Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Why does current decrease when voltage is increased? (transformers) Why is the current in the secondary coil less than in the primary when the voltage is greater in that coil as compared to primary coil? (for transformers)
Well I know that energy should be conserved but listen this is not the cause! There would be some... | If the output from the secondary of a transformer is connected to a fixed load (such as a resistor), an increased voltage will produce an increased current. This will require an increase in the current in the primary (in phase with the input voltage to match the output power).
| {
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"timestamp": "2023-03-29T00:00:00",
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Does Newtonian mechanics work in polar coordinates? Our teacher suggested that Newtonian Mechanics only applies in cartesian coordinates. Is this true?
He gave this example.
Suppose there a train moving with constant velocity $\vec{v}=v_0\hat{x}$, with initial position vector $\vec{r}=(0, y_0)$, where $v_0,y_0$ are con... | This is an example of how operators do not in general commute. That is: if $x$ and $y$ are variables, $xy=yx$, but if $f$ and $g$ are operators, $fg$ does not generally equal $gf$. An operator is a set of instructions for what to do to the expression that follows it. Consider as a simple example $f =$"add 5" and $g =$ ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/684991",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Difference in temperature due to height I observed a strange phenomenon today. I brought my milk and it was steaming hot so i left it for a while so that it could cool down a bit. It was cooled enough and there was cream on the surface and i started to drink after removing the cream. When the glass was approx 1/8 full ... | As the vessel was steel it's possible that the heat was being conducted away through the base of the 'glass'. The base would be in contact with the table.
This would cause cold milk at the bottom, it would stay at the bottom, as it's denser than the hot milk. The top of the glass would be hotter than the bottom.
When... | {
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How to calculate the right path for this spaceship? a spaceship is moving with velocity $v$ in a line, it has a distance P with a planet with $$F=-(mγ)/r^3
(γ=8/9 P^2v^2)$$
now, how can I show this spaceship turns around the planet B for 1 round, and its closest distance to the planet B, and its velocity at that poin... | The Equation of motions are:
$$m\,\ddot r-m\,\dot\theta^2\,r+F_r=0\\
r^2\,\ddot\theta+r\,2\dot r\dot\theta=0\quad\Rightarrow\\
\dot\theta=\frac{h}{r^2}$$
where $~F_r=\frac{m\,\gamma}{r^3}$
form here you obtain
$$r(\theta)=\left[C_1\sin(\omega\,\theta)+C_2\cos(\omega\,\theta)\right]^{-1}$$
where $~\omega=\frac{\sqrt{h^2... | {
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I don't understand Wigner's friend paradox The Wigner's friend experiment goes like this:
Say Wigner instructed his friend to perform Schrödinger's cat experiment in a laboratory while he work from home, his friend made the measurement and email Wigner about the result. The paradox is the state of the cat is defined fo... | The important part of the thought experiment is the time where Wigner's friend knows the cat is dead but Wigner himself has not yet read the email.
After Wigner reads the email, he and his friend will agree that the system has collapsed and the paradox disappears.
I would say that Wigner knowing the result eventually i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/685492",
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What is causing the diffraction pattern on my ceiling? When I wake up in the morning and look at my curtains, I see a pattern on the ceiling made by the light going through the gap between my curtains. I have added a picture of it below. I remember from high school that when a laser was being shot through a very thin s... | It looks as though it may be a reflection off the curtain rod.
| {
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Do light particles have thrust? I understand that nothing is faster than light and that it can not escape a black hole. However, light particles may be fast, but perhaps it can't escape a black hole due to it's lack of thrust power? I can't reasonably push an object with light. a rocket has thrust but can't go as fast ... | As pointed out by joseph, light has indeed a momentum.
Its extremely small, still it is measurable. The origin of this property can be found in the wave particle dualism of electromagnetic radiation.
In space, the momentum of photons is even being utilized as a form of repulsion based thrust with the help of solar sail... | {
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How is classical mechanics recovered when the commutator is zero? If $X$ and $P$ commute, then the rate of change of expectation value of $X$ becomes zero, assuming
$$\frac{d}{dt} \langle X \rangle= \langle [X, P^2+V(x)] \rangle=0.$$
This is not what classical mechanics says, is it?
| One has to be careful in discussing the transition from quantum to classical mechanics. First, by Dirac quantization (see also this post):
$$
[\hat A,\hat B]\to i\hbar \{A,B\}_{PB} +{\cal O}(\hbar^2) \tag{1}
$$
where $\{A,B\}_{PB}$ is the Poisson bracket. Thus, if you naively set $\hbar\to 0$, you get nonsense. In p... | {
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How to add angular velocity vectors? I was reading David Morin's mechanics book and came across this problem.
And here is the solution provided:
I am just wondering why you can express the total angular velocity of the coin with respect to the lab frame by simply adding the different angular velocity vectors. In the ... | Starting with the rotations matrix
\begin{align*}
&[\,_1^3\,\mathbf S\,]=[\,_1^2\,\mathbf S\,]\,[\,_2^3\,\mathbf S\,]\quad\Rightarrow\quad
[\,_1^3\,\mathbf{\dot{S}}\,]=[\,_1^2\,\mathbf{\dot{S}}\,]\,[\,_2^3\,\mathbf S\,]+
[\,_1^2\,\mathbf S\,]\,[\,_2^3\,\mathbf{\dot{S}}\,]\\
&\text{with}\quad \mathbf{\dot{S}}=\m... | {
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Will a planet rotate if it is the only being in the universe? As a senior student , I have been wondering whatever the word inertia mean . Is inertia lying in the interaction between all the objects , or is it the nature of a space even without anything put into it ? In our life it seems like the latter , since whereve... | Rotation is a type of acceleration, and acceleration can be detected in an absolute sense. If the planet was symmetrical and rotating in the way that the Earth rotates, then with the right instruments the inhabitants of the planet would be able to detect the rotation and also the axis of rotation. An object at either o... | {
"language": "en",
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Microcanonical ensemble probability density distribution In microcanonical ensemble the probability density function is postulated as $\rho(q,p)=const.\times\delta(E-E_0)$ so the probability of an ensemble being in an element of phase space $\mathrm{d} q \mathrm{d} p$ is $\mathrm{d} P = \rho(p,q) \mathrm{d} p \mathrm{d... | There are a few concepts that should be better focused, to formulate this question precisely.
An ensemble of Classical Statistical Mechanics is the set of all possible configurations in phase space, each configuration being characterized by the set of its Hamiltonian coordinates $q=(q_1,q_2,\dots,q_N)$ and $p=(p_1,p_2,... | {
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Why are most QM Operator defined as Identity minus Generator? I am currently rehearsing my lectures in quantum mechanics for the exam. I recognized that there is a pattern for different types of operators such as: Rotation operator, Time evolution operator and so on. The way we got it presented in our course is that th... | The identity operator is the same as doing nothing. If you want to construct an operator that is 'small' it better be close to the identity. The goal is to construct a 'big' (read: finite) operator by composing (infinitely) many 'small' operators. We want to do this because these small operators are easy to study and w... | {
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Does anything in an incandescent bulb actually reach its color temperature (say 2700 K)? This question is inspired by a question about oven lightbulbs over on the DIY stack. It spawned a lengthy comment discussion about whether an incandescent lightbulb with a color temperature of 2500 K actually has a filament at a te... | The filament reaches that temperature and acts as a black-body radiator.
