Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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How to superimpose Wood-Saxon and Coulomb potential? I have just written a simple simulation that models the tunnel-effect of alpha-particles for $^{212}$Po and $^{238}$Ur. In this simulation, I approximate the potential of the nucleus by a simple square well. Now I'm thinking about improving the simple model to a more... |
"Do I just add the Woods-Saxon and the Coulomb-potential?"
Do you know any other way of combining potentials? You certainly do just add them up.
Two complications:
*
*You may need to tweak the parameters of your potentials if, for instance, they were set to get a certain $Q$
*You'll need some kind of charge dist... | {
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normalizing a wavefunction I have a homework problem that I can't get started on, below is the first bit. I feel like I should just be able to integrate to find $C$ but I get a divergent integral. Can someone give me a hint as to where to go here?
A particle of mass m is in a one-dimensional infinite square well, with ... | The well is not infinitely wide, just infinitely "deep", meaning that the region outside the well has infinite potential energy. The particle cannot exist in a region of infinite potential energy, so it can only exist within the boundaries of the well, which clamps the integral to $0\le x < a$:
$$1=\int_0^a|Cx(a-x)|^2d... | {
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Can I charge a capacitor using 2 batteries? 1 capacitor, 2 separate batteries (Battery A and Battery B).
Connect A+ to one side of the capacitor and B- to the other side of the capacitor.
A and B are not connected, there is no closed circuit.
looking like:
-A+__________CAPACITOR_______-B+
Can the capacitor be charged... | No. Batteries supply potential difference.
The positive terminal of A(I'll call it A+) is at a higher potential than the negative terminal of A(A-). The same goes for B. However, we don't know if A- and B+ are at the same potential, so we can't conclude that A+ is at a higher potential than B-.
In fact, A+ and B- are a... | {
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Could a planet sized bubble of breatheable atmostphere exist? I'm reading a book (Sun of Suns by Karl Schroeder) that the main location is a planet called Virga, which contains air, water, and floating chunks of rock, and has no or a very small amount of gravity. There is a main 'sun' at the center of the planet, which... | If you look in outer space, you'll see things like giant molecular clouds these clouds are not necessarily in equilibrium, so the factors that cause them to exist for a certain amount of time may be very complicated. E.g., there could be shock waves, star formation, ...
If the cloud is in thermal equilibrium, then the ... | {
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How do you tell if a metric is curved? I was reading up on the Kerr metric (from Sean Carroll's book) and something that he said confused me.
To start with, the Kerr metric is pretty messy, but importantly, it contains two constants - $M$ and $a$. $M$ is identified as some mass, and $a$ is identified as angular moment... | In the limit where $M \to 0$, the Kerr metric reduces to the spherical coordinates form of the Minkowskian metric. In that sense, we recognize it and say it is 'obvious' that is is flat. (The Schwarzschild metric is also flat in the limit $M \to 0$.)
But to show that any given metric is curved or not we have to calcula... | {
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Whats the anti-torque mechanism in horizontal take-off aircraft? In most helicopters there is the anti-torque tail rotor to prevent the body from spinning in the opposite direction to the main rotor.
What's the equivalent mechanism in horizontal takeoff single engine propeller, and jet aircrafts, where the air or the ... | The motor does exert torque on the fuselage.
The pilot, without having to think about it, compensates by applying right aileron, which has plenty of roll authority.
There's more to it.
When a propeller-driven plane is taking off, it has a tendency to yaw to the left, and the pilot automatically applies right rudder to ... | {
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Ground states in the shell model for odd-even nuclei
I understand that even-even nuclei (Z and N number) have zero spin because of pairing.
Even-odd nuclei have the spin of the odd nucleon, and parity is given by $(-1)^L$ - so my question is, how do we work out the state which this odd nucleon is in?
As an example: $... |
How will I know which quantum numbers are the lowest energy?
In general that is a difficult question from first principles. Simulation can often answer it, but the problem can be pretty involved and demanding.
However, as a practical matter the configuration and energy levels of many nuclei are known from extensive e... | {
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Why uncertainity is minimum for coherent states? While reading for quantum damped harmonic oscillator, I came across coherent states, and I asked my prof about them and he said me it is the state at which $\Delta x\Delta y$ is minimum. I didn't quite understand why it is minimum.
Please explain why this happens?
| As you probably know, for any particle the product of the uncertainties in the position, $\Delta x$, and the momentum $\Delta p$ (not $\delta y$ as you state) is bounded below by a positive constant;
$$\Delta x\, \Delta p\geq\frac{\hbar}{2}.$$
(If this doesn't ring a bell, you need to read up on Heisenberg's uncertaint... | {
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Observer effect, do this mean literally someone or just any interaction with other matter? I am a layman and was wondering, the quantum observer effect. The regular notion to laymen seems to be literally "if you look at it", but as I am coming to understand the world I live in better I feel it means just coming in cont... | The "observer effect" does not really have much to do with observation in the every day sense. The effect in question has to do with the fact that some kinds of interaction between systems cause them to stop exhibiting quantum interference: this process is called decoherence. The relevant kind of interaction copies inf... | {
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Why isn't temperature measured in Joules? If we set the Boltzmann constant to $1$, then entropy would just be $\ln \Omega$, temperature would be measured in $\text{joules}$ ($\,\text{J}\,$), and average kinetic energy would be an integer times $\frac{T}{2}$. Why do we need separate units for temperature and energy?
| I've seen temperature being expressed in electron volts (eV) in Plasma Physics. Basically, you can equate $k_B T = e y$, where $y$ is the temperature in electron volts, and $T$ is the "thermal" temperature in Kelvin. $e$ is the quantum of charge and $k_B$ is the Boltzmann factor. So $1\mbox{ eV temperature} \approx 116... | {
"language": "en",
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How can I prevent my son building up static on his trampoline? Whenever my three year old son plays on his trampoline, it doesn't take very long for him to start building up a significant amount of static electricity. His hair stands on end (which is quite amusing), but when I help him down we both get a nasty static ... | Get a grounding rod and bang it into the ground? Get 2 ground clips and 1 meter of 6mm grounding wire. Link 1 clip to the leg of the trampoline and then the other clip to the grounding rod.
| {
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How to calculate beam spread of a non-point light source via an aspheric lens I need to determine the angle, or rate of divergence of light from a single aspheric lens when I place a non-point light source (e.g. LED array) at a given distance from the lens which is less than the focal length of the lens.
This seems to ... | Well, if you were looking strictly at the LED array (no lens) then you can typically find that the intensity of the array will fall off at angle according to the LED manufacturers data sheet AND the cosine of the cross section of your array. Which is to say that an array of LEDs will have a wider viewing angle than a s... | {
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How does a star ignite? I remember reading that X-Rays are generated by 'braking' electrons in a Coolidge tube.
