Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Fuel and heated iron? If I have a pile full of fuel (gasoline) - and I also have heated iron ( very very hot - color orange) and I put the Iron in the pile ,
Would the gasoline will burn ?
I mean - does gasoline need heat or actual fire in order to burn ?
nb - I can't test it since I don't have the means to do it... | I don't know what a "pile" of fuel is. I assume you mean a container full of it.
Gasoline needs oxygen to burn, and it needs the correct mixture. Too little oxygen and burning is impossible. Too much oxygen causes the same problem. To achieve ignition with Gasoline, you need between 1.4 and 7.6% petrol vapour (by volum... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/105741",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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astronomy & light pollution If you were staring to the sky in a big city and electricity is turned off in a big area around you, would you be seeing the sky with little light pollution instantly?
| If you include car lights and similar in what is turned off, then in a big city such as London, which has a radius of about 10 miles, there would be very little light pollution, instantaneously. However, there would still be a lot of atmospheric pollution, and so it wouldn't be possible to see stars as faint as can b... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/105794",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
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Differential equation for evolution of probability density in Quantum Mechanics? I have come up with this differential equation for the evolution of $\vert \Psi \vert^2$, the probability density in quantum mechanics.
Is there a name for this equation? Is the logic sound?
So I start from the conservation of the total pr... | This equation is wrong.
As it has been pointed out in the comments, I can't equate the integrands of two integrals just because the integration limits are the same.
The equation which is of relevance in the context of probability density and quantum mechanics is perhaps the well known continuity equation,
$$ \frac{\par... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/105854",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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How can point-like particles in an ideal gas reach thermodynamical equilibrium? Having learned that the particles of an ideal gas must be point-like (for the gas to be ideal) I wonder how they can reach thermodynamical equilibrium (by "partially" exchanging momentum and energy). First the probability of two point-like ... | Ideal gas does only mean that there are no forces between the particles. They do not have to be point-like. For example 2-atomic gasses could have 3 translatory and 2 rotational degrees of freedom in kinetic gas theory, while still no forces act between the molecules. So ideal but not point-like. For one-atomic gasses ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/105918",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
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Is speed of light ( Sun-to-Earth ) related to the movement speed of solar system? The speed of light has been measured to be 299 792 458 m/s.
Now, the Solar System is traveling at an average speed of 828,000 km/h (230 000 m/s). Summing up the numbers we get close to 300 000 000 m/s
Does it mean, that the speed of light... | No. Speed of light in Vacuum isn't dependent on Solar System's motion. It's a constant. It'd be same even if the motion wasn't there.
Due to your question type problems, we've even calibrated our scales to create Relativistic Physics.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/105974",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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State of constant motion Why does an object remains in its state of constant motion if there are no forces acting on that object?
My understanding is that all the energy of the motion will be kept inside and a change in the speed needs a change in the amount of the energy stored by that object. But how is that energy s... | What is force? It is the transfer of momentum with respect to time. Momentum is the product of mass of a body, and it relative velocity with respect to something. If we imagine, for once, our world made up of tiny uniform particles, then we can take the mass of one particle as one unit mass. This simplifies the situati... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/106158",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Does mass affect velocity when travelling through frictionless medium? I found the following question on an standardized test, and was debating with some friends what the answer would be:
A car of mass M is travelling with a constant velocity through a plane in which friction is non-existent. An object of mass m (m = M... | Let us first simplify a bit, and get rid of the vertical movement of $m$. It is much simpler to assume that $m$ is standing with zero velocity in the path of $M$, which will collide it at $t=0$. This will be the same problem along the horizontal axis, and avoids to superimpose it with another problem in the vertical di... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/106236",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Is an "infinitely sharp blade" possible? A staple of science fiction and fantasy is a blade (knife, sword, ...) that cuts through literally any solid object (wood, steel, concrete, skulls, ...) without effort, often even without the need to apply any pressure.
What (in theory) would be required to construct such a blad... | Pressure is a measure of the force applied to a given area. Blades are sharp because they have a small cross sectional area, allowing you to create very high pressure whilst applying only a modest force. This force generates so much of shear stress on the object getting cut that it crushes through the molecular bonds i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/106390",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Can we think of gravity as space itself moving? So if you move through space with a constant acceleration you experience longer time dilation than when you're at rest, but you also experience the same time dilation when you're under the effect of gravity like on earth, so is it possible that by standing on earth, space... | Yes, in fact that's quite a good way to think of black holes.
Imagine instead of space think about the surface of a lake with a drain hole in the middle. And think of the water flowing into the hole. The nearer to the hole the faster the water will flow.
Imagine a ship on the water which has a maximum speed of 5 knots.... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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The other side of the lever If I have a lever, but I can see only up to the hinge and not the other half, can I know whether the other half is 1 m long with a weight of 3 kg on it, or 3 m long with a weight of 1 kg on it?
| Just for fun let me suggest another rather impractical way to tell the difference.
The diagram shows the far side of the lever. It has a length $L$ that you don't know and there is mass $m$ on the end that you don't know. The torque is equal to $Fd = FL\cos\theta$, and the force is the gravitational force $F = GMm/r^2... | {
"language": "en",
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Does the Sun produce audible sound? Theoretically if I were able to build some sort of device that let me sit 1 foot away from the surface of the Sun (or any star for that matter) without being vaporized, would a star produce any sort of audible sound at that distance? From my understanding, sound waves need a medium... | helioseismology is what you need to learn about. yes, there are sound waves in Sun
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/106652",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Derivation of Lagrangian? I know that the Lagrangian $L$ is defined to be $T-V$, i.e. the difference between kinetic energy and potential energy. Also the Action $S$ is defined to be $\int Ldx$ and from this we can derive Newton's 2nd law of motion.
*
*If we get Newton's second law out, does it mean that the formula... | Newton's second law, $\mathbf{F}_{net}=\dot{\mathbf{p}}$, is the definition of force. Lagrangian and action are defined to be $ T-V $ and $\int L\: \mathrm {d} t$ (and not $\mathrm {d} x $) respectively. You don't derive anything from anything here (however we can talk about how $ T $ and $ V $ come about).
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Normalization of Source Terms in Large-N Gauge Theory Typically when you do the counting for large N gauge theory, you rescale fields so that the Lagrangian takes the form
\begin{equation}
\mathcal{L}=N[-\frac{1}{2g^2}TrF^2+\bar{\psi}_i\gamma^\mu D_\mu \psi_i]
\end{equation}
where I have chosen the original coupling of... | The operator $O^i$ in the source term will in general also contain fields that are rescaled, and the scaling behaviour is supposed to match the rest of the Lagrangian.
If you did not have a factor of $N$ in the source term, you would not need to divide by $N$ when taking functional derivatives. What matters is the res... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/106867",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Can magnetic flux be negative I am studying magnetic flux linkage in an ac generator and it appears to be that magnetic flux linkage is negative half the time, how can this be?? Also with lenz's law why is emf defined as negative when magnetic flux is increasing and how does this relate to the direction of the current?... | Yes, magnetic flux can be negative. It just depends on where the field is going. Say there is a sheet and magnetic field is going through it from front to the back, we can call the flux there as positive and negative when it's the other way round.
