Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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Density of states of 3D harmonic oscillator Consider the following passage, via this image:
5.3.1 Density of states
Almost all of the spin-polarized fermionic atoms that have been cooled to ultralow temperatures have been trapped by magnetic fields or focused laser beams. The confining potentials are generally 3D harm... | The author is working by analogy with the 3D box case. The 3D box worked out easily because $\epsilon\propto k^2$, so that the number of states up to each energy could use the volume of an ellipsoid, which is well known. He/she makes the volume of an ellipsoid work in a "rough way" for the harmonic oscillator. He/she p... | {
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Why does the water bottle not rotate when it is half full? Consider this water bottle:
When it is full and thrown up in the air, it rotates at a constant velocity.
When it is less than 1/8th full, the water bottle rotates even faster than when it was full.
When it is half full, however, the water bottle rotates for o... | I guess, The most important question is wheter you will accelerate the fluid when throwing the bottle. This and conservation of angular momentum will be much more important than dissipation of energy in the fluid.
If it is full, the water, due to the constraints on the system, will be accelerated with the bottle when t... | {
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Soliton solution for a diffusive system With a simple model for bacterial diffusion, I get this partial derivative equation :
$$\frac{\partial n}{\partial t} = D\frac{\partial^2 n}{\partial x^2} + d_1 n -d_2 n^2$$
where $n(x,t)$ is the population of bacteria, $d_1$ the rate of proliferation and $d_2 n $ is the rate of ... | At least for an equilibrium situation, where $\dfrac{\partial n}{\partial t}=0$ and $\dfrac{\partial n}{\partial x}=0$, you would easily see that
$$d_1 n - d_2 n^2=0,$$
with the two solutions you anticipated.
I am not sure what you mean with a soliton solution for an equation like these, as the basis of your equation ... | {
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Determining the three Euler angles from the acceleration I want to know, given the measurement of an accelerometer at rest (so not really an acceleration but a force per unit of mass) the inclination of this accelerometer, along the three axis.
For this, I find this PDF document. However, there's something I can't defi... | The solutions these equations give for the angles are different because they are for different rotation sequences. The first set of equations has the subscript xyz and the second has the subscript yxz, so these angles depend on the rotation sequence.
| {
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Meniscus attached to an inclined plate To be more specific, suppose a hydrophilic infinite plate is stuck into a semi-infinite region of water, above the water is a semi-infinite region of air, when the plate is stuck into the water vertically, the contact angle is $\alpha$, as shown in the figure below:
Needless to s... | the angle will change.
and it will be smaller at the inclination beta.
and greater at the other side
| {
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Number of Nodes in energy eigenstates I have a question from the very basics of Quantum Mechanics. Given this theorem:
For the discrete bound-state spectrum of a one-dimensional potential let the allowed energies be $E_1<E_2< E_3< ...$ with $E_1$ the ground state energy. Let the associated energy eigenstates be $ψ_1,... | The physical interpretation behind the increase of energy with the number of nodes can be understood in a very crude manner as follows:
Nodes are points of zero probability densities. Since the wavefunction is continuous, the probability density is also a continuous function. So the regions in the neighbourhood of node... | {
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Torque in a non-inertial frame How can we calculate torque in a non-inertial frame? Take for instance a bar in free fall with two masses, one on either end, $M_1$ and $M_2$. Taking the point of rotation to not be the center of mass, i.e. $M_1\neq M_2$ and take the point of rotation to be the center, what is the proper ... | Follow the rules of motion:
*
*Sum of forces equals mass times acceleration of the center of mass: $$ \sum_i \vec{F}_i = m \vec{a}_{cm} $$
*Sum of torques about the center of mass equals change in angular momentum: $$ \sum_i (M_i + \vec{r}_i \times \vec{F}_i) = I_{cm} \dot{\vec{\omega}} + \vec{\omega} \times I_{cm}... | {
"language": "en",
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Coulomb barrier in nuclear fusion Suppose there exists an alpha particle in the nucleus.
Within a radius of 2 femtometer, the dominating force is the nuclear force but beyond this radius, the Coulomb force becomes the effective dominating force due to it's longer range force. Outside this radius is a daughter nucleus.
... | The electric potential between two point charges depends on the product of the charge of each.
The charge in the nucleus is due to protons, and the count of protons is given as $Z$ for a total charge of $Ze$.
The alpha decay removes two protons (and two uncharged neutrons). The charge of the alpha particle is $2e$, le... | {
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True randomness? I am a physics high-school student so my knowledge is not very deep on the subject.
We started learnning about quantum mechanics and on some processes that my teacher described as random. I began to think on the concept of randomness and question it, thinking how can a process or an outcome be determin... | Quantum mechanics is a theory where randonmness is inherently present. According to it, it is possible to desing experiments where we can only predict the probabilities of the different outcomes.
It has been argued, in the beggining of the theory, that this must happen becasue QM is an incomplete theory of nature. So,... | {
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Elements of particle mass From what I can tell, it seems that particles have two kinds of mass, the mass inherent in a fundamental particle itself, or for composite particles, additional mass associated with the Higgs field. Is that distinction correct?
If so,is the mass of associated with with the Higgs field equal to... | The Higgs field is a fundamental field in the standard model of particles. The particles which acquire mass due to the Higgs field are shown in the table.
The Standard Model of elementary particles (more schematic depiction), with the three generations of matter, gauge bosons in the fourth column, and the Higgs boson... | {
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What about a surface determines its color? Light falls on a surface. Some wavelengths get absorbed. The other are reflected. The reflected ones are the colors that we perceive to be of the surface.
What is the property that determines, what wavelengths are reflected and what are absorbed? Is it electronic configuration... | Great question -- it opens up a lot of physics. My favorite example is "why do some conducting metals look gold/copper/etc. rather than grey?" Turns out it's due to relativistic effects acting on the various electrons' orbitals.
Then there's the blue jay, whose blue color is entirely interferometric rather than ab... | {
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Two people are holding either end of a couch, is one person exerting more force than the other? I was carrying a couch with my flatmate yesterday, and I started thinking about this.
Often when carrying objects like this, one person will be taller and has thus lifted his end of the couch higher than the other person's. ... | Although Floris made a clear picture involving only vertical forces, this picture is mostly useful when carrying washing machines or large chairs, where the 'height' of the object is more pronounced.
However, you will find that, even when the object is mostly flat, the bottom person will carry most of the weight. The k... | {
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Heating suprecritical water in a closed water tank How does the pressure of water in a closed tank evolve in the following setting:
- closed tank of 2 liters (filled up with water)
- water initially at 25°C and pressurized to 3 bars
The water is now heated up to 130°C, thus remaining a fluid (based on water property ta... | For water, the equation of state is semi-empirical and so the choice depends on how accurate you want to be and the range of temperature/pressure/etc that you're interested in.
Equation 19 in Jeffery et al [1], where the parameters are given in equation 32, seems appropriate.