Is it fundamentally a matter that the extreme gravity immediately before a star ignites is so strong that it affects the hydrogen atoms to the point the velocity of it's components must be let-off in the form... | I was going to put in a detailed answer but the comment above me explains it pretty well. Basically, when the sun gains enough mass (has to be A LOT of mass. Nuclear fusion is a pretty powerful process), the gravity smashes the protons together and fuses them to create Helium nuclei. The 'smashing them together' part r... | {
"language": "en",
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Concerning the curvature of an airfoil (shape) I am wondering about the reasons for the shape of a turbine blade airfoil, see here
Do you know the reason for this shape? Usually, very large curvatures like this are to extract high lift from LOW speed environments. But the conditions inside a turbine is the most strenuo... | Turbine blades can actually have a very complex shape, which changes dramatically from the root to the tip. That diagram is a little misleading as it only shows one cross section.
The shape at the root is indeed at a high angle of attack, and is quite broad - partly as it needs the strength to cope with the large force... | {
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Interval and proper time Is the definition of $$d s^2=-d \tau^2$$ assuming that $c=1$, so that we always have $$\left({ds\over d\tau}\right)^2=-1$$?
Is there a reason for this definition?
Don't we get an imaginary ${ds\over d\tau}$?
| Yeah, you do. The reason $\mathrm{d}s$ and $\mathrm{d}\tau$ are defined this way is that one or the other will be real for any given path. For a spacelike interval $\mathrm{d}s$ will be real (indicative of the fact that the distances we measure in everyday life are spacelike intervals), and for a timelike interval $\ma... | {
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Waveguides (in the ocean?) The speed of sound in the ocean is given by
$$c_s(\theta,z) = 1450 + 4.6\theta - 0.055\theta^2 + 0.016z$$
$\theta$ is the temperature in degrees celcius, and $z$ is the depth. In a simplified model, $\theta$ is constant at 10$\,^\circ $C for the part of the ocean above the "themocline". The t... | You don't need a sharp discontinuity in the speed of sound to guide the waves. Remember that reflection does not occur right at the interface; rather, the wave always penetrates outside the waveguide to "see" what's going on there. A gradual increase in the speed of sound enforces the wave to reflect as well.
Reflectio... | {
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Does entropy alter the probability of independent events? So I have taken an introductory level quantum physics and am currently taking an introductory level probability class. Then this simple scenario came up:
Given a fair coin that has been tossed 100 times, each time landing heads, would it be more likely that tha... | The other answers are good, I just thought this would be a cute opportunity to learn some animation techniques in Mathematica. I start with a hundred heads and make a number of additional, fair, independent tosses. Then I compute the total fraction of heads and repeat this a thousand times and make a histogram of the r... | {
"language": "en",
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Do viruses suffer from quantum de-localization? Consider some microscopic life form. It should obviously be localized in space, in the quantum-mechanical sense, if it is treated as a single particle (though it is composite). If its characteristic length is $l$, then its wavefunction would de-localize in the typical tim... | An experiment to put a virus into a superposition of states was described in this Arxiv preprint. As far as I know the experiment has not been done yet, but I would guess most of us believe it will work and that a virus does indeed obey the principles of quantum mechanics just like a sub atomic-particle. After all a co... | {
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In terms of the Doppler effect, what happens when the source is moving faster than the wave? I'm just trying to understand this problem from a qualitative perspective. The Doppler effect is commonly explained in terms of how a siren sounds higher in pitch as it is approaching a particular observer. I understand this i... | Someone standing on the ground would here a sonic boom. The sound would travel out from the plane as a coherent wave front, all the peaks will be in the same place traveling at the speed of sound (look at a picture on wiki, http://en.wikipedia.org/wiki/Sonic_boom) and will sound like an instant boom. I am not entirely ... | {
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Electric field near a conducting surface vs. sheet of charge I know perfectly well how to derive the magnitude of the electric field near a conductor,
$$E = \frac{\sigma}{\varepsilon_0}$$ and near a sheet of charge, $$ E = \frac{\sigma}{2\varepsilon_0} .$$
In fact, I can explain with clarity each step of the derivatio... | Intuitively, the surface charge on the edge of a conductor only produces a nonzero electric field on one side of itself, whereas the surface charge on an isolated sheet produces an electric field on both sides of itself. The charge on the isolated sheet is filling twice the amount of space (for an appropriate definitio... | {
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Does a current carrying wire produce electric field outside? In the modern electromagnetism textbooks, electric fields in the presence of stationary currents are assumed to be conservative,$$
\nabla \times E~=~0
~.$$ Using this we get$$
E_{||}^{\text{out}}~=~E_{||}^{\text{in}}
~,$$which means we have the same amount of... | Outside a current carrying conductor, there is, in fact, an electric field. This is discussed for example, in "Surface charges on circuit wires and resistors play three roles" by J. D. Jackson, in American Journal of Physics – July 1996 – Volume 64, Issue 7, pp. 855.
To quote Norris W. Preyer quoting Jackson:
Jackson ... | {
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What happens when a star undergoes gravitational collapse? Immediately prior to becoming a supernova the core of some types of stars may suffer gravitational collapse.
*
*What happens to any planets in orbit around the star at the instant the mass is fully collapsed?
*Assuming this sudden change would cause some ... |
"What happens to any planets in orbit around the star"
Why would anything happen to them? There is still a mass there; the same mass as before. It still has the same center of gravity.
Now, when the radiation and shock waves arrive lots of stuff starts happening, including the effect mass around which the planets a... | {
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What is the fastest a spacecraft can get using gravity-assist? Assuming normal spacecraft and space objects (no neutron stars, black holes, etc). To what speed can a spacecraft accelerate using gravity-assist?
For example, if a spacecraft is moving at relativistic speeds, it probably won't get seriously sped up by norm... | A key limitation to how much of a velocity change can occur in a slingshot maneuver is the amount of time the spacecraft spends in the region near the planet. Change in speed is related to force x time/mass. At very high speed, the spacecraft spends only a very short time hear the planet. Moreover, at very high spee... | {
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Negative emf in AC generator At a certain instant in AC generator, when the normal of the plane (rectangular coil) makes an angle of 270 degrees with with the magnetic induction B, the value of emf is:
$E = -NAB\omega$
My teachers would usually say that this is the minimum value of emf that a generator produces. Does i... | Yes. That's why it's named as alternating current. Briefing...
The magnetic flux linked to the coil is $\phi=NBA\ cos(\omega t)$ and the emf induced (according to Lenz' correction of Faraday's law, $$e=-NBA\frac{d(cos(\omega t))}{dt}=NBA\omega\ sin(\omega t)$$
Here, $NBA\omega$ is a constant which can be replaced by $E... | {
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What is the reasoning behind hole carriers being able to carry heat? In the Peltier effect, we consider charge carriers being able to carry heat. As for electrons or ions, this attitude makes sense, since external electric potential drives particles with mass in a direction and effectively transfers heat from one point... | Both free electrons and holes in semiconductor are excitations, i.e. quasiparticles which can propagate under influence of external electric field or temperature due to diffusion or drift. Don't forget that electrons are also characterized by the effective mass. In p-doped semiconductors a gradient of the temperature c... | {
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Voltage of open circuit
A battery with emf $\varepsilon$ and internal resistance $r$ is connected
with a resistor $R$ in the following open circuit. What is the voltage $V_{ab}=V_a-V_b$?
