Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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Help! An 8 year old asked me how to build a nuclear power plant I would really like to give an explanation similar to this one.
Here's my current recipe:
(i) Mine uranium, for example take a rock from here (picture of uranium mine in Kazakhstan).
(ii) Put the rock in water. Then the water gets hot.
(iii) [Efficient way... |
This seems wrong, or the uranium mine would explode whenever there is a rainfall.
A natural nuclear "reactor" probably existed at Oklo, Gabon
The natural nuclear reactor formed when a uranium-rich mineral deposit became inundated with groundwater that acted as a neutron moderator, and a nuclear chain reaction took p... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/244158",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "25",
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Beam Splitter: looking for a "not-typical" second quantization but full-quantum description In all the books of Quantum Optics I read, the theory of beam-splitter (BS) is presented in more or less the same way, e.g. introduction of the transmission-reflection matrix, case study of the single photon and vacuum at the BS... | @TrulyIgnorant
I personally think this is a great question, and surprisingly one that has not yet been fully answered to my knowledge! There are two works that come very close to putting together a first-principles derivation that is fully quantum-mechanical, i.e. by quantizing the modes of a beam-splitter, showing th... | {
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Fourier transform of Hamiltonian for scalar field In the Srednicki notes (http://web.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf) page 36 he goes from
$$H = \int d^{3}x a^{\dagger}(x)\left( \frac{- \nabla^{2}}{2m}\right) a(x) $$ to
$$H = \int d^{3}p\frac{1}{2m}P^{2}\tilde{a}^{\dagger}(p)\tilde{a}(p) $$
Where $$\tilde{a}(p... | Starting from
$$
H = \int d^{3}x a^{\dagger}(x)\left( \frac{- \nabla^{2}}{2m}\right) a(x)
$$
and
$${a}(x) = \int \frac{d^{3}p}{(2\pi)^{\frac{3}{2}}}e^{ipx}\tilde{a}(p)$$
(the second of which follows by inverting the expression above which defines the momentum space $a$ in terms of the position space $a$.
Plugging in fo... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How can you calculate the thrust-to-weight ratio of a gun? Is there some formula I can apply to the weight of a gun, along with the force of thrust it creates, and calculate if it will be able to lift itself off the ground or not? Without actually handling the gun, of course.
| Given the pieces mentioned in your question: the weight of the gun and force it creates, the answer is a trivial yes. If the force is greater than the weight, it could lift.
The problem is in calculating that force. A rocket is designed to produce force continuously for a period, and given the fuel and some other par... | {
"language": "en",
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Units don't match in the torsional spring energy! According to Wikipedia's description of torsion springs and according to my understanding of physics the energy of a torsional spring can be written as
$$U=\frac{1}{2}k \varphi^2$$
where $k$ is a constant with units of $\rm N\,m/rad$.
I am freaking here because if the... | An angle is just the ratio of the length of a circular arc to its radius, so the radian has units of length/length, which means it's a dimensionless quantity.
| {
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"source": "stackexchange",
"question_score": "11",
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Does continuity equation hold if the flow is accelerated? I'm Studying the streamline flow, specifically the continuity equation Bernoulli's Principle.
Consider the following system where a liquid flows through the pipe of a uniform area of cross section A, from high pressure P2 to low pressure P1, both of which are m... | In pipe flow two terms are added to Bernoulli's equation. Major loss and minor loss terms. Major loss is due to wall friction and minor losses are due to shape change in the pipe. (Valves, elbows etc.)
In the system that you draw the pressure difference overcomes the wall friction. The wall friction increases with velo... | {
"language": "en",
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The force felt by a pilot when a package is dropped? Here is a physics question that I wish to prove mathematically.
A 100,000 kg aircraft drops a 1000 kg package of supplies over an arctic research station. What approximate force is felt by the 100 kg pilot at the instant of the release?
Is there a reactive force on t... | He'll feel the release of potential energy, which is equivalent to
$$1000kg*height*gravitational~acceleration$$
The pilot would feel the same effect as if he was dropping an object from his hand weighing 1 kilogram.
| {
"language": "en",
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Why does moonlight have a lower color temperature? Moonlight has a color temperature of 4100K, while sunlight has a higher color temperature of more than 5000K.
But objects illuminated by moonlight don't look yellower to the eye. They look bluer. This holds for indoor scenes (like my hall) and for outdoor. I find it co... | I thought the sun is the yellowest natural source of light we have.
Whatever made you think that? It's pretty much by definition the whitest source of light we have since sunlight is what we judge all colors in.
Now direct sunlight is pretty close to a black body emission spectrum. The moon, not so much. It's reflec... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/244922",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Current operator in continuum model of graphene For the graphene hamiltonian with NNN hopping, the wavefunctions are of the form:
$(\psi_A ,\psi_B)^T$. The current from A(i) to B(j) site in the lattice model is given by:
\begin{equation}
J_{ij}=\mathrm{i}t(c^{\dagger}_ic_j-c^{\dagger}_jc_i)
\end{equation}
where $t$ is ... | The general way to find the current opperator is to gauge the U(1) symmetry and take the derivative of the Hamiltonian with respect to the gauge field $a_{ij}$ or $a_\mu$ and then turn off the gauge field:
$$\text{lattice: }J_{ij}=\left.\frac{\partial H}{\partial a_{ij}}\right|_{a_{ij}\to 0},\text{ continuum: }J^\mu=\l... | {
"language": "en",
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What Keeps a Pendulum Moving In a Circular Path?
From the figure, we know that $F_{net} = mg\sin\theta$. Now, this force $\vec{F_{net}}$ is in the direction of the velocity $\vec{v}$ of the bob, both are tangent to the path. Therefore, the net acceleration $\vec{a_{net}}$ has no component perpendicular to the path, th... |
What might be providing that force? The tension in the string is cancelled by the component of gravity parallel to the string.
I think a correction to the force diagram is required.
One should show the tension in the string and along the string a force called centripetal force is necessary to keep the bob in a circu... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/245223",
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What direction are the decay particles of muons emitted in? If I were to run an experiment where I could measure the neutrino as well as the positron emitted when a muon decays, what direction should i be looking in?
| The decay of a (anti-)muon to a positron is
$$ \mu^+ \longrightarrow e^+ + \nu_e + \bar{\nu}_\mu .$$
As there are three light decay products their directions (in the rest frame of the anti-muon) are only weakly correlated.
The usual experimental procedure for dealing with this is to work with a beam of highly relativis... | {
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What do we exactly mean by a "topological object" in physics? I have been working on topological defects like monopoles, etc. for some time. One think that I have not been able to understand is the physical meaning of the phrase "topological object". I have tried to find answers in many books on topological defects, g... | The broad meaning is: an object which depends on global properties of the system, rather than depending on the metric or other local properties. Therefore these objects are described via topological concepts like homotopy group, fundamental group and so on.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/245395",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
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If gravitons are 'real' and analogous to photons are they also being 'stretched' by the universe's expansion? Since photon wavelengths are stretched by our expanding universe, appearing to us as a redshift, would graviton wavelengths similarly be stretched? For that matter, do gravitons even have a wavelength like pho... | Suppose, there are gravitons, and space is expanding.