It is pretty clear from the statement of Lenz's Law why the emf defined ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/106949",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Are there any QM effects where charged particles are not intimately involved? Are there any QM effects that have been/could be measured from interactions involving non-charged particles?
Elementary QM is all about the electron energy levels in the atom, photon - atom interactions, etc.
When one looks at the nucleus, ... | Weak and Strong interactions do not involve charge. Strong interactions involve color charge, which is a different property than "normal" charge. The weak interaction mostly involves flavor change.
As to your non-charge dependent Quantum Mechanical effects, we have tunnelling. See for example this link.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/107031",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Lepton number conservation in standard model
*
*Why is it said that in standard model lepton number is conserved?
*How do I know that Lepton number is an abelian charge?
*Why is this conservation not as sacred as electric charge conservation.
*How does one mathematically distinguish between lepton number and el... | Let me address your questions one by one.
Why is it said that lepton number is conserved in Standard Model (SM)? How do I know that lepton number is an Abelian charge?
The SM Lagrangian is invariant under the fermion transformations,
$$
\psi \to e^{iL\theta}\psi
$$
where $L$ is assigned such that $e^-$, $\mu^-$ and ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/107128",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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What happens with a tunneling particle when its momentum is imaginary in QM? In classical mechanics the motion of a particle is bounded if it is trapped in a potential well. In quantum mechanics this is no longer the case and there is a non zero probability of the particle to escape the potential through a process call... | There is a detailed description of the behaviour of quantum systems during tunnelling. They do not involve the particle travelling faster than light. The "group velocity" does not correspond to the velocity of anything in that situation. What happens instead is that the wave function undergoes interference inside the b... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/107261",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Does electric field cause changing magnetic field also? According to Faraday's law, changing magnetic field causes eletric field (imprecise wording, but generally accurate). My question is, can Faraday's law be interpreted in opposite way - that is, electric field causing changing magnetic field? Equation itself doesn'... | Yes. You can see this more clearly when working with the differential form of Maxwell's equations. You can consider the simple case of a wire of some radius with current flowing through it. If there's a small gap in the wire the current will accumulate some surface charge density at the ends of the wire at the gap. Thi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/107314",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 3,
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How can I see this equation describes advection? My notes say that this is the equation for the "advection of a quantity A at speed v":
$$ \frac{\partial \mathbf{A}}{\partial t} = \nabla\times(\mathbf{v}\times\mathbf{A}) .$$
Is this true? How can I see (mathematically) that this equation corresponds to advection?
| This term looks like Faraday's law that is used in Ideal magnetohydrodynamics (MHD). So yes, it is true.
In order to see the mathematical advection, you'll need to apply some vector calculus:
$$
\nabla\times\mathbf a\times\mathbf b = \mathbf a\left(\nabla\cdot\mathbf b\right) - \mathbf b\left(\nabla\cdot\mathbf a\right... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/107579",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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A zero gravitational potential and non zero gravitational field Give an example of a situation in which there is a non-zero gravitational field and a zero gravitational potential at the same point?
$$dV=-\vec E\cdot d\vec r.$$
The above equation implies that such a situation is possible.
| The gravitational field $\mathbf g$ equals, by definition, negative of the gradient of a correspondonding potential $\Phi$;
\begin{align}
\mathbf g = -\nabla\Phi.
\end{align}
Therefore, it suffices to produce a gravitational potential $\Phi$ whose value is zero at a point but whose gradient is non-zero at that point.... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/107691",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Lagrangian for relativistic massless point particle For relativistic massive particle, the action is
$$\begin{align}S ~=~& -m_0 \int ds \cr
~=~& -m_0 \int d\lambda ~\sqrt{ g_{\mu\nu} \dot{x}^{\mu}\dot{x}^{\nu}} \cr
~=~& \int d\lambda \ L,\end{align}$$ where $ds$ is the proper time of the particle; $\lambda$ is the par... | It is conceptually possible to have a massless charged particle, although there are none that we know of. It is not true that the Lorentz force has to equal mass times acceleration. The momentum of a massless particle is a quantity indepenedent of its speed as all massless particles travel at the speed of light. ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/107921",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "14",
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If the MH370 black box did sink to 15000 ft, how long would it have taken? I have been following MH370 on the news just as everyone and latest reports seem to indicate that the black-box could be found. A recent info-graphic http://t.co/lyBBE9C2hF shows the insurmountable depth of the oceans and how the black-box could... | You say, ignore currents and I assume, other extraneous factors.
If that is the case, then, considering a hydrostatic balance in the water column where z is the vertical coordinate. Then, the motion of a water parcel with density, $\rho$, displaced upwards by a distance, $\Delta z$, in a fluid with a reference density,... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/107997",
"timestamp": "2023-03-29T00:00:00",
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Why is the divergence of a magnetic field equal to zero? We know due to Maxwell's equations that:
$$\vec{\nabla} \cdot \vec{B}=0$$
But if we get far from the magnetic field, shouldn't it be weaker?
Shouldn't the divergence of the field be positive?
If we define the vector field as a function of distance, then if the d... | Your intuition about the meaning of the divergence operator is wrong.
In physics it's easiest to think intuitively about divergence by using the divergence theorem which states
$$\int_V dV \ \nabla \cdot \mathbf{B} = \int_{\partial V} \mathbf{B} \cdot d\mathbf{S}$$
where $\partial V$ is the surface area surrounding t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/108224",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Loop-the-loop question
Problem: The marble rolls down the track and around a loop-the-loop of radius R. The marble has mass $m$ and radius $r$. What minimum height $h$ must the track have for the marble to make it around the loop-the-loop without falling off?
Express your answer in terms of the variables $R$ and $r$... | Your expression for the velocity looks right; but we have to get a few other things taken care of.
First - the center of the marble doesn't move from 0 to 2R, it moves from r to 2R-r - so the potential energy due to this is smaller than mg(2R) which is what you had in your expression.
On the other hand, you need to tak... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Battery Capacity vs. Battery draw Pardon my ignorance but I just can seem to find an Answer to my question and I hope that you can help me.
What is the equation for calculating how long a Lithium Battery can supply a device?
For instance a Lithium battery has a capacity of 5600mAh, and an Output of 5V 2A. The drawing d... | Yes , that's easy because mAh is presented for a specific voltage that battery can output. Because the battery must output at a specified voltage. Your 5600mAh is for 5 volts. If it's not 5 volts. You must recalculate it. But the voltage shouldn't be change if the battery is not adjustable.
Hope you understand
| {
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"source": "stackexchange",
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What is an intuitive explanation using forces for the equatorial bulge? The earth is not a sphere, because it bulges at the equator.
I tried fiddling with centripetal force equations and gravity, but I couldn't derive why this bulge occurs.
