Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
General idea behind simplifying cube resistors I don't know if "cube resistors" is the right way of putting it, but I am wondering if somebody could walk me through the general procedure for solving problems in which you are asked to find the resistance from A to B through a cube with a resistor of some R on each line ... | The sure-fire guaranteed method, which works even if the 3D network cannot be drawn as a 2D network so that the series and parallel formulas can be used, and even if there is no symmetry to give helpful equipotentials, as in the case with a cube with 12 different resistors along its edges, is:
You apply a voltage $V_0$... | {
"language": "en",
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If the pressure inside and outside a balloon balance, then why does air leave when it pops? Sorry for the primitive question but when we inflate a rubber balloon and tie the end, its volume increases until its inner pressure equals atmospheric pressure.
But after that equality is obtained why does the air goes out when... | For an inflated and tied balloon, the inner and outer pressures aren't equal. The inner pressure is higher by an amount $2 \gamma |H|$, where $\gamma$ is the inflated balloon's surface tension and $H$ is its mean curvature (which is $-1/R$ for a sphere). This is called the Young-Laplace equation.
After the balloon is u... | {
"language": "en",
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A derivation in Jaynes' paper, linking stat-mech and Shannon's entropy I have been going through E. T. Jaynes' 1957 paper, Information Theory and Statistical Mechanics. There is a step in his derivations, which has been giving me headaches for the past day; would appreciate some pointers on how to complete it!
Link to ... | The equation 5.1 in the Jaynes' paper can be understood from basic knowledge in differential equations. $\delta lnZ$ can be written as
$$\delta \lambda_0 = \delta lnZ = \frac{\delta lnZ}{\delta \lambda_1}\delta \lambda_1 + \sum_{i}\frac{\delta lnZ}{\delta f_1(x_i)}\delta f_i(x_i)$$
Here, we know that the first factor ... | {
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How does the inverse-square law work? I'm trying to calculated the intensity of a source that I have done some experiments on using inverse-square law.
$\begin{equation} I(r)=\frac{A \cdot E}{4\cdot \pi \cdot r^2} \end{equation}$
But I'm a bit confused. If A is the activity of the source, it would be 370 kBq (Cs-137), ... | Gamma rays are notoriously difficult to block. As a rule of thumb you need 1.3-foot-thick lead or 6.6-foot-thick concrete to catch 99.9999999% of gamma rays. The detecting part of a G–M tube is made out of air which is worse at blocking (and therefore detecting) gamma rays than lead and concrete.
I suspect your G-M tub... | {
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Why are gold nanoparticles red? While watching the latest computerphile video (https://www.youtube.com/watch?v=FGiBHsUkVzU) I came across a solution of nanoparticles of gold
,
but to my surprise, they appeared as red, shouldn't gold be golden color?
| One thing to note : red back background. How much is that affecting the appearance ? Certainly their will be a great amount of red light to be reflected by the water, glass and particles in the water. Hard to know if this effect is significant or not in this case.
Part of the color (the spectral response) you see in... | {
"language": "en",
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Why do we regard $z$ and $\bar z$ as independent in CFT? I have been studying String Theory and CFT for a while, and I am sad to say I do not know why we treat $z$ and $\bar z$ as independent variables, and why we go on to consider the algebra $Vir\oplus\bar {Vir}$ instead of simply $Vir$. The literature I followed nev... | For simplicity let us consider global conformal symmetry rather than the full Virasoro symmetry. Global symmetry corresponds to the group $SL(2,\mathbb{C})$ acting on $z$ as $z\to \frac{az+b}{cz+d}$. So far $\bar z$ is the complex conjugate of $z$, not independent.
In a quantum theory we want the symmetry algebra to a... | {
"language": "en",
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If the mass of the Earth is decreasing by sending debris in space, does its angular momentum also decrease? We are sending huge amount of debris into space from earth, and also very heavy satellites and rockets, then the mass of earth must be decreasing over time.
If the mass will decrease, then gravitational attractio... | The existing answers are already sufficient, but it is also important to emphasise that if a satellite is sent to Earth orbit, then the launch does not affect the Earth's orbit around the Sun, because the Earth and the satellite continue to interact gravitationally, and the angular momentum of the Earth+satellite syste... | {
"language": "en",
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"source": "stackexchange",
"question_score": "9",
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Why isn't my calculation that we should be able to see the sun well beyond the observable universe valid? I recently read an interesting article that states that a human being can perceive a flash of as few as 5 or so photons, and the human eye itself can perceive even a single photon. The brain will filter this out, h... | The observable universe is actually defined by the speed of light and the time since the universe began to exist in a recognisable form, not by the inverse-square law of light intensity falloff. The reason why we can't see stellar objects from beyond that distance (even with the aid of radio-telescopes) is because the... | {
"language": "en",
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Gravitational field (metric tensor) and speed of light between two massive plates Suppose I have two massive plates of size $l\times h\times w$ mounted parallel to each other with a distance of $d$ and with a mass density of $\rho$. I send a light beam in the middle between them along the length $l$ and in parallel to ... | In Newtonian gravitation there is no field between plates so I would
expect no effect. I don't know what a GR solution would be, nor if
it's feasible. I know a solution for the case of a single thin plate,
but Einstein's equations aren't linear, so I'm afraid it could be of
no help for present case.
| {
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Is there a relation between this function and black holes? I was fiddling with this complex function visualizer and accidentally found this function which looks a lot like the blackhole visualizations that I see on the net:
$$
f(z)=(z\bar{z}-1)^z
$$
and I'm curious if there is a real connection with physics or is it ju... | This is not connected to black holes at all. Complex numbers are 2D objects to you need to be careful when looking at those visualizations as they are trying to represent a mapping from 2D onto 2D, which by definition requires a 4D space.
So you are seeing some form of incomplete picture of the mapping and the page do... | {
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Explanation of covalent bond from physics point of view? We can explain ionic bond as the force between charged particles due to Coulomb electrostatic law. This got me wondering how is then covalent bond explained purely in terms of physics?
| Covalent bonding is a quantum-mechanical phenomenon that can't be explained classically. The basic idea can be demonstrated in the case of a hydrogen molecule if you think of the electrons as two particles in a box. By joining the two hydrogen atoms together into a molecule, you make the "box" twice as long. Let's pret... | {
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Commutation relations in Gupta-Bleuler quantization Quantization of the free electro-magnetic field has essential differences in comparison to quantization of say scalar or massive vector fields. In fact there are different approches to it.
One of them is a covariant approach due to Gupta and Bleuler, see Section 3-2-1... | The standard prescription has the contravariant form of the conjugate momentum:
$$[A_\mu(\vec x,t),\pi^\nu(\vec y,t)]=g^{\nu\alpha}[A_\mu(\vec x,t),\pi_\alpha(\vec y,t)]=i g^{\nu\alpha}g_{\mu\alpha}\delta^3(\vec x-\vec y)=i\delta^\nu_\mu\delta^3(\vec x-\vec y)$$
| {
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Relativity and electromagnetic field I have a question regarding Misner, Charles W.; Thorne, Kip S.; Wheeler, John Archibald (1973), Gravitation ISBN 978-0-7167-0344-0. It is a book about Einstein's theory of gravitation.
