Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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Is Pascal's law applicable in a very large enclosed ocean? Pascal's law states that pressure is transmitted undiminished in an enclosed static fluid. Is this law applicable, say, We apply it to a small scale so molecules push each other to transmit the pressure to the whole fluid say water so what about in a very large... | Yes, it works fine.
Pressure loss is generally associated with restrictions to flow. But when there is no flow, no such loss occurs.
Assume you are in the (again, static) ocean at a particular depth. If there were more pressure from one side than the other, then the pressure difference would accelerate some of the fl... | {
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"url": "https://physics.stackexchange.com/questions/214193",
"timestamp": "2023-03-29T00:00:00",
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Killing Vectors in Schwarzschild Metric Given the Schwarzschild metric with $(-,+,+,+)$ signature,
$$\text ds^2=-\left(1-\frac{2M}{r}\right)dt^2+\left(1-\frac{2M}{r}\right)^{-1}dr^2+r^2(d\theta^2+\sin^2\theta\,d\phi^2)$$
the lack of dependence of the metric on $t$ and $\phi$ allow us to read off the Killing vectors $K_... | Conceptually:
If we leave the mathematical definition aside for a while, we can define the killing vector:
Killing vector $K^\mu(x)$ leaves metric unchanged under infinitesimal coordinate changes
Time coordinate
Change in $t$ does nothing to the metric:
Change in $t\rightarrow t+dt$:
$g_{\mu \nu}=g_{\mu \nu}(t)=g_{\... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/214434",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Effects of inner painting in the temperature of room which room will stay warmer for long time in winter night. The room with inner painting black or white?
| The scientific fact is that white reflects the radiant energy rays of the sun and black absorbs them.
Most major paint manufacturers can tell you the Light Reflectance Value (LRV) of any color paint chip. White reflects 80% of the light, black 5%.
So if you want to have a warmer room paint it black since more of the ra... | {
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"url": "https://physics.stackexchange.com/questions/214503",
"timestamp": "2023-03-29T00:00:00",
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How to find the direction of an eddy current? Suppose there is a magnetic field going from left to right. Suppose a thin sheet of metal conductor (e.g. a 1m*1m square) is dropped through the magnetic field such that the plane of the conductor is PERPENDICULAR to the magnetic field.
Now I know that by Faraday's Law, the... | The first thing to note is that if the loop is moving through a uniform magnetic field the induced emf and hence the induced current is zero as there is change in the magnetic flux through the loop.
The first thing you need to decide is whether or not the magnetic flux through the loop is increasing or decreasing.
The ... | {
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"url": "https://physics.stackexchange.com/questions/214640",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Single Slit Diffraction I am trying to derive the intensity variation function for a single slit diffraction.
Sorry for the poor diagram...
So I decided to take the amplitudes of the waves originating from the slit on the left (wherein the variable that denotes distance within the slit is $l$) and integrate the amplit... | Try using this method.
To study diffraction of light, laser light is passed through a narrow single slit and the
diffraction pattern is formed on a distant screen. An imaginary reference line is drawn
perpendicularly from the center of the slit out to the screen (see Figure 3), which is a
distance L away. The intensit... | {
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Why does a ray passing through optical centre remain undeviated? How can it be explained using the laws of refraction that a light through optical centre of a lens passes undeviated?
If we assume the portion of the lens in the middle to be made of even number of alternately place up and down prisms, then it's clear, b... | Actually the same happens when a ray of light passes through optical centre the perpendicular distance between extended incident ray and extended emergent ray is negligible so...we can say that the ray which passes through the optical centre is undeviate.
| {
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"url": "https://physics.stackexchange.com/questions/214804",
"timestamp": "2023-03-29T00:00:00",
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Are chemical bonds matter? So it recently blew my mind that chemical bonds have mass. And that a spring that's wound up similarly weights a little more.
But there is a distinction between mass and matter.
I believe that a chemical bond, even though it has mass, is not considered matter and is instead a form of energy... | John Custer's comment is the best answer so far, so I'll wait for him to make it into an answer for now rather than copying it here.
Owing to the unified description of the "amount of content" of non quantum ground state systems through the system's total energy, the distinction between what a 1910s scientist would cal... | {
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What it sounds like when I'm travelling at the speed of sound totally hypothetical here:
lets say a man is playing a song on a guitar and I begin travelling quickly away from the guitar, if I were to reach the speed of sound, what will I hear? (my assumption is that I will hear a single note humming in a constant stat... | I'm pretty sure you will hear nothing from the guitar, because you will be traveling at the same speed as the sound so the sound wave will not be able to make vibrations on your eardrum thus you hear nothing.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/215179",
"timestamp": "2023-03-29T00:00:00",
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Liquid electromagnet Would it be possible to make a liquid electromagnet using ferrofluid and Ferris sulfate liquid. Having the core be 3/4s of it be ferris sulfate and 1/4 be ferrofluid. Then just having a normal coil. Would that work and if it does would it be stronger then normal electromagnets?
| If you start with a coil with nothing inside it then introduce a core of relative permeability $\mu$ the effect is to multiply the strength of the generated magnetic field by $\mu$.
So in your case the strength of the field would depend on the relative permeability of your mixture of 25% ferrofluid and 75% ferric sulph... | {
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GR: Pseudo Riemannian or Riemannian? Is General Relativityy described by Pseudo-Riemannian manifold or Riemannian manifold? I cannot understand the vast difference between the two manifolds. In books, General Relativity is looked as a pseudo-Riemannian manifold, though I am not sure after reading some threads on the we... | A pseudo Riemannian manifold is a manifold equiped with a metric of signature $(p,q)$, $p$ indicating the number of positive eigenvalues and $q$ the negative eigenvalues. For a Riemannian manifold, $q = 0$.
A spacetime of dimension $n$ is defined by a pseudo-Riemannian manifold of signature $(1, n-1)$, or alternatively... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/215382",
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Raw data acquirable from amateur astrophotography What raw data can I possibly acquire from an 8" Classical Dobsonian Telescope, and a DSLR? Could anything eye-opening to amateur astronomers be computed or calculated first-hand with such equipment? I'm sure scientists must've considered this equipment "advanced technol... | In addition to CuriousOne's fine answer, I'll point out that Dobsonians, while easy and cheap to build, are rather difficult to combine with a tracking mount. For really good photos (or faint objects), you'll be much happier with a slightly more expensive 'scope with an equatorial mount and a USB interface to your PC... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/215502",
"timestamp": "2023-03-29T00:00:00",
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How do space probes identify molecules? How does a space probe identify molecules without actually obtaining the molecules? The common identification techniques I can think of are spectroscopy and magnetic resonance, but for both of them, the apparatus needs to interact with the molecule and get readings from them (fir... | There are several broadband light sources in outer space such as quasars and blazars which basically can act as a light bulb. Earth bound telescopes as well as satellite telescopes can see absorption features in the light when the light passes through some cloud in outer space that contains molecules before the light r... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/215623",
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Is Earth really a magnet? I am a student of class 9. When I was going through magnetism and read that an earth is a magnet I got some doubts. My question is: is earth really a magnet? Doesn anyone have any proof that earth is a magnet? Is there a magnetic core at the center of the earth? Has anyone reached the core of ... | No there is no magnet inside earth.