Is there
(a) a mathematical explanation using forces (not energies) and
(b... | If you have ever seen a pizza being made by hand, you will know that when the baker throws the disk of dough in the air, he makes it spin. As he does so, the pizza "disk" gets bigger because the dough on the outside experiences a larger centrifugal force (in the rotating frame of reference of the pizza. Don't start on ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/108640",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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In what sense do Goldstone bosons live in the coset? Goldstone's theorem says that if a group, $G$, is broken into its subgroup, $H$, then massless particles will appear. The number of massless particles are given by the dimension of the coset, $G/H$. It is then often said that the Goldstone boson's live in the coset. ... | It is in fact a very simple matter if you use a different parametrization of the fields. Since we care about the Goldstone bosons only, just send $\lambda\rightarrow \infty$ so that the Higgslike state decouples. Moving to the following parametrization
$$
\phi_i(x)=U(x)\langle \phi_i\rangle \,,\qquad U(x)=e^{i \hat{T}... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/108722",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "25",
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Does it make sense to open one window all the way when the other window is much smaller? I can't wrap my head around this idea because I don't know much about air flows.
Say we have this imaginary apartment with two windows, one of which is two times smaller than the other:
Will the first one let more air through than... | If you are familiar with electric circuits in a quite loose analogy you can look at your windows as impedances for the air current. Since current is turbulent (take a look at the Reynolds number if you do not know it) the air does not directly go all the way down through all the windows, but each of them will create so... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/108802",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
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Finding the vacuum which breaks a symmetry I will start with an example. Consider a symmetry breaking pattern like $SU(4)\rightarrow Sp(4)$. We know that in $SU(4)$ there is the Standard Model (SM) symmetry $SU(2)_L\times U(1)_Y$ but depending on which vacuum we use to break this symmetry, in a case you can totally bre... | As I understand the question, it is: what are the possible unbroken subgroups when a symmetry group G is spontaneously broken? If we assume that Lorentz invariance is unbroken, then we can look at the possible vacuum expectation values of a scalar field that transforms under some representation R of the symmetry group ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Converting between (abstract) linear operators and their position representations Just as we have an abstract state vector $|\psi\rangle$ and its position representation $\psi(\vec{x}) = \langle \vec{x} | \psi \rangle$, how do we transform between a linear operator, say $H$, that acts on state vectors thus: $H |\psi\ra... | This simply follows from a resolution of the identity, written (formally) as $\int dy |y\rangle\langle y| = 1$:
$\langle x|HU(t)|x\rangle = \int dy\langle x|H|y\rangle\langle y|U(t)|x\rangle$, which after integrating out the delta function arising from the matrix element of $H$ gives you what you want.
| {
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Can molten metal be suspended in air? I wondered if magnets could be used to hold a drop of molten liquid metal in air (not for any particular reason just because it could be done), but was disappointed when a quick Google search showed the metal would lose its magnetic traits before it melted.
Are there any other forc... | Molten glass is suspended (and spun) on air jets to form "pre-forms" for molding glass optics. I suspect that the same must be possible for metals.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/109163",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
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Why does the Fermi Surface cross the Brillouin zone boundary at right angles? I'm not sure why the fermi surface crosses the Brillouin zone boundary at right angles. I understand that this is normally the case, but not necessarily always.
I'm aware that the fermi surface is a constant energy surface up to the filling p... | I believe it has to do with translation, inversion, and mirror symmetry?
In real space, the potential energy has to share the same periodicity as the lattice. Similarly in k-space, the Fermi energy surface has to share the same periodicity as the reciprocal lattice. Brillouin zone boundaries are like the markers in k-... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/109416",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
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Index Notation with Del Operators I'm having trouble with some concepts of Index Notation. (Einstein notation)
If I take the divergence of curl of a vector, $\nabla \cdot (\nabla \times \vec V)$ first I do the parenthesis:
$\nabla_iV_j\epsilon_{ijk}\hat e_k$ and then I apply the outer $\nabla$...
and get:
$\nabla_l(\na... | First some notation
$$\nabla \times \vec B \rightarrow \epsilon_{ijk}\nabla_j B_k$$
$$\nabla \cdot \vec B \rightarrow \nabla_i B_i$$
$$\nabla B \rightarrow \nabla_i B$$
Now, to your problem,
$$\nabla \cdot(\nabla \times \vec V)$$
writing it in index notation
$$\nabla_i (\epsilon_{ijk}\nabla_j V_k)$$
Now, simply compute... | {
"language": "en",
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Interpretation of Conjugate Momentum in Field Theory The conjugate momentum density, following as a conserved quantity with Noethers Theorem, from invariance under displacement of the field itself, i.e. $\Phi \rightarrow \Phi'=\Phi + \epsilon$, is given by $\pi=\frac{\partial L}{\partial ( \dot{\Phi})}$.
On the other ... | Conjugate momentum in field theory is really just an infinite particle generalization of conjugate momentum in classical mechanics. The reason we impose commutation relations using the conjugate momentum is due to Dirac's canonical quantization prescription. This is well explained by Qmechanic in this answer.
I'll brie... | {
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What's the difference between average absolute error and relative error? I am quite confused by both these terms. I would like to know what's the exact difference between both these terms and which one is more accurate.
| The absolute error can be measured using this formula:
$$\varepsilon_a=\frac{x_{max}-x_{min}}{2}$$
That is the difference between the highest value and the lowest value that you get after some measurements. The Relative error is:
$$\varepsilon_r=\frac{\varepsilon_a}{\bar{x}}$$
where $\bar{x}$ is the average of all your... | {
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Does electricity flow on the surface of a wire or in the interior? I was having a conversation with my father and father-in-law, both of whom are in electric related work, and we came to a point where none of us knew how to proceed. I was under the impression that electricity travels on the surface while they thought ... | I'll try to keep it short and sweet; Stranded wire is capable of delivering high amperage without overheating because the strands devide the load..I.E. battery cables on your car. stranded wire is superior to solid but to expensive for long runs, so solid wire is used for long runs like for your house (easy to snake or... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Work done or not in this case? I have a very simple question. A motorboat directed upstream is seen to be at rest from the bank of a river. Is the engine doing any work? Is it right to say that since it is not causing any displacement, so it is not doing any work.
| It does do work: it's causing the water in the wake of the boat to move downstream faster than the rest of the current. The engine is doing work on the water, rather than doing work on the boat.
| {
"language": "en",
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Why is uncertainty divided by $\sqrt{3}$? Why do we sometimes have to divide uncertainty of the measurement by $\sqrt{3}$?
For example we have the uncertainty of the measurement with a ruler with the smallest scale of 0.01 cm. This 0.01 cm is not our uncertainty of measurement, but we first divide it by $\sqrt{3}$ and ... | I have found out the answer.
When you do a measurement (one measurement) you have many uncertainty sources. But if you want to have the combined uncertainty, you don't add like $1 + 1$, because that would give you uncertainty of $2$, but that doesn't have to be the case. The true value of the measurement may lie in bet... | {
"language": "en",
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Number of planks required to stop the bullet A bullet looses (1/n)th of its velocity passing through one plank. The number of such planks that are required to stop the bullet can be?
Logically, to me the answer seems to be infinity, as always a fraction of velocity will get reduced. But in my book the answer is n^2/(2n... |
Ayush: Isn't the question telling that the bullet always loses 1/n th of its velocity no matter which plank?
Based on the answer provided, it seems the writer wanted you to assume that the energy loss per plank is constant. This is not the same as the bullet losing $1/n^\text{th}$ of its velocity per plank (however... | {
"language": "en",
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Is frequency quantized in the black body spectrum? I'm aware that there're some questions posted here with respect to this subject on this site, but I still want to make sure, is frequency quantized? Do very fine discontinuities exist in a continuous spectrum like the black body spectrum?