[1] Jeffery, C. A., and P. H. Austin. "A ne... | {
"language": "en",
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Why do higher modes propagate more in the cladding of an optical fiber than lower modes? I am trying to understand the theory of inter-modal dispersion in optical fibers. It seems quite obvious that if higher modes have a greater angle of incidence in the fiber than lower modes, the path length of higher modes through ... | At a smaller angle of incidence on the boundary (higher mode), the field of the evanescent wave penetrates more deeply into the optically rarer medium (cladding). See the derivation here, in which the characteristic depth of penetration of the evanescent electric field is given by
$$
\frac{c}{\omega}\left((n_1\sin(\the... | {
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Units of vector differential operator del ($\nabla$) My book says that $\left[\nabla \cdot (\vec E \times \vec H)\right] = \mathrm{W/m^3}$. I see that $\vec E$ is in $\mathrm{V/m}$ and $\vec H$ is $\mathrm{A/m}$, so these multiplied is $\mathrm{W/m^2}$, but how does dotting with $\nabla$ give another $\mathrm{m^{-1}}$?... | Note on notation: I use $[\cdot]$ do denote the units of the quantity in brackets.
Derivatives always have units of $1/[\text{differentiation variable}]$. This can be clearly seen from the definition of the derivative in terms of difference qutionts:
$$ \partial_x f(x) := \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}.$$
So ... | {
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How to determine whether a nuclear transition would be electric octupole, or hexadecapole? The transition from one nuclear state to another is classified as quadrupole/octupole, etc, depending on the units on angular momentum transferred. But depending on the angular momentum of the two states involved, the net J can t... | A way to decide whether a gamma photon emition is electrical or magnetic is from the photon's parity.
Parity conservation requires: $π_i = π_f π_{ph} $ where the parity at the left side is the initial parity of the nuclei, and at the right the final parity of the nuclei and of the photon.
Thus, an electrical transiti... | {
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Why do our ears pop? Have you ever been on a train going through a tunnel or plane and your ears pop?I was wondering why this happens and I know it relates to pressure but don't know exactly the reason
| Measure first, think later. The best tunnel for experiencing ear discomfort around here is a train tunnel under a canal, the Drontermeertunnel. The graph shows the air pressure recordings I made in the train. A and B are the gates of the tunnel. Orange indicates when I experienced ear discomfort (although it wasn't eas... | {
"language": "en",
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Derivation of an ordinary, Lagrangian/Hamiltonian and action formulation I am confused as to how the different formulations in physics are derived.
In many fields of physics, we usually begin with an ordinary formulation (e.g Newton's Laws in classical mechanics), and then move on to the Lagrangian, then Hamiltonian, a... | Regarding your last question, I'd like to add another important point. The Lagrangian is a real scalar function of space and time. Keeping that in mind, one tries to construct scalar objects with the physical fields of the theory, which could be scalars or vector (for instance, in electomagnetism) or tensors, etc. Also... | {
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Why the speed of light in vacuum is same in all inertial reference frames?
If Cathy’s velocity
toward Bill and away from Amy is v = 0.9c, Cathy finds, by making measurements
in her reference frame, that the light from Bill approaches her at speed c, not at
c + v = 1.9c. And the light from Amy, which left Amy at speed ... | It is that the speed of light is the same for all inertial frames that causes Special Relativity, not the other way around. As to why it is the same, nobody knows. Or why it is a finite value. There is some speculation about quantum gravity and a magical æther called spacetime, but nothing has been proven yet.
| {
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How can there be entropy change in this system? How can there be an entropy change in this system?
Suppose if I have a system consisting of liquid water, $1\, \mathrm{kg}$ at $290\,\mathrm{K}$, I stir it, and do say, $10\, \mathrm{J}$ of work on it, I can calculate the temperature change of the system given that:
$$U =... | The integral of dQ/T is equal to the entropy change of a system between two thermodynamic equilibrium states only if the path between the two states is reversible. If you want to determine the entropy change between two thermodynamic equilibrium states for a system that has undergone an irreversible process, you need ... | {
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Explanation of Michelson Interferometer Fringe Shift I have been working on an experiment where 2 glass microscope slides are pinched together at one end (so that there is a "wedge" of air between them) and placed in the path of a laser in one leg of a Michelson interferometer. When I move the glass slides (fractions o... | This answer is based on Floris' insight that the slides might be bent.
Let's say the laser hits the slide at an angle of $\theta$ and travels through the panel at an angle of $\theta'=\sin^{-1}({n_a\over n_s}\sin(\theta))$. Let's assume the curvature is light enough that the laser essentially exits parallel to how it e... | {
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Physical Meaning of Cone used in Conic Section for Orbital Mechanics Does the polar angle (complement of $\theta$ below) of a cone which intersects a plane to yield a conic section have a physical meaning in orbital mechanics?
Note that the angle of incident planes, which form parabolas, ellipses, etc., is not the p... | The polar angle of the plane (the angle of the plane with respect to the symmetry axis) should relate to the eccentricity of the orbit. For $90^o$, the section is a circle and the eccentricity is zero. For an angle between the $90^o$ and the angle of the cone, you will get an ellipse with an eccentricity $0<\epsilon<1$... | {
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Is Gravity a Problem? I was watching the movie "Interstellar" recently and in that a character "Romly" mentions that if he could peep into the black hole "Gargantua" he could solve gravity.
I have a questions, is that a factual statement or is it for the movie's plot.
If yes then can someone explain what he means by so... | There is no problem with gravity. We have general relativity to describe it in full, and it works as far as we can tell.
The "problem" in the movie, as I understand it, was that it was infeasible to evacuate everyone from Earth. It takes an enormous amount of energy to get even a small amount of mass out of Earth's gra... | {
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Is this definition of orthohelium and parahelium incorrect?
"One electron is presumed to be in the ground state, the 1s state. An electron in an upper state can have spin antiparallel to the ground state electron ($S=0$, singlet state, parahelium) or parallel to the ground state electron ($S=1$, triplet state, orthohe... | The definition of orthohelium as having two parallel electron spins is correct. In the state $$\frac1{\sqrt2}\big(|\uparrow\downarrow\rangle+|\downarrow\uparrow\rangle\big)$$ the two spins are also parallel. It may seem that they are not, but note that this state has $m_z=0$, so both spins are perpendicular to the quan... | {
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What would put a harddisk drive (HDD) under 350G's of force? I always see the label and it says 350G's withstandable. What would put this over 350G's? Is it even possible to hit 350Gs of force to a hard drive?
|
Is it even possible to hit 350Gs of force to a hard drive?
Sure is. Drop it on the floor.
You are thinking about sustained forces. 350g sustained won't happen even in rocket launches. But momentary forces can easily peak at this level.
Note that the G limit on the drive is for when it's not running. No spinning drive... | {
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Creation and annhilation operator in the Heisenberg picture I am trying to calculate the time evolution of the creation/anni. operator in the Heisenber picture.