The answer is $- \varepsilon$. "No current. There is no voltage change across R and r.". But I don't really understand why ... I... | Ok , Potential is work done by electrostatic force as you move from A to B per Couloumb. So transfer 1 coulomb from A to B and as you move through the battery, E is directed from +ve plate to -ve plate . So work done by $\vec{E}$ is ($V_-) - (V_+$) , which means $-EMF$.
And yes that is an assumption that charge must re... | {
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Purpose of Grover's algorithm? How is the output of Grover's algorithm useful if the result is required to use the oracle? If we already know the desired state, what's the point of using the algorithm?
So can you give me a concrete example of an oracle function. For example if the indexed items in a Grover search were,... | The oracle doesn't need to know the desired state in order to verify whether a given state is the desired state.
Grover's algorithm can be applied to NP-complete problems. This is the set of problems for which there is no known way to generate a solution in polynomial time, but a given solution can be in recognized in ... | {
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How can anything be hotter than the Sun? I've heard that if a space shuttle enters the atmosphere from a bad angle its surface will become so hot that it will be hotter than the surface of the Sun.
How can that be? It seems to an uneducated mind that Sun is really really hot, how could something seemingly minor such as... | The temperature of our sun is determined primarily by the generation of heat (the fusion process) and the rate of heat loss by various means. When the process reaches equilibrium, a given average temperature is maintained. Any other process that has a higher generation rate or smaller energy loss, or both, would be ... | {
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Electric current streamlines in induction cooking vessel I am looking for a plot of the typical streamlines of the electric induced currents ("eddy currents") in a induction cooking vessel.
How can one theoretically predict the streamlines? How is it possible to measure the streamlines?
I was able to find a plot for t... | The shape of the induced eddy currents in induction cooking will depend on the shape of the fluctuating magnetic field and the shape of the cooking vessel. Certainly there are commonalities though and I suspect the diagram you have is similar. Also, in the case of induction cooking, the field is varying rather than t... | {
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Polarization of sound Sound can't be polarized because the vibration of such type can't be polarized i.e, it can't be limited or controlled by any barriers and so polarization is not possible in them.
This is what my teacher answered me when i asked the question. But i didn't understand what did he mean by "the vibrati... | That happens because electromagnetic waves are consist of electric and magnetic parts
http://www.edinformatics.com/math_science/e_mag_nasa_image.gif
which are running in orthogonal planes. And usually they run in all directions. When You polarize light - You let waves go just in one plane.
But air waves are just vibra... | {
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What materials focus EM radiation in the 2.4GHz range If glass and similar materials refract visible light effectively, what materials would be best for focusing lower frequencies of EM radiation, if any? If not, what other methods exist for focusing these ranges?
The thought was inspired by wondering how you might bui... | Actually, air itself with different water content and density forms refracting layers that can focus microwaves (and other electromagnetic radiation). This is called "ducting"/anomalous propagation.
| {
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I read a book saying bernoulli's flight equations didn't have as much impact on lift as most people think I'm a computer scientist that likes to read about math and physics occasionally. A local author at a nearby aviation center brought bernoulli's flight equations into question.
It was clear enough logic, but I didn'... | It is absolutely true that the Bernoulli effect is not necessary in order for a wing to produce lift. Ultimately a wing produces lift by directing air flowing over the wings downward. The can be achieved by ramming air downward through the wing's "angle of attack" with respect to the air flow. This is why an airplane c... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/63023",
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Escape velocity to intersection of two gravitational fields
Find the minimal velocity needed for a meteorite of mass $m$ to get to
earth from the moon. Hint: the distance between the center of earth
and the center of moon is $\approx 60 R_E$, and the meteorite should
reach a certain point $O$ on that distance, w... | $$U_{g,i}=-G\dfrac{M_{moon}.m}{\underbrace{R_{moon}}_{(\ distance \ from \ moon\ center) }}-G\dfrac{M_{Earth}.m}{\underbrace{(60R_{earth}-R_{moon})}_{(initial \ distance\ from\ Earth)} } $$
You missed $U_i$ due to Earth!
| {
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Reaching the speed of light via quantum mechanical uncertainty? Suppose you accelerate a body to very near the speed of light $c$ where $v = c - \epsilon$. Although this would take an enormous energy, is it possible the last arbitrarily small velocity needed -- $\epsilon$ -- could be overcome with a minor bump in velo... | No. First of all, Planck's constant is not a speed, so you can't compute $c - \hbar$. But you can reword the question to get around that problem, something like this:
Is there some speed $\epsilon$ such that an object traveling at speed $c - \epsilon$ could experience a quantum fluctuation that temporarily takes its s... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/63235",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Definition of electric charge and proper explanation Is there a definition of electric charge and proper explanation of it?
It is said "Electric charge is the physical property of matter that causes it to experience a force when close to other electrically charged matter." How is it though that matter can get charged?... | to be more specific about the definition of charge, charge is an intrinsic property of inherent matter. As we all know the mass which is considered as the fundamental property of every particle in this universe, electric charge is considered as the fundamental property of the particle that is used for electrostatic pur... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/63290",
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Evolution principle of the physical laws I wanted to know if there is a physical theory that considers that the laws of physics undergo an evolutionary process. That see the law of physics or the absence of them, as something dynamic, and that with time they slowly converge to something we know today. A kind of simulat... | All such theories will be perceived as speculative, radical and unbelievable. Darwinian theory of evolution was strongly substantiated and even despite that fiercely attacked.
One example of such theory is MET. It says that every new moment is a result of evolution by necessity arising from information-related (entropy... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Mathematical proof of non-negative change of entropy $\Delta S\geq0$ I understand that we can prove that for any process that occurs in an isolated and closed system it must hold that
$$\Delta S\geq0$$
via Clausius' theorem. My question is, how can I prove this in a mathematical way?
|
I understand that we can prove that for any process that occurs in an isolated and closed system it must hold that
ΔS≥0
via Clausius' theorem. My question is, how can I prove this in a mathematical way?
The Clausius theorem says that when the system undergoes general cyclic process during which it is connected to... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/63416",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Are all points in the universe connected? Is it true that every point in the universe is connected or could be so theoretically? If so how is this mediated?