There is a type of measuring instrument used to measure the temperature at incandescent temperatures- called an "optical pyrometer" or, more specifically, a "disappearing filament pyrometer".
A filament, much like the filament in a bulb, is optic... | {
"language": "en",
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How did Ernest Sternglass’ phenomenologically incorrect model of the neutral pion predict its mass and lifetime so accurately? In 1961, Ernest Sternglass published a paper where, using what seems to be to be a combination of relativistic kinematics and Bohr’s old quantisation procedure, he looked at the energy levels o... | Circular arguments, arguments based on existing assumptions, all demonstrating a reluctance to abandon what you have learned in school. There’s no coincidence here. The strong force is just compressed EM force. Think of this “coincidence” as one data point, Sternglass’ greatness lies in discovering all coincidences acr... | {
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Why do we need the concept of Gravitational and Electric Potential? I understand that we need potential energy for the concept of energy conservation. However, why would we come up with a definition like 'energy required per unit mass/charge to bring the mass/charge from point A to B. The part says 'per unit mass/charg... | It is similar to a system of coordinates. When we want to know the distance between points in a room it is easy to measure directly. But for the short airline route between two cities we can use the information of latitude and longitude for each, and calculate the distance.
In the case of gravitational potential, knowi... | {
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Force of photons from the Sun hitting a football field = weight of 1 dime? I read, I think, some time ago that the "weight" of photons from the Sun hitting an area the size of a football field at noon on a sunny day would be about the "weight" of a dime?
Would appreciate it someone could flesh that out, verify if corre... | "Weight" can be understood as a type of force - standing on the floor, you impart a force on the floor.
Light can impart force on a surface due to the transfer of momentum involved. In other words, if a photon with momentum $p$ strikes a surface and is reflected in the opposite direction, a total momentum of $2p$ is im... | {
"language": "en",
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Would light bend the other way, if I use antimatter instead? Imagine the following setup: an antimatter straw, an antimatter glass filled with antimatter water and we have antimatter atmosphere just in case. My question is: does Snell's law still apply here as though they are regular matter, if I were to observe the st... | It's a no from me.
For light to bend the other way, light in antiwater would have to have phase velocity greater than $c$. This is possible in some systems (called metamaterials) but the optical properties of antiwater would have to be completely different from ordinary water - which is ruled out by existing experiment... | {
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Does SR intend to postulate the one- or two-way speed of light? I have read this question:
It follows that the two-way speed of light is invariant (in the context of relativity, "invariant" is understood to mean "invariant with respect to Lorentz transformations").
Meaning and validity of the mass-energy equivalence ... | The Einstein synchronization convention produces a one-way speed of light that is c. So the second postulate is based on the one way speed. This is justified by the isotropy of the two way speed of light and the isotropy of all known laws of physics.
In Einstein’s seminal paper he says “we establish by definition that ... | {
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Has Rindler horizon already been tested experimentally? For an accelerated frame, there is a Rindler horizon at a distance of $$X = \frac{c^2}{a}$$ where $a$ is the proper acceleration. For $a = g$ it is about 1 light year.
If one of that spacial telescopes, like the James Webb, accelerates for a little while in a dire... | No one has done this experiment because the stars do not suddenly disappear for an accelerated observer - the Rindler observer "outruns" light emitted at a distance $c^2/a$ at the time when the observer is that distance away from it, but the faraway stars have been shining for a long time and there's plenty of light fr... | {
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Centre of mass reference frame of a particle and a photon If we consider the reaction of a gamma photon with a proton, e.g.,
$$\gamma + p \rightarrow p + \pi^0$$
I wonder what would the linear momentum of the initial proton in the center-of-mass reference frame be. I am confused because this reference frame should be l... | Draw an energy-momentum diagram (adding the timelike 4-momentum of the proton and the lightlike 4-momentum photon (tip to tail) to get the timelike 4-momentum of the system). It'll look like a triangle... in fact like a Doppler-effect problem.
Then, find the component of the proton 4-momentum that is orthogonal to the... | {
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Symmetry associated to a part of a separable Hamiltonian The harmonic oscillator in 3D is:
$$H=\frac{p_x^2+p_y^2+p_z^2}{2m}+ \frac{k}{2} (x^2+y^2+z^2) = H_x + H_y + H_z,$$
where $H_x$, $H_y$ and $H_z$ are all constants of motion (alongside $\vec{L}$).
Time translation invariance implies the conservation of $H$. What is... | Well, quite generally for Hamiltonian systems, the infinitesimal symmetry behind a constant of motion (COM) is the Hamiltonian vector field generated by the COM itself, cf. this Phys.SE post.
| {
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Why is the size of image increasing as observer moves away from lens? I was using a convex lens and placed the object at principal axis at a distance from optical center lesser than focal length (between $F_1$ and optical center). Then I started observing the size of the image from other side of lens.
At first I had pl... | I suspect you are looking through the lens rather than looking at the physical image, aka "real image," that the lens would form. The Lensmaker's equation, $ \frac{1}{f} = \frac{1}{p} + \frac{1}{q}$ leads to a smaller image only for a real image (p and q both positive).
Since you are looking through the lens, you w... | {
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Is a single photon a wave plane or a wave packet? According to the definition a photon is monochromatic, so it has a unique frequency $\omega$ and thus it can be expressed as
$\psi(x,t)=\exp i(kx-\omega t)$.
This suggests that a photon is a plane wave which occupies the whole space at the same time.
But why we can say ... | One can derive the longitudinal and lateral intrinsic fields of a photon by equating the expectation values of the field operator in terms of the electric and magnetic field expectation values with the expectation value obtained with the wavefunction of two consecutive number states.
One can have a monochromatic tempor... | {
"language": "en",
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How large does $N$ need to be for statistical mechanics to be a good approximation? About how many components ($N$) does a system need for statistical mechanics to apply to that system?
I took stat mech and biophysics from the same professor in undergrad and I distinctly remember him saying that part of the reason that... | I think it's unfair to ask for an exact value for $N$ to justify all statistical mechanics. There are very many different problems and applications of stat mech, and some of them might have intrinsically low variance and work fine for relatively small $N$, whereas in other problems really require $N \rightarrow \infty$... | {
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Phase difference between two waves in opposite directions Suppose I have two waves travelling along the positive and negative $x$ axis, and are given by : $$y_1=A\sin(kx-\omega t)\,\,\,\,,\,\,\,y_2=A\sin(kx+\omega t)$$
What would be the phase difference between these two waves at a particular point ?
If I define the ph... |
I could have easily defined the waves, by keeping a positive sign in front of ωt instead of kx.
Actually, in this case you cannot do that. Here you have defined the waves in terms of $\sin$ functions. So $\sin(kx-\omega t)$ is not the same wave as $\sin(\omega t - k x)$.