I mean there is not any magnet like we see in our surroundings.Earth itself is a magnet or not is upto you, because there is no direct answer to it.
As explained by some scientists
there are convectional currents of molten iron and nickel in core
which generates magnetic field around... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/215747",
"timestamp": "2023-03-29T00:00:00",
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Why do 3d movies have a red and blue "double image"? My question is why do 3d movies have a red and blue"double image" that is basically just a few inches to the right and left of the real image. And how does this help us see the image as "3d". Does it have anything to do with polarized light. And do you need a special... | red/blue double image is the (very) old technology to see 3D on paints, drawings and ordinary screens. See 'Anaglyph' on wikipedia. It requires red/blue glasses (very cheap on Ebay :-) ).
Polarized display is expensive, and is the one requiring polarized glasses.
| {
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What is the smallest item for which gravity has been recorded or observed? What is the smallest item for which gravity has been recorded or observed? By this, I mean the smallest object whose gravitational effect upon another object has been detected. (Many thanks to Daniel Griscom for that excellent verbiage.)
In oth... | I found a 1988 paper by Mitrofanov et al which describes a Cavendish style experiment where the "big" mass was 706 mg - where Cavendish used balls of over 150 kg. The "small" mass ( the one on the torsion pendulum) was only 59 mg.
This experiment was done to examine possible deviations of Newton's law at extremely shor... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/215997",
"timestamp": "2023-03-29T00:00:00",
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Why can't I push myself in a chair? If I am sitting in a chair with wheels and someone pushes on the back of my chair with sufficient force it will role along the ground. However, if I push on the back of the chair with the same force it will not move the chair. Why?
| Actually, if you don't take into account the friction between you and your friend pushing the chair and the ground, the chair could have any velocity, but it would stay constant. The thing is that the force you exert on the chair is equal and opposite to the force applyied by your friend so the total force (resultant f... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/216094",
"timestamp": "2023-03-29T00:00:00",
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Why do tall buildings have low resonant frequencies? I know that tall buildings have low natural frequencies, hence they're more vulnerable to earthquakes, but why do they have low natural frequencies?
| Excellent answers have been given above, so there may be considerable overlap with mine.
Consider a mass $m$ at the end of a spring with spring constant $k$. Admittedly, this is a very crude model but physicists have a way of making simple models. Let's call it a lumped 1D model of a building. The resonance frequency ... | {
"language": "en",
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What is Pressure Energy? While deriving Bernoulli's Theorem, our teacher said that the sum of KE, PE and Pressure Energy per unit volume remains constant at any two points.
$$P + \rho g h + \frac{\rho v^2}{2} = \text{Constant}$$
In this, he stated that the first term is Pressure Energy per unit Volume. What exactly is ... | When a fluid is squeezed, as in a cylinder by a piston, work is done on the fluid.
This work 1) elevates the pressure (pressure energy), and 2) the temperature (heat energy).
(If the cylinder is insulated, this is called "adiabatic".)
In an ideal gas, these are all related by the ideal gas law,
which says roughly that ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/216342",
"timestamp": "2023-03-29T00:00:00",
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Splitting molecule The photon reacts with the binding electrons orbiting the two atoms.
The photons have the 'correct' wavelength for Bond Dissociation Energy (BDE).
'Splitting' the molecule involves applying the photon wavelength to separate the electron from the molecule.
With the photons being applied between the bi... | This isn't really how it works. A photon doesn't interact with a single electron, it interacts with the entire molecule.
Suppose you take the example of ozone photolysis to $O_2$ and an oxygen atom. We can do a calculation for ozone and come up with a series of molecular orbitals, then put two electrons in each orbital... | {
"language": "en",
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Difficulty understanding the energy transformations during resistance in a circuit I am currently having problems understanding the energy transformations that occur when resistance in a solid conducting wire restricts current flow.
From my understanding, resistance in a solid copper conducting wire, for example, is ca... | The way I imagine it is that the conduction electrons in a wire move under the influence of the applied electric field and then periodically transfer their kinetic energy to the surrounding atomic lattice. But this kinetic energy comes from the applied electric field (i.e, the electric potential energy). So I think tha... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/216496",
"timestamp": "2023-03-29T00:00:00",
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What is the definition of linear momentum? Every where and book I search I get that the definition of linear momentum is the amount of speed (quantity of motion) contained in it or simply it is mass $\times$velocity? So, what is an appropriate definition of linear momentum? What did Newton think when he discovered it... | What you're looking for is an intuitive explanation or how you could visualize momentum.
You can think of momentum as the quantity/amount of motion or "how much would I not want be in the path of this body."
I'm going to try and provide some intuition through a few examples:
A car of mass 1000 kg moving at 5 m/s would... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/216595",
"timestamp": "2023-03-29T00:00:00",
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Why light moves sideways? Greatings!
I'm trying to understand special relativity and have one question bugging me.
In almost every book or video about the subject there is a thought experiment with moving light clock. I hope I need not elaborate on the sutup and the outcome of the experiment.
So the question is this: ... | The components of the velocity vector can change, it's the magnitude c to be invariant.
| {
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Derivation of $E=pc$ for a massless particle? In classical mechanics, massless particles don't exist because for $m=0$, $p=0$.
The relativistic relation between energy, mass and spatial momentum is: $E^2= (pc)^2 + (mc^2)^2$ . So it is said that setting $m=0$ in the first equation you get $E=pc$.
How could setting $m=0$... | For all particles, $p^{\mu}=(E,\vec{p})$ and $p^{\mu}p_{\mu}\equiv m^2$ (using the mostly-minus metric). Thus $E=\pm \sqrt{m^2+|\vec p|^2}$. If you set $m^2=0$, you get $E=\pm |\vec p|$. The non-trivial aspect of these definitions is that $E$ is to be literally identified as the energy, and $\vec p$ as the spatial mome... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Calculating the color temperature and intensity of skylight with an algorithm I think it will be possible to calculate the natural sky light intensity and color balance (CCT) based on time of day/year, GPS location. Has anyone seen a formula/algorithm for this? I would like to work this out for an app that will present... | There are plenty of algorithmic sky models. see for instance paper (and previous work section) https://hal.inria.fr/inria-00288758
But this is not related at all to "color temperature", i.e. Plank's law (or black body). (well, there is the Sun's one at the begining, but after it's about selective absorption, Rayleigh a... | {
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"url": "https://physics.stackexchange.com/questions/217090",
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Why do helium balloons rise and fall? I understand why a regular party balloon filled with helium falls over time due to leakage of the helium. However I've also noticed that recently filled helium balloons put outside rise and fall. At one point in the afternoon they were dropping but later in the evening it was fully... |
Why do helium balloons rise and fall?
At one point in the afternoon they were dropping but later in the evening it was fully upright again. ... The weather did go from a little rainy and overcast to dry and slightly clearer skies later.
Likely many droplets of water adhered to the helium balloons, when the weather ... | {
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"url": "https://physics.stackexchange.com/questions/217209",
"timestamp": "2023-03-29T00:00:00",
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Hyperfine lifetime calculation: what is the spin eigenfunctions?
