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Suppose I have a system composed of two subsystems (each is a 2-state system).
Let $$|\psi\rangle = \frac{1}{\sqrt{2}}(|0\rangle_A \otimes |1\rangle_B - |0\rangle_B \otimes |1\rangle_A)$$ be an entangled state of two subsystems A and B.
Let $\hat{\rho} = |\psi\rangle\langle\psi|$ the same entangled state but described ... |
Assuming that the plank rotate in the red dot and it weights 10kg, how can we calculate the weight or force each leg is supporting?
I tried the following system, assuming the left most leg is supporting F1 and the second is supporting F2, also gravity is 9.8:
5F1 + 3F2 = 9.8 * 10
F1 + F2 = 9.8 * 10
I tried to use the... |
Hey so I know that the phase difference is simply the difference in phase between two points on either the same wave or different waves.
Phase is represented by the letter phi in simple harmonic motion. Now I would like to ask, where can you measure the phase angle from, or is it simply mathametically derived? I am as... |
Everyone knows about the famous Pringle Ring Challenge
Does anyone know how I could develop a theoretical model to predict its stability?
|
When a water bottle rocket accelerates it might leave some water behind, as is (exaggeratedly) shown in Fig 2. The smaller the nozzle the less water is left behind, but let's say the nozzle is rather big for argument's sake.
This left-behind water gives rise to additional mass flow (on top of the mass flow already caus... |
I want to calculate the wire-feed speed only using output current of the welding machine is it possible ? if so what is the formula ?
Known parameters
Weld Current
Weld Voltage
Diameter of wire
Density of material
|
On page 87 of Kittel’s Elementary Statistical Physics, it is claimed for fermions and the grand canonical ensemble:
$$Z
= \sum\limits _{\{n_{i}\}}\prod\limits _{i}\exp\left((\mu-\epsilon_{i}) \frac{n_{i}}{\tau}\right)
= \prod\limits _{i}\sum\limits _{n_{i}=0,1}\exp\left((\mu-\epsilon_{i}) \frac{n_{i}}{\tau}\right).$$
W... |
In a diode at equilibrium, there are Pn holes on the n side of the junction. These are maintained by the dynamic equilibrium of diffusion due to holes = drift due to holes. When a forward bias is applied, the amount of holes diffusing increases. That is an extra amount of holes $ P_n . e^{V_d/V_t} $ found on the n side... |
I’m reading Zeemans 1897 paper on his discoveries of line splitting.
https://articles.adsabs.harvard.edu/full/1897ApJ.....5..332Z
He cited Lorentz who says that a circular rotating “ion” ( electron presumably) will have a different rotational period between Clockwise and counter clockwise rotation but neglects to expla... |
The SSH model is a well-known topological model in one dimension, whose topological invariant is the Zak phase. The Zak phase is defined as:
$$
\gamma = \int_{-\pi}^{\pi} dk\ A(k)
$$
where $A(k)$ is the Berry connection given by:
$$
A(k) = i \langle u(k)|\frac{d}{dk}|u(k)\rangle
$$
and $u(k)$ are the periodic part of ... |
When a very sticky object hits the ground and sticks to it, does the loss of energy simply go to putting stress on the materials and trying to deform the object or ground? If the object is rigid and both the object and the ground are quite strong though, and they don’t get damaged at all (if that is possible), then wha... |
In nonlinear viscoelastic rolling contact problems (assuming a viscoelastic wheel rolling/slipping with zero slip angle on a rigid body with friction), is it possible that the contact stresses (contact pressure and the tangential stresses) become independent of the angular velocity of the wheel? If yes, then under what... |
If in beta plus decay, regular matter such as the up quark can decay into a positron, I have to wonder under high pressure, could it be possible for a quark to decay into the antiquark of its opposite?
For example, if we have a down quark under high pressure, could it decay into say an anti-up quark? Since antimatter h... |
I wanted to check the validity of an expression for the energy required to destroy an asteroid.
Assuming that the asteroid is spherical, the gravitational binding energy can be given as
$U_{GBE} = 3/5 * GM^2/ R$.
However, this is only the energy to remove aggregates away from each other. There is a required energy to d... |
I suddenly got curious in real life.
