you plastically its momentum is what knocks you back.
| {
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$PdV =VdP$ is true for any reversible cycles? My Question:
Does the following equation hold, at least for reversible cycles? If not, are there any special conditions that must be met for this to be true?
$$PdV=VdP$$
The reversible cycle can be drawn as a loop on the PV diagram. In one cycle, the work done by the cycl... | What is true is that
$$\oint P \, dV = - \oint V \, dP$$
because of the area argument you made, noting that the signs are opposite. From this, you can't remove the integral sign to conclude that $P \, dV = -V \, dP$, which is certainly not true.
The integral result is easy to show in general, as
$$\oint P \, dV + \oint... | {
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Can an LC circuit be used to produce and receive FM signal? By simply changing the frequency of oscillation of an LC circuit (which you can do with the capacitor alone) you could emit (and receive) FM signal.
Are LC circuits actually used to do that? If not, why not?
| Yes, indeed, these are the basis of radio and television. Although the actual generators, modulators, and receivers are usually more complicated than a simple LC circuits, the LC is the basis of it (see, e.g., heterodyne, which is the simplest mixing device, used for the amplitude modulation.)
The field of radio wave g... | {
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Are soundproof foam shapes reflective of audio frequencies? I came across a previous question regarding how soundproof foam absorbs sound: How does foam "absorb" sound? where the answer explains the properties of the foam itself rather than the shape.
However, in analyzing audio spectrogram images (and messing around w... | I did a bit of search engine searching with the following search string
shape of sound absorbing material physics
In that search I did not encounter information about the shape of the sound absorbing material. The informative pages I found had information only about the properties of the material itself, such as elas... | {
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Why does closing someone's eyes not give them near-sightedness? When we close our eyes aren't we technically looking a really close up piece of skin? That is, our eyelids? If it's so close to our eyes why doesn't it give us bad vision? We know if screens or books or other objects constantly being close to us causes our... | I think to answer your question you have to think about how the eye works. Light reflects off of an object and strikes the back of the eye to trigger the individual sensors that detect light. When you move your eyelid over your eye there is no light striking the light sensor in the back of your eye and the brain doesnt... | {
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Does universal speed limit of information contradict the ability of a particle to pick a trajectory using Principle of Least Action? I'm doing some self reading on Lagrangian Mechanics and Special Relavivity. The following are two statements that seem to be taken as absolute fundamentals and yet I'm unable to reconcile... | The key to this is that the Lagrangian cannot be just any old function. It has to be a function such that, when the action is stationary, its solution describes the kinematics of the system.
Thus, if we assert that there is a universal speed limit in the real world, then that says something about the Lagrangians which... | {
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Where is the potential energy? I read this question What is potential energy truly? and I find the answers not really satisfying.
When I move an object upward in a gravitational field, I have to work against that gravity. There is not really any energy mysteriously stored inside the object. Conversely, if the object is... | "If I move such a system into a zero gravity zone in space, then the object would still be "above" (even though "above" may not make much sense in zero gravity),but suddenly the potential energy is gone?"
Nope. The potential energy is now stored in the object.
If the object is in gravity it will " fall back" and the p... | {
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Why don't evanescent waves give rise to electromagnetic waves? I'm reading about evanescent waves for the first time. I understand that even thought no electromagnetic wave is transmitted across the boundary, an electric field is transmitted which decays exponentially into the material.
As far as I understand this is s... | Indeed, an evanescent wave only has a wavevector real part parallel to the interface.
| {
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Can pure qubit states be represented in a unit circle in $\mathbb R^2$? How does such representation relate with the Bloch sphere? In this video they are regarding 2D circles denoting real-valued states of qubit, like
Teacher says it can be extended to 3D to Bloch sphere.
But Bloch sphere has |0> at the top and |1> a... | I think what they are doing is representing the (real part of) the complex vector space in which a (pure) qubit is embedded.
Remember that the state of a $d$-dimensional system, which we usually denote via a complex unit vector $|\psi\rangle\in\mathbb C^n$, is more precisely defined as an equivalence class of such vect... | {
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What does it mean for the gravitational force to be "between" two bodies? What is the meaning of the word "between" in the law that the force between two masses at separation $r$ is given by $\frac{GM_1M_2}{r^2}$? I am confused about how can a force be in-between, either it is on body A or on body B, or on both.
Suppos... |
**If A body Exerts force G on Body B,then B body should also exert A force G on A,
but B is also exerting the gravitational force X on A,hence A will
Also exert Force X on B **
Like you said, A experiences a force G towards B , given by $\frac{GM_1M_2}{r^2}$.
B experiences the same force towards A.
These are the 2 ... | {
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What is the formula to determine the change in pressure when there is a change in flow? [Updated to help clarify my question]
I have a current water flow of 9 GPM (gallons per minute) at 50 PSI through a 1/2 inch diameter pipe pouring out at the end.
I understand that if I reduce the flow at the end (exit) of the pipe,... | At a flow rate of 9 GPM translates into 1.2 CFM = 1.25 lb_m/sec. Water viscosity of 0.01 Poise = 0.00067 $lb_m/(ft-sec)$. So the Reynolds number is $$Re=\frac{4m}{\pi D \mu}=\frac{(4)(1.25)}{(3.14159)(1/24)(0.00067)}=57000$$That would give a Fanning friction factor of about f=0.005. Dividing the volume flow rate by ... | {
"language": "en",
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Velocity is relative, which means acceleration is relative, which further implies that forces are relative as well So how would we know whether a force truly exists or not. I can be accelerating a car my 5 meters per second squared but another car accelerating with the same acceleration would think that my car is at re... |
Velocity is relative, which means acceleration is relative
This is not correct. Velocity is relative, but (proper) acceleration is not relative. It is an invariant. Real forces lead to proper acceleration so the existence of real forces does not depend on the reference frame. In contrast, fictitious or inertial force... | {
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Why $U(c,b)U(b,a)=U(c,a)$ instead of $\int_a^c db U(c,b)U(b,a)=U(c,a)$? It's supposed to be a hw&exercise but the proof was in the textbook, in the purpose that one study it. However, somehow the proof in the book was confusing and felt wrong.
Consider a time evolution operator or time ordered product,
$$U(b,a)=T\{\exp... | Essentially because the group property (5) not (7) meet the correct boundary condition (3).
| {
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Is there an alternative to radio waves that can go through metallic objects? Radar can pass through materials such as paper, wood, glass, brick, and concrete, but it reflects off of metal. Is there an alternative to radar that can pass through metal substances? If not, is it likely that we will ever find such a wave?
| For imaging, one alternative is neutrons. Neutrons tend to pass through heavy elements and are absorbed by light elements, so they can be used to image light elements that are present inside or behind heavy elements. You can see an example image here.