However, you could have asked the question in ... | {
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How does potential energy increase with no work? If you're dragging an object up a hill at a constant velocity, work is technically 0 (as acceleration is 0), but potential energy constantly increases. How would you represent this situation mathematically, and how does the potential energy increase despite a lack of wor... | The net force ends up being 0, but you are still applying a force because gravity is pulling down.
Gravity exerts a force down the hill, so to keep the block at a constant velocity, you must exert a force opposite that. This means that work will be applied.
For example, suppose a block is falling down a vertical shaft.... | {
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Elastic potential energy and work equations Elastic potential energy is $\frac{1}{2} k x^2$ and work is $F \cdot d$. Why these numbers do not evaluate to the same value in a problem?
The change in potential energy is the work done on a spring - $W = \Delta U$. However, every time I do an example I always get that the w... | You are missing that the force changes as the spring elongates. It is 0 at the equilibrium position and it is only equal to the final force at the final extension. The factor of 1/2 accounts for the variation in the force, essentially giving you the average force.
| {
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What is the angle of a ray passing through a thin lens? Let's say I have a thin lens model of an optical system. When I have a ray that is parallel to the optical axis, the situation is quite standard - the ray refracts and passes the focal point f (see my bad drawing).
From the triangle in the picture, I can calculat... | I realized that a ray passing through the center of the lens (let's call it ray A) does not deviate from its path. And if another ray (ray B) comes in the lens with the same angle as ray A, but does not pass the center of the lens, it has to cross ray A at the back focal plane of the lens. I drew the situation on a gra... | {
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Why are quantum numbers assigned to electrons? Specifically the principal quantum number ($n$), orbital quantum number ($l$) and orbital magnetic quantum number ($m_{l}$). For systems like the hydrogen atom, these quantum numbers arise from the Schrödinger equation which involves:
*
*A potential energy function, for ... | Yes, these numbers are assigned to the electron-nucleus system. Usually (as in classical mechanics) the treatment of a hydrogen atom starts with separating the motion of the center-of-mass of the atom and the relative motion of the electron and the proton, reducing a two-body problem to a one-body problem in an effecti... | {
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Isotope that decays when ionized Some time ago, I read about a certain isotope that is stable when neutral but decays with electron emission (beta) when being completely ionized, but I can't find which one it was.
Which isotope decays when fully ionized?
| I’m nearly certain you are thinking of beryllium-7, but that you have remembered the condition backwards.
Neutral $\rm^7Be$ can decay to $\rm^7Li$ by electron capture, with energy about $\rm 860\,keV$. Positron-emission decays are always disfavored relative to electron-capture decays, because the final state with an el... | {
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How Would a Car Move in Zero-G? Consider a car floating in a microgravity environment. Assuming the engine can still function (i.e. it is surrounded by normal atmosphere; fuel can still be pumped, etc.), in what ways (if any) will the car move when the accelerator is pressed?
There is air moving into the intake and out... | The movement would depend on several factors, such as wether the engine was transverse or longitudinal. However, the most pronounced motion would be some compound form of rotation. Most of the moving parts in a car rotate, so in the absence of gravity the rotation of parts of the car would generate counter rotations of... | {
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Question about the Wave equation I have a question. I was looking for the Wave equation (first Eq. of this wikipedia page).
I saw for the first time a version of this equation during an Acoustic course, where we obtained it for the sound wave combining the Euler equation, the Continuity equation, the general gas equati... | If you had to write down a generic Lagrangian for a scalar field that is invariant under rotations and space-time translations it would look something like
$$\mathcal L = \frac{1}{2}\left(\frac{\partial \phi}{\partial t}\right)^2 + \frac{1}{2}v^2 \nabla^2\phi + A\phi+B\phi^2 +C\phi^3 + \mu (\nabla^2 \phi)^2 +... $$ The... | {
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"answer_id": 2
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How to affirm whether a frame of reference is Inertial or non-inertial? As far as I know, inertial frame of reference are the ones where the all the three Newton's laws of motion hold. Having this definition we can then identify all such frames of reference which are inertial, if we have an inertial frame of reference,... | You don’t need a second frame to determine if a frame is inertial. Simply compare the coordinate acceleration in the frame to the proper acceleration measured by momentarily co-moving accelerometers. If they match then the frame is inertial. If they do not match then the frame is non-inertial and the difference between... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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What Lorentz symmetries do electric and magnetic fields break? When we turn on an external (non-dynamical) electric or magnetic field in (3+1)-dimensional Minkowski space we break rotational invariance because they pick out a special direction in spacetime. Does this also break boost invariance?
What about in (2+1)-dim... | The electromagnetic field on spacetime is actually Lorentz invariant. It's this conflict between this symmetry group of electromagnetism and the symmetry group of classical mechanics, which is the Galilean group, that led Einstein to special relativity.
The electromagnetic field on spacetime is a single field, it can't... | {
"language": "en",
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Can the Newton's laws be derived from each other in a specific order only(2nd from 1st only and not from 3rd)? In my opinion we can derive Newton's laws in a specific order only that is 2nd from 1st and 3rd from 2nd and first only.
Let us suppose there is a body B which is in its initial state P(i). Now as per Newton's... | This is a common misconception that Newton's first law is unnecessary or that it can be derived from Newton's second law; ''If we put the force equal to zero in Newton's second law then we get the first hence the first law is redundant''. But this is wrong. What is a force? Newton's first law defines what a force is! A... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Can we derive Boyle's law out of nothing? My textbook states Boyle's law without a proof. I saw Feynman's proof of it but found it to be too handwavy and at the same time it uses Boltzmann's equipartition theorem from statistical mechanics which is too difficult for me now.
So to state roughly what Boyle's law is, it s... | The law can be derived from the kinetic theory of gases. Several assumptions are made about the molecules, and Newton's laws are then applied. For $N$ molecules, each of mass $m$, moving in a container of volume $V$ with a root mean square speed of $c_{rms}$, the pressure, $p$, exerted on the walls by gas molecules col... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
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Why is amplitude going to infinity in forced damped oscillator at resonance? I'm trying to find the amplitude of steady state response of the following differential equation:
$$\ddot{x}+2p\dot x + {\omega_0}^2x=\cos(\omega t)$$
A particular solution is
$$x_p=\Re{\dfrac{e^{i\omega t}}{\omega_0^2 - \omega^2 + i2p\omega}... | Without math (or almost ;-)- a system driven by an external forcing function at resonance is accepting energy input that the system cannot easily get rid of. This makes the energy pile up in the system which makes the amplitude of the oscillations grow over time and get big enough to blow it up.
In electrical systems l... | {
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How is conservation of momentum applied even if there is component of $mg$ acting as external force?