The refrigerator stops working when it reaches a set temperature.
If a hot object enters the refrigerator, the temperature of the refrigerator will rise and it will start working again.
Suppose you have two objects that have exactly the same physical properties.(Let's say object A, ... |
I was reading my notes (the topic is called 'nuclear chemistry') today when I noticed a line
"alpha (He2+) and beta (e-) can't be emitted simultaneously. After emission of alpha or beta, gamma photons must be emitted to decrease the energy of Excited Nucleus"
Can someone please explain how emission of alpha and beta pa... |
I am currently learning the basics of quantum electrodynamics. As I was reading through my book of choice on the subject (The Quantum Theory of Light, by Rodney Loudon), it occurred to me that it would be hard to describe the Doppler effect in a QED framework, because the frequencies of individual modes are guaranteed ... |
What is the expression for the covariant derivative of a Weyl spinor?
|
I've looked at the answer to this Math.SE question, but I still can't know the answer to my question here.
The following is the equation of equilibrium: divergence of stress tensor that is the sum of mechanical stress and Maxwell stress.
$$\frac{\partial}{\partial X_j} \left[L_{ijkl}(X) \frac{\partial u_k}{\partial X_l... |
I am unsure if the title of the question is appropriate, but kindly excuse me for that.
And I am also not sure if this would be a homework help problem, if it is, I apologise in advance.
While solving some problems on electrostatics with my friend, we came across a question where we solved it with two approaches and go... |
My problem ist about accelerated motion in SRT.
For example consider a charqed particle with mass m and charge q in an homogeneous Electric Field pointing in x-Direction.
We know that
$ \frac{dp^1}{d\tau} = \gamma E q$ and $m\frac{dx^0}{d\tau^2} = \frac{dp^0}{d\tau} = \gamma E q v$.
Now i've seen that you can use $\... |
This is a very simplistic view from an interested structural design engineer (retired).
Mass curves space. Taking the case of a sphere of uniform density the point at which you have as much mass outside as inside is a spherical shell two thirds the radius of the sphere. Therefore, once you pass through that shell close... |
If gravitational waves interfere with each other, and gravity is the warping of spacetime by the presence of matter, wouldn't thus waves cause the interference patterns seen in the double slit experiment and explain other quantum phenomena? All particles should warp space time, even by a little bit, thus gravity waves ... |
Does the light from my flashlight travel into space?
|
Why does electrostatic force depend on medium as in the formula of electrostatic force the $k$ constant is inversely proportional to permittivity and permittivity changes from medium to medium?
|
Reading through Theory of Elasticity, Landau & Lifshitz, I got stuck in the The equations of equilibrium of rods, on page 82. The part I do not understand is the following:
"We denote by $\vec{F}$ the resultant internal stress on a cross-section. [...] If we regard the two adjoining cross-sections as the ends of the el... |
Suppose that in our universe, there were two initial states which lead to the same outcome state after one time step. How could we possibly remember which of the two steps we came from if the arrangement of our brain cells is exactly the same independent of which state was before? Thus, is not the supposition of time r... |
Suppose we have the full band structure from tight-binding model for a hexagonal (or square) lattice. If there are only two bands, often in literature one band is called hole-band and the other is the electron-band. How does one actually calculate the electron and hole densities as function of Fermi energy? And what ha... |
When a charged sphere (charge = Q1) and an uncharted sphere of same radius are brought in contact, then the final charge on both spheres will be Q/2. But what will happen if different shapes (one charge and other uncharged) are made in contact with each other. What will be the magnitude of charge on both of them ?
|
There's a block of mass $M$ connected to a spring of negligible mass. This is set up horizontally, and there is no friction between the block and the surface. The block oscillates with simple harmonic motion, with an amplitude $A$.
A piece of clay of mass $M$ (the same mass as the block) is dropped on the block from a ... |
Right now I am learning about the first law of themodynamics. But there is a problem which bother me a bit.
As in my chemistry lesson, the teacher introduces $\Delta E =$ $Q+W % $.