On this webpage http://quantummechanics.ucsd.edu/ph130a/130_notes/node191.html, they used the Heisenber equation of motion, but instead of using the operators... | Because (assuming a time independent Hamiltonian, operators without subscript referring to Schrödinger operators, those with the subscript $H$ to Heisenberg operators):
\begin{align*}
[a_H(t), H_H(t)] &= e^{-iHt/\hbar} a e^{iHt/\hbar} e^{-iHt/\hbar} H e^{iHt/\hbar} - e^{-iHt/\hbar} H e^{iHt/\hbar} e^{-iHt/\hbar} a e^{i... | {
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Sound source not in a straight line with the sound receiver - does that make a difference?
Hope the graphics will help me explaining my question better.
Let's say the box would be a room in the fourth floor, and the sound source would come from cars in the street.
It is clear that in case A the sound would enter the... | You will benefit by finding some tutorials on wave theory. In brief, assuming a spherical wavefront from the emitter, you are correct there's no direct path to the receiver. However, the edge of yourabsorber there causes diffraction (Huygen's principle), so thatsome of the sound wave (energy) will make its way to the... | {
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Flaws of Broglie–Bohm pilot wave theory? I recently learned about an oil drop experiment that showed how a classical object can produce quantum like behavior because its assisted by a pilot wave. How has this not gained more attention? What flaws does Broglie–Bohm pilot wave theory have in explaining particle behavior?... | I am not sure if the OP shared the link or not.
I happened to watch this very recently -
https://www.youtube.com/watch?v=WIyTZDHuarQ&t=199s
This is amazing explanation in terms of real visual.
Between 2:35 and 3:15 the video shows how the pattern is built over a period of time, while the jumps appear to be random at a... | {
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Are wavelength and the distance same thing? Can you clarify for me the following question: are wavelength and distance same?
I know wavelength is measured in terms of distance but when we have a look at the two equations:
$$
c=f\,\lambda\\
v=d/t
$$
it actually explains the same thing where $v=c$=velocity and $1/t$ i... | The relationship between wavelength and distance is similar to the relationship between frequency and duration, and no: neither pair is the same. You can see by using dimensional analysis.
Wavelength is distance divided by cycles. Frequency is cycles divided by time. Multiply the two, the cycles cancel out, and you get... | {
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Could some astronomical objects have superconducting properties? The colder it is, the more efficient the superconductivity process works. And as we know, if there is no star nearby, space gets pretty cold.
I do appreciate that many condensed, burnt out, stars may take a long time to cool off, but are there any other ... | Doubtful you'll find anything within the Solar System, but there are neutron stars, which are thought to have regions which are both superconducting and superfluid (that link is one of the original references from almost 50 years ago - there is a ton of literature on the topic since, you could start with some of these)... | {
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Antenna direction I have a router with a wifi antenna that can be turned in any angle. I wonder what difference does the direction of the antenna make to the electromagnetic signals propagation? Where is the signal strength the biggest?
| I had the same question once, and scoured the Internet for advice. All I got was conflicting information, much of it from "experts". I ended up getting a signal strength app for my smart phone and one for my laptop and experimenting. In my house, with my router, I found no detectable difference between horizontal an... | {
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The speed of light/EM waves in vacuum; as if there was another one in non-vacuum? Q1: is there a speed of a photon other than in "vacuum"?
Q2: isn't "speed of light in vacuum" misleading?
If I understand, that light moves with speed of light until there is "something in between" (no matter what) (1)
What I ask for, is... | Speed of light is constant.
But in some substances , still transparent , light is absorbed and retransmitted ( with the same properties ) , spending some time. With not well transparent material, things are more complex. Anyway, between 2 obstacles, it's the vacuum and the speed remains constant and maximum.
How many a... | {
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Difference between a reversible change and a reversible process? Question
In thermodynamics what is the difference between a reversible change and a reversible process?
Additional information
I am new to the topic of thermodynamics and getting confused about the difference, if any, between a reversible change and a re... | A process is something that goes on, has duration. A change has no necessary relation to time. It is a statement of difference between the initial and the final state of the process.
| {
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"url": "https://physics.stackexchange.com/questions/189808",
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Why do sea waves seem to be standing still when you look from the window of an airplane? Looking from the window of a passenger plane even at moderate altitude such that one can still recognize individual waves and even something like white foam, and small boats close to the cost line, it already looks like the water i... | I imagine this effect has to do with the fact that velocity is relative. When you're on the shore, you gauge the velocity of the waves with respect to the shore. When you're in a plane, you're likely gauging the velocity with respect to the other wave crests, which are moving at the same velocity and so there is no app... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/189951",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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How and when are the relativistic corrections applied to GPS satellites? It is known that there is a need to correct the onboard clocks to reduce the time difference from 38μs to 50ns. Where is relativity playing its role here? Why cant the clocks be simply synchronised with the ground clocks through telecommunication?... | Due to relativity, the clocks on the GPS satellites move fast by about 38 µs per day. Which would be a problem, but not that big a problem because they all move fast by the same amount. Still you'd need to synchronize the clocks from time to time, because the satellite's position in space also depends on the clock.
HO... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 2
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Quantum entanglement and the big bang Prior to the Big Bang all matter was compressed into a point of high density. Why isn't all matter already entangled?
| Let $|\Omega\rangle$ be the quantum state that describes the whole universe. Certainly it doesn't make sense to talk about the entanglement of $|\Omega\rangle$ with something else, since $|\Omega\rangle$ describes everything. However, we can meaningfully discuss the entanglement of the marginals of $|\Omega\rangle$:
\b... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/190274",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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I don't understand black body radiation graphs
Let's look at the above graph.
*
*This black body graph is for the temperature of 5000K. Each temperature has a different black body graph?
*How am I supposed to read this graph? Do I start from the left, the right, or the peak?
*As wavelength is approaching zero, i... | *
*The dependence of spectra radiance (y-axis) on wavelength (x-axis) is as follows (Planck's law):
$$I(\lambda,T)=\frac{2hc^2}{\lambda^5}\frac{1}{e^{\frac{hc}{\lambda k_BT}}-1}$$
As you can see, $I$ also depends on temperature T. For each T, we have corresponding curve.
*You should pay attention to the peak first. T... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/190389",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
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Can we find actual rest mass of things on Earth Earth moves around the Sun and the Sun moves around the galaxy and the galaxy moves with unknown speed and direction. We have speed so the mass of us all altered.
Can we know the real rest mass? If so, can we deduce our speed in the universe?
| Earth moves around the Sun and the Sun moves around the galaxy and the galaxy moves with unknown speed and direction. We have speed so the mass of us all altered.