One disadvantage is that neutron radiation is harmful to living thin... | {
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Can a photon be detected by a "lateral" detector? If I direct a laser pointer north and I put a photodetector eastwards (i.e. at $90^\circ$ ), and I wait for a very very long time (in a perfect vacuum if necessary), will the detector ever be triggered by a photon?
| Photons are elementary particles of the standard model. They have mass zero and E=hnu, where nu is the frequency of light the come from, the laser in this case.
As point particles generated by the lasing phenomenon they travel in straight lines because of conservation of energy and momentum. The laser beam will not be... | {
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Kinematic behavior of a flat, a closed, an open universe
according to An Introduction to Modern Astrophysics, 1263p, there is explanation about evolution of scale factor.
“ For the early universe($R<1$) there is little difference among the kinematic behaviors of a flat, a closed, an open universe because the early u... |
For the early universe(R<1) there is little difference among the kinematic behaviors of a flat, a closed, and open universe because the early universe was essentially flat.
Indeed somewhat confusing, because if the early universe were essentially flat, how can it develop in a closed, flat, or open universe? Won't it ... | {
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Why is there no kinetic term in the Hamiltonian of the Ising model? I am used to the Hamiltonian formalism in the context of (quantum) field theory, where as far as I can remember it always has the form of a kinetic term + a potential term. For me the absence of kinetic terms means a theory without dynamics. In Wikiped... | For what its worth, recall that a kinetic term in the Hamiltonian for a rigid body in classical mechanics is $H=\sum_{i=1}^3\frac{L_i^2}{2I_i}$.
Or more abstractly: A kinetic term of the form $H=\sum_{i=1}^n\frac{p_i^2}{2m_i}$.
In that sense a kinetic term for the Ising model would be $\propto \sum_i\sigma^2_i$, which ... | {
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What is the entropy change of the universe for a rock if it falls from a height into a lake? The rock and the lake are at the same temperature According to my textbook, the entropy change of the universe is $+mgh/T$. I'm confused about why this happens.
after falling (without air resistance), wouldn't the rock possess ... | The rock dropping all by itself (without friction) is a completely classical (non-thermodynamic) process, so the stone alone dropping causes no entropy change. The change in entropy comes from excatly the heat absorption process you describe.
At first, the stone has some potential energy. During falling, this is conver... | {
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Does this research paper prove that warp drives are impossible? Does this preprint prove that warp drives are impossible?
J. Santiago, S. Schuster and M. Visser, "Generic warp drives violate the null energy condition"
It states that the NEC (Null Energy Condition) is violated in this paper and many others: E. W. Lentz,... | As Santiago et al say, there have been no-go theorems ruling out warp drives for decades. In fact, as far as I can tell, those earlier results already disprove the claims in Lentz and the other recent articles that Santiago et al are primarily responding to.
This doesn't mean that warp drives are impossible, as you can... | {
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Einstein Equivalence principle & Locally inertial frame Weinberg's cosmology book stated that Einstein Equivalence principle implies that at any spacetime point in an arbitrary gravitational field there is a “locally inertial” coordinate system in which the effects of gravitation are absent in a sufficiently small spac... | There have been some misunderstandings. The 'local inertial frame' is the freely falling frame, as in GR,only freely falling frame can be considered as inertial frame,albeit it has to be confined in a small region. Besides,it is the implications that WEP leads to that is interesting: universality of free fall. Then gra... | {
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What can be derived from the metric tensor? I am working on a computational project about General Relativity. In this process, I want to code 'the stuff' that can be derivable from the metric tensor. So far, I have coded Riemann Tensor, Weyl Tensor, Einstein Tensors, Ricci Tensor, Ricci scalar. What are the other esse... | *
*Metric $ds^2$ in Cartesian/Spherical/... coordinates
*Inverse of the metric
*Angle between $d^{(1)}x^{\alpha}$ and $d^{(2)}x^{\alpha}$
*Christoffel symbols
*Geodesic equations
*Geodesic equations in Newtonian limit
*Components of generalized momentum
*Riemann tensor
*Ricci tensor
*Traceless Ricci tensor
*... | {
"language": "en",
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Elastic collision with one moving object hitting a stationary object In an elastic collision, I understand that momentum is conserved and kinetic energy is conserved. If billiard ball of silver (with velocity $v_{(Ag)}$ impacts a stationary billiard ball of aluminum, I am trying to calculate the velocity of the aluminu... | If the objects have different masses, then there isn't a way to start the collision with object 1 moving and object 2 at rest and then end the collision with object 1 at rest and object 2 moving while also having the collision be elastic. You have over-constrained your system, and so you will find contradictions like t... | {
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How do you differentiate this differential equation? I have to differentiate this equation (Gravitational force between N-Bodies)
$\begin{align}
\frac{d^2}{dt^2}\vec{r_i}(t)=G
\sum_{k=1}^{n}
\frac
{m_k(\vec{r}_k(t)-\vec{r}_i(t))}
{\lvert\vec{r}_k(t)-\vec{r}_k(t)\rvert^3}
\end{align}$
where $\vec{r_{i/k}}(t... | Even for three bodies it's really complicated
https://en.wikipedia.org/wiki/Three-body_problem
Unless someone else knows different, it would seem like a job for computer simulation.
| {
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Why does the intensity of the bright fringes decrease as we move away from the central maxima in Young's Double Slit Experiment? I studied that in Young's Double Slit Experiment the variation of intensity ($I$) of the fringes on the screen with respect to the phase difference ($Φ$) is given by :
$I = 4I_{0} \cos^{2}\fr... | Why do you imagine that the intensity would be the same all the way to infinity? That would require an infinite amount of energy to illuminate an infinitely wide screen.
The best way to think about the observed phenomenon is to imagine what you would see if you had only one slit. You would find that the incident light ... | {
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Why a rotating ball (at the end of a rope) does not fall down? Is the explanation shown in the diagram right?
This is: the net force F1 = tangential + tension is way much bigger than the weight of the ball and, therefore, the resulting force F1 + weight is F1 so that the ball does not fall down.
UPDATE
Thank you very ... | If you were to spin a ball about a vertical axis using a string, it would never rise up to a level above the horizontal level. In fact the angle upto which it will rise could also be calculated. Suppose the length of the string is $l$ and at equilibrium the angle it makes with the vertical axis is $\theta$, $\omega$ be... | {
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Book recommendation: Does anybody know a book adopting a more intuitive approach to the topic of Crystal Vibrations (phonons) than the Book by Kittel? I have tried Simon's 'Oxford Solid State basics' and Kittel 8th edition but I am not impressed by both (I mean the content covered through Chapters 4 and 5 in Kittel)
| I cannot give an explanation but can point to some other sources. Hook and Hall have a decent book on Solid State Physics, here is the link
https://www.wiley.com/en-gb/Solid+State+Physics%2C+2nd+Edition-p-9780471928058 .