The quantization of photon ene... | well, the frequency of a photon is not quantized, we observe all 'kinds of colors (frequencies)'...what is quantized is the quantity of photons of the exact same frequency we may produced, or otherwise exist...for example, lets say we have a photon of 633 nm, then the quantity of photons that may be 'produced' is 1, 2,... | {
"language": "en",
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Why can't an excess of electrons or holes by themselves cause current flow? I am a beginner in electrical engineering. Often times (most cases actually), the underlying physics aren't really explained to us and we are just left to assume that it works "because it works." This is never enough for me in classes etc and I... | An excess of electrons can cause a current flow.
Imagine two spheres of metal. One is neutrally charged, but the other is negatively charged with an excess of electrons. Connect a wire between them, and what happens? The charge re-distributes itself so that the charge on both spheres is equal. As this is happenin... | {
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Exact diagonalization to resolve ground state degeneracies I am studying a perturbed Toric Code model that is not analytically solvable.
On a torus the ground state degeneracy of the unperturbed model is 4.
Once we turn on the perturbation there is a change in the ground state degeneracy.
I would like to detect this... | You must use re-orthogonalization procedure (Gram-Schmidt) at every Lanczos Step in order to correctly capture this degeneracy. I have found that degeneracy will not be captured correctly if you do not orthogonalize your Lanczos vectors. I have used Lanczos on 2D antiferromagnetic Kitaev model that has 4-fold degenerat... | {
"language": "en",
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What is the relation between isothermal process and its surrounding?
In an isothermal process the temperature of a system remains constant but may or may not be similar to temperature of surroundings
How is this possible?
| Isothermal processes can happen in the real-world because of insulation, very little heat exchange, or very little temperature change as the process happens.
For instance, most substances undergo an isothermal process when changing phase. You could even force some processes to become practically isothermal by cooling i... | {
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Why does squeezing a water bottle make the water come out? This seems natural, but I can't wrap my head around it when I think about it.
When I squeeze an open bottle filled with water, the water will spill out. When I squeeze a bottle, the material collapses where I squeeze it, but expands in other areas, resulting in... | Just another approach to visualize it. (two dimensional) If you look on a bottle from above, you can see the round shape. A circle is the optimal shape, where you can have the biggest amount of content per package. If you start to squeeze the circle (no matter how), the amount of stuff you can put into is decreasing. C... | {
"language": "en",
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Interference - the shortest way from the point of constructive one to the point of destructive one So this is a problem from Polish maturity exam.
The image shows 2 speakers (G1, G2) and point B. The wavelength of sound coming from both speakers is 0.155 m, and the wave coming from both speakers is in phase. So point ... | Ignoring the $1/r$ decay, the point source fields can be modeled as
$$f_\mathbf{p}(\mathbf{r})=\exp\left(\frac{2\pi i|\mathbf{r}-\mathbf{p}|}{\lambda}\right)$$
where $\mathbf{p}$ is the speaker location.
The field intensity from the two speakers then becomes
$$I(\mathbf{r})=\left|f_{\mathbf{p}_1}(\mathbf{r})+f_{\mathb... | {
"language": "en",
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Static wave's equation
In my book equation for two advanced wave which created this static wave are
$$y_1=asin{\frac{2\pi}{\lambda}(vt+x)} $$
$$y_2=asin{\frac{2\pi}{\lambda}(vt-x)} $$
and equation for static wave is derived by adding this two equation: $\ Y=y_1+y_2$
Q1: Though this two wave comes from opposite directi... | It doesn't matter whether you add or subtract $y_1$ and $y_2$, because all this does is introduce a phase shift in the resulting standing wave. To see this you need the identities:
$$ \sin(a + b) = \sin(a)\cos(b) + \cos(a)\sin(b) $$
$$ \sin(a - b) = \sin(a)\cos(b) - \cos(a)\sin(b) $$
Let's take your two equations and t... | {
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Trajectory of a photon around a Schwarzschild black hole? Consider a photon coming from the infinity in a unbounded orbit to a Schwarzschild black hole (Schwarzschild radius $r_{s}$) (see this for illustration). Its impact parameter is $b$ and its distance of closest approach is $r_{0}$ with $$b^2=\frac{r_{0}^{3}}{r_{0... | In fact, the problem was that computing the deflection is not very intuitive. So the trajectory in polar coordinates is :
$$\varphi\left(r\right) = \int_{r_{0}}^{r} \frac{dp}{p^2\sqrt{\frac{1}{b^2}-\left(1-\frac{r_s}{p}\right)\frac{1}{p^2}}}$$
and in cartesian coordinates it is nothing else than :
*
*$x=r\cos\left(\... | {
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Why fermions have a first order (Dirac) equation and bosons a second order one? Is there a deep reason for a fermion to have a first order equation in the derivative while the bosons have a second order one? Does this imply deep theoretical differences (like space phase dimesion etc)?
I understand that for a fermion, w... | In fact, the Dirac equation can be expressed as a second-order differential equation of the form
\begin{equation}
\frac{1}{c^2}\frac{\partial^2\psi}{\partial t^2}-\nabla^2\psi\pm\frac{2mi}{\hbar}\frac{\partial\psi}{\partial t}-\left(\frac{mc}{\hbar}\right)^2\psi=0\,.
\end{equation}
| {
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Earphones and electric guitars I remember being in my college dorm, watching a film with a friend. His computer wasn't loud enough and we couldn't hear properly. So he took his earphones and put them on a electric guitar coil. He then plugged his guitar to his amp and voilà, we could listen through the amp.
Why on eart... | Very basically, a speaker driver has a magnet and a coil which move relative to each other when electric current is applied. (The speaker cone is attached to the moving parts and this is what moves the air that causes the audible sound).
When placed close to a guitar pickup, the tiny coil movement itself (not the cone/... | {
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Why doesn't this model plane fly? I have been designing a model plane for Design Technology for the past month or so, and today I laser cut my final design and assembled, it then tested it. Upon testing the plane does not get any lift, whereas the previous testing model which was virtually the same did.
The plane is bu... | It's not easy to tell why a plane does not fly just looking at a couple of pictures of it!
My advice is to go to a soft ground (like >10cm tall grass) and try to launch it by hand like a paper plane and see how it behaves. If it does not get a decent glide there there are very few hopes for it to lift by itself.