The relativistic mass is altered, but this is a somewhat archaic term these days, and is said to be a measure of energy. Nowadays when we say mass without qu... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/190558",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "16",
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Is the scalar magnetic potential continuous? If we have two current-free spaces and separated by a surface current, we can solve the magnetic problem by solving two magnetic scalar potentials and then using matching conditions. My question is, is the general scalar magnetic potential continuous? Why?
| The potential for a static magnetic problem is defined through
$$
{\bf B} = - \nabla \phi
$$
(or you can define another potential for $\bf H$). Then since $\nabla \cdot {\bf B} = 0$ we have Laplace's equation for $\phi$ and that is why it is useful: we have lots of good methods for solving Laplace's equation. (Of cours... | {
"language": "en",
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What is known about Renyi entropy of a probability density function? I see most discussions about Renyi entropy to be using either of these two kinds of definitions, for $\alpha > 0, \alpha \neq 1$
*
*$H_{\alpha}(p_i)=\frac{1}{1-\alpha}\log \sum p_i^{\alpha}$ for a probability measure over a discrete set of events i... | Here is a reference for the continuous versions:
http://arxiv.org/abs/1402.2966
| {
"language": "en",
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Why can microphone be much smaller than wavelength of sound? For sound from 20Hz to 20kHz, wavelength is 17m to 17mm, for sound at 2kHz, wavelength is 17cm.
And I saw tiny microphone which is much smaller than that. In electromagnetic, there is a smallest size for antenna of each wavelength (half wavelength???). And th... | A microphone is a transducer that converts variations in air pressure from sound waves into electrical signals.
Air pressure varies as the wavefront passes into the diaphragm (or the ribbon, or the condenser) of the microphone. The diaphragm needn't be as long as the wavelength, as it senses the wave from a "head-on" ... | {
"language": "en",
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Is it possible to build a thermoelectric nuclear power plant? Current nuclear power plants are essentially an enhanced version of a kettle, which seems like a stupidity caused by a lack of other options. We heat the water which turns to steam which rotates the turbine, which is total waste of energy due to the several ... | The efficiency of a thermoelectric generator is around 5 - 8%.
The efficiency of a large steam turbine power plant aproaches 40%.
In fact the thermodynamic efficiency of a large steam turbine power plant is over 90%, so it's about as efficient as anything could be. The maximum possible efficiency of a steam driven engi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/191425",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "31",
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Does isotropy imply homogeneity? This question comes from exercise 27.1 in Gravitation by Misner, Thorne and Wheeler. They required the following:
Use elementary thought experiments to show that isotropy of the universe implies homogeneity.
I know homogeneity as the universe is the same everywhere at a given time, a... | When MTW say the universe is isotropic, they mean it is isotropic everywhere i.e. at all points in the universe.
It's easy to construct universes that are isotropic at a single point and not homogeneous, for example CuriousOne's suggestion of a ball with density that is a function of distance from the centre. However t... | {
"language": "en",
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"source": "stackexchange",
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How can a material conduct heat but not electricity Mica is a good conductor of heat but an electrical insulator.
According to free electron theory (which applies only to metals) free electrons carry heat and electricity. Therefore, thermal conductivity is directly proportional electrical conductivity.
What about die... | Electricity needs charged particles (or quasi-particles) to conduct it. Heat can be conducted with almost any quasi-particle. Diamond is one of the best conductors of heat in existence, and it's because of phonons, ie quasi-particles of lattice vibrations, which are strong because the diamond lattice is strong.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/191754",
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"source": "stackexchange",
"question_score": "6",
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Is air infiltration a type of convective heat transfer (convection) I have a building / physics question...
A major source of heat loss in homes and buildings is infiltration through cracks (warm air from inside seeping out). Wondering if this falls in the category of convection as a mode of heat transfer?
|
Wondering if this falls in the category of convection as a mode of heat transfer?
Yes.
You are discussing heat transfer due to air traveling through a crack in a wall. Any heat transfer due to a moving fluid is convective heat transfer.
If there is wind, then it is further categorized as forced convection. If the... | {
"language": "en",
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Do electrostatic fields really obey "action at a distance"? In an electromagnetic theory class, my professor introduced the concept of "action at a distance in physics".
He said that:
If two charges are at some very large distance, and if any one of the charge moves, then the force associated with the charges changes ... | To reach the Lienard-Wiechert potentials or to prove Feynman's equation (exposed in his lectures without proof), it's necessary to begin with the so-called retarded potentials expressed here conveniently by the following.
\begin{equation}
\phi\left(\mathbf{r},t\right)=\dfrac{1}{4\pi\varepsilon_{o}}\iiint d^{3}\mathbf{r... | {
"language": "en",
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"source": "stackexchange",
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Water well fluid dynamics In my home village everyone has their own water well at the foot of the mountain (limestone) . The wells are over 100 feet deep but they are not cemented or have the area between the hole and the casing (PVC) sealed with bentonite or anything like it. Even though the well is 100+ feet deep, in... | As posed there is no definite answer to your question.
It is certainly possible for water to enter the well at a depth of 100 feet, and have sufficient pressure that it eventually rises to within 15 feet of the top. That just means that the "water table" in that area is 15 feet below the surface.
If the sides of your w... | {
"language": "en",
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"source": "stackexchange",
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Why, when and where is Gauss's law applicable?
Why is it said that Gauss's Law is mainly applicable for symmetric
surfaces/bodies? Why not for asymmetric surfaces?
I want a logical explanation!
BTW my teacher said that Gauss's law is applicable for any surface/body but in the case where symmetry does not exist, the... | As your teacher says, it holds for every surface, but a look at the law itself, should clear out why some form of symmetrie is desirable:
$$
\iint_S \vec{E} .\mathrm{d}\vec{A}=\iint_S E . \cos\theta . \mathrm{d}A = \frac{Q}{\epsilon_0}
$$
Here, $E$ and $\theta$ are position-dependent, so to calculate the integral, you ... | {
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"source": "stackexchange",
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Is gravity's acceleration rate - squares of all natural numbers? I've seen some science\history documentary in which they made a replica of Galileo's inclined plane experiment.
They rolled a ball down the plane; and it's progressed in length units each unit of time was - 1, 4, 9, 16 etc. I realized it was squares of na... | The distance between successive lines is 1,3,5... making their absolute position 1,4 (1+3), 9 (1+3+5)...
This follows from double integration of the equation of motion with a constant force:
$$v = \int \frac{F}{m} dt = a\; t\\
x = \int v\; dt = \int a\; t\; dt = \frac12 a t^2$$
So the position increases quadratically w... | {
"language": "en",
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Free fall into circular motion If I'm on a roller coaster free falling from height $h$ and then suddenly start going into horizontal motion with a radius $r$ of turn what is the $g$-force I experience?
I worked out the equation like this but am not sure if it is correct:
*
*(1) instant velocity of free-fall $v=\sqrt... |
I don't know if I can use uniform circular motion equation since v is not constant
The equation for centripetal force is independent of whether the motion is uniformly circular or not.
However, irrespective of the radius of the track, the velocity at that point, and the weight of the roller-coaster, or whether the e... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/193042",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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What happens if the load on the electrical generator exceeds its generation power? And why? What happens if the load on the electrical generator exceeds its power generation? and why?