At the page 79, in the Chapter 3.4. about the Maxwell's equation, we assume that we are in a Rocke... | I simply misread the tensor.
The first term is the product of $\Lambda^1_{\bar 1}=1$ and $\Lambda^0_{\bar 0}=\gamma$, while the second is the product of $\Lambda^1_{\bar 1} = 1$ and $\Lambda^3_{\bar 0}=\beta \gamma$.
| {
"language": "en",
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What is buoyancy? I’ve seen answers which cite newton’s third law as the cause for buoyant force, but wouldn’t this mean the moment an object of any weight is placed on a fluid, the fluid would immediately exert an equal and opposing force to the object’s weight? This would result in a 0 net force on any object and thu... | Let me first tell you one thing,Buoyancy is a force exerted on the body just because the fluid does not allow itself to deform because of the body weight.
Now let me give an example,if i have a body having density less than the density of fluid,the body floats.This is because the weight of the body is not greater than... | {
"language": "en",
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Peskin and Schroeder Section 7.1 Mass Shift I'm slowly reading my way through Peskin and Schroeder. Near the end of section 7.1 they compare the mass shift of the electron from QFT to the classical value, both of which are divergent but in different ways.
The calculation from QFT gives:
$$\delta m = \frac{3\alpha}{4\p... | The logarithms in amplitudes are the major consequence of QFT and appear from integrals over 4-momentum. For the hard cutoff regularization integrals like:
$$
\int_0^\Lambda \frac{d^4p}{(2 \pi)^4} \frac{1}{\left( p^2 + \Delta^2 \right)^n}
$$
become
$$
2 \pi^2 i\int_0^\Lambda \frac{d |k|}{(2 \pi)^4} \frac{|k|^3}{\left( ... | {
"language": "en",
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References for Glashow-Weinberg-Salam model I am looking for reference recommendations on the Glashow-Weinberg-Salam theory of electroweak symmetry breaking. In particular, I am looking for a discussion of the $SU(2)\times U(1)$ gauge symmetry "breaking" and its connection to the Higgs phenomenon. I am familiar with th... | Your question is actually unclear, as it instantly multiplexes into four quite different questions, which I will not spend time to parse. Before any discursive bloviations I'll send you to
*
*a classic, ISBN-13: 978-0521476522, Dynamics of the Standard Model by
J Donoghue, E Golowich, B Holstein, a bare mi... | {
"language": "en",
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Regarding notation used for infinitesimal parameters of the Lorentz algebra and generators of the Lorentz group I have confusion regarding the notation that is used for infinitesimal Lorentz transformations and the parameters that define the Lorentz transformation (used in various books such as Srednicki's and Weinberg... | The thing is that by explicit computation, one can find a set of generators $M^{\mu\nu}$ (these are matrices, not matrix elements!) such that $\omega^\mu_{\;\nu}=\frac{1}{2}\omega_{\rho\sigma}(M^{\rho\sigma})^\mu_{\;\nu}$. I admit this is a little miraculous at first sight, but it’s really nothing more than a clever tr... | {
"language": "en",
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Stationary charges and reference frame I've read that stationary charges mean "charges that aren't moving". To me however this definition seems too simplistic.
If the reference frame moves with the same velocity vector of some moving charges, then the charges are considered stationary in respect of the moving reference... | "Stationary in the given reference frame" means exactly that. The charge is stationary in this exact reference frame. Let's consider this example: In our current reference frame $S$ we assume that a stationary rod lies in the $z$ axis and carries an electric current $I$. In another system $S'$ (the $z'$ axis of this sy... | {
"language": "en",
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How does a heated lid in a thermal cycler prevent evaporation? A thermal cycler is a chemistry lab device that increases or decreases the temperature of the material inside it. The lid of the device is heated to prevent condensation and evaporation of the mixture inside.
I understand the condensation bit, as a hot lid ... | The heated lid minimizes net evaporation by preventing condensation.
The liquid water in the sealed sample tube is in a dynamic equilibrium with the water vapour. Liquid water is continuously evaporating and water vapour is continuously condensing. At a constant temperature and pressure the partial pressure of the wate... | {
"language": "en",
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Is the velocity of a string that is being rotated around a central point the same at any point on the string? Say that you have a weight attached to a 2 metre long string, and you are rotating the weight at 5 m/s. Is every point on the string going to be rotating at that same velocity of 5 m/s, or is the velocity of th... | For different points of the string to have same velocities, their direction of movement and speeds would to be the same as well. If the string is taut then all points are moving in the same direction at any given time, but it's easy to show that the speeds are not the same: If you have your 2 meter long string, the end... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Decrease in temperature due to radiation Can radiation cause the temperature to decrease? Because, in my Physics textbook, it is written that:
ln winter nights, the atmospheric temperature
goes down. The surfaces of windowpanes, flowers,
grass, etc., become still colder due to radiation. The
air near them become... | Temperature in a gas is defined as :
the average kinetic energy of the molecules composing it. If you read the link, it becomes more complicated but the basic meaning is the same, kinetic energy in any form contributes to the temperature of an object.
At the same time we have black body radiation, an experimental obse... | {
"language": "en",
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How is it possible to have different answer using two different equation for same condition?
There are two blocks ${(m_1 ,m_2)}$ of different masses placed on a surface, connected with a spring of spring constant $k$. The coefficient of friction between the blocks and surface is $\mu$. Now we have to find the minimum ... | In the first case , when you start applying the force , the block $m_1$ is accelerated , till the equilibrium position, but it has gained some velocity in this process which pushes it forward even further and causes more elongation in the spring.
In the second case , the force that is being applied is for the case of e... | {
"language": "en",
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Units conversion - quanta/cm$^2$/s and photons/cm$^2$/s Can you tell me if there is any difference between these 2 units?
$\log \mathrm{quanta/cm^2/s}$ vs $\log \mathrm{photons/cm^2/s}$
Thanks
| "Number of photons" and "Number of quanta" are both dimensionless so
"quanta" cm$^{-2}$ s$^{-1}$ has the same units as "photons" cm$^{-2}$ s$^{-1}$.
But strictly, both expressions are wrong since:
$\log{x}= (x-1) - (1/2)(x-1)^2 + (1/3)(x-1)^3 - (1/4)(x-1)^4 + ...$
So the argument inside the logarithm should be unit-les... | {
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Rotating coordinate frame connection of coordinates and mass Hello I am still confused about rotating coordinate frames and want to ask a question about it.
Is it correct that strictly speaking the mass must be connected with the axis of rotation in the rotating coordinate frame? For example by a rod, or a rotary disk... |
Is it correct that strictly speaking the mass must be connected with the axis of rotation in the rotating coordinate frame? For example by a rod, or a rotary disk, or whatever. I mean otherwise I do not see how an Euler force or a Coriolis force can act on a particle?