I'm trying to calculate the lifetime of the 21 cm line in hydrogen and have the following expression:
$$\frac{1}{\tau} = \frac{4\alpha}{3}\omega_{if}^3|\langle a_f|\vec{x}|a_i\rangle|^2.$$
The initial state is $a_i = a|{F=1, F_z=1}\rangle + b|F=1, F... | You misunderstood the eigenfunction of angular momentum or spin.
The state vector $|l,m\rangle$ is an abstract notion of the eigenstate of the commutated operators $\hat L^2, \hat L_z$ . They are always orthogonal: $\langle l,m|l',m'\rangle \propto \delta_{l,l'}\delta_{m,m'}$ .
Usually, we do not need to express them ... | {
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Does turning a spoon in water raise the temperature? I read about Joule's experiment proving the transformation of mechanical work into heat. But say I have a bowl with some water, and I start turning a spoon in it very fast, thus doing work — the water won't get hotter! What am I missing?
I think maybe the work I put ... | Do the maths and calculate how much energy is needed to raise the water's temperature by 1K. If you have a fast moving stirrer, you should be able to measure the increase in temperature of a liquid in an isolated pot.
By the way: the microwaves in your microwave oven turn around the water molecules very fast and heat ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/217545",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is the distance between two objects in space as a function of time, considering only the force of gravity? What is the distance between two objects in space as a function of time, considering only the force of gravity? To be specific, there are no other objects to be considered and the objects in question are not ... | The two equations of motion reduces down to one equation of motion by considering the separation $x=x_2-x_1$ and the separating acceleration $\ddot{x} = \ddot{x}_2 -\ddot{x}_1$
$$ \ddot{x} = -\frac{G (m_1+m_2)}{x^2} $$
or $ \ddot{x} = -K/x^2 $ with $K=G (m_1+m_2)$
This can be re-written as $\frac{{\rm d} \dot{x}}{{\rm ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/217633",
"timestamp": "2023-03-29T00:00:00",
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Difference between convexo-concave and concavo-convex lenses? What is the difference between concavo-convex and convexo-concave lenses? We dont say convexo-plane for plano-convex. Does that mean concavo-convex and convexo-concave are essentially the same?
| In both types, (convexo-concave or concavo-convex) the lens has one convex and one concave side.
Convexo-concave : The concave face has a greater degree of curvature than the convex face.
Concavo-convex : The convex face has a greater degree of curvature than the concave face.
The images are as follows:
Now a days ... | {
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"timestamp": "2023-03-29T00:00:00",
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Why is it easier to pull a lawn roller rather than pushing it? Does it have something to do with friction or weight distribution in pulling is favorable or anything else ?
| When you push a lawn mower, you are directing force down as well as forward because of the angle of the handle. This means the wheels of the mower are being pushed into the grass, which increases the rolling friction (when the wheel makes a hole in the grass, you have to "climb out of the hole" all the time; the deepe... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/218052",
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Why don't galaxies orbit each other? Planets orbit around stars, satellites orbit around planets, even stars orbit each other. So the question is: Why don't galaxies orbit each other in general, as it's rarely observed? Is it considered that 'dark energy' is responsible for this phenomenon?
| They do! There's an entire class of galaxy, called a 'satellite galaxy' which is defined entirely based on them orbiting a larger galaxy (which would be called a 'central galaxy'). Our own milky-way is known to have many orbiting satellite galaxies, or at least 'dwarf-galaxies'. If dwarf-galaxies aren't enough, the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/218539",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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FWHM increase with energy (gamma spectra) Below I have two plots from a gamma spectrum which I've been analyzing. The first plot is between a low energy range, the second between a significantly higher energy range. It is clear that the FWHMs (Full Width Half Maxima) of the peaks in the spectrum increase with energy. T... | The answer to the question is due to the fact that the number of charge carriers increased.
Glen Knoll offers the following in pp. 117 of his book "Radiation Detection and Measurement":
The width parameter σ determines the FWHM of any Gaussian through the relation FWHM = 2.35σ. The standard deviation σ of the peak in... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/218813",
"timestamp": "2023-03-29T00:00:00",
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Why can't I see the blue color scattered by the lower atmosphere of the earth? I understand that the blue colour of the sky is because of the scattering of blue light by molecules in earth's atmosphere. The scattering appears to be happening from molecules that are far above in the earth's atmosphere. What about the sc... | It's because you're not looking far enough. From personal experience, it takes at least 10 km of atmosphere to build up a really obvious blue (see, for example, this picture), and if you're not in hilly country, the horizon is only 5km away. In contrast, most of the sky has distances to space on the order of hundreds... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/218962",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "17",
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A false proof of drag force being conservative Consider a particle moving along some trajectory in the $x$-$y$ plane, in a viscous medium.
Then its equation of motion is given by:
$$\mathbf{F}_d = - b \mathbf{v} .$$
it's well-known from the Gradient theorem(fundamental theorem of line integral) that if there exists a ... | To see that your integral expression does not make any sense, imagine that $\vec{r}(t)=( x(t),y(t))$ describes a circle. Then the line integral of the force around the loop gives the change in potential energy, which should of course be zero,
$$\oint \vec{\nabla} \phi \cdot \vec{dl} = \Delta \phi =0. $$
But if you inse... | {
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Why is the blue line in the Balmer series sometimes not visible? So I've conducted an experiment to find the four visible hydrogen emission spectrum lines in the Balmer series in a laboratory. I don't have any background in quantum physics.
When I looked through the eyepiece, I saw the red light, the pale blue light, a... |
Why is the blue line in the Balmer series sometimes not visible?
The human eye has difficulties in distinguishing dark blue lines on a black background.
You can use "Microsoft Word" to draw a black rectangle and a few dark blue lines of different thicknesses on the rectangle. The thinner the dark blue line the less v... | {
"language": "en",
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How does air travel after leaving air nozzle? I am working on a project which involves air nozzles. I am interested in estimating the time it takes for air particles after they leave the nozzle to reach a particular distance away. I have the following information--- a converging nozzle, the speed with which it is comin... | Without more details, we can't find a specific case that will match what you are doing. However, I did find a decent example to show you what to look for to answer your question.
Data for a nearly-sonic round jet can be found in this paper. If you look at Figure 5(a), you'll see how the normalized centerline velocity f... | {
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What constitutes a force? There are a few questions on here about why Gravity is not a force, but I'm having trouble grasping why exactly.
It sounds to me that Gravity is not a force because it is simply a by-product of mass on spacetime. How does this differ from the strong nuclear force? Are the other forces not an... |
It sounds to me that Gravity is not a force because it is simply a by-product of mass on spacetime.
The force in general, including its particular case the Gravity, is a byproduct of mass, space and time because it is measured in $kg*m/s^2$.
| {
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Smallest possible size of nuclear reactor I recently began playing Fallout 4 and asked myself a question: Would it be possible to build a power armor with todays technology?
I did some investigation on servomotors and stuff and came to conclusion that it would be theoretically possible to build such a suit. The main pr... | Considering that the fuel element is called "fusion core", I guess they use fusion reactors, not fission. But in reality fusion reactors are not cost-effective and require extreme temperatures to initiate a fusion reaction (see "tokamak" to get an idea and see the size).