To be more precise, suppose we have a standard induction generator operating at frequency $\nu=50\:\mathrm{Hz}$ and voltage $V_0$, and r... | The generator circuit breaker should trip to avoid damage. But if that doesn't work, or doesn't exist, the generator will not be able to maintain its speed. On a typical AC system, this will cause the frequency to drop from the standard 50 or 60 Hz, as well as drop the output voltage.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/193276",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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Bounds on dimension of a purification? Let $\rho \in H_A$ be a density operator, $H_A$ is finite dimensioal, it is well known that $\rho$ has a purification in some larger hilbert space. Let $b$ be the minimum dimension for $H_B$ such that there exists a purification of $\rho$ in $H_A \otimes H_B$.
Are there special c... | Consider any purification of $\rho$: $|\psi\rangle \in \mathbb{H}_A \otimes \mathbb{H}_B$. This purification necessarily admits a Schmidt decomposition of the form:
$$|\psi \rangle=\sum_i \sqrt{\lambda_i} |\alpha_i\rangle_A |\beta_i \rangle_B $$
with the state $\rho$ being of the form:
$$\rho=\sum_i \lambda_i |\alpha_i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/193475",
"timestamp": "2023-03-29T00:00:00",
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A simple derivation of the Centripetal Acceleration Formula? Could someone show me a simple and intuitive derivation of the Centripetal Acceleration Formula $a=v^2/r$, preferably one that does not involve calculus or advanced trigonometry?
| Imagine a object steadily traversing a circle of radius $r$ centered on the origin. It's position can be represented by a vector of constant length that changes angle. The total distance covered in one cycle is $2\pi r$. This is also the accumulated amount by which position has changed..
Now consider the velocity vecto... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/193621",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "17",
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Does body weight affect the speed when going downhill on a mountain bike? We know heavier objects fall faster when dropped at certain height. I was wondering if I am going downhill on my mountain bike without any peddling, will I travel faster or slower because I am fat?
| No and yes. At first, your assumption is not quite correct. In vacuum, all masses fall at the same speed. The reason is the that the mass cancels in the equations of motion:
$ma=mg$
$a=\ddot{x}=g$
To be more precise: the inertial mass and the gravitational mass are the same. Therefore, they cancel.
However, things chan... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/193839",
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"source": "stackexchange",
"question_score": "1",
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Do black holes violate the uncertainty principle? If black holes have mass but no size, does that imply zero uncertainty in position? If so, what does that imply for uncertainty in momentum?
|
If black holes have mass but no size, does that imply zero uncertainty
in position? If so, what does that imply for uncertainty in momentum?
I mean to say that the particles which were originally separate have
theoretically come to occupy the same point in space. Does the
uncertainty principle apply to this phen... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/193954",
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7/2 versus 9/2 for diatomic heat capacity Question
I calculated the classical heat capacity of a diatomic gas as $C_V = (9/2)Nk_B$, however the accepted value is $C_V = (7/2)Nk_B$.
I assumed the classical Hamiltonian of two identical atoms bound together as
$$
H = \dfrac{1}{2m}( |\bar{p}_2|^2 + |\bar{p}_2|^2)+
\dfrac{\... | The potential energy for a diatomic molecule is not
$$
U(\vec{q}_1, \vec{q}_2) = \frac{\alpha}{2} |\vec{q}_1 - \vec{q}_2|^2
$$
but is instead
$$
U(\vec{q}_1, \vec{q}_2) = \frac{\alpha}{2} (|\vec{q}_1 - \vec{q}_2| - r_0)^2,
$$
where $r_0$ is the equilibrium bond distance. The important difference here is that in your v... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/194075",
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A way to determine if a body accelerates or loses speed at a certain time With given vectors for acceleration and velocity, is there a way to determine if a body accelerates or decelerates at a certain time-interval? Can this be determined, for instance, by simply observing the vectors?
|
With given vectors for acceleration and velocity, is there a way to determine if a body accelerates or decelerates at a certain time-interval?
Given the velocity vectors of a (specific) body (with respect to specific members of a suitable reference system) throughout a trial, in particular the velocity vectors $\math... | {
"language": "en",
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Did the Sun form around a solid core? When Jupiter formed I assume like the other planets it started as tiny clumps of matter that eventually came together, became gravitationally bound and then eventually captured a lot of gas. I've also heard it was capable of collecting a lot of solid ice due to its distance from th... | The Sun did not form around a solid core. Rather, it seems to have formed from a cloud of collapsing gas that may have been further enriched by matter from a nearby supernova. Gravitational force caused the collapsing cloud to start spinning, and the spinning compressed it into a disc with a bulge in the center that ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/194257",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "12",
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Why are most antennas in cellular networks +/- 45° polarized? I've just been asked a strange question that I cannot find an answer to (even on the internet it seems I can't find any explanation for this) and I ended up wondering why most of the antennas which work as "base stations" are nowadays +/- 45° polarized. Whil... | A motive is: "Seen from the front or rear of a handset user, the polarization will be dominated by the vertical component (the most handsets have a linear polarization because they use patch or monopole antennas), but in the lateral direction a handset is typically held at a large angle to the vertical, between the mou... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/194318",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why must heat supplied in the definition of entropy be reversible? Can't it be irreversible after all it is a state function? The definition of entropy contains the term $Q_\text{rev}$ which means the heat supplied or taken out reversibly. I thought yes it can be after all only the initial & final states are important ... | For an infinitesimal heat transfer $\delta Q$ the inequality of Clausius states that
$$\Delta S = S_1-S_0 = \int_0^1 {\dfrac {\delta Q_\text{rev}}{T}} > \int_0^1 {\dfrac {\delta Q_\text{irrev}}{T}}$$
Here $\delta Q_\text{rev}$ and $\delta Q_\text{irrev}$ denote reversible and irreversible heat transfers, respectively... | {
"language": "en",
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Is double-slit experiment dependent on rate at which electrons are fired at slit? I am a mathematician and I am studying string theory. For this purpose I studied quantum theory. After reading Feynman's book in which he described the double-slit experiment (Young's experiment) I was wondering if I send one electron per... | When a time interval between photons or other particles that bombard a foil with two slit is more than milliseconds, the phenomenon of the double slit diffraction/interference will be absent.
For example, in a paper:
V. Krasnoholovets, Sub microscopic description of the diffraction phenomenon, Nonlinear Optics, Quantu... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/194570",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Where does the $(\ell + x)^2\dot\theta^2$ term come from in the Lagrangian of a spring pendulum? I am reading some notes about Lagrangian mechanics. I don't understand equation 6.9, which gives the Lagrangian for a spring pendulum (a massive particle on one end a spring).
$$T = \frac{1}{2}m\Bigl(\dot{x}^2 + (\ell + x)^... | I'm not sure why you're talking about an $x$ and $y$ component of velocity when you're working in a polar coordinate system. Maybe you're confusing $x(t)$ (the extension of the spring as a function of time) with the Cartesian coordinate $x$. These are very different things. To understand what the radial component of th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/194629",
"timestamp": "2023-03-29T00:00:00",
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If gravity were to suddenly change, would the lift generated by a airfoil also change If gravity were to suddenly change, would the lift generated by a airfoil also change?