There is no need for a physical connection. These... | {
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In a circuit having one resistor why do the electrons lose all their potential energy across that resistor and not do so if there are many resistors In a simple circuit which consists of a battery and one resistor, why do electrons lose all their potential energy across this one resistor regardless of the magnitude of ... | Formally, this is called Kirchoff’s current and voltage laws.
But you asked why this happens. What mechanism is it that make sure that the current behaves this way?
Imagine that current goes through the first resistor of two, and then stops before going through the second. This means that charge is building up at that... | {
"language": "en",
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How will Andromeda collide with Milky Way in spite of Hubble's law? According to Edwin Hubble our Universe is expanding because he noticed that other galaxies are moving away from us. But then how Andromeda galaxy will collide with Milky Way in ~4.5 billion years, as it should also move away from us?
I am some bit con... | Because Andromeda is so close, a mere 2.5 million light years away, it is gravitationally attracted to the local group (which incudes the Milky Way), and its proper motion masks the effect of cosmic redshift. As the Andromeda galaxy and the Milky Way are moving toward each other, we see a blueshift in the spectrum of A... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Einstein summation in tensor calculus I am looking at the Schaum's Outlines "Tensor Calculus" by David C. Kay, and on page 3, the following non-identity and identity are presented:
$$
\begin{align}
a_{ij}(x_i + y_j) &\neq a_{ij} x_i + a_{ij} y_j\tag{1} \\
a_{ij}(x_j + y_j) &= a_{ij} x_j + a_{ij} y_j \tag{2}
\end{align... | In (1) the sum $x_i + y_j$ simply doesn't make sense. If you have two vectors $x,y$ you can surely add them, but then you get $(x+y)_i = x_i + y_i$. This is true in general: you can only add tensors with matching indices. That's all there is to it.
| {
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Can quantum communication break the Shannon–Hartley theorem? Just a random stupid thought.
Quantum entanglement cannot be used to transfer information faster then speed of light. But can it "embed" information until a key is received?
For exmample, assume Alice and Bob both have pairs of entangled particles:
*
... | A protocol of the form you have described does exist and is known as superdense coding. It allows Alice to transmit two classical bits to Bob by sending only one qubit through a quantum channel, providing that they already share an entangled state. However, this requires that they already share an entangled state. In o... | {
"language": "en",
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An electrodinamic identity: starting point With this request, I would like to ask you kindly how you can prove this identity. I thank you for those who can help me.
\begin{equation}
\overline{\nabla} \times (\overline{\nabla} \times \overline{E})=-\frac{\partial}{\partial t}(\overline{\nabla} \times \overline{B})\tag{... | Maxwell's version of Faraday's law of induction is
$$
\nabla\times {\bf E}= -\frac{\partial {\bf B}}{\partial t}.
$$
Now apply $\nabla\times$ to both sides. Note that
$$
\frac{\partial }{\partial t}(\nabla\times {\bf X})= \nabla\times\left( \frac{\partial {\bf X}}{\partial t}\right).
$$
| {
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Varying of momentum for constant kinetic energy How is that If the momentum of the particle is constant with time, its kinetic energy ($E_k$) should also be constant with time a true statement but the converse is false...
When momentum is constant,
\begin{eqnarray}
p&=&mv \\
E_k=(mv^2)/2& =& (mv)^2/2m\\
E_k&=&p^2/2m... | Momentum is a vector, but only its magnitude enters into kinetic energy. So kinetic energy can be constant while the momentum vector varies as long as its magnitude stays constant and only its direction changes (for example like in perfect circular motion).
| {
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Do objects besides strings, ropes, and rods have tension? Why do we define tension only in strings and ropes and rods and such? Shouldn't every object experience tension force? Like when you pull a paper from opposite sides, it gets taut, and experiences what seems like a state of tension. If every object does experien... | "Tension" is a simple special case of the state of stress in any solid object.
But you usually start learning about mechanics using simple situations where common-sense ideas like "tension" are all you need, rather than starting by learning about stress and strain tensors and constitutive equations in continuum mechani... | {
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If I stood next to a piece of metal heated to a million degrees, but in a perfect vacuum, would I feel hot? A friend of mine told me that if you were to stand beside plate of metal that is millions of degrees hot, inside a 100% vacuum, you would not feel its heat. Is this true? I understand the reasoning that there is ... |
A friend of mine told me that if you were to stand beside plate of
metal that is millions of degrees hot, inside a 100% vacuum, you would
not feel its heat. Is this true?
Not true. Heat can be conducted through physical medium, or it can be transmitted as electromagnetic radiation, specifically the infrared waves, ... | {
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"url": "https://physics.stackexchange.com/questions/491589",
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Why normal reaction, tension, and friction forces are reference frame-independent? I can not provide a whole manuscript of examples where I can justify that these forces are reference independent.
I don't think that there is any such case where these forces are reference-dependent. What is the main reason that they are... | All the forces you have mentioned here are manifestations of electromagnetic force, with very negligible effect from other fundamental forces. Now if we look at the form of electric and magnetic forces $$\mathbf E = \frac{1}{4\pi\epsilon_0} \frac{q}{ r^2} \mathbf{\hat r}$$ $$\mathbf B = \frac{\mu_0}{4\pi} \frac{\mathbf... | {
"language": "en",
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What is a mass moment? I am currently reading through a document Finding Moments of Inertia from MIT, page 4, and I am a little confused as to one of the concepts that they use.
In this document, there is mention of a mass moment. Could someone possibly define this for me please? I can't find anything too clear on the ... | This is referring to the moment of inertia.
It is similar to how inertia refers to mass, as described in Newton's 1st law, so the tendency of a body to resist acceleration by a force. This is seen as $F=ma$
Now for rotational movements, the physics terms change. The acceleration refers to angular acceleration ($\alpha$... | {
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Why are there many turns in the primary coil of a step-up electricity transformer? Since the voltage in a coil is proportional to the number of turns, the ratio of voltages is equal to the ratio of turns.
So if you need a big increase in voltage, what stops you from having one turn on the primary (instead of a bunch) a... | The transformer with too small inductance can not work normally, the primary is basically equal to shortcut circuit if the number of turns is too small.
| {
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"timestamp": "2023-03-29T00:00:00",
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Electric Flux; Number of lines passing through a unit surface? Most of the definitions on flux and flux density, show a plot consisting of a positive charge emanating a field, and describe that as the number of field lines decrease, the field strength decreases. My question is, If an electric field (which is a vector... | Using electric field lines is just a very efficient method to represent a lot of information about the field in a compact diagram it does not mean that field lines actually exist .