There were some news about a team of scientists... | {
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How do we know that the rate at which a body loses heat is proportional to the difference between its temperature and that of its environment? Did someone do an experiment, or was that fact derived from other ideas we had about how the world works?
| Ultimately, Newton's law of cooling is a simplification that can be obtained from the full heat equation, i.e. $$\rho c\frac{\partial T}{\partial t} = - \kappa \nabla \cdot T.$$
The heat equation itself can be derived from first principles, assuming Fourier's law for heat flow, namely that it is proportional microscop... | {
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Does Newtonian physics work on a galactic scale? I'm currently working on a simulation that aims to use Newton's Law of Gravitation to simulate how a galaxy behaves gravitationally. While I haven't gotten the simulation finished yet, I have had a few people tell me that Newtonian Physics don't work on a galactic scale,... | No, Newton's Second Law of motion is only an approximation and doesn't work on anything larger than a solar system. When you get into the domain where the acceleration is on the order of $10^{-14}\space km\space s^{-2}$, then you can see limits of the approximation. Stars at the edges of spiral galaxies travel much t... | {
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Is there any limit to distance between two waves when used in Huygens principle? Apologising for not being clear.
When I used Huygens principle to determine the spherical wavuefront of radius $R/2$ created by reflection from a spherical concave lens of radius $R$, I got amazingly different results for different size of... | I think that you have found from first principles that a hemispherical lens suffers from spherical aberration?
Later
Here is my attempt.
It might look a mess but I think that it does illustrate the fact that the wavefronts converge towards a region which is about half the radius of the mirror.
The radius of the mirror... | {
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Conflicts between Bernoulli's Equation and Momentum Conservation? The well known Bernoulli's equation states that
$P+\frac{\rho V^2}{2}=c$
However, a simple momentum conservation considering $P_1$ and $P_2$ acting on two sides, and velocity changes from $V_1$ to $V_2$, yields
$P_1+\rho_1 V_1^2=P_2+\rho_2 V_2^2$, which ... | The factor $\frac 12$ comes from the relation $\vec v \cdot\nabla \vec v = \nabla \frac{\vec v^2}{2} + (\nabla\times\vec v)\times \vec v$ in the momentum conservation equation $$\rho \left(\frac{\partial \vec v}{\partial t}+\vec v \cdot\nabla \vec v\right)=\vec g-\nabla p$$
(Sorry to post this as an answer, but I can't... | {
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What mechanism explains the effect of a hot surface on hydrogel balls? Adding little hydrogel balls to a hot surface has an interesting effect as seen in this video. Hydrogels (as the name suggests) contain a lot of water but rather than melt or burst, the little balls are seen to bounce up-and-down on the hot surface ... | Yes, the Leidenfrost effect plays a big part here. As the hydrogel balls aren't perfectly elastic (their restitution coefficient is smaller than one) they would quickly come to a halt but little jets of steam that are ejected by them when they hit the hot surface constantly provide extra upward force to compensate for ... | {
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On a molecular level, how does heat transfer take place? When an ice molecule hits a water molecule, the water molecule adds kinetic energy to the ice molecule. Why do the water molecules lose kinetic energy? In other words, why does heat like to go where there is less heat? I know thermodynamics tells us energy can't ... | Basically a "molecule" of water cannot heat up ice.
I think what you are trying to say is, how does heat transfer take place on a molecular level? If that's the case, then its something like this. In the interface between water and ice, water molecules are moving, while ice molecules are static. on contact, some molecu... | {
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Time dilation in the movie Interstellar I know that the science in movies is questionable and sometimes ridiculous but I would think this question would have been more obvious to the script writers. When they visited Miller's planet they were almost killed by a re-occurring tidal wave. In a few short minutes they ended... | In addition to what should be a miniscule difference in time dilation between the water planet's orbit and the water planet's surface, I still don't understand the tiny difference in subjective time separating the two landers' arriving on the water planet's surface.
If two identical ships start a journey in the same fr... | {
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When does normal force equal to $mg$? Can someone once and for all explain when does normal force equal to mg?
I know for sure that when there is no friction, normal force will be equal to mg.
But, i encountered some questions when there is some mass on an incline with friction, and then the normal force was the y comp... | Normal force $F_N$ is just the force between two surfaces. It's called "normal" because it acts perpendicular (normal) to the surfaces.
Gravitational force is completely unrelated. Gravity always acts with $F_g = -mg$. The minus sign indicates that the force points down.
These two forces often oppose each other, which ... | {
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When sugar is added to water, how does the mass change, and how does that affect the water's density and boiling point? I can't find a good answer anywhere. How does the amount of sugar added change the boiling point, mass, and density of water? Does it affect the mass or the volume? Or both?
| As stated above, the mass of the whole system (sugar + water) doesn't change. In addition, with "ideal" mixing, the total volume of the water plus the total volume of the sugar equals the total volume of the mixture. However, this is not a sure bet, and there are many cases of a volume of one material mixed with a di... | {
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Do a receiving antenna interfers with an emitting antenna? As I understand:
*
*Accelerating electrons generate electromagnetic waves.
*An emitting antenna have an alternating current (electrons are moving) which generates an electromagnetic waves.
*The electromagnetic waves reach the receiving antenna and makes th... | All of these oscillations have the same frequency, so the EM waves have the same wavelength.
Maxwell's equations are linear, and air is a linear medium, so EM waves don't interfere with each other. You can point a laser pointer across the room and it won't affect all of the other light rays flying around the room. So... | {
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How to keep a helium balloon between 1 to 5 meters above ground? (without it being tied) I understand that helium balloons rise because their density is less than air, so they can rise up to a point where the air surrounding it has the same weight as the balloon.
I was thinking to fill it with something like half air a... | Ideal gases (of which real gases are only an approximation) obey the relationship $PV = const$ (at constant temperature). This won't work because pressure falls as altitude increases. As the balloon rises, the pressure outside the balloon falls, and it will expand, increasing its volume, and decreasing the density of t... | {
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Air flow speed and penetration abilities As I understand, two fans with the same diameter and with the same rotor speed(usually measured in RPM) can have different air pressure(usually measured in mmH2O) and air speed(usually measured in CFM) because of fan blades design. Higher air flow speed should provide worse pene... | The most likely explanation is that at lower speeds you get a more laminar flow. To quote the wiki article:
At low velocities, the fluid tends to flow without lateral mixing, and
adjacent layers slide past one another like playing cards. There are
no cross-currents perpendicular to the direction of flow, nor eddie... | {
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Magnetic field at the center and ends of a long solenoid A long solenoid has current $I$ flowing through it, also denote $N$ as the turns per unit length. Take its axis to be the $z$-axis, by symmetry the only component of the magnetic field inside is $B_z$. Find the magnetic field at the center of the solenoid (on the... | since you are concerned about a long solenoid, this problem has a very simple solution.