In this question momentum is conserved along X' direction. But there is a component of mg along the plane which means that there is external force in X' direction. So how is conservation of momentum applied here??
| Gravity is a non impulsive force. it means it takes enough time to cause action and does not change momentum in an instant. So in time just before and after collision, momentum is conserved and gravity is neglected for such small time.
it will work in all horizontal collisions like
BUT
if ball does not strike horizonta... | {
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Easier way to calculate the expected value of $p^2$ I was doing some math with some wave functions when I stumbled upon this one:
\begin{equation}
\phi(x) = \sqrt{\frac{2 a^3}{\pi}} \frac{1}{a^2 + x^2} \mathrm{e}^{i k_0 x}
\end{equation}
I wanted to calculate the uncertainty in the momentum so I changed to $p$-represen... | You don't have to change to p-representation. Just use the fact that p = hbar/i * d/dx and do the math. And your p-representation wavefunction is just an exponential (apart from the absolute value). Use the gamma function (it is really easy).
| {
"language": "en",
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"source": "stackexchange",
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Standing wave in a string clamped at one end *In the case of a standing wave formed with one end clamped (fixed), there is an anti-node at the free end irrespective of the overtone.
My question is why is there has to be an antinode. Is there any intuition behind it?
| At the free end, the restoring force is zero (since it's free). This means the slope of the string at the end must be zero.
Why? The restoring force comes from the vertical component of tension, and tension is tangent to the string always. So if the restoring force is zero, the slope must be zero.
Only anti-nodes have ... | {
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What are the exact axioms to uniquely define the Minkowski metric tensor as a bilinear map? I have read that the definition of a metric tensor is a map with the following axioms:
*
*a bilinear form from the tangent vector space (of a smooth manifold) to the real field
*symmetric
*nondegenerate
[Question] Now, from... | Yes, that's enough.
To be pedantic, though, a metric always has a positive definite signature, aka (+,+,+, ..,+) whilst a semi-metric can have arbitrary signature. A manifold with a metric is called a Riemannian manifold whilst a manifold with a semi-metric is called a semi-Riemannian manifold. Often the qualifier 'pse... | {
"language": "en",
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How to make the Moon spiral into Earth? I recently watched a video of what would happen if the Moon spiraled into Earth. But the video is pretty sketchy on the physics of just what would have to happen for that to occur. At first I thought I understood (just slow the Moon down enough), but my rudimentary orbital mechan... | The easiest way is to slow the moon down progressively until atmosphere does the job. But it would be catastrophic, of course.
Supposing that the moon is spiraling down on earth:
1 - Higher tides, huge waves and probable coast devastation.
2 - Once it get's close to Roche (18,470 km) limit it would star to crumble and ... | {
"language": "en",
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How to use a piecewise acceleration function to get a position function? This should be a relatively easy problem but I think I am missing something somewhere. This problem consists of a object that is being thrown into the air at
$t = 4s$ at a velocity $v_0$
here is my acceleration function:
$a(n) =
\begin{cases}
0, ... | Your integration is correct. It just needs some completing-the-square TLC.
$$
\frac{1}{2} g t^2 - g t t_1 + v_0 t - \frac{1}{2} g t_1^2 + g t_1^2 - v_0 t_1
$$
$$
\frac{1}{2} g\left( t^2 - 2 t t_1 + t_1^2 \right) + v_0 (t-t_1)
$$
$$
\frac{1}{2} g\left(t - t_1 \right)^2 + v_0 (t - t_1)
$$
which is what your PS should hav... | {
"language": "en",
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Differential equation of a series $RLC$ circuit driven by a DC voltage source? From math below it seems no oscillations are possible and the steady state reaches instantly. I know this is wrong but I'm new to differential equations and don't see my mistake.
Summary: For the initial conditions on capacitor
$$v(0) = 0, \... | TL;DR In the procedure you posted you forgot to include particular solution. The homogeneous solution will always evaluate to $0$ when used as a solution to the general differential equation.
Homogeneous solution
The roots of the differential equation
$$v''(t) + 2p v'(t) + \omega_0^2 v(t) = \omega_0^2 V$$
are $q_{1,2}... | {
"language": "en",
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Dirac spinor definition is it right to say that the Dirac spinor is a mathematical representation of a wave-function that satisfy the Dirac equation? or are there more requirements to it?
| Honestly, I somehow dislike this point of view for the simple reason that in order to state the differential equation you must first have a definition of the object which should solve it. Let me state this differently. A differential equation is an equation of the form ${\scr D}\Psi=0$, where $\scr D$ is one differenti... | {
"language": "en",
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How do we find the centripetal forces of 3 planets revolving around a point given that they have the same mass? Let's say we have three planets revolving around a point. We know that the force of gravity acting on all of these planets can be taken from $g = G{m_1m_2 \over r^2}$. We can derive the velocity of these plan... | For fun:
The three body problem in general has to be solved numerically. The mathematical setup is given here.
| {
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Why are kinetic energy of electrons and potential energy of electron - electron interaction universal operators? Time indepedendent Schrödinger equation for a system (atom or molecule) consisting of N electrons can be written as (with applying Born - Oppenheimer approximation): $$ \left[\left(\sum_{i=1}^N - \frac {h^2}... | The Born-Oppenheimer approximation introduces a dependency on the nuclear coordinates. The operator $\hat V = \hat V(R)$ can be seen as function of these parameters. We solve the electronic time independent Schrödinger equation only for one particular choice of $R$ and in that sense, the solution is not universal, sin... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/695373",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Microwave inside-out cooking true/false The wikipedia article on microwave ovens says
Another misconception is that microwave ovens cook food "from the inside out", meaning from the center of the entire mass of food outwards.
It further says that
with uniformly structured or reasonably homogenous food item, microwav... | You guys are complicating the whole thing.
Butter melts at a relatively low temperature. So too, the difference between "solid" and "liquid" is very small. Microwaves penetrate from around outside of a food stuff about ½". How thick is a stick of butter? Just over an inch. If microwaves pass into food ½" then they pass... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/695681",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why should a black hole be infinitely dense? I have been listening to this on Discovery for centuries of my childhood!! That when the heavy core of a star collapses under its own gravity, it shrinks to an infinitely dense point called "singularity". However, recently I was introduced to wave mechanics and The Schroding... | This is one of the currently unanswered questions in physics. The singularity of a black hole is a place where the spacetime curvature is very high (so general relativity is important), and where the size is very small (so quantum mechanics is important). Therefore, the general expectation is that we would need a quant... | {
"language": "en",
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"source": "stackexchange",
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Stress tensor and equality of normal stresses on opposite faces Consider a body arbitrarily loaded as shown,
At a particular point in the body, I take an element and show all the stresses acting on its faces.
To specify a plane I will be using the the axis which is perpendicular to it. For instance, the front face is... | The point is that the claimed identity is valid in the limit of vanishing size $2\delta$ of the considered cubic element. If the element is cetered on the origin and you consider two opposite faces, e.g., normal to the axis $z$, you have, assuming that the stress tensor is differentiable at the origin,
$$\sigma(0,0,\pm... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Gravitational potential energy of a two body system from infinity In determining gravitational energy of a two body system,we define it as the negative work done by gravitational force in bringing those two bodies from infinity to a distance $r$ with respect to the first body.