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/492327",
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Different forces from different inertial frames? I've been having trouble understanding this equation here derived in the picture given below. If I change reference frames to one which is moving at a velocity u with respect to the first frame, then the term $v$ in the equation would change to $(v-u)$ however as far as ... | Okay I got my answer. If I change reference frames to a frame moving with velocity u with respect to the first frame, then the sand is no longer falling vertically but rather it will have a horizontal velocity component of -u in the second frame. So that the equation of motion would be
F = [(v-u)-(-u)]dm/dt = vdm/dt
A... | {
"language": "en",
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How much do ocean currents alone slow Earth's rotation? Tidal friction is commonly spoken of as the reason for the slowing of Earth's rotation. What if the moon didn't exist? We would still have ocean currents and wind due to the Coriolis effect and the resulting friction certainly must be significant. Is it possible t... | As explained in Wikipedia,
the tidal bulge is pushed ahead by Earth's rotation. This offset bulge exerts a net torque on the Moon, boosting it while slowing Earth's rotation. ... energy and angular momentum are transferred from the rotation of Earth to the orbital motion of the Moon
Without the Moon there can be ... | {
"language": "en",
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Coefficient of friction in pulley system
EDIT: Picture doesn't show the mass of $\mathrm A$. It is $60\ \mathrm{kg}$.
My attempt: I placed my coordinate system with $x$-axis parallel to the ramp surface and $y$-axis parallel to the normal force of block $\mathrm A$. Here are my free body diagrams of each block. Note h... | $F_{f,max}<F_f$ implies that the frictional force required to keep the system at rest is too less and, hence, the blocks have to accelerate. Since $F_f$, which was got to be upwards along the wedge, is insufficient in that direction, block A will accelerate downwards along the wedge.
Now you would have to work out the ... | {
"language": "en",
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Is there 100% pure white? Is it possible to have an object 100% pure white without sky blue or sun color tinting the pure whiteness of the photons reflecting/deflecting off an object? Are there any lights that can produce pure white photons (RGB)? And can we see that the color is white or is our eyes going to trick us ... | There is no universal and objective way to define "pure white".
The reason for this is that colour perception has two important aspects:
*
*there is a "base layer" in the physiological response of the human eye and the biochemistry of the retina, but
*there is also a psycho-perceptual component in terms of how the... | {
"language": "en",
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Why is more than one ripple created when a rock is thrown onto the still surface of a pond? I have tried making an analogy with a simple pendulum: if you give it a push it will probably make several oscillations. But why isn't there just one ripple that would carry the energy of the several ripples?
| The surface of the water acts like an elastic bedsheet, if you throw a stone at it the bedsheet will create vibrations and will carry on after the impact of the stone. This situation applies to a ponds surface as it acts like the bedsheet the only difference is that the stone sinks after the first impact with the water... | {
"language": "en",
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Electric field of infinitely extended flat plate I am reading an example how to calculate the electric field of infinitely extended flat plate and I have trouble to understand certain steps
$$
E_{z}=\frac{1}{4 \pi \epsilon_{0}} \int_{0}^{\infty} \int_{0}^{2 \pi} \frac{\sigma}{d^{2}} \cos \beta d \varphi r d r
$$
$$
E_... | *
*$dr d\varphi$ is different from $d(r\varphi)$. The expression for $dA$ comes from considering the tiny orange slice in the image. It has a length of $dr$ and a width of $rd\varphi$. (The difference in the widths goes to zero as you take $dr$ infinitesimally small.)
*There has been a change of variables. You are no... | {
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Flat yet finite Universe I would like to ask you this question:
Let's assume that the universe is perfectly flat and big bang happened as described by our theories some 14 billion years ago. Shouldn´t, therefore, the radius of the universe still be finite, even if the geometry of the universe is flat? Even if inflatio... | Did someone tell you the universe is infinite?
We do not know as the answer lies beyond the scope of the "observable universe".
Extrapolation of big bang theory makes a reasonable argument for a finite universe but there is no way to test it.
No physical infinities have been proven to exist in nature; for example, the... | {
"language": "en",
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What is the difference between position, displacement, and distance traveled? Suppose the question is somewhat like this:
If $v=8-4t$ and the position at time $t= 0\ \rm s$ is $2\ \rm m$, find the distance traveled, displacement, and final position at $t=3\ \rm s$
Since $\text dx/\text dt=v=8-4t$, ... |
*
*$\color{blue}{\text{Position}}$:
$$\color{blue}{\vec p(t)}$$
*$\color{red}{\text{Displacement}}$†:
$$\color{red}{\vec p(t_2) - \vec p(t_1)}$$
*$\color{green}{\text{Distance Traveled}}$:
$$\color{green}{\int_{t_1}^{t_2} \left\|\frac{d\vec p(t)}{dt}\right\|dt}$$
†Displacement is sometimes defined as the scalar $... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/494096",
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Are extra dimensions timelike or spacelike? In special relativity there is a clear difference between spatial and temporal dimensions of spacetime due to the Minkowski metric diag(-1,1,1,1). In higher dimensional theories (10- and 26-dimensional string theories) does this asymmetry continue with additional dimensions b... | From Polchinski's String Theory, Chapter 1:
We want to study the classical and quantum dynamics of a one-dimensional object, a string. The string moves in $D$ flat spacetime dimensions, with metric $\eta_{\mu \nu} = \mathrm{diag}(-,+,+,\cdots,+)$.
So all additional dimensions are spacelike.
Strictly speaking Polchin... | {
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"source": "stackexchange",
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relative acceleration of ball in a train
A boy is standing in a train with a ball in his hand. The train is having a constant acceleration equal to x m/s^2. While still in train he throws the ball with a constant velocity of 20 m/s at an angle of 60 degree with the horizontal and catches it at distance of 1.15 m.(the ... | You can use the train as a frame of reference as long as you take into account that it is not an inertial frame of reference. To account for the acceleration of the train you will have to introduce a fictitious force of magnitude $mx$ N acting horizontally on an object of mass $m$ kg. This fictious force is similar to ... | {
"language": "en",
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Physical meaning of the convection term in the momentum equation of acoustic wave In deriving the acoustic wave equation, the momentum equation is used.
$$\frac{\partial \mathbf{u}}{\partial t}+
(\mathbf{u}\nabla)\mathbf{u}=-\frac{1}{\rho} \nabla p$$
Intuitively, the convection term $(\mathbf{u}\nabla)\mathbf{u} $ repr... | The momentum equation written above is written for an incompressible fluid, otherwise the density $\rho$ would have to be written inside the partial derivative:
$$
\frac{\partial\rho\mathbf{u}}{\partial t}
$$
Hence, the momentum in a Control Volume can change by either:
*
*a change in velocity of the fluid
*convec... | {
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A best definition of proper acceleration In this link of Wikipedia https://en.wikipedia.org/wiki/Hyperbolic_motion_(relativity) there is a definition of proper acceleration:
The proper acceleration to a particle is defined as the acceleration that a particle "feels" while accelerating from one inertial reference syste... | Let's say there is an inertial frame S close to an accelerated frame S'. S' velocity is not constant, but at every moment, we can assume S velocity to be exactly same as S' velocity. Now if S measures S' acceleration, what he will acquire would be proper acceleration. Or if you stay in a rocket that its engines provide... | {
"language": "en",
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Why is "a very silent room" louder than "leaf noise" / "breathing noise"? I recently was at night in my bed room and used the Schallmessung Android App (on a Samsung S7). It showed 20 dB while laying on some furniture. I could not hear anything; to me, the room was completely silent.