Gravitons stretching with stretching space, would loose strength in same way as lower frequency (red shifted) light has lesser energy. That would change laws of gravity constantly. At the least, it would keep changing gravitational constant. That does not seem to be... | {
"language": "en",
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Could you use polarization filters to make a privacy screen? I remember seeing that brusspup video where the polarization filter on the monitor was removed and put it in his glasses, causing only the wearer to see the screen.
(, and)
I was thinking, would another polarization filter set on top of a phone screen to re-t... | Putting a polarization filter of any kind (linear or circular) at any orientation onto your iPhone screen will never be able to turn its display from normal-looking to all-white. Look at it this way: If you have a display on your iPhone screen that has black areas (say, black text on a white screen), then that means th... | {
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"source": "stackexchange",
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Shape of water on top of a thin sheet of stretched plastic Consider a thin sheet of plastic (a square sheet for simplicity) that is stretched taught in a plane parallel to the ground. If a volume of water is then placed on top of the thin plastic sheet, then the water will further stretch the plastic and create a sligh... | Let's first recall the wave equation for a membrane
$\partial_{tt} u = c^2 \Delta u$ where $u(x,y)$ is the vertical displacement. See, e.g., https://en.wikipedia.org/wiki/Vibrations_of_a_circular_membrane.
One can recognize the left-hand side $\partial_{tt} u$ as the acceleration of a membrane element and $\Delta u$ i... | {
"language": "en",
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How to interpret the units of the dot or cross product of two vectors? Suppose I have two vectors $a=\left(1,2,3\right)$ and $b=\left(4,5,6\right)$, both in meters.
If I take their dot product with the algebraic definition, I get this:
$$a \cdot b = 1\mathrm m \cdot 4\mathrm m + 2\mathrm m \cdot 5\mathrm m + 3\mathrm m... | The dot product of two unit vectors can safely be considered a dimensionless quantity, from a dimensional analysis perspective — a unit vector is what you get when you divide a vector by its magnitude, and the dot product is linear in terms of the magnitudes of both vectors, so all of the units cancel out — and for the... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Physical meaning of $Tr(\rho ^2)$ If $\rho$ is the density matrix of a system then $Tr(\rho ^2) \leq 1$. If the equality holds the system is in a pure state and it is in a mixed state otherwise. But, what is the physical meaning of $Tr(\rho^2)$ ?
$Tr(\rho) = 1$ for all valid density matrices. This stems from the norm... | You can interpret $1-Tr[\rho^2]$ as a kind of entropy. If you think of $\rho$ as a classical mixture of quantum states, then $Tr[\rho^2] = \sum_i p_i^2$, where $p_i$ is probability of being found in eigenstate $i$. The more dispersed the states, the smaller the quantity. So for a completely mixed state you have $1/n$, ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/246258",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Airplane on a treadmill - Variant Thought Experiment This thought experiment is in a way related to the (in)famous airplane on a treadmill problem.
If you take a ball and place it on a treadmill, will the ball:
*
*Move backwards relative to the ground at the same speed as the treadmill (as if placing any other non-c... | The treadmill will apply both a non-zero torque and a net force to the ball. Thus the ball will both move backwards and roll. To know precisely how much of each the ball does we need to know more about the initial setting:
Does the treadmill start from rest and then accelerate? How does it accelerate?
Then using th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/246351",
"timestamp": "2023-03-29T00:00:00",
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What causes polarization current density in plasma? Plasma current density is defined as $\textbf{j}=-\mathrm{e}n_e\textbf{u}_e$ where $\mathrm{e}$ is electron charge, $n_e$ is electron concentration and $\textbf{u}_e$ is electron velocity. What exactly causes polarization current density and why we do not consider oth... | A polarization current can be driven by something that causes a time-varying electric field, like a gradient drift which forces positive and negative charges to drift in opposite directions. This can be similar to a displacement current, but it is generally driven by bulk particle motion.
Side Note:
The current densit... | {
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Quantum versus classical computation of the density of states If I consider for instance N non interacting particles in a box, I can compute the energy spectrum quantum mechanically, and thus the number of (quantum) microstates corresponding to a total energy between $E_0$ and $E_0 + \delta E$. In the limit of large qu... | For particles in a 1-D potential $V(x)$, we can connect the volume of phase space to the number of quantum states via the WKB approximation. Under the usual WKB assumptions, it can be shown (see, e.g., Liboff or Griffiths) that to have a well-defined wavefunction we must have
$$
\int_{x_1}^{x_2} p(x,E) \, dx = \left( ... | {
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"timestamp": "2023-03-29T00:00:00",
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Angle of a pendulum as an explicit function of time What would be the solution for the angle $\varphi(t)$ and angular speed $\omega(t)$ on pendulum without the small angle approximation - not as differential, but as an explicit function of time?
The pendulum starts at angle $\theta_i$ with the arbitraty initial angula... | You can predict that as the initial angle of deflection increases so does the period: Look at the special case for a bob held by a stiff wire, when the angle is exactly $180^0$ then the bob will remain in the upright position for ever (ignoring any small perturbations). Continuity suggests that as the initial angle of ... | {
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Double slit with opposite circular polarizers Let's say I'll send linearly polarized light onto double slit but in front of one slit I'll have quarter wave plate and before the other I'll have 3/4th wave plate (half+quarter? minus quarter?) oriented in such way that the light will get polarized clock-wise before going ... | Circular polarisation can be though of as a horizontally polarised wave together with a vertically polarised wave which is $\frac \pi 2$ out of phase with the horizontally polarised wave.
With the two slit arrangement that you have described let the horizontal components of the circularly polarised light from each slit... | {
"language": "en",
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Wigner-d matrices for higher (than 1/2) spins I’ve been reading
¨Halzen, F., and A. D. Martin. Quarks and Leptons. New York: Wiley Text Books, January 1984. ISBN: 9780471887416¨,
and I’d like some clarification of a concept, please: I’m looking at Problem 2.6, and the question asks us to show that the rotation matrice... | *
*Your feeling looks very misguided. Whatever you do, stay away from SU(3) for rotations. The rotation group and its Lie algebra are always linked to SO(3) ~ SU(2), to avoid formal forays into double covers and half angles. Read up on the spin matrices for any representation of the very same group (any spin).
*There... | {
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Ohm's law deviation In terms of superconductivities and diodes (I do not know anything else except these), Ohm's law deviate from a linear relation. I search many titles or tags for this but I did not understand properly how it becomes. I wonder somethings related with this.
*
*What is the basic of this deviation? ... | Ohm's law is a misnomer. It is not actually a true law, in the sense of Coulomb's of Ampère's; rather it is a 'rule of thumb' that applies pretty well in most circumstances. You will certainly not get a nobel price for finding an exception! A more general form of Ohm's law is
$$\mathbf{J} = \sigma \mathbf{E},$$where $... | {
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What is $\langle \phi | H | \psi \rangle$ in QM? I know that $\langle \phi | \psi \rangle$ is the probability of going from the $\psi$-state to the $\phi$-state, and that $\langle \phi | H | \phi \rangle$ is the expectation value of the energy for the $\phi$-state.