I realise that if gravity were to increase, then weight would also increase, leading to a change in the resultant force on the object (say a aeropl... | If gravity changes, then so will the density of air. Air pressure at the surface is proportional to the weight of the column of air above it, so if gravity increases, the pressure would, too. That will in turn affect the lift from an airfoil. NASA says lift varies linearly with density. I suspect the two effects woul... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/194787",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Does a propeller being pushed through the air have more friction if free to spin? I just passed a boat being pulled on a trailer and noticed the propeller spinning in the wind. I began considering the possibility that a propeller free to spin might cause less friction against the forward motion of a force pushing the p... | The net drag force on the surface of the propeller is a function of the relative velocity of the fluid against the propeller's surface.
The simple model for drag force that can be (loosely) applied to the question regarding the propeller is
$$F_d=C_dA\frac{1}{2}\rho v^2$$
where $v$ is the relative velocity, $A$ is the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/194897",
"timestamp": "2023-03-29T00:00:00",
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What is the viscosity difference between a solid and a liquid The pitch drop experiment, for example, shows bitumen as a liquid, even though it appears to be a solid, and then there is the "glass: solid or liquid" debate. Is there a numerical value in viscosity that defines the boundary between a solid and a liquid?
O... | No.
The elasticity of the solids is a liquid kind of character. The non newtonian fluids provide a solid kind of character.
As everything is just electromagnetism, you can split your thoughts down the an single atom level, and play it with magnets on real scale. You can push your hands between magnets, and you can ma... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/194948",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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Is it normal for radiation levels to be elevated near a medical imaging lab? I work in a general-purpose, commercial office building where the first floor is dedicated to an x-ray / imaging lab for medical diagnostics. The public lobby of this building is routinely experiencing radiation level increase from 0.10 uSv/h ... | I don't think 0.96 $\mu$Sv/h or 365.25$\times$24$\times$0.96 = 8.5 microsieverts/year is a problem. To put this in perspective,
*
*Every year, we receive natural radiation : 2,000 microsieverts
*CT scan : 7,000 microsieverts
*Additional radiation in a life time for those living around Fukusima : 10,000 microsiever... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/195319",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Force division of moving pulleys? I am a second grade at a middle school and I was reading a physics workbook to prepare for a test. And I was solving pulley problems and one problem made my brain stop.
The problem asked me what would the minimum force of F would be when the weight of the pulleys were 30N. I checked t... | This is a mechanical advantage problem. For fixed pulleys, only the direction of motion is changed, and there is no mechanical advantage. A 1 N force directed downward on one side of the fixed pulleys (the small ones) produces a 1 N force directed upward on the rope on the other side of the fixed pulleys.
For a movab... | {
"language": "en",
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What would happen if we tried to run a motor in space when it is not attached to anything to provide support to it? I know that a when a motor runs it generates torque and that torque can be used to do useful work. On the other hand, the motor needs strong support that absorbs the reaction torque. In our case let us a... | Your intuition was correct - the shaft will rotate in one direction and the housing/stator will rotate in the other.
If you look up "moment of inertia" you will find that it is the rotational equivalent of mass. For almost any reasonable motor the moment of inertia of the shaft/rotor windings will be smaller than the m... | {
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Is Gauss' law valid for time-dependent electric fields? The Maxwell's equation $\boldsymbol{\nabla}\cdot \textbf{E}(\textbf{r})=\frac{\rho(\textbf{r})}{\epsilon_0}$ is derived from the Gauss law in electrostatics (which is in turn derived from Coulomb's law). Therefore, $\textbf{E}$ must be an electrostatic field i.e.,... | No we cannot prove it; Maxwell postulated that it would hold dynamically because it made the most sense for it to do so as he pondered the displacement current problem. As you likely know, Maxwell pondered the inconsistency between Ampère's law for magnetostatics and the charge continuity equation. Ampère's law for mag... | {
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Question about Planck's constant
*
*How did Dirac or whoever came up with it know that the momentum operator in quantum mechanics is $-i\hbar\frac{d}{dx}$?
*How did he know the $\hbar$ was in there?
*How did all these physicists know they had to put $\hbar$?
*Does it go back to Planck's paper on blackbody radiat... | Note: This is a brief summary.
Wikipedia is helpful, if you can't look anywhere else at the moment. It notes that
$$\hat{p}=-i\hbar\frac{\partial}{\partial x}$$
because of the de Broglie relation,
$$p=\hbar k$$
where $p$ is momentum and $k$ is the wave vector.
de Broglie's equations, in turn, relate to the de Broglie w... | {
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Where does the equation $p=\frac{1}{c}\sqrt{T^2 +2mTc^2}$ come from? Where does the relativistic formula
$$p~=~\frac{1}{c}\sqrt{T^2 +2mTc^2}$$
come from? What is the derivation from Einstein's formula? $T$ is the kinetic energy $m$ is the mass $p$ is the momentum.
| We can write total energy $E$ two ways:
\begin{equation}
E^2=p^2c^2+m^2c^4 \\
E=T+mc^2,
\end{equation}
where $T$ is kinetic energy.
Eliminating $E$ from those two equations will give you the desired result.
| {
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Why does humidity cause a feeling of hotness? Imagine there are two rooms kept at the same temperature but with different humidity levels. A person is asked to stay in each room for 5 minutes. At the end of experiment if we ask them which room was hotter, they will point to the room with the higher humidity. Correct ri... | For the thought experiment in your question, the answer is: it depends on the temperature of the room!
Cold Room
If the room is cold, humidity will actually make it feel colder! This is because water vapor has a much higher heat capacity than dry air, meaning that it takes more heat to raise or lower its temperature. S... | {
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In general, why do smaller guns have more felt recoil? Why is recoil easier to control on a more massive gun compared to a smaller gun with the same bullet. Presumably the bullet leaves both guns with the same momentum, but the larger gun seems easier to control. Since the momentum you have to control is the same in bo... | Felt recoil is partly a matter of momentum, partly a matter of force.
When a bullet with mass m leaves a gun with a velocity v, the gun must have an equal-but-opposed momentum MV, where M is the mass of the gun and V is the recoil velocity, or $$mv + MV = 0$$. If there are two possible gun sizes, $M_1$ and $M_2$, each ... | {
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How and why the phrase "quark force increases with distance"? I have seen that phrase "force between quarks increases with distance" at many resources, some even relatively credible (albeit written for general audience).
What is the reason behind that, when the area law for the confining phase clearly gives the potent... | Perhaps the resources you have seen are confusing "force" with "energy", which is a common misunderstanding that frequently leads to mistakes in terminology. Energy must be applied to overcome the color force and increase the distance between quarks. The formation of a new quark/anti-quark pair when the gluon field b... | {
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Travelling near the speed of light, will radar give me sufficient warning of approaching debris? If I’m travelling in space near the speed of light, I would like to use radar to give me advance warning of approaching hazards. However, will I have enough time to be able to react?