Now I looked at some examples of no... | A silent room is not perfectly silent, but contains sound from ventilation sources and vibration sources inside the building plus outside sounds being transmitted into the room through its walls and windows. These sources are accounted for in the (textbook) citation of the sound level inside a "typically quiet" room.
| {
"language": "en",
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Is the acceleration of car greater when hitting the accelerator, or the brakes? Is acceleration of car greater than when pedal the pushed to the floor or when break pedal is pushed hard? I do understand that the signs would change in either but I am more considered about the magnitude....
| Assuming that you have enough of a variety of gear ratios available, every car should theoretically be able to "burn rubber" when accelerating, up to a certain critical speed $v_0$. On a level road, with the standard model of friction, $v_0=P/\mu_s mg$, where $P$ is the maximum power the engine can supply.
So below $v_... | {
"language": "en",
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What is the most efficient single-photon detector to date? (This question depends on the current time period, so the reader should make note and be aware of the date of the posted answers.)
I am wondering what is the most efficient state-of-the-art single-photon detector we have currently achieved. There are two things... | Superconducting nanowire single photon detectors and transition-edge sensors (>95% end-to-end measured at 1550nm) Both operate near a phase transition superconductor - normal metal, where absorption of a photon changes the resistance.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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$n$-body problem = many-body problem? Are the terms "$n$-body problem" and "many-body problem" synonymous? Or does one refer to a numerical problem an the other to an analytical problem?
| The Mathematics Subject Classification (MSC2010) classifies "many-body" under quantum mechanics:
81-XX Quantum
theory 149997
81Vxx Applications to specific physical systems 33023
81V70 Many-body theory; quantum Hall effect
4367
Whereas "$n$-body" appears to have more extension:
70-XX Mechanics of
... | {
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Particle moving on ellpse with foci as origin I'm reading the book "An introduction to Celestial Mechanics" by Forest Ray Moulton. In the first chapter, I got stuck on the following problem:
A particle moves in the ellipse whose parameter and eccentricity are $p$ and $e$ with uniform angular speed with respect to one ... | Start with the following polar-coordinates equation for an ellipse with focus at the origin:
$$r=\frac{p}{1+e\cos\theta}.$$
Note: The parameter $p$ is often written in terms of the semi-major axis $a$ and the eccentricity $e$ as $p=a(1-e^2)$. Another name for $p$ is the semi-latus rectum.
Differentiate to find Moulton’... | {
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Is reversal of velocity always equivalent to reversal of time? Let us imagine there is a container full of small particles which are allowed to collide with each other and the container walls (in 2D). If I initialise the system with given velocities and positions at $t = 0$, and reverse the velocity of every particle a... | You are rediscovering the chaotic behavior of non-integrable systems.
The reason the system does not recover exactly its original state is due to the unavoidable round-off which makes the final dynamic configuration slightly, but definitely different from the exact evolution. Even after a few steps. When velocities ar... | {
"language": "en",
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The limit of the Universe that we'll ever be able to see After watching Neil Turok's talk at 13:00 - 13:20 he says that the Universe expands and there is a limit beyond which we will never be able to see anything.
And that's due to the Dark Matter which (as I understood) interferes with the light.
So the question is t... | It is not directly because of dark energy (he said dark energy, not matter), it is because of the accelerating expansion of the universe, which is believed to be caused by dark energy. The distance between opposite sides of the universe is increasing faster than the speed of light, so the light can never reach the othe... | {
"language": "en",
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"source": "stackexchange",
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Calculating mean velocity: using time or velocity? Background
I have been running tests which involve timing an object moving a certain (fixed) distance, $s$.
Each test has been repeated 3 times, and the 3 times ($t{_{1}}, t{_{2}}, t{_{3}}$) for the object to travel $s$ m are recorded.
However, when calculating average... | Your question is not clear in particular part ,wether you want to find average velocity at distance s(which is nothing but the average of three experiment) or you want average velocity of the experiment where the object travel distance 3s in time interval t1,t2,t3
Which is calculate by total distance /total time that... | {
"language": "en",
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Are laws of Physics same in frames having zero relative acceleration? If two frames have the same acceleration, then they'll be moving with a uniform speed with respect to each other. Are laws of Physics the same in these two frames?
| The laws of physics are not frame dependent. What is free dependent is the equations of motion. And, indeed, we will find that the equations of motion will be the same in two frames that are accelerating the same. You can do the frame transform and find that all vectors transform by the identity transform (other tha... | {
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Does the Second law of thermodynamics violate the First law of thermodyanmics? Since entropy has the units of Joules per Kelvin, and the net entropy of the entire universe is always increasing. Does it mean that the energy of the universe is always increasing?
Edit1: To be more precise. Consider two systems. A glass of... | This is not how physics works. Units tell us nothing about how a quantity behaves. There are a million examples but here is one: kinetic energy has units of Joule but is not conserved (only the total energy is).
But to answer the question directly:
The first and second laws are two independent statements and one does ... | {
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Does an object storing more internal energy emit more thermal radiation? There are two objects of the same material, similar geometry but different dimensions and same temperature. The larger object is supposed to contain more quantity of heat because it has larger volume.
Now I know that the quantity of emitted therma... | @Andreas Sundstrom is correct that the equation for radiation does not depend on the volume (mass) of the radiating object. But that is because the equation assumes the temperature of the emitting body is constant.
As the body radiates heat its internal energy is reduced thus reducing the temperature of the body and t... | {
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Why is the electric field of a conducting sheet of charge double the electric field of just a sheet of charge? I was reading Feynman's Lecture on the Application of Gauss' Law and I came across this:
Source
This really confused me. What are the "other" charges he talks about? How does the additional field make the el... | I will admit that the language he is using is slightly confusing at first, but if you read on, it makes more sense. The "other" charges he is talking about are the charges outside the tiny Gaussian surface.
In the middle of a charged sheet, by symmetry, the charge distribution produces an equal and outward (for positiv... | {
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From where do electrons gain kinetic energy through a circuit? Supposing an ideal wire, How do electrons accelerate and gain kinetic energy?
What I understand:
When a circuit is opened ,electrons are crowded at the negative term of the battery and have high electric potential energy, when we close the circuit electrons... |
Supposing an ideal wire ,How do electrons accelerate and gain kinetic energy ?
An ideal wire is an abstraction that is used to simplify calculations in physics and electrical engineering.