In th... | {
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Does electrical current have a measurable momentum? If I were to build a levitating super-cooled superconducting loop of wire with a electrically charged circuit that would discharge its stored energy to produce a large circulation of current around the superconducting loop levitating off the ground, would the loop of ... | Not only is the experiment possible, a version of the experiment at the atomic level was done by Einstein and de Haas[1]. Einstein and deHaas showed that the angular momentum inhering in the aligned electron spins in a ferromagnet can be exhibited on a macroscopic scale when the sample is demagnetize. Apparently, his... | {
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The "replica trick" initial formula In Spin-glass theory for pedestrians by Castellani and Cavagna, the initial formula used to introduce the replica trick is written as:
$$\overline{\log Z}=\lim_{n\rightarrow0}\frac{1}{n}\log\overline{Z^{n}}\qquad(1)$$
where the overbar denotes average over quenched disorder. I don't ... | Try to look at Introduction to the Replica Theory of Disordered Statistical Systems by V. Dotsenko. In the following, I've written a possible answer to your question:
\begin{equation}
f=-\lim_{N\rightarrow\infty}\frac{1}{\beta N}\mathbb{E}\left[\ln Z_{J}\right]
\end{equation}
where:
*
*$\mathbb{E}\left[\mathcal{O}\r... | {
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Why are popcorn seeds soft after popping? When a seed of popcorn is heated up in oil, it pops like this:
You can take one of these popped pieces and eat it with little to no problem. However, if you get an un-popped seed and sink your teeth in, it is noticeably harder. Why is this?
| Normally I feel uncomfortable giving Wikipedia-based answers since it seems lazy, but the Wikipedia article does a good job explaining it. It appears that the heating itself, rather than the popping, causes the popcorn starch to soften:
Under these conditions, the starch inside the kernel gelatinizes, softens, and bec... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/112015",
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Twin Paradox: Still a Paradox? Alright, so David Griffiths in his "Introduction to Electrodynamics" states that the Twin Paradox is not a paradox at all since the traveling twin returns to Earth. By returning to Earth, the twin had to reverse direction, thus undergoes acceleration, and therefore cannot claim to be a st... | I believe the twin paradox is truly a paradox in that the same problem approached different ways gives different answers. So if the travelling twin accelerates from near earth at 1g, he will be close to the speed of light (relative to earth) in one year. If he then turns 180 degrees and continues acceleration at 1g, he... | {
"language": "en",
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How to calculate the energy freed in the reaction: $^{10}_5Be +\space ^2_1H \rightarrow \space^{11}_5B + \space ^1_1H$? I have the following reaction: $^{10}_5\mathrm{Be} +\space ^2_1\mathrm{H} \rightarrow \space^{11}_5\mathrm{B} + \space ^1_1\mathrm{H}$
And I know that I have to use the formula: $E = \Delta m\cdot c... |
How do I calculate $m\left(^{10}_4\mathrm{Be}\right)$ and $m\left(^{11}_5 \mathrm{B}\right)$?
The masses and various other properties of isotopes are available freely at Wolfram Alpha. They are,
*
*$m\left(^{10}_4\mathrm{Be}\right)=10.013533818u$
*$m\left(^{11}_5 \mathrm{B}\right)=11.009305406u$
where $u$ denot... | {
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Gauss’s Law inside the hollow of charged spherical shell Use Gauss’s Law to prove that the electric field anywhere inside the hollow of a charged
spherical shell must be zero.
My attempt:
$$\int \mathbf{E}\cdot \mathbf{dA} = \frac{q_{net}}{e}$$
$$\int E \ dAcos\theta = \frac{q_{net}}{e}$$
$$E \int dA = \frac{q_{net}}{... | It isn't enough to show that the net field over some randomly chosen surface within the shell is zero. After all, this is also true of a closed surface between the plates of a capacitor, but the field is not zero there.
You need to use the spherical symmetry and choose a sperical shell centred at the centre of your sph... | {
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Clebsch-Gordan Coefficients for two spin-1 particles - Why is there a ∣0⟩∣0⟩ ket? I have used the rules for addition of angular momenta to work out the Clebsch-Gordan coefficients, which all seem right except for state $\lvert0,0\rangle$:
For n = 1
\begin{align}
\lvert1,1\rangle & = \frac{1}{\sqrt 2} \left( \lvert0\ran... | If you have two spin-1 particles, there are $three$ states where the projection of the total angular momentum is zero:
$$
\begin{align}
\left|2,0\right> &= \frac1{\sqrt6} \left(
\big|1,1\big>\big|1,-1\big>
~~+~~
\big|1,-1\big>\big|1,1\big>
~~+~~
\sqrt4\cdot
\big|1,0\big>\big|1,0\big>
\right)
\\
\left|1,0\right> &= \fra... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Constant power in rotational dynamics I am having trouble understanding and applying the concept of constant power (e.g. a motor) in rotational dynamics. We have that:
$$P=\tau\omega$$
Therefore if we imagine a physical system with a motor, supplied with a constant voltage and current such that $P=P_{0}$ is a constant,... | Wolfram Alpha wont give you the coefficients of integration properly.
The solution is
$$ t = \int \frac{1}{\dot \omega}\,{\rm \omega} = \int \limits_{\omega_0}^\omega \frac{I \omega}{P-\gamma \omega^2}\,{\rm d} \omega $$
$$ t = - \frac{I}{2 \gamma} \ln \left( \frac{P-\gamma \omega^2}{P-\gamma \omega_0^2} \right) $$
wh... | {
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Which clock is the fastest inside an accelerating body? The picture shows an accelerating spaceship with two clocks inside it. It is so far away from all other bodys that gravity is of no importance.
Will the bottommost clock be slower than the topmost one? Or will both clocks have the same speed?
| The clock ahead is behind in time by an amount depending on the speed of the inertial frame of reference theyare in. If the acceleration is thought of as moving through faster and faster inertial frames of reference then the amount that the clock ahead in distance is behind in time increases as the speed of the inertia... | {
"language": "en",
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Snells Law: Does the $k$ vector change on the boundary between mediums? I was using Waves - Berkley Physics Volume III, and in explaining Snell's Law the author claims that as a wave is on the boundary between glass and air (going from glass to air) that the number of wave crests per unit length along the $y$-axis must... | Asuming I've understood your setup correctly it looks like this:
The red line shows the spacing between crests, and the number of crests per unit length is just the reciprocal of this distance. The red line is obviously constant on both sides of the interface because the wavelength otherwise there would be mismatches ... | {
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Which side of wave-particle duality to choose in a given situation How does one know whether, in treating a certain problem, one should consider particles as waves or as point-like objects? Are there certain guidelines regarding this?
| It will depend on the results of your experiment, the results will tell you whether you are seeing the wave nature or the particle nature.
Take the scattering of an electron on a proton producing an electron and a proton and a pi0 meson. Your experiment measures "particle" interactions, in the form of classical particl... | {
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$\Delta^+$ decay in GZK process The dominant channels in the GZK process are
$$p+\gamma_{\rm CMB}\to\Delta^+\to p+\pi^0,$$
$$p+\gamma_{\rm CMB}\to\Delta^+\to n+\pi^+.$$
According to the pdg, $\Delta\to N+\pi$ makes up essentially 100% of the branching ratio (BR). It doesn't, however, say which process is favored: the p... |
[...] $\Delta^+ \rightarrow p + \pi^0$, [...] $\Delta^+ \rightarrow n + \pi^+$,
which process is favored: the proton and neutral pion or neutron and charged pion [?]