But how should I interpret $\langle \phi | H | \psi \... | This is a scalar value that is a projection of the state $H|\psi \rangle$ on the state $|\phi \rangle$. The state $H|\psi \rangle$ results from the action of the operator $H$ on the state $|\psi \rangle$. If the state $|\psi \rangle$ is an eigenstate of the operator $H$, the expression can be rewritten as $E \langle\p... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Why don't stars re-emit the photons they absorb, thus restoring a continuous emission spectrum? If you shine white light through a gas, electrons can absorb sufficiently energetic photons to reach higher excited states. This produces gaps in the spectrum and it's how Helium was discovered. So goes the story.
But an exc... | When the electron falls to its ground state, it will emit the photon in a random direction.This means that the photon might not travel in the direction as the rest of the white light.
In the absorption spectrum of the sun, there will be some photons of the characteristic frequency of helium, but significantly less than... | {
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Is it always possible for an observer to realize to be in a non-inertial frame? Galilean relativity principle states that two frames moving with uniform linear motion cannot be distinguished. But is it always possible to realize to be in a non-inertial frame?
In a rotating frame it is surely possible for the observer t... | In a non-inertial frame, observers will see fictitious forces with no reaction pair. For example, in a frame accelerating linearly forward, there appears to be a force acting backwards, and one cannot find the reaction (or source) of this force.
| {
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Understanding role of friction in block on block problems Consider two blocks stacked on top of one another. There is friction between the blocks but there is no friction between the lower block and the table. So the only frictional force that tends to retard the lower block is due to the friction between the blocks ri... | As long as the two blocks move together as one whole block, it does not matter you apply accelerating force to the upper or lower block.
But, if the accelerating force is greater than a threshold, the two bodies move in relative to each other, in this case, the threshold value and the resulting movement depend on which... | {
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Why does limiting friction have to act when a block tied to a wall is pulled? A block lying on a rough surface, is connected to a wall by a mass less, inextensible string and an unknown amount of force is applied to the block opposite to the side of the wall. Now, if it is given that there is some tension in the string... | Because the tension force of a string is a reaction force (like the friction force). This means there is no tension force until the string isn’t stretched. The string will be non-stretched until the force F is lesser than the limiting static friction force. There is a same state for friction force. The friction force i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/248265",
"timestamp": "2023-03-29T00:00:00",
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Why do constants have dimensions? I am just a beginner in dimensional analysis, and I see that $G$, the universal gravitational constant, is independent of everything. Speed, for example, depends on distance and time, but $G$ does not depend upon anything.
Then why is $G$'s dimensions not $M^0 L^0 T ^0$, as it is not ... | Speed doesn’t depend on distance and time. We measure it by measuring distance and time. We should understand the difference between physics and mathematics. We use mathematics because we want to live better in nature. Speed is a abstract concept that we created it. We never can discover how the nature works or what ar... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/248376",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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relationship between torque and potential energy for electromagnetism It is well known that the energy of a magnetic dipole in a magnetic field is taken as
$$U = - \bf{m}.\bf{B}$$
The dipole also experiences a torque
$$\bf{\tau = m \times B}$$
In classical mechanics, the torque is given as
$$\bf{\tau} = \bf{r \time... | A conservative force is one for which the curl is zero, i.e: force $F$ is conservative if and only if it satisfies the following condition,
$$\nabla \times F=0. $$
This is true for electrostatic forces. However, if at a point in space the magnetic field is changing with time, then the electric force will, in general, b... | {
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Can lasers lift objects? I have been fascinated by a very intriguing question - Can lasers push objects up?
I have done the below math to find out
Lets say we have a $1000~\text{mW}$ laser and we would like to lift an object of weight $100~\text{g}$.
By definition: $1~\text{W} = 1 \frac{~\text{J}}{~\text{s}}$
That mean... | Your approach is incorrect. You cannot do this calculation by considering that the energy absorbed by the object is converted into a change in gravitational potential energy. For one thing the object would just get hot and radiate away most of the energy and for another this is a dynamical problem, you have to be able ... | {
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What is the moment of inertia really? Is moment of inertia or second moment of inertia, simply the resistance of a body to rotate it over an axis? What is radius of gyration? What if the axis is via the center of mass or somewhere different? can you give me please an overview of these issues with SIMPLE words, and with... |
simply the resistance of a body to rotate it over an axis?
Gosh, I dislike the word resistance in this context since resistance is, in general, dissipative and, in particular, resistance to rotation would imply that an isolated object that is rotating would eventually stop.
Think of moment of inertia (rotational iner... | {
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Different definitions of the parity transformation for the Dirac spinors There are two definitions of the parity transformation acting on the Dirac spinors: $\Psi_P = \eta \gamma^0 \Psi$ with $\eta = i$ ($P^2=-1$ as in Srednicki) and $\eta=1$ ($P^2=+1$ as in Peskin & Schroeder).
Both definitions result in the same pari... | For non-hermitian products of Dirac field operators the parity is not well defined and depends on the phase $\eta=\pm1,\,\pm i$ of the parity transformation $\eta \gamma^0$. For example, $I_P = -\eta^2 I$, where $I = \overline{\Psi_C}\Phi$.
In the $S$-matrix elements, however, all phases go away eventually, because cr... | {
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Quick question on weight/mass (In the US, just to clarify)So, from a physics perspective weight and mass are different, but when people are talking about weight in everyday(non-physics) situations ("how much do you weigh" etc.), are they actually talking about mass and it's just common to refer to it as 'weight'?
Expan... | When you are looking at the car speedometer you are actually measuring AN ANGLE between the zero and dial hand. Nevertheless, you read SPEED units.
This is because scale is CALIBRATED in units of speed.
Similarly, when you are looking at mercury thermometer, you are actually measuring the DISTANCE. Nevertheless, you... | {
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Why doesn't a swing make a full revolution on a swingset in a park? I'm familiar with the concept of swinging of a swing in a park, but I'm confused why it doesn't it swing at a complete circle around the center bar?
| You mean go all the way around? It could if you had enough force to overcome gravity and like a tether ball swing all the way although most humans do not have the strength to apply the force needed to push another or them selves to a full revolution around the bar of a swing with out a jerk, but if the chain was replac... | {
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Do gravitational waves affect light? Gravity "bends" light, predicted with theory of relativity and subsequently observed: how does gravity and gravitational waves achieve this effect, and shouldn't this effect be present wherever there's gravity, for example shouldn't there be a "shimmering effect" when observing dist... | Gravity "bends" light, predicted with theory of relativity and subsequently observed: how does gravity and gravitational waves achieve this effect
I conceive the question as one referring to General Relativity (GR) which is an entirely classical theory, and not to a (thus far missing) theory of Quantum Gravity.