There are also numerous sets of lecture notes that come up when you google 'Solid state physics pdf... | {
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Since the speed of light is constant and also the speed limit; would you, in your reference frame, have no upper bound on your speed? Let us imagine you are in a vacuum and after having maintained a speed of 0 km/s (standing still) you accelerate to 297,000 km/s (99%). You know this is now your speed because you have a... | In your reference frame you are always at rest, so you can always accelerate to a new reference frame.
Suppose you were at rest in some reference frame. Then suppose you were accelerated to 0.9999999999999999999999999c in that initial reference frame.
In your new reference frame you are stationary. You can now accelera... | {
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An algebra step in the Quantum Partition Function for the Harmonic Oscillator On page 183 of Altland Simons, we are told:
$$ \prod_{n = 1}^{\infty} \Big[ \Big( \frac{2\pi n}{\beta} \Big)^2 + \omega^2 \Big]^{-1} \sim \prod_{n = 1}^{\infty} \Big[ 1 + \Big( \frac{\beta \omega}{2\pi n} \Big)^2 \Big]^{-1} \sim \frac{1}{\sin... | $$
\newcommand{\qcl}{q_{\rm cl}}
\newcommand{\ket}[1]{| #1 \rangle}
\newcommand{\bra}[1]{\langle #1 |}
$$
This is a source of very sloppy work which appears in many textbooks. You are completely correct that it makes no sense to divide by this diverge factor ad hoc. The reason they are doing this is because they weren'... | {
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What happens to entropy when half the particles are removed? Curiosity question. What happens to entropy in the following situation?
A gas fills an entire container and is in equilibrium. Suddenly all particles are removed from half the container. As such, there are now 1/2 the original number of particles, but all ... | With the thermodynamic definition of entropy:
$$dS = \frac{dQ}{T},$$
where $Q$ is heat and $T$ the temperature, the answer of what is the entropy of half the volume of your container will be , half of the entropy of the full one.
Now saying
Suddenly all particles are removed from half the container.
the state stops b... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How to calculate the centroid of a simple shape but rotated? Question:
Locate the centroid $y$ for the cross-sectional area of
the angle.
I tried to use four triangles, two of them are the bigger ones $(a+t)$ and two of them are the smaller ones $(a-t)$. I then used the idea of proportionality and Pythagoras, but I am... | The rotation matrix is overkill here. Simple geometric reasoning helps.
If you add a dotted square to L-shape, you will get a bigger square. Thus, if you put a pivot at $O_2$, then the small square (with CoM at distance $O_1O_2$) would be balanced by L-shape (with CoM at distance $O_2C$). Can you know find the distance... | {
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What is the force pair for the normal force? Clarification on Newton's 3rd Law In the process of trying to wrap my head around Newton's 3rd law I've come across 2 definitive statements.
*
*Forces must occur in pairs
*Forces must act on different bodies
This is confusing to me when applied to the classic box on a fl... | The reaction to the normal force is the normal force generated by the box pushing into the table. The table experiences a downward normal force from the box, just as the box experiences an upward normal force from the table.
| {
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"url": "https://physics.stackexchange.com/questions/637378",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How to measure the speed of an electric current? We all know that the definition of a current is the amount of charge flowing per second, that is often expressed by the equation $i=dq/dt$. But is it possible to measure the speed of an electric current in m/s? And also how can we measure such speed?
| From two other answers you know how the speed, $v$, of the charge carriers is related to the current, provided that you know $n$, the number of charge carriers per unit volume.
The Hall effect gives you an independent way to measure $v$. Send a current in the $z$ direction through a cuboid of the conducting material of... | {
"language": "en",
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Does a object gain heat faster the colder it is? Does an object at $-273°{\rm C}$ gain heat faster than an object at $-1°{\rm C}$
| Heat transfer by conduction, convection and radiation is a function of the difference in temperature between two objects, or an object and it's surroundings (for radiation it's the difference between the fourth powers of the temperatures, but the effect is the same). So if you have two objects, one at $0^o$C and one at... | {
"language": "en",
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How to translate from a state/density matrix formalism to matrix product state representation? From what I understand, MPS is just a simpler way to write out a state, compared to the density matrix. But how do I get those $A_i$ matrices? From all the examples I read, people just somehow "have" the matrices in their poc... | Any state can be written as a matrix product state. There are systematic procedures to construct such a description, based on sequential SVDs, see e.g. Section 4.1.3 of this review.
On the other hand, this description is usually of interest if the resulting MPS description has much less parameters than the $2^N$ parame... | {
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Regarding the charge configuration on a spherical shell based on the atomic level behavior With regards to the fundamental theories in Electrostatics, when a spherical shell of inner radius $a$ and outer radius $b$ with a $+q$ charge at the center is considered, there will be no electric field lines within the region $... | You don't even need to consider a specific charge in the center. (Reasonably low) static electric fields cannot penetrate any material containing free electrons (i.e. metals). Free electrons, by definition, are free to move if exposed to a force. If you try to put an electric field through such a material, the electric... | {
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Wick's theorem, contracting field operators at the same point I want to calculate the amplitude for nucleon meson scattering $\psi \varphi \to \psi \phi$ in scalar Yukawa theory, with interaction term:
$$H_{I} = g \int d^{3}x \psi^{\dagger} \psi \varphi.\tag{3.25}$$
This involves dealing with a time ordered string of o... | There is an implicitly written normal ordering symbol $:~:$ in the Hamiltonian (3.25), and therefore 2 implicitly written normal ordering symbols in the expression (3.46). The answer to OP's title question is that there are no contractions among operators within the same normal ordering symbol, i.e. belonging to the sa... | {
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Where is energy in energy density? I was learning about energy density and it seemed to be defined as the potential energy per unit volume in an electric field
$\frac{dU}{dV} = \frac{1}{2}\epsilon E^2$
But how can just the electric field have a potential energy on its own without presence of any charge? What is causing... | There are some reasons for believing that fields are real as well as being a mathematical convenience; and that they do contain energy. A prime example would be the electromagnetic wave, which consists of fields that can carry energy from one point to another. Another example would be a magnet, which can push or pull ... | {
"language": "en",
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Why intensity of light reaching the sensor or film with a particular lens directly proportional to $\frac{D^2}{f^2}$? The following is quoted from my book:
"The intensity of light reaching the sensor or film is proportional to the area viewed by the camera lens and to the effective area of the lens. The size of the are... | Since we are talking about a camera, it's more appropriate to talk about the illumination of an image which translates to the amount of light per unit area of the image. The dependence on D$^2$ is straightforward as that is proportional to the area of the lens aperture.