Is it through the quantum nature of the fabric of space or is it through the interrelationships of the gravity fields throughout the universe. From the gravity fie... | On space-time, the useful notion of points are events. Only events that are separated by time-like curves are causally connected. Causal connectedness implies that fields happening at one of the events can influence fields happening at the other. Events that are separated by space-like curves are not causally connected... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/63523",
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If everything in existence were increasing in size at some rate, would we be able to detect it? Would our eyes observe any changes?
What about electronic measurement devices?
| Depends.
If you simple assume matter growing we would see the distance between the surfaces of celestial bodies diminishing. Given that we regularly monitor the distance between the surfaces of the Earth and Moon by laser ranging to accuracies of less than one cm (which means less than one part in $10^8$ over the time... | {
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Is there a way to create a flickering frequency to be dependent on speed of the person looking at it? Is there a way to make a screen or a road sign flash at different rates, depending on the velocity of the observer looking at it?
*
*I would like to achieve a state where two observers going at different speeds wou... | You can use a reflector with gaps. Then the light from a car will alternate between reflecting and not reflecting at a rate dependent on their velocity towards the reflector. Please excuse my crude diagram:
As the car moves right to left, gaps in the reflector will cause it to appear to flash on an off.
| {
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If particles can find themselves spontaneously arranged, isn't entropy actually decreasing? Take a box of gas particles. At $t = 0$, the distribution of particles is homogeneous. There is a small probability that at $t = 1$, all particles go to the left side of the box. In this case, entropy is decreasing. However, it ... | Even though the answer you chose is very good I will add my POV
Take a box of gas particles. At $t=0$, the distribution of particles is homogeneous. There is a small probability that at $t=1$, all particles go to the left side of the box. In this case, entropy is decreasing.
Take the statistical mechanics definition ... | {
"language": "en",
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"source": "stackexchange",
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Temperature of glowing materials As I understand it, Stars emit visible light, OBAFGKMRNS, in the range of $10^3 - 10^4 K$.
Yet materials such as steel emit similar frequencies at much lower temps; red is around 800K.
Why the difference? I thought black body radiation applies to all materials and environments.
I am an ... | The peak wavelength at which a body emits light is governed by Wien's displacement law, which states that this wavelength is inversely proportional to the temperature, as
$$\lambda \, T=\text{const}=0.003\text{ m K}.$$
More graphically, in the stellar-surface sort of temperature range, this looks like
You'll notice th... | {
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Does relativistic mass have weight? If an object was sliding on an infinitely long friction-less floor on Earth with relativistic speeds (ignoring air resistance), would it exert more vertical weight force on the floor than when it's at rest?
| First off, your question is phrased in terms of relativistic mass, which is an obsolete concept. But anyway, that's a side issue.
The question can be posed in terms of either the earth's force on the puck or the puck's force on the earth. We expect these to be equal because of conservation of momentum.
In general relat... | {
"language": "en",
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Why don't black holes within a galaxy pull in the stars of the galaxy? visit http://www.nasa.gov/audience/forstudents/k-4/stories/what-is-a-black-hole-k4.html
If black holes can pull even light, why cant they pull the stars in the galaxy?
| Why would you assume they do not ? Of course they do. But as you probably know, the gravitational pull decreases with distance (inverse square law). From a safe enough distance any other object (star, galaxy) would feel the normal gravitational pull of an object of the black-hole's mass at that distance; it makes n... | {
"language": "en",
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"source": "stackexchange",
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The Preference for Low Energy States The idea that systems will achieve the lowest energy state they can because they are more "stable" is clear enough. My question is, what causes this tendency? I've researched the question and been unable to find a clear answer, so I was hoping someone could explain what's going on b... | Large systems with many degrees of freedom (e.g. a ball consisting of many molecules) tend to settle into low energy states. This is a direct consequence of two fundamental laws, the first and second laws of thermodynamics: energy conservation and entropy increase.
A system with many degrees of freedom can be in many d... | {
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Reflection of a polarised beam The past days I've been trying to understand how AutoFocus(AF) works on photographic cameras. There is a statement that says AF systems are polarisation sensitive. This means that they can only work with circularly polarized light.
Trying to understand why, I came accross this article whi... | Reflection polarizes light. A reflected ray becomes linearly polarized perpendicular to the plane containing the incident and reflected rays. This is why polarized sunglasses are effective for reducing glare. The autofocus may not be working as expected because much of the scene is polarized light.
| {
"language": "en",
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What's the physical significance of using fourier transform for diffraction? I am studying some basic idea of diffraction and there mention in far field, the diffraction pattern could be understood by Fourier transform. But I just don't understand what's the physical fact for that. And why cannot use Fourier transform ... | To make it short, my interpretation of the Fourier transform in optics is that is transforms positions (and phase) of the rays at some given plane, to their angles. One given angle corresponds to one given oscillation of the phase, i.e. one point on the Fourier space.
| {
"language": "en",
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"source": "stackexchange",
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Displacement current - how to think of it What is a good way to think of the displacement current? Maxwell imagined it as being movements in the aether, small changed of electric field producing magnetic field. I don't even understand that definition-assuming there is aether. (On the topic of which, has aether actually... | The displacement current is the 'phantom' current that passes through a capacitor in a circuit, since no real current runs between two plates of a capacitor. This is given by finding the rate of change of the electric flux with respect to time, and multiplied by epsilon nought. A great video on this can be found here: ... | {
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Is it possible to obtain higher order corrections to the ideal gas law when one allows realistic phenomena to make their way into the equations? I had an interesting thought today that caused me to ask whether it'd be possible to make corrections to the ideal gas law via introducing terms derived from more realistic ph... | See van der Waals' Gas Equation :
$$\Bigg(P+\dfrac{an^2}{V^2}\Bigg)\Big(V-nb\Big)=nRT$$
$ a,b$ are constant dependent on gas properties.
| {
"language": "en",
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Different batteries connected in parallel If we have 2 batteries one of emf x and the other is of emf y and we connect them in series we get an effective emf of x+y.
But what if we connect them in parallel, how to calculate the emf now?
| The other answers are good (especially the I = (V1 - V2) / (R1 + R2) equation that we will use) but I just wanted to give you ballpark estimates of some numbers that you can expect to see. Imagine that you are going to do this to a 9V battery and a 1.2V AA battery, then:
V1 - V2 = 7.8V
For internal resistances, it's h... | {
"language": "en",
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What is our estimated running speed on Moon's surface? I was wondering if we have the chance to run on the Moon's surface, how would you expect it look like?
I expect our velocity will increase for the same work we do on Earth, but not sure if this will be multiples in term of gravity variations.
How do you think our m... | There are a few videos of astronauts running on the moon, e.g. here and here. Note that they have to adopt quite different gaits from on Earth. However, they were encumbered by space suits that were heavy and stiff, and they were probably moving fairly carefully in order to avoid the danger of a puncture.