The poi... | {
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Deviation of free falling objects (Coriolis effect) using conservation of angular momentum I read this pdf on non inertial frame, in particular I have a question on the deviation of free falling object due to Coriolis effect.
Consider a ball let go from a tower at height $h$. The displacement due to Coriolis effect, ... | The error is just to consider an average speed $h\omega$.
When the particle is at height $z$, its horizontal (relative to the Earth) speed is $v=2z\omega$, ignoring higher order terms in $z$.
During the time interval $dt$ the particle falls $dz$ with vertical speed $u(z)$. Hence
$$dt=\frac{dz}{u(z)}=\frac{dz}{\sqrt{2gz... | {
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Were the Michelson-Morley results a surprise? How unexpected were the Michelson-Morley experiment results?
Did physicists have theoretical reasons to predict that the speed of light would result to be invariant?
| It was a completely unexpected result at the time. The principle of the MM experiment hinged on the hypothesis that Maxwell's equations of electromagnetism were valid only in a special frame of reference called the aether frame.The speed of light was equal to its standard value only in this frame and its speed in any o... | {
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How does the viscosity of a non Newtonian fluid (ooblek) affect its resistance to electricity? I know the conductivity of water is based on whatever is dissolved into the solution, hence pure water does not conduct electricity.
However, these ions in solution must also be free to move around.
If I keep a non Newtonian... | The thickening of oobleck and similar materials is due to a phenomenon called dilatancy. This happens because shearing the suspension forces the water to flow at very high shear rates through the restricted gaps between the solid particles, and that requires a very high shear stress.
However the water itself is not thi... | {
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Rolling without slipping in absence of friction force I'm confused about a rolling without slipping situation. Suppose to have a disk of radius $R$ on a floor, and exert a horizontal force at a certain distance $r$ from the center of mass.
I would like to see in which situation I obtain that the disk rolls without sli... | There's one thing in you question that doesn't quite add up and that is when you say exert a horizontal force at a certain distance r from the center of mass. If you are pushing a disk anywhere you push it (on the curved surface at least) is going to be a distance r from the centre of mass because the whole surface is... | {
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Atmospheric Pressure inside a closed room
Even though they’re too tiny to see, all the molecules of air in the atmosphere above your head weigh something. And the combined weight of these molecules causes a pressure pressing down on your body of 10,000 kg per square metre. This means that the mass of the air above the... | From Pascal's law, we know that pressure is isotropic, which means that at a given location in a fluid, it acts equally in all directions. So, at a given location, the horizontal force per unit area acting on a small vertical surface is the same as the vertical force per unit area acting on a small horizontal surface.... | {
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How much load does an aqueduct support? Recently, I found out about /r/InfrastructurePorn, and I found a particularly interesting photo of the Gouwe Aqueduct in Gouda, NE:
It seems like the bridge that is supporting the boat wouldn't be able to do it. Is the weight of the actual boat being supported by the aqueduct? ... | Yes -- because if the boat displaces xx tons (however many tons it is) of water, then if the ship weren't there then the water would be (where the boat is now) -- and it's IMO clear that the weight of that water is being supported by the aqueduct.
I guess the boat looks relatively heavy, but it's mostly hollow.
Another... | {
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Producing gravitational waves in labs Can gravitational waves be created on very small region of vacuum with quadruple movement of atom or subatomic particles?
| Yes, even tiny objects produce gravitational waves as they move. It's just that their gravitational waves will be way too tiny to measure.
Just consider that the recent gravitational wave detection was caused by 2 black holes weighing 36 and 29 times the mass of our sun. Even those enormous black holes only caused a ti... | {
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Meaning of a certain value at Fourier Transform Define the Fourier Transform of a certain signal in the time domain FT[$x(t)$]=$X(j\omega)$
$X(j\omega)$ = $\int$ $x(t)$ $e$^($j\omega$$t$)$ $dt
I'd like to ask what is the meaning of the value obtained from $X(j\omega)$ with certain frequency $\omega$
for example if w... |
I'd like to ask what is the meaning of the value obtained from X(jω)
with certain frequency ω
Consider for a moment, the synthesis equation where we 'construct' $x(t)$ out of a weighted 'sum' (integral) of the orthonormal basis functions of time: $e^{j\omega t}$
$$x(t) = \frac{1}{2\pi}\int_{-\infty}^{\infty}\mathr... | {
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How is a mass, suspended vertically by two springs in parallel, kept stable? Consider a mass suspended vertically from above by two springs in parallel with different spring constants. Wouldn't the tension be different in each spring? How is this system kept in equilibrium?
| I've simulated the case
The two springs had the same initial length, and the block in the picture is in equilibrium. See how it is deviated towards the spring with bigger stiffness to decrease the resultant moment, and stop the rotation of the block.
| {
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Free Expansion Of and Ideal Gas We know that in free expansion of an ideal gas, no heat enters or leaves the system.
We also know that
$P_\text{initial}V_\text{initial}=P_\text{final}V_\text{final}$
is valid.
If heat exchange is zero, then we can call this process to be adiabatic.
Then why the following is not valid? ... |
Are isothermal free expansion and adiabatic free expansion different?
No. They are the same.
Your mistake is in thinking that $PV^\gamma = \text{constant}$ applies to a free expansion. That expression is for a reversible (i.e., isentropic) adiabatic process. A gas that has undergone a free expansion has more entropy ... | {
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What is the minimal G-force curve in 2-dimensional space? Given two parallel roads, which need to be connected, what shape of curve would produce the minimum overall horizontal G-force(s) on travelers?
Is it a $sin$ or $cos$ wave?
Is it a basic cubic function?
Is it something else?
I'm working on an engineering projec... | The answer is two arcs. One arc with a constant gee loading in one direction and then flipping to the opposite direction. This is called the bang-bang method, and it is no very smooth, but the gee forces never exceed the specified maximum.
Given a path $y(x)$ the instantaneous radius of curvature at each x is
$$ \rho =... | {
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Hamiltonian or free energy corresponding to 2+1D Kuramoto-Sivashinsky model I am trying to understand if the deterministic 2+1D Kuramoto-Sivashinsky equation
$$
\partial_t h =
-\nu \nabla^2 h - K \nabla^4 h + \frac{\lambda}{2} (\nabla h)^2,
$$
where $\nu$, $K$, $\lambda$ are constants and $h=h(x,y,t)$ is a time-depen... | Comments to the question (v2):
*
*On one hand, the Kuramoto-Sivashinsky (KS) equation is a dissipative differential equation (DE). Each term has an even number of spatial derivatives. It's a non-linear version of the heat equation. Dissipative systems rarely have variational action formulations nor Hamiltonian formu... | {
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May a point rotate about itself? Suppose we have two equivalent rigid cylinders. Cylinder 1 is moving (translating) with constant velocity of v. Cylinder 2 is rotating without slipping and its center’s velocity is constant and equal to v. So, the motion equations of both centers of cylinders are same (x=vt). If we cons... | "What is the difference between these two points (centers of cylinders)? "
1) there is no difference in the motion of the points (lines that extend down the cylinder, actually). They each translate in space with the center of the cylinder as you might expect.