The mobile charge in an ideal wire respond instantaneously to external fields so that the skin depth is zero. Clearly, this can't ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/497325",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How to get the Bertotti-Robinson metric into its conformally flat version? The Bertotti-Robinson metric is a very nice exact solution to the Einstein-Maxwell field equations in vacuum. It is usually stated into these equivalent versions (where $r = \sqrt{x^2 + y^2}$ and $\bar{r} = \sqrt{\bar{x}^2 + \bar{y}^2 + \bar{z}... | I found a solution to my question. I consider A.V.S.'s answer (thanks dude!):
(4) can be written this way, using spherical coordinates, with $\bar{r} = \sqrt{\bar{x}^2 + \bar{y}^2 + \bar{z}^2}$:
\begin{align}
ds^2 &= \frac{R^2}{\bar{r}^2} \, d\eta^2 - \frac{R^2}{\bar{r}^2} \, \big( \, d\bar{r}^2 + \bar{r}^2 \, (d\vart... | {
"language": "en",
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What are the pros and cons of Einstein-Cartan Theory? As an alternative to General Relativity, i hear that it can avoid the initial big bang singularity as well as the singularities in black holes, so why does it appear to be talked about so little? If anyone can enlighten me a bit on the successes and shortcomings of ... | One main reason why the ECKS theory (Einstein-Cartan-Kibble-Sciama) is so unpopular even today is its extreme mathematical complexity. The connection isn't symetric anymore, so it changes a lot of things in the mathematical formalism (for example: the covariant derivative applied to a simple scalar field doesn't commu... | {
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Does the postulate of equal a priori probability apply only to equilibrium states or to all states satisfying the constraints? In deducing the zeroth law of thermodynamics in micro-canonical ensemble, there is a frequently-mentioned example. Suppose we put two isolated system, system 1 and 2, in contact and allowing th... | The equal a priori probability postulate says:
all microstates in the big box are equally probable
Here is what this means. If we collect all possible microstates of the big box what we will find is that the overwhelming majority of them are such that the part 1 has energy $E^{eq}$ and part 2 has energy $E-E^{eq}$. I... | {
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Why do all fields in a QFT transform like *irreducible* representations of some group? Emphasis is on the irreducible. I get what's special about them. But is there some principle that I'm missing, that says it can only be irreducible representations? Or is it just 'more beautiful' and usually the first thing people tr... | The premise of the question is just false. When doing phenomenology it is useful to split a field into its irreducible components, essentially because each irrep carries its own coupling constant. But when analysing QFT from a theoretical point of view, it is convenient to consider a single "big" field in a reducible r... | {
"language": "en",
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If an earthquake can destroy buildings why it cant kill us according to physics? Most earthquakes with magnitude 5.5 and higher can damage or destroy buildings. However, according to my knowledge and experience, I have never seen someone dying from an earthquake itself. Rather, they die from an associated tsunami, dama... | Force is the rate of change of momentum (the product of mass and velocity of the object):
$$ F = \frac{dp}{dt}$$ where $p = mv$ is the momentum. An object with twice the mass has twice as much momentum compared to an object moving with its same velocity.
So a building of a million kilograms will have ten thousands time... | {
"language": "en",
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From Poisson's equation to Laplace's equation I want to understand how exactly $$ \nabla^2 V = - \frac{\rho}{\epsilon_0}$$ turns into $$ \nabla^2 V = 0.$$
Of course it is by setting $ \rho$ equal to $0$ but what does setting $ \rho$ equal to $0$ mean?
$$ \int_{S} \vec E \cdot d \vec a = \int_{V} \nabla \cdot \vec E \,... | Following specification should help: In electrostatics, Laplace's equation holds at any point where the charge density is zero, i.e. $\rho = 0$, even if $\rho \neq 0$ elsewhere. It informs us about how potential behaves locally at a point of consideration.
| {
"language": "en",
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Force on a charge particle due to magnetic field Why is Force perpendicular to the velocity and magnetic field ?
I know it's a cross product whose magnitude of force is given by
$$\vec{}= \vec{}\times\vec{}$$
but why is that ? I mean when an electrically charged particle with initially velocity perpendicular to electr... | This in some sense has got to do with the fact that nature does not have magnetic charges. Only dipoles. These dipoles can be thought of as an arrow pointing perpendicular to the plane that the charge is rotating in.
The action of the magnetic field is to get this magnetic dipole to align with it. In order for the dip... | {
"language": "en",
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How can the charged object move towards the reference charge , without acceleration while measuring the electric potential of a point? It is given in the defination of electric potential in a website that we bring a charge from infinity to that point slowly(without acceleration). But if the charge placed at infinity i... | Obvious to move a charge from infinity without accelerating it is not a very practical proposal if the charges attract. You can also let it fall in, measure its speed and subtract the kinetic energy. For the repulsive case I see no issue other than that infinity is very far off.
| {
"language": "en",
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Does the equivalence principle imply that light must move slower when moving away from a massive object? Thought experiment: Elevator going up at an extreme acceleration, pulse of light bouncing up, and down between mirrors on the floor, and the ceiling. Won't it take light longer to travel from the floor to the ceilin... | Your reading of the thought experiment is not correct.
The equivalence principle implies that locally the laws of physics are described by special relativity, hence locally the speed of light is $c$.
The thought experiment means the ceiling (receiver) is moving away from the floor (source) and thus measures a lower... | {
"language": "en",
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Covalent bonding in cuprates In high temperature cuprate superconductors like YBCO, there are intermediate copper-oxide planes, where $Cu$ and $O$ atoms are arranged alternatively in a square lattice. In this arrangement, the $Cu$ atoms generally make 4 in-plane and 2 axial bonds, and each $O$ makes 2 in-plane bonds (s... | The square-planar coordination is typical for a Cu(II) ion. Also when there are six ligands which could form an octahedral crystal field, the Jahn-Teller effect on a $3d^9$ configuration generally leads to the hole occupying the $3d_{x^2-y^2}$ orbital, and the bonds in the $z$-direction becoming longer.
| {
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Why doesn't mercury flow in the thermometer? Nowadays digital thermometers are used, but in the past mercury based thermometers were used. From my experience the mercury does not flow in the thermometer tube. Mercury is a liquid, so it must have tendency to flow. Why does it not flow when tilted?
| This is because the thermometer tube it is contained in is so small in diameter that surface tension effects dominate over gravity and inertia effects. If you were to smoothly increase the diameter of the thermometer tube, there would come a critical point at which for that diameter, tilting the tube would cause the me... | {
"language": "en",
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If magnetic force can't do any work, then how can we define a potential? I am confused about the idea that magnetic forces do no work. If something has a potential, then it has energy and hence can do work. I am using the logic of electric fields for this reasoning. I have seen the mathematical proof of why magnetic fi... | The vector potential describes potential momentum per charge unit. A better name would be "momentum potential". The confusion arises when one tries to interpret this quantity as another energy potential.
| {
"language": "en",
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How can Schrödinger's cat be both dead and alive? So, this goes to something so fundamental, I can barely express it.
The Schrödinger's Cat thought experiment ultimately asserts that, until the box is opened, the cat is both dead AND alive. Now, this is obviously ludicrous. The cat either died or lived at some point; ... | Short answer: the cat isn't dead and alive. It's dead or alive.
When faced with a quantum superposition of more than one state, e.g.,
$$
|\phi\rangle = \frac{1}{\sqrt{2}}\left(|a\rangle + |b\rangle\right),
$$
interpret the plus to mean that when measured the state could be found to be $a$ or $b$, with probabilities go... | {
"language": "en",
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Confusing work done on a particle I'm going to ask a simple question, but it's bothering me. We all know that work done by a force which is perpendicular to its path of motion is zero.