The magnification due to the camera lens is given... | {
"language": "en",
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Why is the number of isotopes of an element bounded? Is there a known reason why any given element has finitely many isotopes? Here I mean both stable and unstable isotopes.
If we know this, do we have a reason why, for a given element, are the isotopes limited to that particular number?
| I think this is a good question -- after all, if there's no extra Coulomb repulsion penalty for adding more neutrons, unlike for protons, why can't nuclei have lots of neutrons?
One model for the nucleus we use is called the Semi-Empirical Mass Formula (SEMF), which has a bunch of terms describing the energy contributi... | {
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Why is power transmission carried out at low current high voltage? My textbook states that power is transmitted at high voltage and low current since $P=I^2R$ and as the current has a small magnitude, the heat dissipated across the transmission lines is less than when we carry it out at high current and low voltage. Bu... | Here are the possible ways of writing power
Look at how resistance exists in wires. The power is inversely proportional to resistance if one uses the voltage as a criterion, the more resistance in the way the smaller the power transferred for the same voltage. The smaller the current the less power is dissipated by a ... | {
"language": "en",
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The nice Veritasium video about a wind-powered vehicle that can go downwind faster than the wind itself Today Derek Muller posted a video about a wind-powered vehicle that can go downwind faster than that downwind itself.
The vehicle is custom made for that case only: the case of going straight downwind.
The vehicle ha... | One should note the difference between reaching faster-than-the-wind travel and being able to maintain faster-than-the-wind travel (i.e. is the vehicle in steady-state when going faster than the wind).
The difference is in whether energy can be continuously harvested from the air (i.e. the wind) once the vehicle has re... | {
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Is it possible to replace the welding machine with a light beam? Using mirrors, lenses, and a battery of any power?
Yes, it can be expensive, yes, it can be inefficient, but it is absolutely not important.
Not about laser
| That was the basis of a rather known Russian sci-fy novel from 20s: The Garin death ray (at least known in Russia). Notably, the novel discusses the docusing system based in a parabolic mirror, which is mistakenly called hyperbolic (hence the Russian name of the novel is literally The Garin's hyperboloid). Russians phy... | {
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Do materials sort in order of density in space the way they do near Earth? Obviously, if you drop materials into water near the surface of the Earth, they sort according to densities, with the least dense materials near the surface, and the most dense materials near the bottom. Common sense suggests this is due to grav... | Yes that is more or less the correct explanation. The configuration with highest density materials at the bottom and lower density materials at the top is the one with the lowest potential energy, and thus the one favoured at equilibrium.
In space, far away from massive objects, there is no direction called “up” or “do... | {
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Why doesn't current flow through an open branch? I know that current doesn't flow through open branch because current can't flow through air due to its high resistance .But i was thinking , what's the problem if current flows through an open wire (assumed 0 resistance for matter of circuit solving). I mean, isn't there... | Current (or more properly, conduction current) can flow into an open wire and charge accumulate at the end IF there is displacement current to continue the circuit. Displacement current is not the flow of charge, but a change in the electric field. Two situations where this might happen is in an antenna, where the disp... | {
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In LED's do the number of charge carriers (electrons and holes) decrease with time? According to page-1268-69 of Halliday, Walker & Resnick's Fundamentals of Physics (10th edition),
To emit enough light to be useful as an LED, the material must have a
suitably large number of electron-hole transitions....What we need ... | You won't run out of electrons and holes. There are two main processes through which you will get more.
Thermal energy will naturally generate electron/hole pairs in your semiconductor. That's where they come from in a semiconductor at thermal equilibrium. However, this process is slower than we would like for an LED, ... | {
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Can information travel faster than speed of light in this situation? I know the answer is no but I have a thought experiment that seem to be violating that. Imagine two persons living on two different planets namely A and C which are 10 light years apart. There is a planet in between, B, which is located exactly at the... | The principle is that information cannot move from Point 1 to Point 2 faster than the speed of light. In the example you give, information moves from the initial positions of the two participants to Planet B at less than the speed of light, so the principle is not violated.
| {
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Trying to show new matrix elements of momentum operator after unitary transformation of $|x \rangle$
The problem is this. Given that I have a new x basis
$$|\tilde{x} \rangle = e^{i g(X)/ \hbar} |x\rangle$$
I have to show that
$$\langle \tilde{x} | P | \tilde{x}' \rangle = \left(-i \hbar \frac{d}{dx} + \frac{dg}{dx}\r... | We know that for any function $f$, we have :
$$[P,f(X)]= -i\hbar f'(X)$$
In particular :
$$\left[P,e^{ig(X)/\hbar}\right] = g'(X)e^{ig(X)/\hbar}$$
Now, we can compute :
\begin{align}
\langle \tilde x |P |\tilde x'\rangle &= \langle x|e^{-ig(X)/\hbar}Pe^{ig(X)/\hbar}|x'\rangle \\
&= \langle x |g'(X) + P|x'\rangle \\
&=... | {
"language": "en",
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A cylinder doing pure rolling in the front collides Consider a cylinder rolling in the forward direction with velocity of $v$ and angular velocity of $v/r$. There is a wall in front and the cylinder collides with the wall. The collision is perfectly elastic.
Here I am unable to judge what will happen next.
Will it sto... | It should stop rolling instantaneously and then start rolling in the opposite direction.
When the cylinder collides with the wall, the point on the cylinder's surface in contact with the wall is moving instantaneously in the downward direction. Elastic collisions reverse velocities, so the instant after the collision, ... | {
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How to generate electric current without a permanent magnet? The question is pretty simple:
Can we build a device that coverts mechanical work in electric current1 without employing a permanent magnet and without access to any external source of current?
The restrictions in place seem to rule out the possibility of c... | Piezo electric cells convert mechanical energy to electric energy
| {
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Can it be shown in experiment that the momentum (or position) states of the electron and proton in hydrogen are entangled? The states of the electron and proton in hydrogen are entangled. Which means that the momentum and position of both are entangled. Can this be shown in an experiment, so if you measure the momentum... | In a two body bound state, (quantum mechanical or not) from conservation of energy and momentum, once the masses are known, measuring the four vector of one particle , the four vector of the other is known.
| {
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Does energy of a capacitor means energy stored in both plates? I've a doubt in this,
Does the term potential energy of a parallel plate capacitor means the energy stored in both the plates or a single plate, since the formula $E=Q^2/2C$ , $Q$ is the charge of only one plate?