2) "Can we define rotation for a point about an axis that c... | {
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Eddington-Finkelstein coordinates, how to tell which is ingoing and which is outgoing? The Eddington-Finkelstein coordinates in case of Schwarzschild metric are defined as
\begin{align}
u&=t-r^*\\
v&=t+r^*
\end{align}
where $$r^*=r+2GM\ln\left|\frac{r}{2GM}-1\right|$$
The question is that how to understand which one is... | $du,dv$ are light-like, i.e. they could, in principle, be viewed as some affine parameters of some light-rays. However, we will focus (in the spirit of the usual coordinate-nature analysis) on what is the nature of either $u,v$ constant. I.e., we want to know what is the nature of $u,v$ constant hypersurfaces and deriv... | {
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How do we know WHEN to get the result from quantum computers? So I always hear that you can't disturb quantum computers because this will ruin the particles superstate.
Well, how do we know WHEN to retrieve the result from the calculation?
How can we determine when the calculation is finished, without observing it?
| As explained on page 7 of Deutsch's first paper on quantum computation, you can set aside one of the qubits of the computer as a flag for completion of the computation. The qubit starts with the value 0 and the computer doesn't interact with it unless the computation terminates, at which point it sets the bit to 1.
| {
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Why current in series circuit is the same? I have read in the internet that the charges do not have any other path to go and they must go through the same in a series circuit,hence the current is same.
It was quite convincing but what confused me was:
"A resistor is a passive two-terminal electrical component that impl... | What this means is that the resistor reduces the current compared to a circuit that didn't have the resistor in it.
Say you have circuit with a bulb and a battery in which 0.5 A of current flows. If you then introduce a resistor in series with the bulb the current everywhere in the circuit will be less than 0.5 A. Th... | {
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Time taken for a layer of ice to form The book I have gives the following derivation:
Let the temperature of the atmosphere be $-\theta$ and the temperature of the water be $0$.
Consider unit cross sectional are of ice, if layer of thickness $dx$ forms in time $dt$ with $x$ thickness of ice above it,
heat released due... | You assume that the temperature difference between the air at $-\theta^\circ C$ and the water directly under the ice $0^\circ C$ is constant.
So looking at the thermal conduction equation $\dot Q = K A \frac {\theta}{x}$ if you increase the thickness of the ice $x$ by a factor of two you reduce the rate of heat flow $\... | {
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Twin paradox in special relativity: length contraction Can the concept of twin paradox be applied to length contraction as well? meaning that the twin which is in spaceship will have its meter rod "actually" contracted while he will see his brother's meter rod contracted which is in fact will be an "apparent" effect.
| This might or might not be responsive to the question you intended to ask:
Suppose you've got a meter stick. Over a period of time, I apply identical forces to the front and back ends of that meter stick, causing them to accelerate in the same direction. Therefore the entire stick, being a rigid body, accelerates in ... | {
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non constant acceleration problem
The acceleration of an arrow from a bow falls from $6000m/s^2$ to zero when it leaves the bow after travelling a distance $x=0.75m$. Assuming that this acceleration can be expressed by the linear equation $a=6000[1-(4x/3)] m/s^2$ determine the speed of the arrow when it leaves the bow... | This is the setup described in the equation:
The acceleration is defined in terms os the displacement of the bow $x$ by:
$$ a = 6000 \left(1 - \tfrac{4}{3}x\right) \tag{1} $$
So initially $x=0$ and when we substitute this into equation (1) we get $a = 6000 \text{ms}^{-2}$. When the arrow leaves the bow so $x=\tfrac{3}... | {
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Derivation of TKNN's main result from Kubo formula I have a question about a small but meaningful (to me at least) step in the original TKNN paper (http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.49.405). I understand the construction of the magnetic translation operators and the use of the Kubo formula to get... | The OP's main concern is about:
But why must there exists an r-independent phase factor when
translating to the boundary of the magnetic Brillouin zone? The values
of $k_1$ and $k_2$ are only defined modulo $2π/a$ and $2π/b$ to begin with.
Answer: for "$k_1$ and $k_2$ are only defined modulo $2π/a$ and $2π/b$", t... | {
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Thermal de Broglie wavelength - definition The thermal de Broglie wavelenght is often defined by the formula
$$\lambda=\frac{h}{\sqrt{2\pi mkT}}$$
but equally frequently is it defined as de Broglie wavelength for a free ideal gas of massive particles in equilibrium, but in this case we obtain
$$\lambda=\frac{h}{\sqrt{3... | I see two ways in which the thermal de Broglie wavelength is defined. In both cases we can get it from the probability distribution and partition function of an ideal gas. We will consider a 3D ideal gas with non-relativistic dispersion.
First Way
Consider the partion function of an ideal gas:
\begin{align}
Z &= \int_{... | {
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gradient strength units in MRI This may not be the appropriate forum for this but seemed to be the closest.
I am trying to understand some concepts around MRI physics and it is common to use external magnetic fields created using gradient coils to manipulate the main magnetic field strength at different locations.
Now,... | A 'gradient' measures how quickly something changes with respect to something else. In this case, it's how much the magnetic field strength changes per unit length.
| {
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What is the best way to calculate impact time with collisions? I've been teaching myself physics and I've been wondering about the impact time in collision calculations. The scenario I've been using to learn is an object with a mass of 4000 kilograms colliding with a human being, while travelling at 17m/s. The object h... | In general you need to establish some sort of stiffness, or more importantly an natural frequency for the system of two bodies. You can hear impacts and distinguish between slow thuds with fast pings.
For example if a short duration force has a harmonic shape (with frequency $f = \frac{\omega}{2 \pi}$) and peak force ... | {
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Decompression sickness In decompression sickness why does nitrogen gas come out as bubbles? Is it because under high pressure the nitrogen gas was converted into liquid nitrogen and during the process of coming to the surface (depressurisation)the liquid nitrogen evolved out as gas bubbles in the arteries and veins?
I ... | Nitrogen is not liquefied in these conditions at all.
What happens is that when pressure increases, nitrogen's solubility in blood increases (this is a general property of gases: their solubility in liquids always increases with pressure)
When a diver decompresses properly (i.e. quite slowly) the nitrogen is released f... | {
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Why does a pot start rotating when coffee is stirred inside? I usually make Turkish coffee as my morning coffee. I have a small somewhat rounded pot with handle on one side. I noticed that when I pour water in and start stirring, pot has a tendency to start rotating in the same direction as I'm stirring.
Why is that?
| You have made a model of a viscous fluid coupling which was used in a number of four wheel drive vehicles to transfer torque. The system relies in the fact that adjacent planes of moving liquid experience a viscous force between them.
| {
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Is static friction the only force causing a car to move (without sliding)? A car is moving without sliding means that the friction between wheels and the ground is static friction. This is the force causing an object to move forward, therefore, its direction is the same as the moving direction of the car.
My question i... | A free body diagram will show a car in motion has air drag force, gravity force and friction force on it. The net force keeps the car accelerated, decelerated, or moving at constant speed.