Suppose you have two identical long solenoids, each of them having magnetic field $B$ at the ends. You join them end to end, such that their magnetic moments are in same direction. Thus, at the junction the magnetic field adds up to... | {
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Can we find a vector if its dot product and cross product with another vector is given? If I have two vectors $\vec{b}$ and $\vec{v}$, and I know that
$$
\vec{b} \times \vec{v} = \vec{c}
$$
and
$$
\vec{b}\cdot\vec{v} = \lambda
$$
can I find the $\vec{v}$ vector in terms of the $\vec{c}$ vector, $\vec{b}$ vector, and $\... | Yes. If $\bf B \times V=C$ and ${\bf B \cdot V}=\lambda$, the BAC-CAB rule tells you:
$\bf B\times C=B\times(B\times V)=B(B\cdot V)-V(B\cdot B)$
So
${\bf B\times C}={\bf B}\lambda-{\bf V}B^2$
and
$${\bf V}=\frac{{\bf B}\lambda-{\bf B\times C}}{B^2}$$
| {
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Conservation of energy and angular momentum I'm writing a java program to simulate the solar system. All planets are modelled as point masses. How do I check if my solar system is conserving energy? I'm not sure how to calculate the energy of the system at the start of the simulation, let alone at the end!
And given t... | The conserved quantities in your problem are: total mechanic energy $T+U$, total linear momentum $\vec P$, and total angular momentum $\vec L$ of the $N$ point masses.
They are defined as:
$$E=T+U \quad\text{ total mechanical energy}$$
$$U=-G\sum_{i}^N \sum_{j}^N \frac{m_i m_j}{|\vec r_i -\vec r_j|}\quad\text{ total... | {
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Infinite pulley system Infinite Atwood Machine Harvard Solution
Hi, I've been trying to solve this question for a while. I understand the first solution and also the solution to the second problem but I don't understand how to apply the second problem to solve the infinite pulley system.
In particular, I don't understa... | No, an Atwood's machine with masses $m$ and $3m$ has acceleration of $g \frac{3m -m}{3m+m} = g/2$, as explained in https://en.wikipedia.org/wiki/Atwood_machine#Equation_for_constant_acceleration
| {
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Principle behind electrostatic shielding? If we have a solid conducting sphere with charges around it, then the electric field inside the sphere is zero, otherwise the electrons of the sphere would not be in equilibrium as there would be a net force acting on it. However, if its a hollow sphere, then why does the elect... | Okay, draw a circle around the spherical void; done?
Then see is there any charge?
If not, there should not be any divergence of electric field, know that?
So, from Gauss Law, $$\text{div} \mathbf{E} \cdot dv= 0$$ which implies $$\mathbf{E}\cdot d\mathbf S= 0 \implies \mathbf E= 0$$ over that volume .
Edit:
Don't know ... | {
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Nature of Pressure Pressure is defined as force per unit area. Therefore, pressure = force divided by area. Since force and area are both vectors, how can we perform this division without violating the rule of vectors?
If pressure is a scalar quantity, how did this scalar nature came about from the vector nature of for... | Only the force component that's perpendicular (90 degree angle) to the surface will create a pressure. Let's consider a toy car on a track that has a 45 degree incline. Gravity exerts a force on the car. We can split this force into two components: one that is parallel to the track and the other one is perpendicular to... | {
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The anticommutator of $SU(N)$ generators For the Hermitian and traceless generators $T^A$ of the fundamental representation of the $SU(N)$ algebra the anticommutator can be written as
$$
\{T^A,T^{B}\} = \frac{1}{d}\delta^{AB}\cdot1\!\!1_{d} + d_{ABC}T^C
$$
where $\delta^{AB} = 2\text{Tr}[T^AT^B]$ is the normalization c... | For a general representation $t^{A}$ of the generators of $SU(N)$ it is possible to deduce the following form of the anticommutator
$$\{t^{A},t^{B}\} = \frac{2N}{d}\delta^{AB}\cdot 1_{d} + d_{ABC}t^{C} + M^{AB}$$
where
$$
\mathrm{Tr}[t^{A}t^{B}] = N\delta_{AB}\\
d_{ABC} = \frac{1}{N}\mathrm{Tr}[\{t^{A},t^{B}\}t^{C}]
$$... | {
"language": "en",
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What is meant by the word "length" in definition of surface tension? Surface tension is defined as the force applied per unit length. What is that "length" belonging to? I can imagine force being applied per area but not length.
"It would take a force of 72 dynes to break a surface film of water 1 cm long." Film is tw... | Image you have a U shaped piece of wire with a soap film inside it, and a straight piece of wire inside the U:
The red line is the stright piece of wire that is free to move in the U - in effect a 2D version of a piston.
The surface tension of the soap film $\gamma$ pulls on the wire so it produces a force $F$ on it w... | {
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Earth as a conductor In a lightning rod or other safety devices, charge is directed towards the earth.
How the surface of the earth can be used as a conducting path despite being composed of material that is not a good electrical conductor?
| Small currents do pass for example when we want to create charges in a metallic sphere by induction.Earth has both insulating and conducting minerals like aluminium oxide,organic matter and aluminium iron etc respectively and moisture in the soil will do more good by dissolving ions.Talking about electric discharge fro... | {
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Velocity of a leak in a closed water tank Bernoulli's equation states
$P_1+{1\over2}\rho v_1^2+\rho g h_1 = P_2+{1\over2}\rho v_2^2+\rho g h_2$
In a classic "water tank with an open top and a leak" scenario, "point 1" is the surface water in the tank, and "point 2" is the leak. The equation could be rewritten for $v_2$... | It seems more complicated but I would just take the force which is pushing the water out (Gravity) minus the force by the difference in air pressure.
| {
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What is the root cause of elasticity of a material? I know that there exist some interatomic and intermolecular forces in the material but why does stretching a material will enhance attractive force over repulsive force and vice versa.
| The bonds between atoms will 'break' if they are pulled apart even a short distance; however, the angles between adjacent bonds can be distorted a fair amount. If the molecules have a zigzag chain structure, or better yet a helical chain structure, you can stretch the material more without breaking the bonds. If the ... | {
"language": "en",
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"source": "stackexchange",
"question_score": "4",
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Moment of inertia of solid cube about body diagonal How do I find the above mentioned moment of inertia?
Steps I've tried:
1.) Triple integrations that proved to be to big.
2.) I noticed that the if we split a $2\times 2\times 2$ into individual $1\times1\times1$ components, the body diagonal of the $2\times 2\times 2$... | One of the big tricks that you find helpful is that the inertia matrix of a sphere is of the same form of that of a cube. I'll describe what this means.
For a sphere, imagine the moment of inertia (MoI) about three perpendicular axes through the centre of mass. Each MoI will be the same due to symmetry. Now, rotate the... | {
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How does one get the first few terms of the $S$-matrix expansion? According to a set of notes I'm reading
$$\langle p_f | S | p_i \rangle = \delta(p_f-p_i) + 2 \pi \delta(E_f-E_i) \bigg[\langle p_f | V | p_i \rangle + \cdots\bigg]. \tag{1.29}$$
I don't understand where the $2 \pi \delta$ factor comes from in the second... | The first expansion term is $\langle p_f | V |p_i\rangle$. If you assume energy and momentum conservation between initial and final state, namely $E_f = E_i$ and $p_f=p_i$ then the only possibility for the above to be non-zero is in correspondence of
$$
\delta(E_f-E_i)\delta(p_f-p_i)\langle p_f | V |p_i\rangle = \delt... | {
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How do you determine if the spin is up or down? Fundamental particles such as quarks and leptons can have a spin either up or down. These spins are (obviously) opposite of each other. But what differentiates them? Let's say you examine a pair of electrons and you find out they're opposite (one up and one down). How do ... | There's no universal notion of "up" or "down", just like there's no universal notion of "left" or "right" in the universe.