Please help me in this.
| It is the total energy stored in the entire system.
Consider that you have an uncharged parallel plate capacitor and you decide to charge it up such that the charge on one plate is $+Q$ and the charge on the other plate is $-Q$ where $Q>0$. At any point in time, the charge on the positive plate is $q$, where $0\leq q\l... | {
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Are the accelerations the same at either end of a moveable pully? Given a moveable pulley with a fixed pulley on either side,
Is the acceleration of the left weight (m1) the same as that of the right weight (m2)?
Intuitively, I would imagine it to be, since if m1 drops by 10 metres, then m3 would rise by 5 metres, and... | Hint: The tension in the string is the same throughout.
Hope this helps.
| {
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A K-theory isomorphism I found this identities in a paper on Floquet topological classification which the author mentioned as a "well-known K-theory isomorphism"
$$K_{R}^{0,n}(S^1\times X, \{0\}\times X) = K_R^{0,n+1}(X).$$
Here $S^1$ is a circle (corresponding to time) and $\{0\}$ is a point in the circle (the initial... | I found an identity in Karoubi (4.11 page 87)
$K^{-n}(X,Y):= K((X-Y)\times \mathbb{R}^n)$
Applying this,
$K^{-n}(S^1\times X,\{0\}\times X) = K((S^1-\{0\})\times X\times \mathbb{R}^n)=K(X\times \mathbb{R}^{n+1})=K^{-(n+1)}(X)$
I just blindly applied the identity so I'm not completely sure.
| {
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Are charged particles cold? Are charged particles colder than neutral ones?
If a charged particle is vibrating due to temperature, it will release some of its energy as electromagnetic waves. So that means it's losing energy, cooling itself off. Is there an error in my logic?
| Temperature is defined for a system in (at least local) thermal equilibrium. The electromagnetic field is present everywhere and, when in thermal equilibrium, has a blackbody spectrum. Thus, a body made of charged particles "vibrating" at temperature $T$, in the presence of an electromagnetic field at the same temperat... | {
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If photons have also particle properties why should they not collide with each other? If photons have also particle properties why should they not collide with each other? Collisions between fermions are possible as collisions between fermions and photons(bosons) except collisions between photons (that are described by... | If photons are neutral particles with a very small size, the interaction may be very improbable (small cross section). But there is a more long-distance interaction of photons - they are bosons and thus somewhat "attract" each other, roughly speaking. Lazers are typical devices using this effect.
| {
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"source": "stackexchange",
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Is energy really quantised? I'm currently doing an introductory course to quantum mechanics, and came across an assumption that Planck used in solving the UV catastrophe. From what I understand, he essentially stated that that the change in energy cannot be smaller than $hf$. So generally $\Delta{E}$ = $n*hf$ where $n$... | The crucial insight made by quantum mechanics is that electromagnetic waves in the cavity can be described by simple harmonic oscillators. If the angular frequency of the mode of oscillation is $\omega $ (FIXED) , then the energy associated with this mode is given by
$$E_n=\hbar \omega \left(n+\frac{1}{2}\right)\ \ \ ... | {
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Mechanical energy in a body moving upwards Why is it that mechanical energy is always conserved, I mean when an object is thrown in air, why does the kinetic energy convert to potential energy and not any other form of energy?
| Energy forms are associated with forces. Gravitational forces cause the presence of gravitational potential energy. Therefor we might expect this energy form to be involved.
Had other types of forces, such as electrical forces, elastic forces etc., been involved then we would have expected electric potential energy, el... | {
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Graph Interpretation of Gravitational Waves In the image is the data recorded by the LIGO's 2 observatories in USA. What is its interpretation? I mean what does the zig zag lines represent? Similarly, what does the blond red and blue lines (that seem like exponentially increasing up) represent? Could you please clarify... | LIGO works essentially by monitoring the separation of two large mirrors.
The zig-zag lines could be thought of as by how much the separation of the mirrors changes over the course of the 0.2 seconds represented along the x-axis. The separation oscillates in response to the passage of the gravitational wave. Confusingl... | {
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Why do I feel centrifugal force If I move with constant speed on a turn? Title sums it up pretty much, I'm studying for my physics exam right now and I just can't wrap my head around this
| Acceleration is the change in velocity $$\frac{d\vec v}{dt}$$. Importantly $\vec v$ is a vector, meaning that it has both magnitude and direction. So changing the direction of your velocity vector is indeed an acceleration. In uniform circular motion your velocity vector is not constant because its direction is changin... | {
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Scalar field displacement from the minimum of the potential gives rise to particles/dark matter, why? In This paper (Kobayashi et al -- Lyman-alpha Constraints on Ultralight Scalar Dark Matter: Implications for the Early and Late Universe) it says, at the beginning of Section 3.1:
A light scalar field stays frozen at ... | If there is a non-zero particle field in the early universe, this means there are particles present. These particles are driven away so fast from each other (by inflation) that they can't return to the zero-field configuration anymore. So they are "frozen".
| {
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Why don't the Earth's oceans generate a magnetic field? Many questions have been asked here about why the Earth has a magnetic field, e.g.,
*
*What is the source of Earth's magnetic field?
*How does Earth's interior dynamo work?
*How can an electrically neutral planetary core be geodynamo?
*Why does the Earth e... | Maybe it's good to point out how this field comes about. You would expect no field as the currents are both equally positively and negatively charged. On their own they don't produce a magnetic field. This only comes about if tboth currents interact with magnetic field of the Earth. These currents are separated because... | {
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Explain the theory behind this problem(if possible using number line or graph or any other method of pictorial representation) In a situation in which data are known to three significant digits, we write 6.379 m = 6.38 m and 6.374 = 6.37 m. When a number ends in 5, we arbitrarily choose to write 6.375 m = 6.38 m. We co... | When we are using order of magnitude estimates we are typically using logarithmic scales, and when we are dealing with powers of ten we specifically use base ten logarithms. So $\log_{10}(10) = 1$, $\log_{10}(100) = 2$, $\log_{10}(1000) = 3$ and so on. Then the "mid point" of $100$ and $1000$ would be the number given ... | {
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A space ship has maximum proper acceleration of $a_0$. How close can it fall freely towards a black hole before it can no longer accelerate away? Edit: To clarify, all motion is radial only.