Now in doing this, we say that work done b... | Gravitational potential energy in a two body system is a function of the separation of the two bodies, not their absolute locations. So if you want to use a work-energy argument to determine the potential energy at a separation $r$ then your initial condition is that the two bodies are separated by an infinite distance... | {
"language": "en",
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In radiotherapy, why do normal tissiue or organ cells not die of radiation? In radiotherapy, why don't normal tissiue cells or organ cells in the way of incoming radiation die, but tumours die instead?
| There are two main reasons for this. First, there isn't a single direction the radiation is applied from. Instead, beams from multiple directions are directed at the affected body part. The part where all the beams overlap is the volume recieving the highest radiation dose. Ideally this is where the pathological tissue... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is power a cumulative quantity? Is the power needed to do a particular work cumulative? Like, the power needed to do work W for one second is P, is the power needed to do the same work for 2, 3, 4... seconds equal to 2P, 3P, 4P...?
| Power is work divided by time. Or the rate at which work is done. So the average power required to do the same amount of work in twice the time would be $\frac{P}{2}$
I exactly don't know what cumulative quantity means. But I feel a cumulative quantity is something which adds up over time or space (like mass, distance,... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/696619",
"timestamp": "2023-03-29T00:00:00",
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Why does plane mirror form image of same size as object?
Plane mirror form images of the same size as of the object.
Also if we need to see ourselves completely in mirror, we would require a mirror of at least half out height.
Assume I am 6 feet tall then if I use a mirror 3 feet tall then how come me and my image ha... | The optical ray diagram of a plane mirror may help
Also here:
Let’s say you have a toy car, and it’s sitting in front of a regular bathroom mirror. The distance between the car and mirror is called the object distance, and it’s always positive. If you look at the image of the toy car in the mirror, it will appear to... | {
"language": "en",
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Is potential difference always required for current? Say we use a cell to give rise to a current in a circuit and then remove the cell such that the circuit doesn't break. It means that no potential difference exists between any two points in the circuit since a circuit wire with current is neutral. So will the circuit... | . . . . we use a cell to give rise to a current in a circuit and then remove the cell such that the circuit doesn't break.
The circuit whether there is a break or not can now being considered as having an inductance, resistance and capacitance with the capacitance easier to visualise if there is a break in the circuit... | {
"language": "en",
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Nature of force between two permanent magnets When we put two permanent magnets close to each other they repel or attract each other and this process increase their kinetic energy. I know that magnetic force can't increase kinetic energy so plz explain which type of force is this.
|
I know that magnetic force can't increase kinetic energy so plz explain which type of force is this.
Assuming you meant potential energy when you said, "kinetic energy."
If two magnets are oriented so that they repel each other, then you increase the potential energy of that system when you push them closer together.... | {
"language": "en",
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Interpretation and units of propagators Quantum field theory is usually expressed in natural units in which $\hbar=c=1$. This simplifies equations and one can always get back to other units by inserting $\hbar$ and $c$ in appropriate places. However, to me this is not always straightforward.
In the second edition of th... | Yes, it's logical. With natural units $c=\hbar=1$ we usually work in mass dimension, so lengths and times are $-1$ (in other words, change signs in what follows if you prefer to think in terms of length), $\partial$ is $+1$, $\delta^{(4)}$ is $+4$, and $D$ is $+2$. This is the only way to determine the propagator dimen... | {
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Why is enthalpy discussed exclusively as $\Delta H$ and doesn't make sense as just $H$ For a chemical reaction, it is well-known that
$$\Delta H = H_{\text{products}} -H_{\text{reactants}}$$
Are we physically unable to determine an absolute $H$?
| Yes; since we are unable to determine an absolute energy $U$ and since enthalpy $H\equiv U+PV$, we are unable to determine an absolute enthalpy (or Helmholtz free energy or Gibbs free energy or chemical potential or anything that includes $U$).
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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How to find the velocity of point of intersection?
My approach: The velocity of the point of intersection u will be in horizontal direction due to symmetry about x-axis.The velocity v of the rod makes angle $\theta$ with the vertical.Thus, $v\sin \theta=u$.
But the correct answer is A. Can anyone please point out wher... | TL;DR You have correctly identified that the intersection point does not travel along the vertical axis, but your conclusion about the horizontal velocity is not correct. I show here how to solve this problem by following: (i) geometric approach, from which you will see what is the problem with your conclusion, and (ii... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Would a head-on collision between two stars create heavier elements? I was thinking about Przybylski's Star, and I was wondering how it was possible that so many heavy elements ended up in the star, such as einsteinium, californium, berkelium, etc. But there is unusually low amounts of iron and nickel. Also, I read abo... | Whether we consider the usual gravitational in-spiral case or an unlikely head-on collision, two neutron stars that are close enough to collide will also have powerful gravitational forces between them, accelerating them to high speeds.
By conservation of energy, you can expect their velocity to be roughly the escape v... | {
"language": "en",
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Can observation by animals collapse the wave function? In Schrodinger's cat, somehow the cat is dead and alive at the same time until someone opens the box, observes that cat's state, and collapses the wave function. Of course, something can't be dead and alive at the same time (unless...), so this makes no sense.
I st... | Let's suppose the cat will be killed when an atom undergoes radioactive decay. What happens is:
*
*A live cat goes in the box.
*The cat knows it is alive. From the cat's point of view, the wavefunction has collapsed and the atom has not decayed. From the human's point of view, outside the box, the wavefunction ha... | {
"language": "en",
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Covariant derivative with an upper index in terms of Christoffel symbols I have encountered expression
$$\frac{1}{2}\left(2 \dot{g}_{\mu}{}^{\lambda ; \mu}-\dot{g}_{\mu}{}^{\mu ; \lambda}\right)$$
in a GR paper.
Here we assume to be working with the de Sitter metric $g$ and $\dot{g}$ is some two tensor.
I know that in ... | In General Relativity, the covariant derivative is always taken to be compatible with the metric. In other words, $\nabla_{\mu} g_{\nu\tau} = 0$ and $\nabla_{\mu} g^{\nu\tau} = 0$. This implies that $\nabla_{\alpha}(g^{\lambda \gamma}\dot{g}_{\mu \gamma}) = g^{\lambda \gamma} \nabla_{\alpha}\dot{g}_{\mu \gamma}$.
As fo... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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QM perturbation degenerate case $$
\begin{aligned}
0 &=\left(E-H_{0}-\lambda V\right)|l\rangle \\
&=\left(E-E_{D}^{(0)}-\lambda V\right) P_{0}|l\rangle+\left(E-H_{0}-\lambda V\right) P_{1}|l\rangle
\end{aligned}
$$
We next separate (5.2.2) into two equations by projecting from the left on (5.2.2) with $P_{0}$ and $P_{1... | On the LHS of your 4th equation, the last term is $-\lambda P_1 V P_1 |l>$. Since $P_1^2=P_1$, this is equivalent to $-\lambda P_1 V P_1^2 |l>$. Then the rest is just a rearrangement of your 4th equation. you move the 1st term to the RHS, and multiply by the inverse operator in the parenthesis (its inverse exists in th... | {
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Why does the vapour bubble in an inkjet printhead collapse so fast? I am studying the inkjet printer in detail. I have come across thermal inkjet printing technology (bubble inkjet technology) and this short discussion below.