Speaking of "spin up" and "spin down" involves two completely arbitrary choices - a choice of axis and then a choice of "up" and "down" along that axis. You can swap the meanings of "up" and "down... | {
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Can we speed up the evaporation of black holes manually by accelerating it? If we throw an object to pass near a black hole, to bypass it, it will change the speed of the black hole, just like gravitational assist for a space probe. Does an accelerating black hole evaporate faster because:
*
*When object accelerates... | Black holes emit radiation through what is essentially a modified case of the Casimir Effect. That is what we know as Hawking Radiation. Most black holes would only emit in the microwave band, which is why a stellar black hole will outlive most of the matter in the universe. It also must be taken into consideration tha... | {
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Photon absorption and Sight If light is made by emitting photons and photons are absorbed by our eyes to see light
then i have this question:
if there is one person in the room and he looks at a light source (L) with x photons emitted
then there is another room and there are 10 people who look at light source (L) which... | Two people cannot view the same photon of light, because it is destroyed in effect upon being absorbed. However this does not decrease the overall brightness of the light source if more than one person observes it because your eye was not going to capture those photons anyway. Think about it this way. The brightness of... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Velocity-time-distance problem In my book the formula for the $y$-component of velocity during the upward projectile motion is given:
$$V_y=V_{iy}-gt$$
and next to it the formula for $y$-component of velocity during the downward projectile motion is given, differed only by a conjugate,
$$V_y=V_{iy}+gt$$
I think it must... | It's customary to use small $v$ for velocity (but not mandatory).
Notations like $v_y$ and $v_{iy}$ make little sense without defining them. Here it implies the velocity component along the $y$-axis but without specifying this axis nothing makes much sense either.
So I'll define the $y$-axis as a vertical axis, pointin... | {
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Can you compress pure carbon into diamonds? I'm doing a science project, and we're wondering if it is possible to compress pure carbon (C) to the point where it becomes diamonds? What would the process have to be and how much energy would this take? Has this been done and is this feasible?
| my profesor of structure of matter told us that is widely done in Russia, where there is a surplus of explosives and so the price is low.
The procedure consists in filling a container with graphite on the borders and with explosives in the center, and make the expolsive blow up.
This procedure will produce diamonds $10... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Electrostatic induction, induced charges Is it true that if a conducting object is not grounded, the nearby charge will induce equal and opposite charges in the conducting object?
It is mentioned on Wikipedia (electrostatic induction) but it is also mentioned that charges will appear such that the total electric field... | If a conductor is ungrounded, then the charge on the conductor cannot change (unless touched by an electrically charged object).
Now, we know that every charge has electric field around it. So, if a charge is brought near an ungrounded conductor, (we are assuming that the conductor is uncharged), the will tend to devel... | {
"language": "en",
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"source": "stackexchange",
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Energy of classical ideal gas in the grand canonical ensemble The canonical partition function for an ideal gas is
$$
Z(N,V,\beta) = \frac{1}{N!} \left(\frac{V}{\lambda^3}\right)^N
$$
where $\lambda = \sqrt{\frac{\beta h^2}{2 \pi m}}$ is the thermal De-Broglie wavelength. It is straightforward to obtain
$$
\langle E \r... | You may take derivative by assuming constant fugacity i.e $e^{\beta\mu}$. Because the Main formula for calculation of partition function in grand canonical ensemble is $Q=\sum\,e^{-\beta(E-\mu N)}$. So when you want calculate mean Energy or $\langle E\rangle =\sum p_i E_i =\sum\frac{e^{-\beta(E_i-\mu N_i)}}{Q}E_i $.
W... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is it possible that a person with myopia will see a blurry picture as normal? I am trying to process an image in good quality to appear blurred to a normal person and good to a person suffering from myopia
as seen in this source.
Is it possible that a picture that is blurry will appear normal to a person suffering from... | No, it's not possible, sorry. This is because blurring (or more generally, convolution) is a lossy operation, meaning that information is lost when an image is blurred, such that it can never be completely retrieved. While there are ways to sharpen a blurred image, these are either very non-trivial or else they're only... | {
"language": "en",
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"source": "stackexchange",
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How do I figure out the totally airborne height for a given machine? Technically "airborne" can just mean to move through the air, but I would like to know how high you have to be before you are entirely supported by air in a helicopter-like machine, as opposed to benefiting from the reaction from the earth (or whateve... | The usual rule of thumb in flying is that ground effect starts to appear within about one wingspan of the ground. av8n always has a good intuitive explanation.
He explains it as a mirror-image aircraft beneath you.
In flight training, it becomes important in soft-field takeoffs, where you transfer weight to the wings a... | {
"language": "en",
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Origin of radio waves In the same way as the origin of X rays is the excitation of electrons, what is the origin of radio and infrared radiations in this respect?
| Infrared and radio radiation has the same origin as X rays. When a photon 'crashes' with an electron, that electron gains the energy from the photon (if the photon has high frequency it gains a lot of energy, if it has low frequency it gains little energy). Then, the electron goes to a more energetic energy level, fart... | {
"language": "en",
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How can I convert Right Ascension and declination to distances? I am calculating galaxy rotation curves for various galaxies in the Ursa Major cluster and I want the distance of those galaxies from the center of the Cluster. The values referred to as coordinated are RA and dec and I don't know anything about these coor... | Right Ascension and declination are angular measures, RA * 15 gives degrees &c.
Basically, RA is where the siderial zenith is at any time, declination is the distance from the zodiac. You multiply RA by 15, and get angles.
Neither of these are distance, you have to get a radial term from somewhere else. What they a... | {
"language": "en",
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"source": "stackexchange",
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Is moment of inertia numerically additive?
NOTE: The following argument is being made for square only, not any general shape.
We have this square plate:
From Perpendicular Axis theorem,
$$I_1 + I_2 = I_z \\ I_3 + I_4 = I_z$$
Also, $$I_1 = I_2 \\ I_3 = I_4$$
Therefore, $$2\ I_1 = I_z \\ \text{and }\ \ 2\ I_3 = I_z \... | The equations you derived, especially the last two are true only for the square shape. Because it has inherent symmetries as mentioned by ja72 and others. But your instructor told you that those equations were not true for squares also. He probably did some mistake. The most probable case is the following:
We know that... | {
"language": "en",
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Does Quantum Mechanics say that anything is possible? I may be incorrect in this, but doesn't Quantum Mechanics state that everything has a probability of occurring (with some probabilities so low that it will essentially never happen)?
And if I am correct in my thinking, could it mean that, quite literally, anything h... | You have probably heard a garbled version of Murray Gell-Mann's totalitarian principle:
Everything not forbidden is compulsory
In quantum mechanics some processes are forbidden usually because they violate conservation laws. This is what CuriousOne refers to in his comment. Gell-Mann's principle states that unless a ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Lens combination Suppose there are two lenses touching each other as shown in the diagram below. the focal length of the lenses are $f_1$ and $f_2$ respectively. Now by using the formula for lens combination I obtained the final focal length as $$\frac{f_1f_2}{f_1+f_2}$$.