Friction force is due to relative motion between wheel and ground. Engine output spins the wheels (torque from power train system ... | {
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Why does the classical Doppler formula make a distinction between movement of the source and movement of the receiver? I've tried rewriting the Doppler formula to include only the relative velocity between the source and the receiver of sound waves. However, when I compare the results with the results of the formula th... | That's correct. Imagine a sound emitter and receiver traveling at twice the speed of sound in the same direction with the emitter behind the receiver. Even though the relative velocity is zero, the sound will never reach the receiver because sound doesn't travel fast enough. At this point, the frequency calculated from... | {
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Relativistic Mass and Potential Energy In the chapter 16–4 of the Feynman Lectures, Feynman employs a thought experiment to explain why "if two particles come together and produce potential or any other form of energy; if the pieces are slowed down by climbing hills, doing work against internal forces, or whatever; the... | Energy is stored in electric and magnetic fields. There's a little bit stored at each point in space. It's proportional to the square of the electric field at that point. The total energy stored that way is just the integral (i.e. sum) of that the energy at each point.
As you move charges around, you change the field v... | {
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Spinning top fixed point I have seen many explanations about the movement of a spinning top. The explanations were in a varied level, from basic newtonian mechanics to Lagrangian formalism. But I do not understand why some people consider different fixed points. In same cases it is the point of contact with the surface... | When a top rotates, it rotates about its centre of mass. The centre of the mass is a point on the axis of rotation. Since the axis is also stationary as is the centre of mass, therefore all the points in the axis are eligible to be considered fixed about which the top is rotating.
Besides,I would prefer to use the ter... | {
"language": "en",
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Luminosity of an accretion disk? With reference to Black holes in particular, how can you approximate the luminosity of an accretion disk? It is possible to quantify the temperature at a given point, but as the disk is not a black body, and this temperature is at a specific point, I am unsure how to equate this to lumi... | The simplest answer is that you integrate the emission from annuli radiating at various temperatures. Explicitly, the luminosity per wavelength in this approximation is
$$L_\lambda = 2 \int_{r_{\rm in}}^{r_{\rm out}} 2 \pi r [\pi B_\lambda(r)] dr$$
where the overall factor of 2 is for the two sides of the disk, $2 \pi... | {
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Is a falling leaf an example of a chaotic system? Let´s assume is a wind still day in autumn. When a little change is made in the initial motion of a leaf at the time it falls off a tree, the resulting path of motion of the leaf is very different from the path that would develop if these changes wouldn´t have been made... | It depends on your exact definition of chaos:
*
*We certainly have a strong sensitivity to initial conditions (butterfly effect), which is the one property of chaos everybody seems to agree upon.
*We do not have topological mixing.
*The falling to the ground is only a short-lived transient compared to the non-chao... | {
"language": "en",
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What is beyond gamma rays and radio waves in the electromagnetic spectrum? The electromagnetic spectrum is commonly referred to as consisting of;
radio-waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays - of increasing frequency from left to right.
But is it possible to get radiation of higher ... | Beyond radio waves are mega-giga-super-long waves as the wavelength approaches infinity; the longer they are, the more they dissolve into nothingness because once half the wavelength $\frac{λ}{2}$ gets more or less bigger than the radius of the entire universe, they cannot really interact with anything. In other words,... | {
"language": "en",
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Why doesn't orbital body keep going faster and faster? If we consider the change in velocity during an infinitesimal interval of an orbit:
where body B is orbiting body A, we can see that the magnitude of the resultant vector (the green arrow) is greater than the magnitude of the original tangential velocity. Why does... | Since you still seem puzzled I'll try a different tactic here:
You're showing the tangential velocity (A) and the radial acceleration (B) and adding them to get the green arrow. What you're missing is that this occurs in a gravity field. As the initial path climbs away from the object it's orbiting it loses velocity.... | {
"language": "en",
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What is the difference between metallic hydrogen and plasma of hydrogen? As far as I know, metallic hydrogen and plasma seems share some common properties, eg:conduct electricity, nuclei share electrons, high temperatures...
So my question is, is metallic hydrogen in fact plasma state of hydrogen? If not, what is the d... | In metallic hydrogen, the protons share an approximately fixed location relative to each other - energetically, a lattice is more favorable than an randomized state. Because of this, the substance is not a plasma - in a plasma, the positive and negative charges both flow freely.
Metallic hydrogen only exists at very lo... | {
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Why does the sign of Delta H indicate whether the reaction is exothermic or endothermic? If $\Delta H = Q + W$ (assuming constant conditions), then there are two terms involved in calculating $\Delta H$, only one of which measures heat gained/released. It is possible then for $\Delta H$ to be negative (if $W$ were very... | The symbol $\Delta$ (here) simply means difference, e.g.:
$$\Delta H=H_2-H_1$$
So, enthalpy of the end state minus enthalpy of the initial state.
In the case of an exothermic reaction the system has lost enthalpy, so:
$$H_2<H_1$$
Thus, for an exothermic reaction:
$$\boxed{\Delta H=H_2-H_1<0}$$
It is possible then for ... | {
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Difference between inviscid and viscous flow In my lecture notes, I have a load of examples and I want to sort out which egs are viscous flow and which are inviscid flow. It is not always said if the flow is viscous or inviscid. Please can someone tell me what other things determines the difference rather than just the... | Quite simply, a viscous flow is a flow where viscosity is important, while an inviscid flow is a flow where viscosity is not important.
Gases and liquids alike are considered fluids and any fluid has a viscosity. So a gas bubble surely has a viscosity, albeit relatively low compared to some liquids; liquids are genera... | {
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Pressure on the sides of a container? Sorry if this is an incredibly basic question for these categories. Basically, I don't understand these types of problems. I'm sure it's something really simple I'm missing.
Let's say there's an open swimming pool with width $w$, length $l$, depth $d$, and density $\rho$ (equal to ... | Pressure is indeed F/A however force varies upon the depth of the water therefore to find the force you need to
"divide each area into small bands of areas, each having its own pressure (rho)gh, then add up those little forces you have got to gain the total force on the wall"
Which this is actually the concept of int... | {
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De-merits of the application of Laplace's Equation to find electrostatics potentials QUESTION: What are the de-merits of the application of Laplace's Equation to find electrostatics potentials?
Our professor told us that the answer was as follows:
It can be used only when the charge distribution is at the boundaries
... | Well, if there were charge between the boundaries, you would be solving Poisson's equation rather than Laplace's equation. However, boundary conditions for the potential function are also crucial, because there could always be distant point charges that modify the field in the region of interest, without changing the d... | {
"language": "en",
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Where are the photons coming from? Particles and Antiparticles can annihilate, and they are completely destroyed in the process, which creates photons.
From wikipedia:
An unstable atomic nucleus with an excess of neutrons may undergo β− decay
n → p + e− + -νe
neutron decays into proton, electron, and electron antineutr... | I had similar stupid doubt.
It's coming from binding energy.
The equation you give:
Unstable atomic nuclei with an excess of protons may undergo β+ decay
$$p → n + e^{+} + \nu_{e}$$
proton decays into neutron, positron, and electron neutrino.