We create a water vapour bubble by heating a resistance, which displaces ink and forms a drop ... | I can't compete with Niels' years of experience in the field, but I'll add a note explaining why the bubble collapse is so fast once the heating is turned off.
If you have ever inflated a party balloon then you will know that the tension in the rubber skin of the balloon exerts a pressure on the air inside. That's why ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/698471",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Derivatives of exponential operator I'm reading the paper (eq.(14) and eq.(10)) and got curious how the paper uses this equation:
$\frac{\partial}{\partial c}\exp(-i\Delta t (X+cY)) = \exp(-i\Delta t (X+cY))(-iY\Delta t + \frac{\Delta t^2}{2}[X+cY, Y] + \frac{i\Delta t^3}{6}[X+cY, [X+cY,Y]]+ \cdots )$
Can anybody help ... | The standard identity for the derivative of the exponential map is
$$
\partial_c e^{M(c)}= e^{M} \left (1-\frac{1}{2}[M,\bullet]+ \frac{1}{6}[M,[M,\bullet]]+... \right ) \partial_c M,
$$
where $\bullet$ pipes the argument on the right in case you were not familiar with the adjoint map.
So, just plug in, $M= -i\Delta t ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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If the creation operator has no eigenstates, then what happens when you "use" it? According to Is there a simple way of finding the eigenstates of the creation and annihilation operator in QM?
The creation operator has no eigenstates. But one postulate of QM says that the state of a system after measuement using an ope... | Not all operators are observables. Only self-adjoint operators are observables. A property of self-adjoint operators is that they have real eigenvalues.
The creation operator is not an observable and is not a self-adjoint operator. It's okay for an operator not to have eigenstates and not to be an observable.
Only obse... | {
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Ehrenfest theorem proof I'm using this resource along with Griffith's Introduction to Quantum Mechanics to try and reproduce the Ehrenfest theorem.
From equation $(176)$ in the link above, we have:
$$\frac{d\langle p\rangle}{dt}=\int_{-\infty}^{\infty}\left[\frac{-\hbar^2}{2m}\frac{\partial}{\partial x} \left( \frac{\p... | Fun fact; it's not true in general! For example, this answer lists an example of a function that is totally square-integrable and therefore viable as a wave-function but whose derivatives do not have a well-defined limit at infinity.
The real reason you can get away with doing this approximation is that we assume impli... | {
"language": "en",
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In a capacitor, is there energy in the electric field, is there potential energy, or both? The electric field between two capacitor plates is very simple.
$$
\vec{E} = \frac{Q}{\epsilon_0 A} \vec{e}_z
$$
I can get the energy stored in the field by integrating the energy density, $u_e$, over the volume (between the pl... | Energy stored in a capacitor is electrical potential energy, and it is thus related to the charge $Q$ and voltage $V$ on the capacitor. We must be careful when applying the equation for electrical potential energy $\Delta PE = q \Delta V$ to a capacitor. Remember that $\Delta PE$ is the potential energy of a charge q g... | {
"language": "en",
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EFT unitarity violation Standard Model Effective Field Theory is said to not be a complete model because the presence of nonzero anomalous, say, Quartic Gauge Couplings would violate tree-level unitarity at sufficiently high energy, i.e. if you don't constrain the energy considered
Can someone explain why exactly? is t... | There are no couplings in the Standard Model that violate tree-level unitarity at any energy. The reason we know the Standard Model is incomplete is experimental, not theoretical: it does not contain gravity, or dark matter.
In the Standard Model without the Higgs, there are couplings that violate tree-level unitarity;... | {
"language": "en",
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Work of a spaceship in circular motion Say a spaceship is traveling though space in a uniform circular motion.
It's not orbiting any planet, it just flies in circles in an empty space.
The only force working on the spaceship would be the centripetal force caused by the ship's engine.
Thus, the work would be $0$, as the... | This is a continuation of Andrea's and Claudio's answers:
From this link
Work refers to an activity involving a force and movement in the direction of the force. A force of 20 newtons pushing an object 5 meters in the direction of the force does 100 joules of work.
Energy is the capacity for doing work. You must h... | {
"language": "en",
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What does the Lorentz factor represent? How can the Lorentz factor $\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$ be understood? What does that mean? For example, what is the reason for the second power and square root? Why not $\frac{1}{1-\frac{v}{c}}$, or what would happen if it took that form?. Can you point me to other physi... | The Lorentz factor can be understood as how much the measurements of time, length, and other physical properties change for an object while that object is moving.
What you have named $r^2$ is indeed known as $\beta^2$ which is the ratio between the relative velocity between inertial reference frames and $c$ the speed o... | {
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Notation for rule of thumb, without breaking dimensional homogeneity? I'd like to know how to write rules of thumb in a concise way, without breaking dimensional homogeneity.
For example, if a runner has an average speed of ~10 km / h, an approximation of the covered distance would be
$\mathrm{distance} \approx \mathrm... | My preference for such things is
$$\left[\frac{\mathrm{distance}}{1\ \mathrm {km}}\right] = 10\left[\frac{\mathrm{duration}}{1\ \mathrm{hr}}\right]$$
As another example, the electron plasma frequency is given by $\omega = \sqrt{ne^2/\epsilon_0 m}$. Since all but one of the quantities on the right-hand side are constan... | {
"language": "en",
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Regarding the action of Time reversal on Dirac spinors I'm inquring about the difference between notions of time reversal found in Streater & Wightman's "PCT, Spin and Statistics, and All That", and this accepted answer from Chiral Anomaly. While both agree $\mathcal{T}$ is anti-unitary and $\mathcal{C}$ is unitary, an... | There are two definitions of time reversal, one of which changes particle to antiparticles. The second, the Wigner definition, does not and is the one usually used these days.
| {
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Quality factor of LCR circuit If we are given a parallel or series LCR circuit, we know the quality factor of these circuits ( which we can see in many books). But if we are given a LCR circuit with the three components connected in series or parallel as we like, say resistor is connected in series to both inductor and... |
Now here we have a simple deviation from our traditional series or parallel circuit. so wouldn't this change in configuration also change the quality factor of the circuit.
Yes, of course it would. It's not the same circuit anymore. There would be similarities, but you can't use the common equations for series or... | {
"language": "en",
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What is the meaning of an object having an uncertainty of velocity of 2 $\rm m/s$? In several questions we are given the uncertainty in velocity of an object and are asked to calculate the uncertainty in position of an object?
Well my doubt is that,as when we say that the uncertainty in position (of an let's say electr... | When you say that electron position is uncertain by $\pm 2\,\rm nm$, it means that whatever electron position you have calculated/measured, you may be wrong by 2nm offset. That is, in reality electron could be anywhere within 2 nm radius of your target position coordinate in position vector space.