Since the kinematics (and corresponding "phase space" factors) for the two final states are presumably as good as equal, the evaluation of the branching... | {
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Specific Heat equations - paradox! We know that enthalpy is $h = u + pv$. Where $u, p, v, h$ are internal energy, pressure, volume, and enthalpy respectively. Now specific heat at constant volume is calculated as $c_v = \frac{\partial u}{\partial T}$, and specific heat at constant pressure as $c_p = \frac{\partial h}{\... | $pv$ is not "a form of energy". It is just product of pressure and volume. Specific heat is the amount of heat needed to increase temperature by one unit. This heat can be expressed as $Tds$ for quasi-static processes. In constant volume case this can be expressed as $du$, because $du = Tds -pdv$ generally and $dv=0$. ... | {
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Is it possible to produce gamma radiaton using radio emitter? As in the title, I'm wondering is it possible.
I think it is possible, because we have powerful enough radiotechniques and gamma radiation are just EM waves, not particles. However I think is useless, because it costs too much.
Can anyone say something more ... | The 0.51 MeV photon from positron-electron annihilation is considerd a gamma ray and industrial X-Ray tubes emit photons that are over 1 MeV. So there is some overlap in the terminology. If your radio produces electric fields of 500 KeV or more, there is SOME way to make gamma rays come from something loosely called an... | {
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Measurement using Vernier Callipers
The diameter of a cylinder is measured using a Vernier Callipers with no zero error. It is found that the zero of the Vernier scale lies between 5.10 cm and 5.15 cm of the main scale. The Vernier scale has 50 divisions equivalent to 2.45 cm. The 24th division of the Vernier scale ex... | When the zero lies between 5.10 and 5.15, it means that the diameter is more than 5.10 and less than 5.15. The length of the vernier scale is not important. Since the 24th mark (out of 50) lines up with another mark, then the additional amount is 24 parts of 0.05, since each mark is 0.05 (5.15 - 5.10) cm. The reading o... | {
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Examples of Weyl transforms of nontrivial operators I've been able to find examples of Weyl transforms of operators like $\hat{x}$,$\hat{p}$, and $\hat{1}$, but not anything more complicated. Are there derivations of the Weyl transforms of more complicated operators, like the Hamiltonians of the Hydrogen atom or harmon... | The Wigner-Weyl transform of a function $f(x,p)$ is given by,
$$\Phi[f]= \frac{1}{4\pi^2}\iiiint f(x,p) \exp \left[ i \left( a(X-x)+b(P-p)\right)\right] \, dx\, dp\, da \, db$$
As you suggested, let us take the Hamiltonian of the harmonic oscillator, i.e.
$$\Phi[H]=\frac{1}{8m\pi^2}\iiiint p^2\exp \left[ i \left( a(X-... | {
"language": "en",
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Photobombing without app used by Harley Davidson Here we see a photobombing trick, used by Harley Davidson.
They achieve to incrust a logo on a photo you take. The logo is invisible with naked eyes and only revealed on the photo you take.
How does it work?
| The camera in a smartphone is sensitive to wavelengths of light that the human eye cannot see. Have a look at this picture from this article:
This is actually a Canon EOS 40D SLR, but the idea is the same. The human eye can't see any wavelengths longer than about 700nm, but the graph shows the camera can detect light ... | {
"language": "en",
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What would cause a spinning fluid to stop spinning? I once saw a demonstration where an electric current caused a drop of mercury to spin. The drop contained bits of iron, which could be seen flowing around in a circular pattern. As soon as the current was turned off, the spinning slowed fairly quickly. What caused ... | Friction forces seem much stronger on small objects than expected from experience. If the momentum of the moving object is not larger than the average (thermal) momentum of the surrounding material, it will get stopped quickly.
Some funghi can eject their spores at supersonic speed, but still these spores have a reach ... | {
"language": "en",
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What technological advance would allow LEP3 to surpass LEP2? I learned that for electron accelerators synchrotron radiation and acceleration are the limiting factors.
This article, that I found in one answer to this question mentions that one would not use the superconducting acceleration elements that were developed i... | There is nothing really surprising here. The limit is basically how much energy you can add to the beam in the space left after you have installed all your bending and tuning magnets.
Both magnets and cavities are better now than they were then. More over, the size of both items has gotten slightly smaller allowing mor... | {
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Road to String Theory I have a question for our theoretic SuperUsers. How much knowledge and which fields of physics you have to know to start studying string theory? I am now on QFT, after I think I'll start study Supersymmetry or maybe special cases of QED. How much more should I know to start Strings? :)
| You need to master algebraic geometry (in particular derived functor cohomology of sheaves, say EGA 1-3), algebraic topology (characteristic classes, say the entire book of Spanier), commutative algebra and algebra in general (say Lang's book and A/M), and also homological algebra (the entire book of Weibel).
| {
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Which Force would help find the mass? Two masses, A and B, are connected to a rope. A constant upward force 86.0N is applied to box A. Starting from rest, box B descends 12.1m in 4.70s . The tension in the rope connecting the two boxes is 32.0N.
What is the mass of B?
What is the mass of A?
My work and what I am stru... | Split the rope and see what force are acting on B
$$T-M_b g = M_b a$$
and on A
$$F-T-M_a g = M_a a$$
Since you know $T=20\,{\rm N}$, $F=86\,{\rm N}$, and you have calculated $a=-1.09955\,{\rm m/s^2}$ it is trivial to find $M_a=\frac{F-T}{a+g}$ and $M_b = \frac{T}{a+g}$.
| {
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What's the efficiency of real heat engines? Real heat engines always have lower efficiency than the Carnot efficiency.
I wonder how efficient real engines can be? Can their efficiency get anywhere near the Carnot-limit?
| The efficiency of heat engine cycle greatly depend on the individual processes that make up the cycle are executed. Thus cycle efficiency can be maximized by using the processes that require the least amount of work and deliver the most that is by using reversible process.
In 1824 French engineer Sadi Carnot pr... | {
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What does the work on a current carrying wire in a Magnetic Field? We consider that the force acting on a current carrying wire placed in a uniform magnetic field perpendicular to the length of the wire is given by $IBl$. If the wire moves by a distance $x$ in a direction perpendicular to its length the raise in its ki... | Your wire must be part of an electrical circuit (no closed loop = no current). Let us assume that the "return wire" is far away, where there is no magnetic field. So we have a large loop.
Now the motion of the wire in the magnetic field will induce a current that will oppose the magnetic flux change. What happens is th... | {
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Is Newton's third law always correct? Newton's third law states that every force has an equal and opposite reaction. But this doesn't seem like the case in the following scenario:
For example, a person punches a wall and the wall breaks. The wall wasn't able to withstand the force, nor provide equal force in opposite ... | (As suggested in Classical Mechanics by H. Goldstein, 3rd edition in chapter 1 : Survey of the Elementary Particles )
No, the third famous law is not always valid. As pointed out above, in the case of electromagnetism, take for an example, two charged particles A and B are in motion.
B is just travelling perpendicular ... | {
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Why is the ratio of velocity to the speed of light squared in the Lorentz factor? Why is the ratio of velocity to the speed of light squared in the Lorentz factor?
$${\left( {{v \over c}} \right)^2}$$
My only guess is the value must be positive.
| It's due to the Lorentz invariance of the spacetime interval:
$$\Delta s^2 = (c\Delta t)^2 - (\Delta x)^2 = (c\Delta t')^2 - (\Delta x')^2$$
Assume that, for example, $\Delta x = 0$ such that $\Delta t$ is the elapsed time according to a clock stationary in the unprimed frame of reference.