How do you think a proton can be converted to neutron which has greater ma... | {
"language": "en",
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estimating deviations from ideal gas behaviour How can one estimate the pressure at which argon atoms show deviations from ideal gas behaviour due to the finite size of the atoms?
I have tried Taylor expanding the hard sphere gas equation:
$$P'(V-b)=NkT $$
to get $P'=P(1+b/V)$ to first order, where $P$ is the ideal ga... | For a bit more empirical approach, try the compressibility factor. With this factor, the ideal gas equation becomes PV = znRT, where z is described in very great detail by https://en.wikipedia.org/wiki/Compressibility_factor.
For places on the "z plot" that differ substantially from a value of z=1, you will find that ... | {
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Why do liquids exert pressure on the sides of a container? What makes a liquid push against the walls of a container if the liquid is completely static?
I was thinking a comparable situation would be a bin full of baseballs. Unless the balls were perfectly stacked they would be rolling off one another and the walls of... | The reason is because liquids don't have preferred directions.
It's true that if you squeeze a regular solid by pushing down on it, it'll push back up on your hand but it won't exert any force to the sides (though it might bulge out a bit). If you model a solid as a cubic lattice of masses connected by springs, this ma... | {
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Why does the interference pattern change with given relation when the source slit changes? Why should the dependence relation be like $${\frac{s}{S}}<{\frac{\lambda}{d}}$$ for the interference condition to be seen?
Where $s$ is the width of the source slit and $S$ is the distance between the source slit and the double ... | Answer
Interference pattern is formed by diffracted-on-double-slits beams. When your condition is not met beams of different orders of diffraction superpose and interference pattern becomes blurred and disappears.
Explanation
Angular spacing of the fringes:
$$(tan)\theta_{fringes} = \frac{\lambda}{d}$$
Angular spacing ... | {
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Why does the 'Jacobian of at least one combination of $n$ functions shall be different from zero'? I've started reading The Variational Principles of Mechanics by Cornelius Lanczos; here is the concerned excerpt from p. 11:
The generalized coordinates $q_1,q_2,\ldots, q_n$ may or may not have a geometrical significanc... | The conditions about
*
*(i) differentiability of the functions and
*(ii) the maximal rank of the corresponding rectangular Jacobian matrix
are regularization conditions imposed to simplify the mathematical analysis of the physical problem, in particular to legitimate the possible future use of the inverse functi... | {
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Maxwell velocity distribution, in 1D or otherwise I learned from my textbook that Maxwell's velocity distribution gives: $$v_{rms} =\sqrt{\frac{3kT}{m}}$$ $$v_{avg} = \sqrt{\frac{8kT}{\pi m}}$$
Presumably this is for a three dimensions. This confuses me because for one-dimensional distributions the values are $$v_{x,rm... | The definition of $v_{avg}$ for 3 dimension is $$v_{avg}=\int_0^\infty |v|f(v)dv$$ However, it needs to be clear that $$v^2=v_x^2+v_y^2+v_z^2$$
For 3D, the distribution can be derived from 1D distribution but a little different. $$f_{3D}(v) = \left(\frac{m}{2 \pi k T}\right)^{3/2} \exp\left(-\frac{m v^2}{2kT} \right)$$... | {
"language": "en",
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Speed of Sound in matter So basically when it comes to the speed of sound, it is said that speed of sound in media is based on two main factors - 1)elasticity and 2)density from the formula
V= $\sqrt{E/\rho }$
where E is the modulus of elasticity and $\rho$ is the density.Now this represents that Speed of Sound is in... | Adiabatic bulk modulus of air $=1.4\times 10^5$ Pa and Young's modulus of steel $=1.8 \times 10^{11}$ Pa.
Density of air $= 1.2 $ kg m$^{-3}$ and of steel $8050$ kg m$^{-3}$.
The interaction between the atoms within steel is via the bonds whereas the interaction in air are by molecules colliding with one another and l... | {
"language": "en",
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Rotational movement at the equator What is the centripetal acceleration if you are moving with $100\frac{km}{h}$ on the equator if you are are moving a) east b) west?
Shouldn't the acceleration be the same given with $a_{cp}=\frac{v^2}{r}=\omega^2r$. Has the angular speed of earth $\omega_e=\frac{2\pi}{r}$ any influenc... | For the first part of your question, you have to realize that your net velocity (the one that you plug into the expression for centripetal force) is the vector sum of the surface velocity and your velocity relative to the surface. If you were running West as fast as the earth turns East, you would "stay in place" and t... | {
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What are the differences between the differential and integral forms of (e.g. Maxwell's) equations? I would like to understand what has to be differential and integral form of the same function, for example the famous equations of James Clerk Maxwell:
How to know where to apply each way?
Excuse the ignorance, but alwa... | I would like to point out also, the differences between the Maxwell-Faraday equation, and Faraday's law itself ( emf = -d/dt(magnetic flux)). Faraday's law, combined with the Maxwell-Faraday equation, can show that the total emf due to ANY change in flux is equal to Emf =int (e+Vxb).dl
which corresponds to transforme... | {
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What is the nature of equilibrium between water and air in a sealed container that is heated above 100C? In the case of a single substance (water), looking at the phase diagram is enough to conclude what happens upon heating:
(source: WolframAlpha)
But what if I have water and air (or some other gas) in the same seale... | Let's say that you have a vessel containing water and air and you start heating it. The temperature of the water and air inside will start to rise and so will the pressure, because the air would like to expand (but volume is fixed and water is almost incompressible). Since the boiling point of a substance depends on bo... | {
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Two Black Holes held stationary by EM forces If two black holes with large enough mass (so that the tidal forces are minimal and the intersection is large) that are held apart by like charges (saddle point stability). Imagine the black holes in a vacuum placed such that there event horizons are overlapping. Is this ove... | Traversable - Overlapping (actually intersecting) region would not be Traversable even if the gravity at some parts of the region may be zero. For exampple, between earth and moon, gravity will be zero at some point. That does not mean something in that region can go out of earth/moon system. As soon as an observer lea... | {
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Modern interpretation of wave-particle duality As far as I understand, in the early days of quantum theory there was quite a lot of debate over how to interpret what it meant for a quantum mechanical object to exhibit both wave-like and particle-like properties.
Is it correct to say that the modern interpretation (as ... | I think what you wrote is fine, and interpretation matters a lot to answer this question. However, I think the notion of "wave particle duality" is still meaningful. There are two ways a wave function can evolve, via time evolution given by the Schrodiner equation, or randomly via external measurement. When not being m... | {
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Why are the electric force and magnetic force classified as electromagnetism? I confuse the four kinds of fundamental interactions, so I think the electric force and magnetic force should not be classified as a big class called electromagnetism.
Here is my evidence:
*
*The Gauss law of electric force is related to t... | The classical electromagnetic effect is perfectly consistent with the lone
electrostatic effect but with special relativity taken into consideration.