Now suppose I assume there is a very small di... | If there is a small gap between two optical components you have to do your calculations for a small separation. If the elements are touching each other then you have to set the separation $d$ to $0$.
If I understand your question correctly then the answer is yes, you can set the distance to $0$ before or after solving ... | {
"language": "en",
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What is the trajectory of a photon moving through a vacuum? Since electromagnetic energy is carried by photons and moves in forms of waves, does it mean that a single photon when propagating through space doesn't follow the straight path but instead always moves up and down, up and down like a wave. If so another quest... | Photons can be regarded as stable particles depending on perspective. In the Sun's core hydrogen atoms break down into a mixed plasma which includes protons and deuterium atoms. If these collide they form a helium-3 nucleus and a gamma ray is released. The gamma ray is a highly energized photon. It is very difficult fo... | {
"language": "en",
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"source": "stackexchange",
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Operator Product Expansion I wonder why in OPE in CFT terms like
$$ \frac{:O(z) O(w):}{(z-w)^2} $$
occur, for example in the OPE of Energy-momentum tensor with itself:
$$T(z) T(w) = \frac{c/2}{(z-w)^4} + \frac{T(z)}{(z-w)^2} + \frac{\partial T}{z-w}$$
Here we have term $:\frac{T(z)}{(z-w)^2}:$, where for free scalar f... | The question (v4) is a bit unclear, so here are some general comments, which may help:
*
*In CFT, an OPE is calculated via a Wick-like theorem changing an (implicitly written, operator-valued) radial order ${\cal R}(\hat{A}_1\ldots\hat{A}_n)$ into combinations of c-number-valued contractions and operator-valued norm... | {
"language": "en",
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Is there any physical interpretation for $\nabla\cdot(\nabla \times F)=0$? It is well known that the divergence of the curl is always 0. Mathematically I understand why this happens ($d^2=0$ where $d$ is the exterior derivative) but today I was wondering what is the physical meaning of this.
The divergence represents t... | It quite simply means that the radial direction is orthogonal to the tangential direction.
The universe in which we live behaves, as far as we can tell and measure, as a 3D volume (time aside for now:). A 3D volume is defined by 3 orthogonal directions. We can choose to look at a 2D cross-section of this volume, and we... | {
"language": "en",
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Current from Middle Battery in a Two-looped Circuit
With this question, as with many tutorials of similar questions I’ve found online, my textbook only mentions three currents: $I_1$, which flows through the left loop from and to the 19 V battery, $I_2$, which flows through the right loop from and to the 19 V battery,... | Forget about the circuit details of the batteries and resistors for the moment and focus just on the circuit layout: You have three paths by which current can travel from the top to the bottom of the shown circuit. So you need three independent parameters, $I_1$, $I_2$, and $I_3$ to fully describe the current flow in t... | {
"language": "en",
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What will happen to a human being exposed to Martian atmosphere? Mark Watney, in the movie The Martian, says that,
If the HAB breaches, I'm just gonna, kind of... implode.
The corresponding novel, by Andy Weir, says he will explode (as pointed out by @MikaelSundberg).
I think he will neither explode, nor implode, bu... | The Martian atmosphere is effectively vacuum. He would be unconscious in less than 20 seconds and the he will end up freeze dried.
| {
"language": "en",
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"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
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Why do we only feel the centrifugal force? After spending some time researching about the centrifugal force, I now understand that it is needed in a non-inertial reference frame for Newton's Laws to hold true. However, I don't understand why we only feel the centrifugal force when moving in a circular path. For example... | When you are standing upright imagine a downward external force on your head and an equal magnitude upward force on your feet.
These two forces will compress you and you “feel” being compressed as a result of these two forces acting on you.
Imagine that you are being spun round in an apparatus as shown in @JohnRenni... | {
"language": "en",
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How to show period is defined by $T=dS/dE$ (V.I. Arnold Mathemtical Physics) I'm looking at a book by VI Arnold on mathematical physics and I've hit a roadblock pretty early on. I'll quote the question:
"Let $S(E)$ be the area enclosed by the closed phase curve corresponding to the energy level E. Show that the period... | Notice that the "speed" in the phase space is given by
\begin{equation}
v_{\mathrm{ps}} = \sqrt{\dot{q}^2 + \dot{p}^2} = \sqrt{H_{p}^2 + H_q^2}.
\end{equation}
Here, $H=H(p,q)$ is the Hamiltonian, and $H_p$ and $H_q$ are shorthand for $\partial H/\partial p$ and $\partial H/\partial q$. Provided that there exists a clo... | {
"language": "en",
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"source": "stackexchange",
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Closing a switch in series with a capacitor Suppose we have the following circuit:
Such that for $t<0$ the switch M was open. If we close the switch at $t=0$ what will the voltage on the capacitor, $V_C$, be at $t=0^+$? What about $\dot V_C$ at $t=0^+$? Will there be a current passing through $R$ the moment the switch... | There are some mistakes with your assumptions. When $t<0$ a current $I =V/R$ will be flowing through resistor and no current would be flowing through capacitor. As soon we close the switch the capacitor will get charged instantaneously (yes it could lead to $I = \infty$ at $t=0$ but it can be avoided if even a small r... | {
"language": "en",
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Correct Yukawa Term with a SU(2) Higgs Triplet? Given $SU(2)$ doublet fermions $\Psi^1$ and $\Psi^2$ and a $SU(2)$ triplet Higgs $H$, how does the correct Yukawa term look like in tensor notation?
Schematically, we have
$$ 2 \otimes 2 \otimes 3 \stackrel{!}{=} 1$$
and
$$ \Psi^1 \otimes \Psi^2 \otimes H $$
A first gu... | The first thing to notice is that composing two spin 1/2 particles (doublets) symmetrically yields spin 1 (a triplet) and anti symmetrically, spin 0, a singlet. So to suppress the singlet component in the Clebsch -Gordan reduction, you just symmetrize. What you are seeking has already been written down in 1964, in the ... | {
"language": "en",
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What is electron? In quantum mechanics, we easily talk about some "particles" or "somethings" like electron and photon. Besides, in classical mechanics we talk about particles that have mass. As we know, one can formulate axiomatically the meaning of a particle in Newtonian mechanics. Is there any similiar approach to ... | There was a lot of temptation and attempts to present the electron as a wave or as a wave packet. But the problem arose, because such waves and wave packets are quickly destroyed because of dispersion.
But there is a case where the dispersion disappears. This is the case when the group velocity of wave propagation beco... | {
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Applying Kirchoff voltage law to a short circuit If you consider an ideal wire with no resistance that shorts an ideal battery, the only voltage drop that exists is the emf of the battery, with nothing to balance it.