Classically, the answer to this is pretty obvious. You just find the distance from the black hole at which the gravitational acce... | Assuming you are talking about radial motion the limit is when the proper acceleration for a stationary observer is equal to $a_0$. This is calculated in twistor59's answer to What is the weight equation through general relativity? The proper acceleration at a distance $r$ is given by:
$$ a = \frac{GM}{r^2}\frac{1}{\sq... | {
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How do sound waves cause air molecules to oscillate? I would like to clear up some confusion about the mechanics of air particles that are propagating a sound wave.
I understand that there is no net movement of air molecules when a sound wave passes through air. Instead, the particles oscillate and the wave is propagat... | Without the random movement of molecules, it is true that a vibrating membrane for example would create a depleted region around. It is like a fight in the middle of a crowd. Suddenly there is a clear region around the event and a wave of pressure that extends for some distance.
But because of that random movements, an... | {
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Why is difference of points not a valid definition for a vector in curved space? In page-49 of MTW (1973 edtn), the following picture is shown:
After seeing this picture, the question which arose in my head is why exactly can we not define a vector as difference of points in curved space?
| For one thing, vectors obey linear structure, i.e. we can write $\vec{v}$ as sum of two vectors $\vec{v_1}$ and $\vec{v_2}.$
So if we want to have operation $A=B+\vec{v},$ we should also demand that operations $$A=B+\vec{v}_1+\vec{v}_2=(B+\vec{v}_1)+\vec{v}_2=C+\vec{v}_2$$ and
$$A=B+\vec{v}_2+\vec{v}_1=(B+\vec{v}_2)+\... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/646316",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
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What is the drag coefficient of a semi-cylinder travelling at laminar region but with high Reynolds number?
For Laminar flow along a cylinder, the drag coefficient is about 1.
Question:
Can we assume that for Laminar flow along a semi-cylinder, the drag coefficient is about 0.5 because the pressure drag dominates grea... | The variation of drag coefficient of a semi-circular cylinder with orientation angle is shown below, taken from Yamagata et al. 2016. The case you are interested in is $\theta=0$. The measurements were taken at $Re=6.4\times10^4$. Taking the drag coefficient to be $0.5$ is a reasonable approximation.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/646535",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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How to reconcile time dilation in relativity with what you actually see?
If a traveler is moving at $0.5c$ towards a clock which is located one light year away, his relativistic time dilation is $1.15$. But in the time he takes to arrive at the clock, he must catch up the 1-year lag that he saw when the clock was 1 li... | You are being downvoted unfairly. Your answer is logically OK (in the sense that there is more to it than just the Lorentz Transform), but the calculation is wrong. Use the doppler effect, and you will see the clock appearing to move $\sqrt {1.5 / 0.5}$ times (1.73) normal speed as you approach (it will also appear t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/646666",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 3,
"answer_id": 2
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What is a bulk state and bulk bands? I am a bachelor student and I started studying topology and I came across two terms I have never seen before: Bulk band structure and bulk states.
Can someone explain these two terms or provide me a reference where I can check? Everything I found on the internet is for people who al... | The bulk states are the quantum states of electron inside the volume (bulk) of a crystal, obtained from Schrödinger equation. These states are usually labeled by the two indices, n and k representing respectively the band index and wave number. The plot of the energy of these states versus k for various values of n is ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/646777",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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If $E=mc^2$, then why do different substances have different calorific values? Today during a classroom discussion, I realised that if we consider the equation $E=mc^2$, then we are establishing a relation between energy and mass but we often observe that different substances produce different amount of energy when the... | Although often used, I would not use the term "conversion to energy". $E=mc^2$ says that energy and mass are the same things (in the center of mass frame).
If a system at rest has some mass $m$, it has, at the same time, a corresponding total energy $mc^2$. No conversion is going on. I would rather say that in any reac... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/646875",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 6,
"answer_id": 4
} |
How is Noether's theorem applied in fluid dynamics? As the title says, I'm trying to understand the applications of Noether's theorem in fluid dynamics. I was looking for references in this context, but I only find very old papers, where explanations are very limited. Are there any recent studies for the application of... | You can find a nice discussion about the virtual (added) mass force that arises when a submerged body accelerates relative to the its surrounding fluid in Gregory Falkovich’s Fluid Mechanics book. Apparently, this force is a consequence of the conservation of quasimomentum, which is the conserved quantity associated to... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/647000",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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How does stroking metal with a magnet magnetize the metal? How does stroking metal with a magnet magnetize the metal? I have thought about it for a while and got absolutely no clue as to how the magnetic domains in the steel rod got shifted to the same direction (regions of metallic ions pointing the same direction, in... | If a ferromagnetic material is placed in, and then removed from, a magnetic field, the “remnant” magnetization within the material will depend on the strength of the field. Stroking a bar will bring the strong field from the pole of the magnet into close proximity with each part of the bar. Then the magnetic “domains... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Can you exit the event horizon with a rocket? The reason given in most places about why one cannot escape out from an event horizon is the fact that the escape velocity at the event horizon is equal to the speed of light, and no one can go faster than speed of light.
But, you don't really need to reach the escape veloc... | It should be nearly impossible to do. You have to be roughly the speed of light to escape. But If your position is far from the black hole, it looks like you can still escape.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/647487",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "48",
"answer_count": 6,
"answer_id": 5
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Quantum mechanics and logical statements I am a math student and currently working on my bachelor thesis with a philosophy professor. The subject is paraconsistency and thus also dialetheism which is the believe that a statement can be true and false at the same time.
I had a general/introductory course to QM and one e... | Let us say that the setup is such that you can get up or down with some probability. Then the truth of your statement depends on who do you ask, that is, on the interpretation of QM that that person has. If he is a local non-realist, the statement, before the measurement, is false because the particle has no determined... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
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Will there be potential difference across a resistor if the circuit is open?
In such an open circuit, will there be potential difference across the resistor? More specifically, will charges accumulate on the left side of the resistor? or will it be able to flow through the resistor and stop at the open end, resulting... | Both sides of the resistor will be at the same potential, so there will be no potential difference. We use the term potential difference because potentials are only defined up to the addition of an arbitrary constant. Thus, if we say the potential on each side of the resistor was zero before the cell was connected then... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/647952",
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"source": "stackexchange",
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Why is everything not invisible if 99% space is empty? If every object is $99$% empty space, how is reflection possible? Why doesn't light just pass through?
Also light passes as a straight line, doesn't it? The wave nature doesn't say anything about its motion. Also, does light reflect after striking an electron or at... | Yes, atoms are mostly empty, comprising a nucleus with electrons surrounding the nucleus$^1$.
But electrons are not to be considered point particles that follow fixed orbits. In fact electrons are probability clouds that are smeared around the nucleus, and fill the volume of the atom.