Thus
$$(c\Delta t)^2 = (c\De... | {
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Photons and perfect mirror A perfect mirror means, that all the photons which collided with the mirror will be reflected in the same amount, with the same energy and with the same - except sign - angle. Will the mirror get an impulse from the photons?
| Yes it will.
Assuming the light is incedent normally the change in the photon momentum is $2h\nu/c$, and consequently the momentum of the mirror will change by the same amount.
If the mirror is free to move it will be accelerated by the light and as a result the light will be slightly red shifted. There is more discuss... | {
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Why does magnet attract iron but not other metals? While searching, i found this page: http://timesofindia.indiatimes.com/home/stoi/Why-does-a-magnet-attract-iron/articleshow/4298171.cms but it does not have full explanation. So Please tell full explanation of why this happens?
| Materials (including some non-metals) that are strongly attracted to magnets are known as ferromagnetic. If you Google for this, or just search this site, you'll find lots of articles on this subject, thoughly surprisingly I don't think the question how does ferromagnetism arise has been asked before.
Electrons have a ... | {
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Is it more efficient to stack two Peltier modules or to set them side by side? Is it more efficient to stack two Peltier modules or to set them side by side?
And why?
I have a small box that I want to cool down about 20 K below ambient -- cold, but not below freezing.
(I want to keep my camera cool, so I'm putting in t... | For a 20 degree Celsius differential, parallel devices will be more efficient, if the devices are operating in their normal range of heat removal. If your camera box is extraordinarily well insulated and you can wait for hours and hours for it to cool down, then a series arrangement with both devices running at less th... | {
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Inertial navigation system: am I doing it wrong? I'm trying to develop an inertial navigation system.
I can access data from an accelerometer sensor (acceleration on three axes) and gyroscope sensor (angular velocity on three axes).
First of all, I integrate my angular velocity data with respect of time, and get angles... | One possibility is that your approach is hugely sensitive to measurement uncertainty: integrating noisy signals can be a huge problem. You might think about ways to average the measurements over time, so that they're (hopefully!) more stable.
Another possibility is that your instrument doesn't output the data in quite ... | {
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Finding out the Potential difference
Find the potential inside and outside a uniformly charged solid sphere whose radius is $R$ and whose total charge is $q$. Use infinity as your reference point. Compute the gradient of $V$ in each region, and check that it yields the correct result.
The above one is a question crop... | Considering $R$ as the radius of the sphere, The work done in taking a point charge from $\infty$ to $r(0\le r\le R)$ will involve moving the charge through the field outside the sphere and also indside from $R$ to $r$ (Note that is a solid sphere and field will also be present inside it).
| {
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Mechanical waves edge between material and vacuum I have been thinking about the propagation of EM waves vs. mechanical waves and some of their odd cases. One such case that I haven't been able to puzzle out is what happens when a mechanical wave reaches the end of a medium (such as the outer layer of the atmosphere) ... | the materials are elastic, so when it reaches the end it would reflect, because the last layer won't have other layer to collide and the elastic properties of the material would make it bounce back, making the wave reflect back. Unless the wave energy is sooo large that would break the material and in that case the par... | {
"language": "en",
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"source": "stackexchange",
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Normal reaction - force without acceleration When a body lies on the surface of the Earth it is under the influence of gravity. The force on the body due to gravity causes it to exert a force on the ground and the normal reaction acts in the opposite direction causing the resultant force on the body to be zero.
However... | Newton's second law of motion states this (verify on Wikipedia):
$$\vec F_{net} = m\vec a$$
Here, $\vec F_{net}$ is zero, so $\vec a$ is zero too. Going back in reverse (what you did in question), $\vec a = \frac{\vec F_{net}}{m}$ can only deduce that the body is experiencing no net force. That's it.
Feel free to use L... | {
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Dielectric boundary I am trying to determine why electric field may be confined to a certain region if there is a large difference in the permitivity for example if electric field flows through water and then reaches a water air boundary.
I have also been reading about EM waves, is it possible to model electric field ... | The answer to the second part of your question is yes your approach is OK. I have gone through the link you have posted and want to say that the inferences drawn from formulae written above are for non collisional case i.e. dielectric constant $\epsilon$ is real. However if $\epsilon$ is complex you can not draw the ... | {
"language": "en",
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What will happen after escaping earth's gravitational field? Suppose that I escaped the gravitational field of earth.
Then: am I going to be pulled by Sun's gravity?
| When at distance $R$ from the center of earth, the minimum velocity needed to escape from earth's gravity is $v_{esc} = \sqrt{2GM/R}$. Here, $G$ denotes Newton's gravitational constant, and $M$ earth's mass.
As should be obvious from this equation, regardless the distance $R$, the escape velocity never vanishes. So no... | {
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Are diffeomorphisms a proper subgroup of conformal transformations? The title sums it pretty much. Are all diffeomorphism transformations also conformal transformations?
If the answer is that they are not, what are called the set of diffeomorphisms that are not conformal?
General Relativity is invariant under diffeomor... | A general diffeomorphism is not part of the conformal group. Rather, the conformal group is a subgroup of the diffeomorphism group. For a diffeomorphism to be conformal, the metric must change as,
$$g_{\mu\nu}\to \Omega^2(x)g_{\mu\nu}$$
and only then may it be deemed a conformal transformation. In addition, all conform... | {
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Does the general topology of Minkowski space-time change under a Lorentz transformation? Does the general topology of Minkowski space-time change under a Lorentz transformation? Open balls in $\mathbb{R}^{4}$ (with the standard topology) are not invariant under Lorentz transformations. Does this mean for example that o... | This is simply a short addendum to Robin Ekman's answer and response to your comment
So I could phrase it this way: Lorentz transformations are homeomorphisms, so even though they open sets not invariant, all topological notions are still preserved?
Homeomorphism is indeed the key concept here, and I wish to add a v... | {
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A strange audio phenomenon, could there be a physical interpretation to it? https://mathoverflow.net/q/165038/14414
Motivation : Here is a motivation as to why this problem is so important.
Let $f(t)$ be an audio signal. We can safely asume it to be bandlimited to 0-20kHz as we cannot hear anything above that. Capture ... | You can express your signal as the series expansion:
$$f(t) = \sum_k a_k \cos(kt) + b_k \sin(kt)$$
The Hilbert transform is a linear operator, so:
$$f_h = \sum_k a_k H[\cos(kt)] + b_k + H[\sin(kt)] = \sum -a_k \sin(kt) + b_k \cos(kt)$$
So, $f_h$ has changed the phases f the different frequencies, but leaving the mangit... | {
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Why doesn't a block rotate due to friction? In a horizontal surface, a block (cube) is sliding due to a sudden push. When the block slides, there is frictional force which is acting on the block.
Frictional force will have a torque around the center of mass, so why does the block not rotate/roll around (a horizonta... | The image below shows a rough diagram of the forces on a box just as it would begin to rotate.
In this case we can consider the normal force to the surface as focused on the leading corner about which the box would rotate.