It's difficu... | {
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Why does increasing the temperature of a thermistor decrease it's resistance? Surely, upon an increase in temperature, the atoms within the thermistor would vibrate with more energy and therefore more vigorously, hence making the electrons flowing through the electric circuit more likely to collide with one of the atom... | Olly, the first part of your thinking is correct, as the atoms receive more energy, the electrons do collide more energetically, but they also move "away" from the atom's center. The further they are from the center, the easier it is for an electric field to "move" them. This means that for the same effort (voltage),... | {
"language": "en",
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Does inertia increase with speed? I have heard that when the speed of the object increase, the mass of the object also increase. (Why does an object with higher speed gain more (relativistic) mass?)
So inertia which is related to mass, increase with speed?
So, if I accelerate on a bus, my mass will increase and my iner... | I think inertia doesn't depend on speed, it depends on rate of change in speed, i.e. acceleration. The higher you accelerate the more will be the inertia.
It can be understood by taking an example of a motorcycle, in which lower gear gives more traction than the higher one. The higher the acceleration you want the mo... | {
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What is the derivation for the exponential energy relation and where does it apply? Very often when people state a relaxation time $\tau_\text{kin-kin}, \tau_\text{rot-kin}$,, etc. they think of a context where the energy relaxation goes as $\propto\text e^{-t/\tau}$. Related is an approach to compute it via
$$\tau=E... | This form of $dE/d\tau$ is valid only when the system is not too far from equilibrium and linear response assumption is valid. The fact that $dE/d\tau$ depends on the difference $E - E(0)$ alone is a consequence of assuming a linear response.
| {
"language": "en",
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"source": "stackexchange",
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The motion of a spring
I have a question about the force set by this spring, I saw many times that $\overrightarrow{F}=-Kx\overrightarrow{i}$.
I'm asking why not using $\overrightarrow{F}=Kx\overrightarrow{i}$ without the minus.
And supposing that $\overrightarrow{F}$ is changing during the motion of the solid object ... | $x$ measures the difference in length of the spring in relation to its relaxed state. If you increase the length (positive $x$), the spring creates a force in the negative $x$ direction, because it wants to return to its relaxed state. Accordingly, if you compress the spring (negative $x$) the spring wants to expand (f... | {
"language": "en",
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Hilbert space of harmonic oscillator: Countable vs uncountable? Hm, this just occurred to me while answering another question:
If I write the Hamiltonian for a harmonic oscillator as
$$H = \frac{p^2}{2m} + \frac{1}{2} m \omega^2 x^2$$
then wouldn't one set of possible basis states be the set of $\delta$-functions
$\p... | *
*The Hilbert space ${\cal H}$ of the one-dimensional harmonic oscillator in the position representation is the set $L^2(\mathbb{R})={\cal L}^2(\mathbb{R})/{\cal N}$ (of equivalence classes) of square integrable functions $\psi:\mathbb{R}\to\mathbb{C}$ on the real line. The equivalence relation is modulo measurable ... | {
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Determine the velocity and acceleration of the vertex $B$ 1) The bent rod $ABCD$ rotates about the line $AD$ whit a constant angular velocity of $90 rad / s$. Determine the velocity and acceleration of the vertex $B$ when the rod is in the position shown in Figure.
2) Determine the velocity and acceleration of the vert... | Your angular velocity vector is
$$ \vec{\omega} = \Omega \frac{ \vec{r}_D - \vec{r}_A }{|\vec{r}_D - \vec{r}_A|} $$
where $\vec{r}_A = (0,0.2,0.12)$, $\vec{r}_D = (0.3,0,0)$, $\vec{r}_B = (0.3,0.2,0.12) $ in meters and $\Omega = 90\;{\rm rad/s}$.
Your velocity kinematics is
$$ \vec{v}_B = \vec{\omega} \times ( \vec{r}_... | {
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How can a car's engine move the car? Newton's First Law of Motion states that an object at rest or uniform motion tends to stay in that state of motion unless an unbalanced, external force acts on it.
Say if I were in a car and I push it from the inside. It won't move. So how is the engine of a car capable of moving t... | The friction force between the tyres and the ground makes the car change positions or move,if the road is slipperly cars find it difficult to move sometimes they can be just spinning on the same spot but again the energy supplied by the engine makes the crankshaft to rotate in the process making the tyres to rotate too... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/65001",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Derivation of Dirac equation using the Lagrangian density for Dirac field How can I derive the Dirac equation from the Lagrangian density for the Dirac field?
| The Lagrangian density for a Dirac field is
$$
\mathcal{L} = i\bar\psi\gamma^\mu\partial_\mu\psi -m \bar\psi\psi
$$
The Euler-Lagrange equation reads
$$
\frac{\partial\mathcal{L}}{\partial\psi} - \frac{\partial}{\partial x^\mu}\left[\frac{\partial\mathcal{L}}{\partial(\partial_\mu\psi)}\right] = 0
$$
We treat $\psi$ an... | {
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Why the magnetic flux is not zero? If $\vec{\mathbf B}=B\vec{\mathbf a}_z$, compute the magnetic flux passing through a hemisphere of radius $R$ centered at the origin and bounded by the plane $z=0$.
Solution
The hemisphere and the circular disc of radius $R$ form a closed surface, as illustrated in the figure; there... | the net flux is always zero , and it's satisfies the Maxwell equation , in the answer firstly the flux through disc has been calculated next using the fact that the net flux must be zero we can conclude the flux of hemisphere must be equal to the flux though the disc but with opposite sign namely : flux through hemisph... | {
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Physical representation of volume to surface area I was looking at this XKCD what-if question (the gas mileage part), and started to wonder about the concept of unit cancellation. If we have a shape and try to figure out the ratio between the volume and the surface area, the result is a length. For example, a sphere of... | For the case of a sphere the ratio you found is:
$$ \frac{V}{S} = \frac{ \frac{4}{3} \pi R^3}{4 \pi R^2} = \frac{R}{3} $$
We can actually pass off the volume as being the integral of the surface area here. That's passable when you check the calculus.
One approach is then to ask "what is a function divided by its deriv... | {
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what sort of set up would i need to create an electro magnetic chair with no legs I am a furniture design student therefore please keep it simple. a system strong enough to hold the avergae male of say 90 kg is this possible even....
| Some has done this with a bed http://www.dvice.com/archives/2012/05/maglev-bed-lets.php. With the use of the naturally strong rare earth magnets (neodymium magnets). For a chair it would be hard to levitate the chair any reasonable distance, as you would need a decently powerful magnet.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How to directly calculate the infinitesimal generator of SU(2) We commonly investigate the properties of SU(2) on the basis of SO(3). However, I want to directly calculte the infinitesimal generator of SU(2) according to the definition $$X_{i}=\frac{\partial U}{\partial \alpha_{i}}$$ from Lie group theory. But, where a... | The problem is that your coordinates aren't well defined at $\theta=0$ and $\phi=\pi/2$. Note in particular that
$$
U|_{(0,\frac{\pi}{2},\gamma)} = \begin{pmatrix}1&0\\0&1\end{pmatrix}
$$
for any value of $\gamma$. A simpler choice is
$$
\tilde{U} =
\begin{pmatrix}
x+iy & z+iw \\
-z+iw & x-iy
\end{pmatrix},
$$
with
$$... | {
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How can the big bang occur mathematically? As we know time began with the big bang. Before that there was no time, no laws, nothing. Mathematically how can an event take place when no time passes by? How did the big bang took place when there was no time?