Same goes about speed... | {
"language": "en",
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Force between two protons Yesterday my teacher was teaching about the production of photons, he told that photons are produced when the electron move from a higher energy level to a lower energy level then suddenly a idea struck in my mind that if electrons are responsible for photons and photons are responsible for el... | Photons are the carrier of the electromagnetic force. So any charged particle exchanges photons with another charged particle to transmit the force. Electrons aren't the only particles that can emit virtual photons , any charged particle can do it.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Why doesn't the non-degeneracy definition of the metric tensor assure $g(v,v)=0\implies v=0$? We know that a defining property of the metric tensor is that it is non-degenerate, meaning $\forall u,\, g(v,u)=0\implies v=0$. Yet from a textbook I read that $g(v,v)=0$ does not assure $v=0$. Why is this? Can't we simply le... | I think this is a question of logic:
Suppose $$g(v,v)= 0 \Longrightarrow v=0 \tag{1} $$ holds. Then we can conclude
$$\forall u:\quad g(u,v)=0 \Longrightarrow v=0 \quad, \tag{2}$$
by choosing $u=v$. However, the converse must not be necessarily true: Even if $(2)$ holds, we cannot conclude from $g(v,v)=0$ alone that $... | {
"language": "en",
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Electromagnetic forces due to a current carrying wire on a stationary charge due to length contraction Consider a current carrying wire. There is a stationary charge $q$ at a distance $r$ from wire.
In lab frame when the electrons in wire are moving at $v_1$ velocity we say that there is some linear charge density of ... |
But it doesn't happen. Why?
The electrons don’t have a fixed separation in their rest frame. So when you change the current you also change the separation in the electron’s rest frame. Changing the current in the wire is not a boost.
| {
"language": "en",
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Why do we use different differential notation for heat and work? Just recently started studying Thermodynamics, and I am confused by something we were told, I understand we use the inexact differential notation because work and heat are not state functions, but we are told that the '$df$' notation is only for functions... | $ df,\,\Delta f$ and $\delta f$ are associated with the idea of a change from an initial value to a final value.
So $\Delta f$ or $\delta f$ are equal to $f_{\rm final}-f_{\rm initial}$ and $df$ when the change is infinitesimal.
As you have pointed out with work and heat there are no initial and final states but it is ... | {
"language": "en",
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A question regarding excitation of electrons in atomic orbitals In Bohr's model of an atom, the formula used to find the energy between the 2 orbits and wavelength of emitted photon was valid only for single electron species like hydrogen.In the case of a multi-electron system like in the picture given above will the e... | The electron can go to any state allowed by the selection rules for the corresponding type of transitions considered (e.g. electric dipole transitions). So this means there are in general different decay channels available for the electron. Which channel it takes is a random process, with a statistical weight given by ... | {
"language": "en",
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Do the components of a force written for a purpose actually exist? On an inclined plane if you put a box, the force of gravity $mg$ is written as sum of two forces $mg\sin\theta$ and $mg\cos\theta$ where $\theta$ is the angle the incline is making with earths surface. Do these forces $mg\sinθ$ and $mg\cosθ$ actually wo... | I am tempted to say that in the larger picture, given that the force $m\vec g$ comes from interaction with the earth, the components of the vector we are considering simply happen to be in the direction in which something of our interest is happening, the direction of the incline plane in this context, and thus $mgsin\... | {
"language": "en",
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Why is Avogadro constant used to calculate the number density? My book says:
The number density of particles is $nN/V$, where $n$ is the total amount of molecules in the container of volume $V$ and $N$ is Avogadro's constant.
I can do something with the concentration $n/V$, it tells me how many moles of a particle I ... | You are converting between absolute number of particles per volume and mol of particles per volume. The total number of particles is obtained by multiplying the moles with Avogardro's constant. Lets say I have 1 mol per volume. How many particles in absolute numbers do I have per volume? To answer that question you mul... | {
"language": "en",
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Difference between 2 points a circuit I am asked to find the voltage difference between points A and B, namely $V_a - V_b$ of the following circuit:
I don't exactly know how to approach this however. Is it as simple as going counter clock wise from A to B (since this path doesn't have an opening) and counting the volt... | I recommend you setup the potential-difference equations. From your schematics it follows:
$$\varphi_Y - \varphi_B = +10 \text{ V}$$
$$\varphi_Y - \varphi_A = +20 \text{ V}$$
From this you can easily find what is $\varphi_A - \varphi_B$.
| {
"language": "en",
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Is it possible to derive Navier-Stokes equations of fluid mechanics from the Standard Model? We know that the Standard Model is a theory about almost everything (except gravity). So it should be the basis of fluid mechanics, which is a macroscopic theory from experiences. So is it possible that we can derive equation... | The answer is no, here is why.
The Standard Model lets us predict (among other things) experimental outcomes of tests run in particle accelerators, at the scale length of ~much smaller than a proton and truly gigantic energy scales (billions of electron volts), where the number of particles in the system is of order ~a... | {
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Why do the electric field lines not originate from a positive charge in the following situation? Consider two fixed positive point charges, each of magnitude $Q$ placed at a finite distance apart. Let point $O$ be the midpoint of the two charges. We can see that the electric field at $O$ is zero, but for any other poin... | Electric field lines do originate only at charges, but they can cancel out.
*
*Consider point O. From the top charge, a field line points downwards in this point. From the bottom charge, a field line points upwards in this point. Their effects cancel out and there is no net field at this point O.
*Now look slightly... | {
"language": "en",
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More general propagator of a real scalar field I have some Lagrangian containing a real scalar field $\phi$ with mass $m$. Let $A \in \mathbb{R}$ be some constant. The Lagrangian takes the form:
\begin{equation}
\mathcal{L} = -\frac{A}{2} (\partial_\mu \phi)^2 - \frac{1}{2}m^2 \phi^2 + \mathcal{L}_{\phi \phi \phi} + \m... | *
*On one hand, if $A\equiv 0$, then the field is non-propagating, and one cannot construct a scattering theory. This is OP's case.
*On the other hand, if one makes a field-redefinition
$$ \phi^{\prime}~=~\sqrt{|A|}\phi, \quad m^{\prime}~=~\frac{m}{\sqrt{|A|}}, \quad g_3^{\prime}~=~\frac{g_3}{|A|^{3/2}}, \quad g_4^{... | {
"language": "en",
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Gravitational wave radiation power from dimensional analysis Let us try to find a formula for the power emitted through gravitational waves (GW) from a binary system in quasi circular orbit. The relevant quantities are the Newton's constant $G_N$, speed of light $c$, a mass scale $M$, orbital frequency $\omega$. So I w... | The short answer is no. The problem is that a simple dimensional analysis argument tells you that you need the power to be energy per unit time, given the mass $M$, frequency $\omega$, and $G$ and $c$. Well, the energy part is "easy" in the sense that $Mc^2$ has the right dimensions. However, the problem is that there... | {
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Conservation of symmetrization in quantum mechanics I recently read about the symmetrization requirement, which my book states is axiomatic of quantum mechanics:
$$
\psi(\mathbf r_1, \mathbf r_2) = \pm \psi(\mathbf r_2, \mathbf r_1). \tag{*}
$$
It further states that if a system starts out in such a state, then it will... | If the Hamiltonian is symmetric in $r_1$ and $r_2$, then we can show that its eigenfunctions can be taken to by symmetric or antisymmetric. If we start with a symmetric state at some time $t_1$, then we can expand it over the symmetric eigenstates only. We see that it will remain symmetric at any other time $t$. The s... | {
"language": "en",
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Determining initial conditions for central force question
Question: A particle of unit mass is acted on by an attractive force of magnitude $k/r^2$ directed toward origin O. It is projected from infinity with speed $v$ along a line whose perpendicular distance from O is $d$. Find and sketch the path of the particle.