It is similar for bonds between a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/648041",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "31",
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"answer_id": 4
} |
Why is acoustic intensity inversely proportional to density of the medium? The definition of sound (acoustic) intensity is given by
$$ I = {p^2 \over {\rho c}} \;\;\;\; \text{or} \;\;\;\; I = {p^2 \over {2\rho c}}$$
I've seen both definitions in different textbooks and am not sure which equation is more accurate. But... | Your intuition is in the right direction. Nevertheless, you are only considering the amplitude and the intensity is the power per unit area. So, you need to consider that when a material is more dense you need a higher increment in pressure to get the same increment in particle speed.
If we write it mathematically, we ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/648325",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
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Do Newton's laws of motion hold true in non-inertial frames of reference? My book derived the formula for the acceleration of a rocket at any instant in the following way:
$v_r=$ velocity of gas released from the nozzle relative to the rocket
$dt=$ infintesimal time interval
$dm=$ mass of the gas released from the nozz... | This derivation makes the most sense in momentarily comoving reference
frame.
Say you want to derive the equation at some arbitrary time $t$.
At this particular time, there exists an inertial reference frame where
the velocity of the rocket is exactly zero. In this reference frame, the
rocket was moving backwards and d... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/648688",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 5,
"answer_id": 4
} |
How can I find the angle after the last lens from in the last lens?
I want to find the angle after the last lens when the beam diffracts. How can I do that? Is it the field of view? But for the field of view formula it takes account the size of the sensor. I want to find the relation of this angle and the origin of th... | If this is a camera with a lens, the angle $\alpha$ you are interested in is really the angle of view, which can be calculated as
$$\alpha = arctan \left( \frac{d}{2f} \right) $$
You may have a look here for details about this equation https://en.m.wikipedia.org/wiki/Angle_of_view (for angle of view in photography you ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/649105",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Why is the absolute magnitude of a source negatively correlated to its luminosity? The absolute magnitude $M$ of a source of luminosity $L$ is given by $M = -\frac{5}{2}log(L) + constant$. Why is $M$ defined with a negative correlation to the luminosity? Wouldn't it be more intuitive to have a larger absolute magnitude... | The definition of the magnitude $M$ is such that smaller values correspond to brighter objects. Hence, the larger the luminosity $L$ the smaller the absolute magnitude $M$.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/649465",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Does real life have "update lag" for mirrors? This may sound like a ridiculous question, but it struck me as something that might be the case.
Suppose that you have a gigantic mirror mounted at a huge stadium. In front, there's a bunch of people facing the mirror, with a long distance between them and the mirror.
Behin... | As the speed of light is finite, sure enough there is some lag, but let's evaluate how big that lag is. Considering that the mirror is 100 meters away, than the lag will be $$2\times 100\: \mathrm{m}/(3\times 10^8\:\mathrm{m/s}) = 667\:\mathrm{ns}.$$ Comparing it to average human reaction time of about $0.1\:\mathrm{s}... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/649738",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "23",
"answer_count": 7,
"answer_id": 1
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What does it mean for a nucleus to be more stable? When we say that a nucleus is more stable than another nucleus, are we saying that the nucleus is at a lower energy level than the other nucleus? In chemistry, a more stable compound is one that is at a lower energy level, is this the same when we talk about a nucleus?... | Wnen a nucleus (or a particle) is called stable, it usually means that it does not decay, i.e., it is not radioactive. In practice one would describe as stable the nuclei and particles that decay over very long times, so long that their decay rate can be considered negligeable for practical purposes. The stabilities of... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/650010",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
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Can we cool Earth by shooting powerful lasers into space? In a sense, the climate change discussion revolves around the unwanted warming of the earth's atmosphere as a whole.
It seems a bit too obvious to be true, but could we cool the atmosphere by simply shooting that unwanted energy somewhere else?
Energy might be c... | Like other answers say... Your problem is that the act of forcibly pumping energy one place to another, beyond what nature itself would do, takes additional energy.
So for example, moving the warmth from inside your fridge to outside it, costs extra energy. Informally (not literally to scale), you can think that the f... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/650490",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "24",
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Gravitational wave and 1st law of thermodynamics Introduction:
A prediction of the general relativity is that any moving mass produces fluctuation in the space-time fabric, commonly referred as Gravitational-Wave.
This prediction was recently confirmed by the LIGO experiment.
The generation of such gravitational waves ... | The energy comes from the binary system itself and ultimately from the mass-energy of the binary components.
The binding energy of a binary system (the sum of its kinetic and potential energies) is negative. The acceleration of these masses, or more precisely, the accelerating mass quadrupole moment, produces gravitati... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/650879",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 3,
"answer_id": 2
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Does the physical singularity of the Reissner-Nordstrom metric have a ring structure? The physical singularity of the Kerr metric has a ring structure due to the axi-symmetric nature of the metric.
The Reissner-Nordstrom metric is the solution for a non-spinning, electrically charged black hole, and has two horizons: a... | It's worth noting that the Reissner-Nordstrom singularity is timelike, like how the Kerr singularity is. (and unlike the Schwarzschild singularity, which is spacelike)
but the metric is spherically symmetric, so the singularity cannot be a ring, because that would choose a special plane in the spacetime.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/650955",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 2
} |
Can a material have high permittivity and low permeability or the other way around? Since the electric and the magnetic fields are interrelated, can a material have high permittivity and low permeability or the other way around? Would it be possible to have a material that would be highly magnetized upon an applied mag... | It all depends from the temperature of the material and of course from the existence of unpaired electrons in the outer shell of the atoms.
For permanent magnets below the Curie temperature a stable magnetic field do to the alignment of the magnetic dipoles of the involved subatomic particles exist and on higher temper... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/651118",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Proton Electron Merger Can somebody explain what would happen if an electron & a proton, very close to each other are left to "fall" to each other in a straight line?
| They would form a hydrogen atom.
They would not merge, because merging would result in a neutron, which is heavier than a proton and an electron combined. However, if they are sufficiently forcibly "slammed" into each other, they might form a neutron (and an electron neutrino, which has an negligible mass). The neutron... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/651283",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 5,
"answer_id": 1
} |
True or False: energy is conserved in all collisions Using introductory physics, how would you answer this question? (I have a disagreement with my instructor and I’m curious to hear your input)
One of us says true because the question doesn’t specify “kinetic energy,” or a “system” and all energy is always conserved. ... | The correct answer is that energy is conserved. It is not pedantic, but simply correct, to insist that if the questioner meant kinetic energy, or mechanical energy, which would be conserved only in an elastic collision, then they should have said so. The conservation of energy is such a fundamental property of nature ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/651797",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "13",
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What forces act on a droplets hanging from surfaces? What are the different forces acting on a hanging water droplet (tension of the droplet itself, surface adhesive forces, meniscus formation, etc)? What is the direction of each force, and how does each affect droplet stability?