Note my question is not about weather big bang took place or not... | According to dictionary.com:
An event is an occurrence that is sharply localized at a single point in space and instant of time.
An event can't take place without time. Yet, many scientists claim that there was no time before the big bang. But, that is completely illogical. How can there be no time and then suddenly ... | {
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Work on Ferromagnetic Object Due to Solenoid I've been going through some equations and such trying to determine the work done by a solenoid on a ferromagnetic object. I have the following:
Magnetic field due to solenoid:
$\vec{B} = \langle0,0,\mu_0nI\rangle$
(Assuming coils are on xy-plane and current is counter-clock... | I think you're right to consider the magnetic permeability of the object. However, I don't think the equation for force you have is valid here as the object may neither be charged (q=0) nor initially moving (v x B = 0), conditions which according to the equation would result in zero force.
| {
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Where does the extra equation come from to determine the forces from an object on a table? I have a question about basic statics but somehow I cannot manage to find the answer on my own (btw, this is not a homework. It's been so many years since school for me...).
The problem is very simple: we have an object with wei... | The simple answer is that you can't fully solve this problem--because as you note it is under-constrained--under the assumptions that are made when you first start doing statics (that objects are completely rigid).
The introduction of finite strains bring in additional relationships.
| {
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Geometrical Representation Grover algorithm I am studying the Grover algorithm and in my and others lectures, I've come across this picture.
If the dimension of the computational basis is greater than 2, why does the evolution algorithm have this geometrical representation in the plane?
| The plane is enough because all the vectors – before and after the operations (which are really simple rotations) – belong to a two-dimensional plane. The Hilbert space has many more dimensions but they're orthogonal to the plane of the picture and the coordinates (amplitudes) in these additional directions don't chang... | {
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Expectation value - Zetilli vs Griffith I know that an inner product between two vectors is defined like:
$$\langle a | b\rangle = {a_1}^\dagger b_1+{a_2}^\dagger b_2+\dots$$
but because a transpose of a component for example $a_1$ is again only $a_1$ the above simplifies to:
$$\langle a | b\rangle = \overline{a_1} b... | If the wave function $\Psi$ is normalized, then $\langle\Psi|\Psi\rangle$ should equal 1. Griffiths' definition assumes the wave function is already normalized, while Zetilli accounts for all possibilities by dividing out the normalization constant. So if the wave function $\Psi$ is normalized, Zetilli's definition wil... | {
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Can one of Newton's Laws of motion be derived from other Newton's Laws of motion? Can one derive Newton's
second and third laws from the first law or
first and third laws from the second law or
first and second laws from the third law
I think Newton's laws of motions are independent to each other.
They can not be de... | Newton's laws of motion cannot be derived from each other. They are the building blocks of Newtonian mechanics and if fewer were needed, Newton would simply formulate fewer.
The first law postulates the existence of an inertial reference frame in which an object moves at constant velocity if the net force acting on it ... | {
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A Musical Pathway Using a small number of sound emitters, could you create a room where certain nodes emitted particular tones, but no meaningful sound was heard anywhere else.
So, for example, by walking down a certain path, you could hear the tones for "Mary Had a Little Lamb." Is there a generalized algorithm to ma... | I suppose you could use destructive interference and set up speakers in just the right positions for it to work, but I also assume the calculations needed to achieve it would be complicated (luckily, you're not asking for that).
It should be possible in theory
| {
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Physical interpretation of different boundary conditions for heat equation When solving the heat equation,
$$
\partial_t u -\Delta u = f \text{ on } \Omega
$$
what physical situations are represented by the following boundary conditions (on $\partial \Omega$)?
*
*$u=g$ (Dirichlet condition),
*$n\cdot\nabla u = h$ ... | Different boundary conditions represent different models of cooling.
*
*The first one states that you have a constant temperature at the boundary.This can be considered as a model of an ideal cooler in a good contact having infinitely large thermal conductivity
*The second one states that we have a constant heat fl... | {
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Field At Magnetic Dipole Suppose I have a pure magnetic dipole $\mathbf{\vec m} = m\hat z$ located at the origin. What is the magnitude of the field $|\vec B|$ as $r\to 0$? In other words, what is $\lim_{r\to 0}\frac{\hat{r}\cdot \vec{p}}{4\pi\varepsilon_0r^2}$? Is it just zero? $\infty$? Do I have to use some sort of ... | The magnitude of the fields would go to infinity at zero. However, dipoles are an approximation, at large distances, of the fields created by smaller object (e.g. a current loop). If you zoom closer, the B field does not diverge.
| {
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Does potential energy in gravitationall field increase mass? I was just taught (comments) that any type of energy contributes to mass of the object. This must indeed include potential energy in gravitational field. But here, things cease to make sense, have a look:
*
*I have object at some distance $r$ from radial s... | The total energy of the test mass in the Schwarzschild gravitational field depends on the time-like component of the metric tensor $g_{00}$. This is how the gravitational redshift is derived (see, for example, Hartle J B, Gravity). In this case for the test particle (at rest) with the rest mass $m$ it is possible to wr... | {
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Guitar strings and temperature I am investigating Mersenne's law with a guitar by varying tension (hanging weights) and string length. Will temperature change (room temperature to ~4°C) effect the frequency noticeably? If so, is the string oscillating differently or is the change due to a variation of the speed of soun... | The speed of sound according to this chart would change as much as 330.4/358.0 = 8% .
The air behaves closely to an ideal gas, therefore this kind of change would hardly change the pitch, let alone be noticeable to a human ear.
However the change in temperature would effect the stiffness and length of the string dramat... | {
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What happens when a photon hits a beamsplitter? Yesterday I read that we can affect the path and the 'form' (particle or wave) of a photon after the fact (Wheeler's delayed choice experiment). Part of what is puzzling me is the beam-splitter. Are the individual photons actually being split into two new photons of less... | Very short and "axiomatic" answer: You indeed can "split" one particle. In QM particles are treated as a "wave functions", maybe it will be more easy for you to imagine a splitting wave. However, only at the point when the photon is detected the particle is measured in one point of space. This is the very foundation of... | {
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Circuit Loop Law Doubt In a circuit with a solenoid/inductor and a resistor and a battery .
Books say that $\Sigma \Delta V=0$ around a closed loop . That means work done by electrostatic field per unit charge is $0$ around a closed loop .