Suppose I keep a chunk of mass in a perfectly frictionless sack, and I start moving from place A to place B. I am applying a force wh... | If the particle is starting from rest, then you can't apply only a force perpendicular to its motion because there is no motion, and you have to do real work to get the particle started, i.e. the work required to go from 0 to some kinetic energy. You can later do negative work to stop the particle, but the required fo... | {
"language": "en",
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How does instantaneous velocity or acceleration have any other numerical value than 0? Instantaneous velocity is defined as the limit of average velocity as the time interval ∆t becomes infinitesimally small. Average velocity is defined as the change in position divided by the time interval during which the displacemen... | $$v_\text{average}=\frac{\Delta s}{\Delta t}$$
$$v_\text{instantaneous}=\lim_{\Delta t\to0}\frac{\Delta s}{\Delta t}$$
*
*If the time interval gets infinitesimally small $\Delta t\to 0$, then you are dividing with something very, very tiny - so the number should become very big: $$\frac{\cdots}{\Delta t}\to \infty \q... | {
"language": "en",
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Doubt about Entropy of solar radiation on Earth This paper $[1]$ gives the following statement:
On Earth, the low-entropy energy is provided by solar radiation and the high-entropy energy is disposed as infrared radiation emitted into the cold space.
So, what suppose to mean "low-entropy energy"?
$$ * * * $$
$[1]$ h... | In a black body radiation, entropy of a photon gas is proportional to the cube of its temperature (see e.g. Wikipedia), which is itself an increasing function of frequency (or decreasing function of wavelength), so indeed, visible light has more entropy than infrared.
| {
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Derivation of Conservation of Energy from Newton's Second Law Given Newtons's Second Law: $$ \frac {d}{dt} (m \boldsymbol{\dot r}) = \mathbf F $$
How is it possible to derive the conservation of energy equation with a constant mass?
That is how can you derive $ \mathbf F = - \nabla V(\mathbf r) $ where $V(\mathbf r)$ i... | Defining $\vec{v}=\dfrac{d\vec{r}}{dt}$ and $\vec{a}=\dfrac{d\vec{v}}{dt},$ we have:
$$\dfrac{dE}{dt}=\dfrac{d}{dt} \left(\frac{1}{2}m\vert \vec{v} \vert^2+V \right)=m\vec{v} \cdot \vec{a}+\dfrac{dV}{dt}.$$
Next notice that because of the chain rule we have:
$$\dfrac{dV}{dt}=\nabla V \cdot \vec{v},$$ so that we have:
... | {
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Does the curvature of light around a "centre star" in gravitational lensing affect the age at which we view the object being "lensed" It occurred to me that during gravitational lensing, the light curves around a given object, creating a curved path. Because the path of light is curved, and thus, longer than a straight... | Yes it does. Thus if a background lensed source is varying in time, then this variability can be seen at different times in the variously lensed images with a distinct lag between them that is related to the optical path length of the lensed light.
Such time delays can be hundreds of days and have been measured in the ... | {
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Determine canonical fields of action I'm working on an exercise which asks me to determine the canonical fields, and their equations of motion, of this invariant action:
$$
S = \int d\tau \sqrt{g_{\tau\tau}}\left( \frac{\tilde m}{2} g^{\tau\tau} \frac{d}{d\tau} x^\mu \frac{d}{d\tau} x_\mu - V \right),
$$
where $\tilde... | I suspect you need to derive the pair of coordinates and their corresponding momenta.
The coordinates are just the variables your action is formulated in so $x^{\mu}$ and $g_{\tau \tau}$.
The definition of canonical momenta is
$$ p_{\mu} = \frac{\partial \mathcal{L}}{\partial \dot{x}^{\mu}}, $$
where $\mathcal{L}$ is t... | {
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Heuristic derivation of air resistance - why should the velocity of the air be equal to the velocity of the car? David MacKay gives a heuristic derivation of air resistance of a driving car in his book Sustainable energy without the hot air.
He starts with a tube of air with the cross sectional area of the car $A_{\tex... | He is referring to the air behind the car, the air in front will collide with the car and be pushed away, but behind the car some air will be dragged along with the car at a similar speed to the car.
| {
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How to calculate pole strength for this magnet? I know magnetic mono poles don't exists and a magnetic poles always have equal strength. But what about a magnet which looks like this?
This is picture of magnet whose thickness is constantly decreasing
Will it have poles of unlike strength or such magnets cant exist?
| A magnet consists of subatomic particles with aligned magnetic dipoles. More precisely, with more or less aligned dipoles, which together form a macroscopic magnetic field.
Faraday introduced the lines of force and modeling a magnet with such lines of forces is a good way to understand what is happening. First at all t... | {
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Why don’t I see proper time? Say we have my friend blasting off in a spaceship to Planet Physics and I’m sitting here on earth. I think it’s quite obvious that I will measure the proper length between the planets (because I could use a meter ruler and measure it all) and that he will measure the contracted length (bec... | Special relativity is not special. It is simply a process where an observer A measures observer B when they are in relative motion. There is no preferred frame of reference. Thus observer A cannot say they are stationary (preferred frame) while observing B. They both move away from each other. That is what relativity i... | {
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If a thermodynamic cycle on a Pressure-Volume diagram has internal irreversibilities, what does the area enclosed by the cycle represent? When a cycle is internally reversible, the area enclosed by its P-v or T-s diagram is the net work, but what about when the cycle is internally irreversible? Is it net useful work on... | For both internally reversible and internally irreversible processes, the area enclosed in a plot of $P_{ext}$ vs V determines the work . However, to do this for an internally irreversible process, you need to know $P_{ext}$ vs V (either specified or controlled). For an internally reversible process, $P_{ext}$ is equ... | {
"language": "en",
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Does vacuum energy have an average temperature of 0° Kelvin? Vacuum energy has zero-point energy. Does this imply that vacuum energy [has] an average temperature of 0° Kelvin?
| There are various ways to define temperature, but a simple way to understand it is that some medium has a temperature greater than zero if heat can flow from that medium to a colder medium.
But even though the vacuum does indeed have a zero point energy, that energy is still the lowest energy state possible. So there i... | {
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Linear Regressions vs Algebra & Averaging in Solving for a Constant I'm current taking AP Physics, and in both of the labs performed so far (Snell's Law/Refraction and Galileo's Inclined Plane), I have been trying to calculate some constant from a linear relationship between two variables, with some form of $y = mx$, w... | Normally, a linear regression assumes no uncertainty in the independent variable (e.g., x). If this assumption is valid and the relationship is actually linear, a linear regression drives a line through the data such that the errors in the dependent variable normally distribute themselves around the regression line. ... | {
"language": "en",
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Michelson-Morley Experiment as evidence for Special Relativity Context: Our state (NSW, Australia) recently got a new syllabus for the year 12 physics course, and as such we are the first year going through with the new course.