Obviously in the real world such a scenario is impossible, for the wire will have some resistance, but ... | No, it doesn't break. All it means is that all the voltage is on the ideal wire. According to Ohm's law there will be infinite current to account for the zero resistance. That's what happens in a real circuit - if you short a battery the current is very high.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/227054",
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"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
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Expansion of wave function and energy in terms of small parameter In time-independent perturbation theory, the Hamiltonian is perturbed with a perturbation of the form $\lambda V$, and the eigen-energies and wave-functions of the unperturbed Hamiltonian are expressed as series in powers of $\lambda$:
$$E =E^{(0)} + \la... | The perturbation is usually written in the form $\lambda V$ to make its dependence on a small parameter explicit. Clearly, the eigenstates and eigenvalues of your hamiltonian must depend on $\lambda$ as well and therefore one may hope that it can be expanded around $\lambda=0$ (yes, you can think of it as a Taylor expa... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Sliding along a circular hoop: work done by friction
Assume a point object of mass $m$ slides along a hoop of radius $R$, starting from a position which makes 90 degrees with the line of radius connecting the center and the ground. Let the coefficient of kinetic friction between the hoop and the object be $\mu$. Assum... |
Set up an equation of motion for the rotation of the mass around the centre-point.
$$\tau=I\alpha$$
Where:
$\tau=mg\cos\theta-\mu mg\sin\theta$
$I=mR^2$
$\alpha=\frac{d\omega}{dt}=\omega\frac{d\omega}{d\theta}$
So:
$$mg\cos\theta-\mu mg\sin\theta=mR^2\omega\frac{d\omega}{d\theta}$$
$$R^2\omega d\omega=g(\cos\theta-\mu... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/227354",
"timestamp": "2023-03-29T00:00:00",
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How does one show Maxwell's equations in vector calculus form describe the same motion in all reference frames? The covariant form of Maxwell's equations is Lorentz invariant.
$$\partial_{\alpha}F^{\alpha\beta} = \mu_{0} J^{\beta}$$
$$\partial_{\alpha}F_{\beta\gamma} + \partial_{\beta}F_{\gamma \alpha} + \partial_{\ga... | The "motion of stuff" is not the same in all reference frames.
Each frame has it's own coordinate system, and so the physical process you are looking at will be described by different variables. (This is true even when you think of Galilean coordinate systems).
What Griffiths means is that you can use the vector form o... | {
"language": "en",
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Quantum circuit and Witness preserving amplification for QMA My question is about the witness preserving amplification scheme for QMA proposed by Marriott and Watrous in 2005 (see http://arxiv.org/abs/cs/0506068 and http://www.cims.nyu.edu/~regev/teaching/quantum_fall_2005/ln/qma.pdf).
The original (quantum verifier) c... | Since we measure the output in step 1, we do not apply $AA^\dagger$, but rather
$$
A\vert0\rangle\langle 0\vert_1 A^\dagger
$$
or
$$
A\vert1\rangle\langle 1\vert_1 A^\dagger\ ,
$$
depending on the measurement outcome,
which is generally not equal to the identity.
| {
"language": "en",
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"source": "stackexchange",
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Do free-electron lasers actually lase? Free-electron lasers are devices which use the motion of highly energetic electron beams to produce bright, coherent radiation in the x-ray regime. More specifically, they start with a high-energy electron beam and feed it into an undulator, which is an array of alternating magnet... | If you use "population inversion" as an essential part of the definition of what a laser is, then you're right it's not a laser. But that doesn't deny that the properties of light can be just light from any "laser." So, this is a bit of semantics issue, and less about the physics.
Some other "non-laser" coherent ligh... | {
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How exactly does a bulb light up?
A typical value for the electron drift velocity in a copper wire is $10^3\ \mathrm{m\ s^{-1}}$. In the circuit below, the length of the copper wire joining the negative terminal of the batter to the lamp is $0.50\ \mathrm{m}$.
(i) The switch S is closed. Calculate the time it would t... | A single electron takes some time to move from the battery to the bulb but the lamp lights up faster than that. The reason is due to the fact that it is not the electrons travelling from the battery that light up the lamp when it is first lit, rather due to nearby electrons. The electric field is set up almost instanta... | {
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Negative powers of operators This may sound like a strange question, but just to be sure: Suppose I have a general Hermitian operator in Hilbert space whose action on an eigenvector is given by $R|r\rangle = r|r\rangle$. Then, I assume that the following is true:
$\frac{1}{R}|r\rangle = \frac{1}{r}|r\rangle$ and simila... | If you have $R|r\rangle=r|r\rangle$ then you have, where $I$ is the identity operator,
$|r\rangle=I|r\rangle=R^{-1}R|r\rangle=rR^{-1}|r\rangle$ and you immediately have
$R^{-1}|r\rangle=\frac{1}{r}|r\rangle$
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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How to move a bubble which is trapped by the capillary pressure? I have a question about how to move a trapped bubble in a tube.
If we assume to have a horizontal tube, with water on each side of the bubble. The point to the left of the bubble is point 1, while the point to the right is point 2.
The capillary pressure... | The stuck bubble problem happens when there is static equilibrium between the circumferential contact forces of surface tension and the forces due to the pressure difference upstream and downstream of the bubble. The gas pressure inside the bubble is uniform and between the upstream and downstream liquid pressures. In ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/228202",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why is the Fourier transform more useful than the Hartley transform in physics? The Hartley transform is defined as
$$
H(\omega) = \frac{1}{\sqrt{2\pi}}\int_{-\infty}^\infty
f(t) \, \mbox{cas}(\omega t) \mathrm{d}t,
$$
with $\mbox{cas}(\omega t) = \cos(\omega t) + \sin(\omega t)$.
The Fourier transform on the other ha... | *
*On the set ${\cal L}_1(\mathbb{R})$ of integrable functions $f:\mathbb{R}\to \mathbb{C}$, we can define the sine and cosine transforms
$$\tag{1}\left\{\begin{array}{ccc} ({\cal C}f)(\omega) &:=& \int_{\mathbb{R}}\! dt ~\cos(\omega t) f(t),\cr
({\cal S}f)(\omega) &:=& \int_{\mathbb{R}}\! dt ~\sin(\omega t) f(t).... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/228401",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 3,
"answer_id": 0
} |
Why doesn't gravity mess up the double slit experiment? So let's say you are doing a double slit experiment. Also, let's use electrons.
My question is, won't the gravity of the electron affect the earth, thereby causing it decoherence and its wave function to collapse (or for MWI, entanglement and loss of information t... | "everything is a detector"
This can't be true, or else there would be no such thing as persistent entanglement.
As @Conifold points out, the electron's charge should be a far more potent source of environmental disturbance, anyway. Why doesn't the charge of the electron leave a trace as it passes through the slits - s... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/228714",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 2,
"answer_id": 1
} |
Why there aren't gluons with charges like $b b$ or $r r$? So my principal question is the one in the object above. But then I have another question related.
Supposing I have a $bg$ gluon.
How may I write it in the octet basis?
Thank you for your help!!
| Gluons carry color in color-anticolor pairs and form an octet and a singlet representation as seen below:
As you see the octed is filled with a color and an anticolor. The anti has to be a different color otherwise the gluon would be color neutral, and no strong force would be transferred.
Since to be exchangeable a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/228772",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Why is the speed of sound lower at higher altitudes? At sea level the speed of sound is 760mph, but at altitudes like the Concorde would fly at (55,000ft) the sound barrier is at 660mph, so 1000th slower. Does it have to do with lower pressure?
| it has to do with the temperature lapse with altitude. since the speeed of sound is related to temperature by:
$a = \sqrt{\gamma RT}$, where $\gamma$ and R are gas properties and T is temperature
and the temperature profile follows (generally) like the left of these three plots:
The area of interest for airliners is i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/228883",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 0
} |
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