... | You are given two quantities that are conserved throughout the motion:
(a) The mechanical energy $E=\frac{1}{2}mv^2-\frac{k}{r}.$
(b) The angular momentum about the force center $L=mvd.$
| {
"language": "en",
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Recommendations for Algebraic quantum mechanics book I am familiar with quantum mechanics and quantum information at the level of Sakurai and Preskill's lecture notes / Nielsen and Chuang. I want to study the $C^*$ algebraic formulation of quantum mechanics. Are there any good books on that? Mathematical rigour is not ... | I can recommend "Araki: Mathematical Theory of Quantum Fields." The first two chapters describe an algebraic formulation of quantum mechanics (and can be read without knowledge of quantum field theory). The book begins with an outline/motivation of how an algebraic formulation of a quantum theory should look like, and ... | {
"language": "en",
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Does amplitude really go to infinity in resonance? I was recapping the forced oscillations, and something troubled me. The equation concerning forced oscillation is:
$$
x=\frac{F_0}{m(\omega_0^2-\omega^2)}\cos(\omega t)
$$
I don't understand why this equation predicts that the amplitude will approach infinity as $\omeg... | It is instructive to analyze the problem in time domain. When the driving force is $F_0 \cos(\omega_0 t)$ and the mass is initially at rest at its equilibrium position, the solution is
$$x =\frac{F_0}{2\omega_0m}t\sin(\omega_0t) $$
which represents oscillations that grow in amplitude over time.
It isn't necessarily rel... | {
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"source": "stackexchange",
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Formula For Finding Electric Field I am currently studying AP Physics and have a question about a formula. I know that from $E = \frac{F}{q}$, we get $dE = dF/q = \frac{1}{4 \pi \epsilon_0} \frac{dQ}{r^2}.$
However, I also see a formula: $$E = \frac{1}{4 \pi \epsilon_0} \int \frac{dq}{r^2} (\hat{x} \cos \theta + \hat{... | Electric field and (Coulomb) force are vectors, meaning they have a direction. So from your first equation for electric field you could have written $$d{\bf E}=\frac{1}{4\pi\epsilon_0}\frac{dQ}{r^2}{\bf\hat r}$$ where ${\bf\hat r}$ is a unit vector pointing in the direction of the electric field (or force). Now your ma... | {
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What are the differential equations that model a self-propagating gravitational wave in space-time? Light is a self-propagating wave, but it's very complicated.
Imagine, if you will, a wave in space-time that by assumption was self-propagating like light, except that it was a gravitational wave.
What are the differenti... | Light as a self-propagating wave in vacuum is governed by the free Maxwell equations:
$$\nabla^aF_{ab}=0$$The electric and magnetic fields which shows the oscillatory behavior are actually the components of the Maxwell tensor $F_{ab}$. One could ask - what are the analogues of $F_{ab}$ in GR? Note that one can express ... | {
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Quantum and classical physics are reversible, yet quantum gates have to be reversible, whereas classical gates need not. Why? I've read in many books and articles that because Schrödinger's equation is reversible, quantum gates have to be reversible. OK. But, classical physics is reversible, yet classical gates in clas... | Irreversibility comes from friction. Frictionless classical systems are (theoretically) reversible.
Practical computer design exploits friction to remove unwanted perturbations to the computer's state. Imagine that 3V is supposed to represent a "1", but for some reason a "1" at a particular node in the circuit is at 2.... | {
"language": "en",
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Can positrons attract electrons? Now, it is established that positrons and electrons have the same mass but opposite charges. Since they have opposite charges, do they create a force of attraction and collide thus annihilating each other? Or do they just "happen" to interact? If an attraction exists, can it also occur ... | As per Coulomb law,
$$ |\mathbf {F} |=k_{\text{e}}{\frac {|q_{1}q_{2}|}{r^{2}}} $$
any charged particle $q_1$ affects any other charged particle $q_2$ (unless distance between them is infinity).
So the answer is yes, positrons are attracted by electrons, and upon collision they annihilate, according to reaction:
$$ e^{... | {
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Why doesn’t horizon distance move exactly proportional to the height of the observer? For instance if someone is 8 inches above the surface of the Earth, they can see approximately 1 mile to the horizon. However, if someone is viewing the horizon at an eye level of 5’5 they can only see about 3 miles out. If the height... | On earth, the distance to the horizon, say $d_h$ and the height of an observer, say $h_o$ cannot have a linear relationship $$d_h=\text{constant}\cdot h_o$$ or proportional relationship you speak of, since this would assume the earth has some geometry other than spherical.
Instead, in reality, since the earth has curv... | {
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No net charge in conductor or no charge at all? Electrostatics I understand that there can be no net charge in a conductor because any moving free electrons would induce a countering electric field that would then cause the net E field inside a conductor to be zero. I also understand that net charge is distributed on t... | Since conductors are made of atoms, which are made of particles with charge, there are still charges in conductors. There is no net charge within a conductor; any net charge resides on the surface(s).
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/705887",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Energy to momentum Is there anyway to convert energy to motion IN SPACE? Let's say a satellite collects electric energy from sun using solar panel. Is it possible to convert it to Linear motion? The only way I know to change linear motion in space is by throwing stuff out (Ions, burned propellants etc).
| Yes, light has momentum, so you could use your collected electrical energy to create a beam of light to propel the satellite. However, you need to bear two points in mind- firstly, the recoil from the beam would be tiny compared with the energy taken to produce it, and secondly the collection of light from a solar pan... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/706069",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 6,
"answer_id": 0
} |
Are there two work-energy theorems (rotational and translational) or just a single theorem for both? Suppose a body is able to rotate. If work is applied to it along a path $C$, the traditional work-kinetic energy theorem states that
$$W_{\mathrm{translational}} = \int_{C} \vec{F} \cdot d\vec{r} = \Delta \left(\frac{m ... | To make a clarification, I am unsure about relativistic effects, so I assume we are only considering non-relativistic speeds.
To answer your question, it is important to define our translational and rotational kinetic energy. For a body undergoing both translational and rotational kinetic energy, a suitable definition ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/706701",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 0
} |
Meaning of "$=$" in $\vec{F}=m\vec{a}$ (for example) I don't understand how the two could really be one and the same. E.g. we can exert forces $\vec{F}$ and $-\vec{F}$ on a body and it's acceleration will not change. I don't think it makes sense to say that a body at rest is accelerating equally in all directions. So w... |
I don't understand how the two could really be one and the same. E.g.
we can exert forces $F$ and $-F$ on a body and it's acceleration will
not change.
$\vec{F}$ in the $\vec{F}=m\vec{a}$ is the net force acting on the body. In other words, Newton's second law of motion should be written
$$\vec{F}_{net}=m\vec{a}$$
Ho... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/706947",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 0
} |
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