One of the things we need to learn is evidence for Einstein's Special Theory of Relativity. ... | The null result of M-M experiment actually tells you that there is some problem with Galilean transformation of Maxwell's equations for electrodynamics. For further details refer to Tests of special relativity
. For a much detailed discussion on relativistic electrodynamics refer to Liénard–Wiechert potential and Feyn... | {
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Why does transition from one electron shell to another shell always produce massless photon? When electrons transition from a higher energy state to a lower energy state (energy difference $E$), they produce massless photon with frequency $\nu$ where
$ \Delta E= h \nu$
(h is Planck constant). We know energy-mas relati... | It's just a conservation of energy equation.
An example of such a case when an electron jumps to a lower shell it emits a photon and this photon itself is captured by an electron in the outer shell and that electron gets emitted from the atom. So in principle till all the conservation laws are satisfied there is always... | {
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Percent difference when both negative In an experiment, I was asked to find the percent difference between theoretical and experimental $y$-intercept (which I have). It is known that its formula is
$$\text{Percent Difference} =\frac{|x_t-x_e|}{\frac{1}{2}\left(x_t+x_e\right)}\cdot100\%$$
But what if both values (in my... | It should be $\%=\frac{|x_t-x_e|}{\frac{1}{2}\left(x_t+x_e\right)}$. You dont have to worry about negative values as ${|x_t-x_e|}$ will take care of all possible values + or - Just plug the values as they are and the difference will be correct.
| {
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Is the Olympic running race fair? I noticed that the 200-meter sprints are conducted on curved tracks. (See this video: world championship semifinals 2009)
Isn't that weird? I mean, just look at the curvatures of each lane!
(Source)
Since they use staggered start lines, the total track length is the same. But the p... | From the point of view of an ideal machine that is not slipping on the ground, friction does not do any work. $W = \vec F \cdot \vec d$, but as the shoe does not slip, the distance moved against friction is zero, so the work is also zero.
Another way to think about it is that in a constant-speed turn, the velocity is ... | {
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If $\mathrm df$ is an inexact differential, how would the function $f$ look like? I am studying thermodynamics and in the first chapter the concept of exact and inexact differentials were used to talk about the differences between internal energy, work and heat.
From Blundell and Blundell: $\Delta f=\int_{x_i}^{x_f}\ma... | The definition of $df$ being an inexact differential is that $f$ is not a function of any sort. It's a small quantity of something. The classic example of this is the first law of thermodynamics
$$\mathrm{d} U = dQ - dW.$$
In this law, the left hand side is an exact differential, it's the difference in internal energy ... | {
"language": "en",
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Work done by friction in a complicated path
A block of mass $M$ is taken from point $A$ to point $B$ in a complex path by a force $F$ which is always tangential to the path. We also have coefficient of friction as $K$. What will be the work done by force $F$ when it reaches point $B$ from point $A$? Given that the ve... | Here, at any instant of time, the normal force on the body is $mg\cos\theta$, where $\theta$ is the angle made between the downward direction and the normal force on the wedge direction. Therefore, the work done by friction on moving distance dl is $\mu mg\cos\theta.dl$. Notice, however, that $dl$ could also be written... | {
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Does the magnetic part of the Lorentz force do work? The magnetic part of the Lorentz force is
$$\vec F_L=q\left(\vec v\times\vec B\right)$$
As this force is always perpendicular to the direction of the movement, we learned that no work is done by it.
However, it's easily observed that permanent magnets attract each ot... | Are you asking how magnets do work? I would say that when you pull magnets appart you are putting potential energy into the system. And when magnets snap back together, the energy is released as sound and heat.
| {
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Navier-Stokes Derivation Someone knows a physical derivation of the Navier-Stokes equation? Mainly the stress tensor. A lot of authors simply "jumps" the stress tensor and it's the more important of physical motion and deformation of the fluid.
| Most books on continuum mechanics and/or fluid mechanics will have a section devoted to the stress tensor. I personally like the derivations in Lin and Segel's Mathematics Applied to Deterministic Problems in the Natural Sciences (Chapter 14) or in Gonzalez and Stuart's A First Course in Continuum Mechanics (Chapter 3)... | {
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Does it take more force to press two springs in series? Let's say I have a spring that takes force $F_1$ to fully compress it from a relaxed state with spring constant $k_1$ and total displacement from relaxed state $x_1$, which I believe is related through Hooke's Law $F_1 = k_1 x_1$.
Now say I have a second spring wi... | So you are in a situation like this:
Split the springs into their own free body diagrams
and notice that they share the same force $F$ and that the combined displacement is the sum of each displacement
$$ \delta = \delta_1 + \delta_2 = \frac{F}{k_1} + \frac{F}{k_2} $$
The above is solve for the force to get the combi... | {
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How do we calculate the force applied by a ball on a wall which bounces back? If we have a ball which we throw toward a wall which touches the wall and bounces back then how will you calculate the force applied by the wall on the ball because the the contact time of the ball and the wall is infinitely small so force mu... | It is not in fact infinitely small. If you look at slow motion video of the collision, you can see that the ball and the wall are in contact for reasonable amount of time. During that time, energy of motion is stored as elastic energy od the ball (some is naturally lost) and then converted back to the kinetic energy of... | {
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How are quarks assigned color charge? As always, I'll preface that I am wildly undereducated, so i may be overlooking something or be completely unaware of another relevant property.
Color Confinement dictates that to "assemble" a baryon or meson it must be color neutral. Eg q -q, or qqq.
Looking at a proton it has a c... | Colour is independent of flavour. An up quark can be red, green or blue. Since gluons also carry colour, the colour of a quark isn't fixed. When a blue quark interacts with a green quark (of whatever flavour) they do so via a gluon that carries "blue-antigreen" (or green-antiblue) colour, and this has the effect of swa... | {
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Has the gravity a negative value? We all know that the acceleration of the gravity is equivalent to 9.81 m/s². But the gravity attract everything that have a mass (everything as far as i know) to the center of a planet.
As an magnetic field that attract another magnetic with a opposite pole, is the gravity an negative ... | Outside involved masses gravitational energy potential is ~ -1/r for distance r; in this sense YES. The offset of the absolute energy of a system does not contribute to the laws; regarding this neither YES nor NO.
| {
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} |
Is there any physical evidence for motion? Let's say that we have 2 tennis balls in space, one being in motion (say, pushed by an astronaut), and the other one still.
If we could take a snapshot of both tennis balls, would there be any evidence that could suggest that one is moving and the other one is still? Is there ... | If we look past your example with snapshots we can just look into modern technology and find a little thing called videos. They can record motion pretty easily. "Is there any physical evidence for motion", videos?
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/508066",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "44",
"answer_count": 12,
"answer_id": 11
} |
Are operator matrices of $x$ and $p$ the same for all systems? I recently read Computing quantum eigenvalues made easy . In that article, the author used the position and momentum operator's matrix form in terms of the normalized eigenstates of a harmonic oscillator(truncated to some finite dimension ofcourse) and some... | From a theoretical point of view, a quantum mechanical system consists of a Hilbert space $\mathcal H$, which consists (roughly) of the possible states of the system, and a special choice of operator which governs how the system evolves in time. When we make a choice for this time evolution operator, we call it the Ha... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/508222",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
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