Will these forces be affected if the su... | *
*Adhesion, normal to the solid-liquid interface, found only very near
the solid-liquid interface, increasing with proximity to the
solid-liquid interface. Makes the droplet stick to the solid surface.
*Cohesion, radially inward and uniform
throughout - each little bit of water is pulling on all the adjacent little ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/652003",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Doubt concerning biot savarts law Why do we calculate $dB$ for an infinitesimal part of a wire instead of a point?What is the reason behind that?Why can't we determine the magnetic field of a point with respect to a point of the wire instead of an infinitesimal part?
Also why is $dB$ proportional to $dl$ where $dl$ is ... | A point cannot produce any magnetic field, it should have some length for it to produce any field.
Now coming to the second question. As pointed out by @Angry Refrigerator in their answer, dlXr shows the direction of the magnetic field, while I and distance from wire show its magnitude. It is not correct to say dB is p... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/652121",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Negative energy solutions in Klein Gordon and Dirac equations It is often read that Dirac equation poses the problem of negative energy solutions (later solved by antiparticles and second quantization/QFT schema). My question is: negative energy solutions were obviously present also in the previous KG equation. Why the... | In QFT, when making a field operator, negative frequency solutions correspond to annihilation operators while positive frequency solutions correspond to creation operators. Not worrying about normalizations and things like that,
$$
\hat \phi(x) \propto \int d^3 k \left( \hat a(k) e^{- i k \cdot x} + \hat a^\dagger(k) e... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/652283",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Why is the gravitational potential energy lost not subtracted from the required work done in the given problem?
An elastic string of natural length $l \;\text{m}$ is suspended from a fixed point $O$. When a mass of $M \;\text{kg}$ is attached to the other end of the string, its extension is $\frac {l}{10} \;\text{m}$.... | You are calculating the EPE as if there is no tension in the string before it is stretched from extension $\frac l {10}$ to extension $\frac l {5}$. But we know there is already tension $Mg$ In the string, and so the EPE initially stored in the string is $\frac {Mgl}{20}$.
The additional energy stored in the string by ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/652427",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 0
} |
Why do physicists like to put the imaginary unit $\:i=\sqrt{-1}\:$ everywhere? There are many disagreements of convention between mathematicians and physicists, but a recurring theme seems to be that physicists tend to insert unnecessary factors of $i = \sqrt{-1}$ into definitions.
I understand this is only convention,... | Real classical observables are quantized as Hermitian operators, and $\partial_\mu$ is anti-Hermitian. So:
*
*Structure constants We seek Hermitian generators.
*Transformations We seek real $\theta$, unitary $R_z$ and Hermitian $J_z$.
*Covariant derivative We seek Hermitian $A,\,V$.
*Curvature/field strength We se... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/652545",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
"answer_count": 2,
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Why doesn't charge escape from capacitor? A charged spherical capacitor kept in air do not loose charge because air is a bad conductor and increase in charge results in Corona Discharge. Is it because the nucleus of air molecule repels the charge in sphere and after a limit the repulsion is less than the attraction by ... | A charged sphere stays charged in vacuum because it takes a minimum energy for an electron to exit the physical material. This is called the work function.
Indeed, if you would just have a spherical shell distribution of truly free charges this would fly apart.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/652668",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 0
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Does gravity get stronger the higher up you are on a mountain? So I saw this article stating that gravity is stronger on the top on the mountain due to there being more mass under you however I have read some questions other people have asked and most of the responses state that the mass is concentrated at the middle o... | The strength of gravity does vary from point to point on the Earth's surface, because the earth is not of even mass distribution. The images in the link you have provided are evidence of this.
The strength of the earth’s gravitational field is given by $$a=\frac{GM}{r^2}$$ where $M$ is the mass of the earth, $G$ is the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/652752",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "27",
"answer_count": 6,
"answer_id": 3
} |
Energy stored in the electric field of an electron Energy stored in the electric field or self energy of a solid sphere of radius $r$ and uniform charge distribution $q$ would be
$$\frac{3}{5}\frac{1}{4\pi\epsilon_0}\frac{q^2}{r}$$
This result could be derived if we take electrostatic energy density $u = \frac{1}{2}\ep... | It's simply wrong!
An elementary particle or fundamental particle is a subatomic particle with no (currently known) substructure, i.e. it is not composed of other particles.
That means you can't consider an electron as a sphere of the finite radius with charge $e$. This is question is beyond the range of classical el... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/652927",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
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Why does $dG < 0$ imply that processes involving chemical reactions are spontaneous? Here is a short proof/derivation of why $dG < 0$ implies that a process is spontaneous (for constant temperature and pressure):
But this derivation assumes that only mechanical work is done on the system. If the process involves chemi... | We have, for the Gibbs free energy $G=\sum_i \mu_i N_i$ for species $i$ with numbers $N_i$ and chemical potentials. For a set of reactions denoted in stoichiometric notation
$$
\sum_i \nu_i X_i -\sum_f \nu_f X_f = 0
$$
and imposing conservation of species: $\frac{dN_i}{\nu_i} = dN = -\frac{dN_f}{\nu_f} = $ constant for... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/653042",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 2
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Why does water contract on melting whereas gold, lead, etc. expand on melting? My book mentions that water contracts on melting, but the book doesn't give any reason why it does so. It is mentioned that:
$1\,\mathrm g$ of ice of volume $1.091\,\mathrm{cm}^3$ at $0^\circ\mathrm C$ contracts on melting to become $1\,\ma... | The structure of ice comes from hydrogen bonds. These occur because the electrons are more strongly attracted to the oxygen atom, so this atom is slightly negative, whereas the hydrogen atoms become slightly positive. You can think of the electrons as spending more time near the oxygen atom. When you put this together ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/653220",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "21",
"answer_count": 7,
"answer_id": 0
} |
Law of conservation of energy using work done vs maxwell theory of electromagnetic radiation Consider the motion of a charged particle in a uniform magnetic field. $\vec{B} = B_0(-\hat{k})$. Let the initial velocity with which it enters the field be $\vec{v_i} = v_0(-\hat{i})$. It is well known that it follows a circul... | There is a formula for the Power of the emitted radiation due to an accelerating charge, the Larmor formula
$$P=\frac{q^2a^2}{6\pi\epsilon_0c^3}$$
where $a$ is the acceleration of the charge also $\frac{Bqv}{m}$.
In calculations the energy lost by radiation can often be ignored, you can put in various numbers to see th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/653328",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 1
} |
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