The simplest hypothetical experiment would be two identical parallel
infinite lines of charge (with charge per unit length of $ \lambda \ $
and some non-zero mass per un... | {
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Question on doing the integral for Fermi golden rule Today in the lecture, my professor did something which confused me
As an example, we consider the photoelectric effect, in which an
electron bound in a Coulomb potential is ionized after interacting
with an external electromagnetic field. [...] The absorption ra... | The delta function $\delta(x)$ has unit area, but the function $\delta(2x)$ is "half as wide" and thus has half as much area; thus you can pick up extra factors from 'how fast' you cross the peak of the delta function. The general identity is
$$\delta(f(x)) = \sum \frac{\delta(x-x_i)}{\big| df/dx|_{x=x_i} \big|}$$
wher... | {
"language": "en",
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What does it mean that the laws of physics are time reversible?
The Universe, as far as we can tell, only operates according to laws
of physics. And just about all of the laws of physics that we know are
completely time-reversible, meaning that the things they cause look
exactly the same whether time runs forwar... | Only the mathematical formulas are time reversible. That does not mean that the law itself is reversible. You can understand it this way - Every law/formula has an implicit condition that says - "time flows only forward".
Other way to understand can be that when the coffee cup falls, universe (gravity in this case) mak... | {
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What does a voltmeter actually measure? For time varying fields (even quasistatic ones) the electric field is given by
$${\bf E} = - \nabla \Phi - \frac{\partial {\bf A}}{\partial t}$$
So what does a voltmeter measure? Does it measure a difference in $\Phi$ between two points $a$ and $b$, or does it measure $\int_a^b ... | A voltmeter does not measure $\Phi$ (the electrostatic potential), nor the difference $\Phi_A - \Phi_B$ where $A$ and $B$ are arbitrary points in a material. It also does not measure $-\int \vec E \cdot d\vec l$.
A voltmeter measures the difference in the electrochemical potential between point $A$ and point $B$, divi... | {
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Where does $\hat{P}\psi(x) = -i\hbar \partial_x \psi(x)$ come from? It's a very basic question, where does the relation $$\hat{P}\psi(x) = -i\hbar \partial_x \psi(x)$$ for any square integrable $\psi(x)$ come into existence? Some texts I found states that the above relation comes as a consequence of momentum being defi... | That $\hat{P} = - i \hbar \partial_x$ generates translations comes from a straight-forward computation: if $\psi$ is continuously differentiable, and $\Psi$ as well as its derivative are square integrable, then you can prove that
\begin{align}
i \frac{\mathrm{d}}{\mathrm{d} y} \bigl ( \psi(x - y) \bigr ) \big \vert_{y... | {
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Accelerations of Cylinders I got a box hanging from a rope that passes through an ideal pulley that attaches to the superior part of a Cilynder and makes it rotate. An exercise asks me two things:
a) determine the magnitude of the acceleration of the block
b) what is the magnitude of the acceleration of the center of... | If you see on the cylinder as a wheel then note that its center moves twice slower than top point attached to the block. Same is for acceleration.
In each moment the cylinder rotates around the point of its touch to the table, so radius from touch-point to the center is twice less than radius to the cylinder top point... | {
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Why would a spinning space station create a centrifugal force on an astronaut rather than simply spinning around him/her? We often see films with spinning space station that create artificial gravity by having the astronauts pulled outwards by centrifugal force.
I'd like to know if this would really happen, and if so, ... | In your scenario, your 3 statements are correct, and if nothing changes, your astronaut will not move from its spot as the wall of the cylinder moves past him. However, if somehow the astronaut "attaches momentarily" to the cylinder wall (the floor), then he will acquire the tangential velocity of the spot he attaches... | {
"language": "en",
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Non-abelian current commutators There many articles, in which non-abelian current commutators are computed. The general result is that quantum corrections lead to additional term in commutator
$$[J^a_\mu (x), J^b_\nu (y)] \delta (x^0 - y^0) = [J^a_\mu (x), J^b_\nu (y)]_{classical} \ \delta (x^0 - y^0) + A_{\mu \nu} (... | Restrictions can be imposed on the anomalous terms from general considerations even without fully solving the Feynman diagrams. In fact, the restrictions on the Schwinger term in the commutator given in the question are explicitly described in detail by Roman Jackiw in his review article: Field theoretic investigations... | {
"language": "en",
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Does Heat Cause Time Dilation? Since heat is defined as the movement of molecules, and because of relativity time slows for faster moving objects, would a hot object be in a slower time frame then a cooler object, because the hot objects molecules are moving faster?
| Just to add some influences of heat on a stationary clock on the surface of a star.
Heat is energy, and energy increases the energy-momentum tensor, so effectively increases the mass. With everything else remaining equal, this would increase time dilation.
On the other hand, heated bodies increase their volume. The ... | {
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Why would two inertial frames be distinguishable, if the coordinate of an event perpendicular to the motion would be different? This question arises from the classical example: imagine a laboratory frame, and a space shuttle frame, the space shuttle moving in the laboratory frame with a constant velocity, let's say in ... | What is meant is that physical laws are the same between (inertial) reference frames so that if you observe two bodies undergoing an elastic collision then you will experimentally determine that the momentum before the collision is the same as the momentum after the collision. An observer in another frame will also not... | {
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Effect of a nuclear weapon on the Moon In some science fiction novel, there is the scenario of using nuclear weapons to deflect an Earth-approaching asteroid.
But the question is, is a nuclear weapon really as useful on the moon or an asteroid as on Earth?
The point is that, on the Earth, there is the atmosphere. The... | Indeed, a nuclear bomb works a bit differently in a vacuum than in the atmosphere. If you want to generate momentum, an atmosphere or some material with a low boiling point (e.g. ice) is probably better than bare rocks in vacuum, because all the heat will be converted directly into gas with a high momentum, without "wa... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/258558",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
What is more basic thing to explain phenomenons : Energy or Force? You know many physical happening are explained by considering forces or we can explain these phenomenon using energy (like energy conservation, etc.).
so i was wondering that explaining the physical phenomenon using energy method is more fundamental or... | As @CuriousOne quoted, the concept of energy and force are both fundamental. The choice depends on how you need to analyse the system. As a simple example, consider a collision between two identical particles. One is at rest and the other has a definite momentum. Obviously, the one at rest is set to motion. There the m... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/258757",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
Why does Bernoulli's equation only apply to flow along a streamline that is in viscid, incompressible, steady, irrotational? I am learning about hydrofoil on this website.
In a later video I watched, I learned that in the process of deriving Bernoulli's equation, $$constant=P/d+gh+1/2v^2$$ has to multiplied through by ... | I think a derivation of the Bernoulli equation will help clarify things.
We begin with the Navier-Stokes equations
$$\frac{\partial \vec{u}}{\partial t}+\vec{u}\cdot \vec{\nabla}\vec{u} =-\frac{1}{\rho} \vec{\nabla} p +\nu \nabla^2 \vec{u},$$
where $\rho$ is the density, $p$ the pressure, and $\nu$ the kinematic visc... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/258876",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 3,
"answer_id": 1
} |
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