Now as we go pass through a solenoid $\Delta V= -L\frac{di}{dt}$ . Suppose I t... |
Books say that ΣΔV=0 around a closed loop
KVL holds only if the magnetic flux linking the circuit is unchanging.
In ideal circuit theory, it is assumed that circuit elements are ideal lumped elements and the self inductance of the circuit is zero.
In other words, we assume that the dimensions of the circuit and circu... | {
"language": "en",
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Sum of all forces Let us glue up these two images, where we get closed loop thrust of water. Force $F_3$ has direction $-x$ and force $F_2$ has $x$ direction. What is the sum of all forces? Can it be more than zero? Speed of water is constant.Angles are the same.Half circle is not exactly circled at the ends due to the... | Newton's second law was originally formulated as $S_F$=$dp/dt$. P is momentum, which equals mass multiplied by velocity and that quantity divided by time. $S_F$ is the sum of the forces. Although $S_F$ is usually expressed as ma, to which it is mathematically equivalent, the original form is actually more descriptive, ... | {
"language": "en",
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Generalizing a relativistic kinematics formula for spatial-acceleration dependence I'm starting from this expression
$$ \alpha dt = \gamma^3 dv $$
where $\alpha$ is proper acceleration of a point particle, $dv$ and $dt$ are coordinate differentials of velocity and time, and $\gamma$ is the relativistic factor of the p... | In your equation $\alpha dt = \alpha(x) \frac{dt}{dx} {dx}$, just multiply each side by v before you integrate.
| {
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Action Reaction when I pushing a trolley? I tried to explain how those force work but I can hardly figure it out.
I exerted a force on the trolley and there will be a force on trolley on me as well. This is the newton's third law. But why the trolley will move? Where's the force come from
| The trolley only moves because of forces acting on it.
The reaction force acts on you, not the trolley.
It is the force of you pushing on the trolley that makes it move.
Learn about 'free body diagrams'.
| {
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Maximum angular velocity to stop in one rotation with a known torque I have an object I can rotate with a given torque. I would like to stop applying torque once I've reached a defined maximum rotational speed. The maximum rotational speed should be defined so that applying maximum torque will stop the rotation of the ... | Building off of Zen's response, the energy will be $E_r = \frac{1}{2}I\omega^2$. The work done in one rotation is $\tau\Delta\theta$. These two terms are equivalent in your case. I.e. you will have the following expression
$$ E_r = \frac{1}{2}I\omega^2 = \tau_\text{max} \Delta\theta$$
$$ \omega_\text{max} = \sqrt{\... | {
"language": "en",
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Is play-dough liquid or solid? At room temperature, play-dough is solid(ish). But if you make a thin strip it cannot just stand up on it's own, so is it still solid?
On a more general note, what classifies or differentiates a solid from a liquid?
| Play-Doh is mostly flour, salt and water, so it's basically just (unleavened) dough. There are a lot of extra components like colourings, fragrances, preservatives etc, but these are present at low levels and don't have a huge effect on the rheology.
The trouble with saying it's basically just dough is that the rheolog... | {
"language": "en",
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Which quantity gives the resistance of a component? In a current vs potential difference graph, we can obtain the value of the resistance of the component. There are books that say gradient-inverse is the resistance and also books that say the value of $\frac{\text{current, I}}{\text{potential difference:V}}$, which co... | The rate of change of voltage with respect to current is known as the dynamic resistance. The ratio of voltage to current at a point is the static resistance.
For an ohmic circuit element, the static resistance and the dynamic resistance are equal.
For non-linear circuit elements, the dynamic resistance is more useful... | {
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Where can I find the full derivation of Helfrich's shape equation for closed membranes? I have approximately 10 papers that claim that, from the equation for shape energy:
$$ F = \frac{1}{2}k_c \int (c_1+c_2-c_0)^2 dA + \Delta p \int dV + \lambda \int dA$$
one can use "methods of variational calculus" to derive the fol... | In the paper by Lin et al. (2003) Progress in Theoretical Physics they mention in the abstract that they extend the work of Ou-yang and Helfrich by expanding the bending energy to fourth order. That means you should be able to work out the lower order solutions from their paper as well.
| {
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Is heat flux density and heat flux the same thing? Heat flux and heat flux density is the same thing, while electric flux density and electric flux is not the same thing?
It makes me confused since we compare Fourier's law with Ohm's law.
Here is a statement from Wikipedia.
To define the heat flux at a certain point i... | If we take the definition of heat flux given here seriously, then heat flux is defined as a vector field $\vec\phi$ with units of energy per unit time, per unit area. At every point $\vec x$ in space, the vetor $\vec\phi(\vec x)$ tells you the direction and magnitude of heat flow in a neighborhood of that point. In p... | {
"language": "en",
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What could magnetic monopoles do that electrically charged particles can't? I understand the significance to physics, but what can a magnetic monopole be used for assuming we could free them from spin ice and put them to work? What would be a magnetic version of electricity?
EDIT
Sorry this wasn't clear. The questio... | Magnetic monopoles are thought to be carriers of magnetic force similar to electrons and electrical charge. If you can generate and use these particles you could expand the number of ways we can manipulate electromagnetic waves. Two ideas that spring to mind immediately are the creation of a DC transformer that does no... | {
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Membrane-reversed black holes and their relationship to white-holes We usually think of white holes as 'thermodynamically reversed black-holes', and this kind of membranes have not been observed in our universe. However, there is some other kind of 'topologically reversed black hole' which we know exists: our cosmologi... | A cosmological horizon isn't the same thing as a black hole horizon--the black hole horizon is an essential feature of the spacetime that is located where it is due to special geometry. A cosmological horizon is an observer-dependent phenomenon that describes when two observers are out of causal contact with each othe... | {
"language": "en",
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Is a proton collision (collisions like in the LHC) visible to the human eye? I was curious if a proton collision is visible to the human eye.
(This might sound like a really basic question and forgive me if it is. I am very inexperienced in Physics and just wanted an answer to my curiosity)
| A spinthariscope is a simple device consisting of a minute amount of an alpha-emitter and a zinc-sulphide screen. It often includes a magnifier to view the screen. The amazing part is that a dark-adapted eye can clearly see the flashes of light produces as individual alpha-particles hit the screen! There's probably ... | {
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How does energy convert to matter? To my understanding, matter and energy are one and the same. Shifting from $E$ to $M$ in Einstein's famous equation requires only a large negative acceleration. If $M$ really is $E/c^2$, does that make matter the solid state of energy? I've read a lot about positron-electron collis... | The thing about energy becoming particles is not entirely true. Quantum mechanics explains that particles themselves are waves. The energy that forms mass, however, is not a part of the particles themselves. For subatomic particles such as electrons and quarks, their mass is caused by their interaction with the Higgs... | {
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How to cut a stone on a White Dwarf? I've heard that white dwarf stars are extremely dense and hard. So, if I had a piece of white dwarf matter, would it be possible to cut it (or otherwise) into a custom shape? How could one do that?
| The "surface" of a white dwarf is a mixture of hydrogen, helium and perhaps a trace of heavier elements. It is never (read this as many, many times the current age of the universe) going to cool down enough to solidify.