This results in 2 torques on the box. The first from friction which is causing the box to rotate... | {
"language": "en",
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Moment of inertia of a cylinder When I tried to calculate the moment of inertia ($I_C$) of a cylinder (mass M, height H, radius R) around the rotating axis going symmetrically through its middle, I came up with a different result than expected ($\frac{1}{2}MR^2$), but I do not spot my mistake, since my calculation make... | You are missing an r in the dV. So it's $dV=r dr d\phi dh$ and in the integration you get $I_C=\int_{0}^{H}dh\int_{0}^{2\pi}d\phi \int_{0}^{R}\rho r^3 dr =2\pi H \rho R^4/4=\frac{2}{4} \rho (\pi R^2 H) R^2=\frac{1}{2}M R^2$
| {
"language": "en",
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Tritium decay is spontaneous even if the binding energy of tritium is higher than the binding energy of 3He. Why? Given this nuclear reaction:
$^3_1\mathrm H\to {}^3_2\mathrm{He}+e^-+\bar{\nu}$
and knowing the binding energies:
$BE(^3_1\mathrm H)=8.48 \,\mathrm{MeV}$
$BE(^3_2\mathrm{He})=7.72 \,\mathrm{MeV}$
If I calcu... | Binding energy simply isn't the right metric (because it is calculated from different starting points on account of the differing masses of the constituent nucleons).
Proper energy (AKA mass) of the states is the right metric.
Wolfram Alpha gives the masses as
$$M_{\mathrm{T}} = 2809.432 \,\mathrm{MeV}$$
$$M_{^3\mathr... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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What is is a molecular/microscopic explanation for why a balloon rises in water? If we consider a balloon full of air submerged in water then we all know that it will rise rapidly. I am having trouble understanding this at the level of individual molecules of air and water. What is a molecular/microscopic explanation... | I will give it a try but remember I am new here.
Pressure in the end is brownian motion, therefore more pressure more motion, more total force. Therefore left and right forces are compensated, left and right recoils are compensated.
What is not compensated is on the vertical axis therefore the water above the balloon w... | {
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Is tea weaker if you make it in a half full cup of water? Imagine you put a tea bag in a cup and half fill it with boiling water. Then after one minute you take the tea bag out and then fill the cup up to fill with hot water. Will the tea be weaker than if you had filled the water up to the normal level with boiling w... | In answer to your question - the math you seek is somewhere in the Noyes-Whitney equation as pointed out in the following link analysis of teabag dynamics unfortunately the author doesn't expressly calculate the rate of dissolution but the ammount of detail will either A/ give you a good start on figuring it out - or B... | {
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Moon's pull causes tides on far side of Earth: why? I have always wondered and once I even got it, but then completely forgot. I understand that gravity causes high and low tides in oceans, but why does it occur on the other side of Earth?
| Let us try to find the acceleration at points A and B with respect to the centre of the earth O due to the influence of moon and earth, as shown in the figure.
O and X are the center of the earth and moon respectively. Let the radius of earth be $R_E$, distance between earth and moon be $d$, mass of earth and moon be... | {
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What does an applied force on an already accelerating object do? I'm a big beginner having only taken Grade 11 high-school physics.
Imagine this situation: an object is accelerating north, and while it's accelerating, it's 'hit' by a northward force.
To me it would make sense that the acceleration of the object would... | The acceleration of an object is a result of the sum of all the forces. If it was accelerating before you hit it, there must have been a force. If an object is falling in air, there are forces of gravity and air friction on it. When all forces even out the object continues with the same velocity.
Simply take the vector... | {
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Entropy was created after inflation? I'm puzzeled by a statement in Big Bang Cosmology-review about the reheating phase subsequent to the exponential expansion during inflation:
In this reheating process, entropy has been created and the final value of $RT$ is greater than the initial value of $RT$.
(Taken from sect... | A form of the first law of thermodynamics:
In a thermodynamic process involving a closed system, the increment in the internal energy is equal to the difference between the heat accumulated by the system and the work done by it.
It is a form of conservation of energy.
Thermodynamics developed and has been validated a... | {
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Gravitational Constant in Newtonian Gravity vs. General Relativity From my understanding, the gravitational constant $G$ is a proportionality constant used by Newton in his law of universal gravitation (which was based around Kepler's Laws), namely in the equation $F = \frac{G\cdot M\cdot m}{r^2}$. Later, Einstein set ... | Since in the limit of weak gravitational fields, Newtonian gravitation should be recovered, it is not surprising that the constant $G$ appears also in Einstein's equations. Using only the tools of differential geometry we can only determine Einstein's field equations up to an unknown constant $\kappa$: $$G_{\mu\nu} = \... | {
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Can we say there are 2 EM radiation types? EM radiation seems to come from two different sources:
*
*According to the Maxwell, by acceleration of electrons
*According to the Bohr, by jumping of electrons between energy levels?
Are these two, completely different things?
| These are different causes of radiation, but they both produce the same kind of radiation: electromagnetic radiation.
When an electron is accelerated, it loses energy and emits one or more photons. This is a purely classical view of what happens.
When an electron falls from a higher energy state in an atom to a lower ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/118840",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 5,
"answer_id": 1
} |
Inverting the equation for $T_{\mu\nu}$ in terms of $F_{\mu\nu}$ The Stress-Energy Tensor for electromagnetism is given by:
$$ T_{\mu \nu} = F_{\mu}\,^{\alpha}F_{\nu\alpha}-\frac{1}{4}g_{\mu\nu}F_{\alpha\beta}F^{\alpha\beta} $$
How can I find $F_{\mu\nu}$ in terms of $T_{\mu\nu}$?
Rewriting the above equation using:
$... | The easiest way I can think of in Minkowski space, short of doing the algebra in terms of matrices, is to use $$\begin{split} f^a &= \rho E^a + \epsilon^{abc} J_b B_c = \partial_b T^{ab} - \epsilon_0 \mu_0 \partial_t S^a\\ \frac{\partial T^{00}}{\partial t} &= - \vec{J}\cdot \vec{E}- \vec{\nabla} \cdot \vec{S} \end{spl... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/118975",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
"answer_count": 2,
"answer_id": 1
} |
Particle in a box: simultaneously bounded momentum and position While writing an answer to this question, I started doubting about the interpretation of the uncertainty principle for the particle in a box.
In the 1-dimensional particle in a box problem, explicit solutions for the energy eigenstates exist, and are essen... | But the momentum is not definite.
The standing wave state is a mixture of waves with wave number $k$ and $-k$ (here I am assuming a square-well for simplicity of notation). In more than one dimension we have to write those as vectors, but the same principle applies: there is a mixture of multiple states with different ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/119035",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 1
} |
Difference between matrix representations of tensors and $\delta^{i}_{j}$ and $\delta_{ij}$? My question basically is, is Kronecker delta $\delta_{ij}$ or $\delta^{i}_{j}$. Many tensor calculus books (including the one which I use) state it to be the latter, whereas I have also read many instances where they use the fo... | These Kronecker symbols have the same matrix representations, as you said, just the unit matrix. The indices are placed at upper or lower positions to suit Einstein summation convention (http://en.wikipedia.org/wiki/Einstein_notation). They are always used together with covariant and contravariant vectors (http://en.wi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/119126",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "19",
"answer_count": 4,
"answer_id": 1
} |
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