From a perspective on the spaceship, the... | Per Bort's comment, this is easier to think about from the spaceship's frame rather than the debris's frame. A rock is traveling toward your spaceship at .99 times the speed of light. You send out a pulse of light that intercepts the rock when it's one light-minute away from the ship. The pulse bounces back and arri... | {
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Conical train wheels I've been reading about how the conical shape of train wheels helps trains round turns without a differential. For those who are unfamiliar with the idea, the conical shape allows the wheels to shift and slide across the tracks, thus effectively varying their radii and allowing them to cover differ... | Shift the upper configuration to the left a short distance at equilibrium. Result: the left wheel goes a little up, the right goes a little down, the train tilts clockwise, the center of mass is to the right of the centerline between the wheels, and therefore the center of mass provides a restorative force to push the ... | {
"language": "en",
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Why is the index of refraction different for different wavelengths? The index of refraction can be written as
$$n=\frac{\lambda_v}{\lambda_m}$$
where $\lambda_v$ is the wavelength in a vacuum and $\lambda_m$ is the wavelength in the medium. I’ve been told that since wavelength appears in the definition of an index of r... | You are mixing up two different things.
The refractive index is usually defined in terms of the velocity of light:
$$ n = \frac{c}{v} $$
where $v$ is the velocity in the medium. However the velocity is related to the frequency and wavelength by:
$$ v = \lambda f $$
so:
$$ n = \frac{\lambda_0 f_0}{\lambda f} $$
The freq... | {
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What determines the probability of creating a particular particle in a collision? When discussing events at the quantum level, we deal in probabilities and not absolutes. Articles I've read on particle physics state that a particle has a probability of being created in a collision. What determines this probability?
Ass... | Once one specifies a quantum field theory, typically in the form of a Lagrangian density, one can calculate the probabilities of various outcomes in collisions.
A quantum field theory is a theory based on fields that obeys quantum mechanics and special relativity. The so-called Standard Model is perhaps the most famous... | {
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Can a magnet damage a compass? I've heard the claim before that a magnet can ruin a compass, and was about to repeat it to my son when I realized it sounds like complete nonsense. Googling turned up such unsubstantiated and illogical answers as this one and unanswered questions as this one but nothing that sounded rea... | If the field is big enough it can physically destroy the compass needle. But that might be the least of your problems at that point
| {
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Wavelength vs Wavenumber etiquette When am I supposed to use the terminology of EM "wavenumber", instead of "wavelength" (or frequency)?
The concepts of wavelength and frequency are no problem for me, but wavenumber (number of wavelengths per unit length) seems redundant to me as a student engineer and proto-physicist.... | Traditionally wavenumber is used in molecule spectrums such as infrared spectrums in organic chemistry where it is given in the incoherent SI-unit $\textrm{cm}^{-1}$. Mostly because one obtains convenient numbers on the axis. Also in most of the wave equations it is used, because again you can make the convenient subst... | {
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Pointwise and uniform convergence. Examples from physics I am a first-year mathematical student, and from a mathematical perspective I understand the difference between pointwise and uniform convergence of sequences and series of functions. However, I have been wondering about what phenomenons from physics (or other sc... | Sciences use mathematics only as a tool. In almost all such applications, mathematical problems (such as pointwise vs uniform convergence) are not inherent to the scientific problem at hand, but arise from the mathematical model and are indicative of its limitations.
For example, when modelling a large collection of pa... | {
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Is wave-particle duality not clear from the single-slit experiment? In experiments it is easy to discern between 2 and more-than-2 fringes on a screen, making the double-slit experiment the default one for wave-particle tests.
Let's say we shoot massive particles (e.g. electrons) towards a slit. Would the image behind ... | There is still interference at a single slit resulting in a Fraunhofer pattern. Just consider both edges of the split as starting point of a new wave.
Generally you're right. But, in a single slit, the electrons could still be deflected by the atoms that make up the slit. This - I think - leaves more room for discussio... | {
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Are Hubble Telescope Images in true color? Like many others, I have marveled at the images made available from the Hubble Space Telescope over the years. But, I have always had a curiosity about the color shown in these images. An example is shown below. Are the colors we see, such as the yellows, blues, and so on t... | The classic color mapping for Hubble is described in Flase-color astrophotography explained.
What you have is (in the Hubble palette):
Line Freq True False
Ha (656.3 nm) Red -- Green
S-II (672.4 nm) Red -- Red
O-III (500.7 nm) Green -- Blue
An example of this for true color from John Nassr at St... | {
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How do I know what variable to use for the chain rule? In my textbook the tangential acceleration is given like this:
$$a_t=\frac{dv}{dt}=r\frac{dw}{dt}$$
$$a_t=rα$$
I understand that the chain rule is applied here like this:
$$a_t=\frac{dv}{dt}=\frac{dv}{dw}\frac{dw}{dt}=rα$$
What I don't understand is why we have to ... | In general you are allowed to use any parameter $q$ to describe the motion of an object as $\vec{r}(q)$ where the parameter changes with time $q=q(t)$. The parameter can be an angle or a distance or any combination that best makes sense.
So now you have expressions for velocity and acceleration defined from the chain r... | {
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What is the ratio of cosmic ray energy to dark matter energy in our solar system? In any cubic meter of space in our solar system there is predicted to be some amount of dark matter. Also in a cubic meter of space is a known average amount of cosmic ray energy. What is the ratio of cosmic ray energy to dark matter ener... | The integrated local interstellar cosmic ray energy density is claimed by Webber (1998) to be about 1.8 ev/cm$^3$. The energy density of dark matter (mostly rest mass energy) in the solar system is thought to be around $0.43\pm0.1$ GeV/cm$^{3}$ (Salucci et al. 2010).
Both numbers likely have quite big error bars, but a... | {
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How to estimate if an image is in focus I am building a test measurement (optics) to look a rectangular slit opening (1mm x 15 microns). The slit opening is illuminated by a white LED and using a microscope objective to magnify it to 10X on an image sensor.
What would be the possible method to estimate if the image is... | Since you're imaging something that is basically a 2D rectangle function you would need an infinite amount of spatial frequencies reconstruct it in the Fourier domain.
You could take the FFT of the image and vary the image or object distance until you got the highest possible spatial frequencies.
| {
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Why aren't calculation results in error propagation at the center of the range? We have two copper rods, with $L_1$ and $L_2$ as their lengths respectively, and we want to glue the two bars together, with glue that's infinitesimally thin.
$$\begin{align}
L_1 &= 20 ± 0.2\ \mathrm{cm} \\
L_2 &= 30 ± 0.5\ \mathrm{cm}
\end... | I think you should have a look in this http://ipl.physics.harvard.edu/wp-uploads/2013/03/PS3_Error_Propagation_sp13.pdf it should clear up how to do error estimation in a more rigorous manner. I would only worry about the first two sections on addition and multiplication if you haven't covered calculus yet.