Solids exist inside the approximately isothermal interiors$^{1}$ of white dwarfs, at densities $\geq... | {
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Why does the Sun feel hotter through a window? I have this big window in my room that the Sun shines through every morning. When I wake up I usually notice that the Sunlight coming through my window feels hot. Much hotter than it normally does when you're standing in it outside. I know if the window were a magnifying ... | Whenever you are near a window with solar radiation, you will feel hotter even if the room you are might be cooled(lets say 65F), and its not your AC fault.
That's why even if you are near a fan like you said, the heat gain from the sun still is superior.
From ASHRAE Fundamentals Handbook 2017:
Direct solar load has a... | {
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Integrable equations of motion Suppose that a force acting on a particle is factorable into one of the following forms:
$$\text{a)}\,\,F(x_{i},t)=f(x_i)g(t)\,\,\,\,\,\,\,\text{b)}\,\,F(\dot{x}_{i},t)=f(\dot{x}_{i})g(t)\,\,\,\,\,\,\text{c)}\,\,F(x_{i},\dot{x}_{i})=f(x_i)g(\dot{x}_i)$$
for which cases are the equations o... | You can't integrate the right hand side because $f=f(x_i)$ and you've got a differential on $t$. As for a), if you rearrange terms, you can verify that
$$m\frac{d\dot{x_i}}{f(x_i)}=g(t)\,dt$$
so that now you can't integrate the left hand side because $f$ depends un $x_i$ and you've got a differential on $\dot{x}_i$.
| {
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How general relativity gets to an inverse-square law I understand that a general interpretation of the $1/r^2$ interactions is that virtual particles are exchanged, and to conserve their flux through spheres of different radii, one must assume the inverse-square law. This fundamentally relies on the 3D nature of space.... | I found many explanations for this type of questions
http://settheory.net/cosmology
http://settheory.net/general-relativity
It's better than "The Meaning of Einstein's Equation" (John Baez).
In particular
- It is directly applied to an important example (universal expansion)
- The expression is simpler (relating 1 co... | {
"language": "en",
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Why do stars flicker? Why do stars flicker and planets don't? At least this is what I've read online and seen on the night sky. I've heard that it has to do something with the fact that stars emit light and planets reflect it. But I don't get it, isn't this light, just "light"? What happens to the reflected light that ... | Much closer than stars are the distant lamps (polychromatic or monochromatic), say 2 to 3km away, also twinkle. this cannot be related to change of index of refraction due to temperature's variations , since the frequency of this twinkling does not vary strongly with air turbulence.
the accepted explanation for this i... | {
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Why doesn't an electrometer's capacitance influence the measurement of voltage? I've read on the subject in several books, and none of them mentioned whether we can neglect electrometer's influence on the measurement of the voltage or not. Maybe my question sounds a bit stupid, but I really can't understand why they do... | For low frequency measurements the capacitance in the circuit is much higher than the probe's capacitance (100pF-10uF+ vs 10pF). The slight temporary effect of connecting the meter is quickly compensated for by the circuit because you're talking about a very small amount of charge that is pulled off in a quick transie... | {
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Why are particles in harmonic motion in normal modes? Why do we assume that in normal modes, particles oscillate in form cos (wt) ?
How do we know that the general motion of particles can be expressed as a superposition of normal modes?
In both French and Crawford, the assumption of harmonic motion is made without any ... | In most cases, this is related to an assumption of small displacements from equilibrium.
Assume that the system is described by a potential function $V(s)$, where $s$ represents
the coordinate(s) associated with the normal modes. Let $s_0$ represent value of the coordinates the equilibrium state. Taylor expanding the... | {
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Uncertainty in path integral formulation In Feynman's path integral formulation, in order to calculate the probability amplitude, we sum up all the possible trajectories of the particle between the points $A$ and $B$.
Since we know precisely that the particle will be at $A$ and $B$, does it mean that the uncertainty of... | If you are using non-relatavistic quantum mechanics then yes the momentum uncertainty is infinite. If you want to include Lorentz invariance you need to use quantum field theory in which case you describe the evolution of a field with the path integral formalism and interpret particles as disturbances in the field.
| {
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Is my boss wrong about our mechanical advantage from our pulley system? I work on a drilling rig as a roughneck and we had a lecture today (at the office) about mechanical advantage in pulley systems. Now, I know that my boss is well educated in oil drilling, but my instincts tell me that he may have this one wrong.
A ... | To put it simple let's say the pipe is 1 ton and you have a 4 to 1 then your lifting 1/4 ton, if the pipe was 2 ton you would be lifting 1/2 ton, although heavier you still have a 4 to 1 pull so will need more
power to lift it. So no matter the weight or strain it remains 4 to 1 advantage.
| {
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How can we describe the electrons of multi-electron atoms (i.e. not Hydrogen) when equations/analytic solutions only exist for Hydrogen? I've been digging into emission spectra of different elements and found that such things as the Rydberg equation, Bohr's model, and quantum mechanics can only fully describe the singl... | The only atoms for which the Schrodinger equation has an analytic solution are the one electron atoms i.e. H, He$^+$, Li$^{2+}$ and so on. That's because with more than one electron the forces between electrons make the equation too hard to solve analytically. However, over the 90 or so years since Schrodinger propose... | {
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To what extent are quantities fundamental? Arguably the most well-known and used system of units is the SI-system. It assigns seven units to seven ‘fundamental’ quantities (or dimensions). However, there are other possible options, such as Gaussian units or Planck units. Until recently, I thought that these different s... | The Si - Units are just a definition which are related by euqations. Take for example the speed of light $c \approx 3\cdot 10^8\frac{m}{s}$. Now what does $\frac{m}{s}$ mean? You can take it as a parameter that is connected to other units by equations like the famous $E = m c^2$. Since only the equation is important an... | {
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"answer_id": 1
} |
Why can't we obtain a Hamiltonian by substituting? This question may sound a bit dumb. Why can't we obtain the Hamiltonian of a system simply by finding $\dot{q}$ in terms of $p$ and then evaluating the Lagrangian with $\dot{q} = \dot{q}(p)$? Wouldn't we obtain then a Lagrangian expressed in terms of $t$, $q$ and $p$? ... | A fairly basic remark to make is that usually we can plainly identify
$$L = T-U$$
where $T$ is the kinetic energy and $U$ is the potential energy, and
$$H = T+U$$
Expressing these quantities for e.g. a Hooke-like spring (or any system where $U\neq 0$) would give you a problem with the sign of $U$ if you simply substitu... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/69133",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 5,
"answer_id": 2
} |
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