This method... | {
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Is heat conduction impeded at interfaces between dissimilar materials? Sound in air essentially echoes off concrete walls, rather than penetrating them, because of the difference in the material properties of air and concrete.
By analogy, are there pairs of solid materials where their interface would be very inefficien... | Sound in air is a percussion wave - way different. Heat via conduction does not have an interface barrier. It would just be the sum of the resistance.
| {
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thin film interference of light
In a thin film interference (reflective system) I know that condition for maxima is
$$2\mu t\cos(r)=(2n\pm 1)\frac{\lambda}{2}$$ and for minima is $$2\mu t\cos(r)=n\lambda$$ and for transitive system it's just the opposite.
but what happens if then film is very small such that $$\lim_... | At the reflection in an interface from low to high refractive index, a phase shift of $\pi/2$ occurs; no such phase shift occurs on the second interface (high to low). As a consequence, for sufficiently thin films, there is indeed destructive interference- so your very thin film looks dark. You can sometimes see this o... | {
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Eddy Currents – Tubes with slits When a magnet falls down a tube, eddy currents form and flow around the tube, perpendicular to the direction in which the magnet falls.
However, when there is a vertical slit in the tube, are either no eddy currents formed (since they cannot complete a rotation), or alternatively do mu... | Probably in the last case of slit direction of magnetic field is on the side walls upwards as shown and thus there is no interaction of this field with the magnet. Here it seems it is to be considered to neglect radial magnetic field (even though it do exist). In complete loop magnetic field is centralized so it intera... | {
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Any fractal physical model that generates time series which demonstrate heavy-tailed (non-Gaussian) behavior in some form? I know that fractal structures have power-laws in various forms "hidden" in them. I am looking for the most simple fractal model that I can find that generates time series with, say, Pareto-distrib... | your answer is hidden in the self organized criticality (SOC) concept.
there is many model that have applied in many branch of science that obey SOC.
this concept for the first time was introduced by Bak et al with "Abelian Sand pile model".
this model is the simplest model can receive to critical state (showing power... | {
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Probing beyond the black hole event horizon Black holes are interpreted to have a "break down" of general relativity at their point of singularity. The region near the singularity is expected to be described by some theory of quantum gravity.
Since quantum gravity is expected to describe the physics near the black hol... | There are a number of attempts at constructing theories of quantum gravity, of which string theory and loop quantum gravity are the most developed. However none of these theories have been developed to a point where they can make uncontroversial predictions about what happens near a black hole singularity.
The only eve... | {
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What is blocking the magnetic field of this neodymium magnet? I opened up my hard drive and pulled out (among other things) the top and bottom braces for the reading arm.
Each bracket contains a really powerful neodymium affixed to its underside.
When the two undersides come within a few inches of eachother, they acc... | Those are nickel/steel brackets that have high magnetic permeability and saturation. Due to the magnets shallow thickness the magnetic fields are completely diverted into the bracket preventing any mag fields from penetrating through it. Notice how the magnet is strongly attracted to the bracket due to magnetic attract... | {
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Which power equation to use: $P = I^2 * R$ or $P = V^2 / R$? Given are ideal max voltage $V = 200\;\mathrm{V}$ and max current $I = 5\;\mathrm{A}$.
Therefore:
*
*ideal resistance is $$R = \frac VI = \frac{200 \;\mathrm{V}}{5\;\mathrm{A}} = 40 \;\mathrm{\Omega}$$
*ideal max power is $$P=IV = 5 \;\mathrm{A}* ... | Both equations are valid. You just made an error in taking suddenly 20 $\Omega$ instead of 40 $\Omega$.
$$P = I^2 \cdot R = 25 A^2 \cdot 40 \Omega = 1 kW$$
$$P = U^2 / R = 40000 V^2 / 40\Omega = 1 kW$$
The power is always determind by the current that runs through the part of interest times the voltage drop over ... | {
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What makes neutron heavier than a proton? The mass of proton is 1.672 × 10−27 kg while it is 1.675 × 10−27 kg. Both are made up of 3 quarks each. Then what makes proton lighter than a neutron?
| Note that the combined rest masses of the quarks (~10 MeV/$c^2$) account for about 1% of the proton and neutron mass (~938 MeV/$c^2$), the main contribution to the mass are the gluons from the Strong Force. Since the composition of the proton and neutron are different, so is the force that binds them.
| {
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Why is heat flux sometimes assumed to be proportional to surface temperature? Suppose a fluid flows over a heated surface. In "Newtonian heating", it's assumed that the heat flux through the surface, $q$, is proportional to the surface temperature, $T_\text{surface}.$
Written as an equation, it's$$
q ~=~ h \, T_{\text{... | I guess you wanted to say
$$
q ~=~ h \, \left(T_\text{fluid} - T_\text{surface}\right)
\,,$$
right? So this means that the heat flux density $\left(\mathrm{W} \cdot {\mathrm{m}^{-2}}\right)$ is proportional to the temperature difference between the fluid and the wall. It seems reasonable since when $T_\text{fluid} = T_... | {
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Is the change in orbital of an electron the only way a photon is created I would like to know if there are any other ways in which photon's are being emitted other than in the case an electron's orbital around a nucleus changes.
| That's a give and take. The emission of photons is always based on an energetic level of particles higher than the surrounded world. To reach this higher level it needs an receive of photons.
A moving electron will be deflected in a non parallel to the movement magnetic field and emit photons. How the electron reach th... | {
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How to calculate tide times? How do I calculate the time of the tides at a given location?
I'm not interested in the amplitude of the tides, just the times when they occur.
| There is a lot more to it than just astronomy. For example, the tide times inside Boston Harbor are significantly different from those on the southeast coast of Cape Cod.
It is true that the primary force behind tides is the position of the Moon, but the macro tidal bulges take a long time to propagate around/across o... | {
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Can you huddle next to a fridge in sub-zero temperatures and keep warm? There's a saying I've heard in so many places.. "It was so cold that we used to huddle next to our refrigerator to keep warm..." I had heard this phrase uttered some 30 or so years ago, and it's stuck with me ever since...
Which gets me thinking...... | Suppose you would actually go sitting inside your refrigerator and close the door, so that you are in an environment of +4 degrees Celsius. If you are literally warming up, then you was colder than 4 degrees Celsius in which case you probably had died from hypothermia.
If you are wearing protective clothing, the clothi... | {
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"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 2
} |
Car Crash Scenario Two vehicles travelling at 80mph in the same direction.
Vehicles are directly behind each other.
12 meter distance between them.
Front door of car in front rips of and hits the front window of the car behind.
At what speed did the door make contact with the car?
How would one go about calculating thi... | The door is not slowing down because of its mere detachment from the front car. It is slowing down because of air drag on the door. That drag would depend on the area of cross-section interaction, the mass of the door and whether the door is tumbling. One might be able to estimate a worst-case scenario, but there isn... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/200799",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 0
} |
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