However in the physics textbook, it introduces $\Delta E =$ $Q-W % $
Is the difference between the both equation is due to different perspe... |
If two point charges $q1$ $q2$ of same charge approach from infinity and we want to know work done in some distance between q1 and q2. Can we just integrate Coulombs law? Or is this increasing force between charges some how ”contained” in electric field of q2 and just solve potential difference?
|
Chern-Simons theory has action $$\tag{1} S = \frac{k}{4\pi}\int_X tr(A\wedge dA + \frac{2}{3}A\wedge A\wedge A).$$
Here, $X$ is some compact 3-manifold, perhaps with boundary, and $A$ is a connection 1-form on a principal $G$-bundle for some compact Lie group $G$.
At first glance, the theory seems to be topological, fo... |
Short Version: when we say that $(\pmb{q},\pmb{u}):TQ_{(q)}\to\mathbb{R}^{2n}$ are local coordinates for the tangent bundle of $Q$, which can be viewed as an embedded submanifold of a higher dimensional euclidean space, what is the extrinsic view of the coordinate basis vectors $\pmb{\partial}_{u^i}$ associated with t... |
For each of these 3 cases, I'm having trouble understanding...
If light is reflected, does that mean that there was not sufficient energy by the photons to excite the electrons of the surface to their higher orbitals? If that's the case, why would blue light sometimes be reflected, but not lower energy frequencies suc... |
For the first time, I'm seriously trying to put to use differential forms and exterior algebra I learned long time ago in the context of GR calculations. I found two uses: 1. for the computation of connection coefficient functions $\Gamma^i_{jk}$ and Riemann tensor in the tetrad method, and 2. for integration theory on... |
I'm taking introductory, undergraduate-level E&M, for which we're following Griffiths. In his chapter on the conservation laws, he gives the following as the statement for conservation of momentum under electrodynamics:
$$\frac{d\vec{p}_{\textrm{mech}}}{dt} = \oint_S \overleftrightarrow{T}d\vec{a} -\epsilon_0 \mu_0 \fr... |
lets say a fountain shoots water at some height $y$ then why the formula relating the initial velocity of water at the base that is required to achieve that height is:
$$\frac{1}{2}V_0^2 = g(y - y_0).$$
where does this formula came from how it is derived?
|
For a physics project , I will try to study the deviation of a sliced tennis ball after its bounce. So I'm looking at the influence of the linear speed and the speed of rotation of a ball on its deviation angle after the bounce. I need to do some experiments to verify a physics model (can be a theory or an equation). U... |
Say there's an object that becomes electrically charged and then stuck on a wall using the electrostatic attraction between the object and the wall. For the object to stay in place, there is a friction force acting from where the wall and object meet going upwards, equal to the force of gravity acting from the center o... |
I have found P=eeoV/(ktd33t), but this has "P" pressure. I need frequency vs. voltage.
|
Another mystery facing cosmologists is the accelerating expansion of the universe. In 1929, astronomer Edwin Hubble showed that the universe was expanding, but for this expansion to be justified, there must be much more mass or energy in the universe than we can see. One possible explanation for this was provided by Pe... |
What I understand after reading all answers from physics stack exchange related to residual gauge freedom and complete residual gauge fixing are as follows;
The gauge transformation is:
$A'_{\mu}$=$A_{\mu}$+$\partial_{\mu} f$, $f$ is any gauge function.
Here we can choose those four potentials only if it satisfies the ... |
lets say we have some sphere under some pressure and I want to find what is the force pressing one-half of the sphere toward the
opposite half?,lets take one piece of area then the pressure force exerted in this area is:
$$p\Delta A$$
and the horizontal component is:
$$p\Delta A cos\theta$$
book says the following:
A ... |
I am attempting to solve the equation of motion for single field inflation. The equation of motion is given by
\begin{equation}
\ddot{\phi} + 3H\dot{\phi} + \frac{dV}{d\phi} = 0
\end{equation}
In conformal time, $\eta$, with $d\eta = d t/a$:
\begin{equation}
\frac{d^2\phi}{d\eta^2} + 2H\frac{d\phi}{d\eta} + \frac{dV}{d... |
In quantum mechanics, one could write Hamiltonians for a given quantum system both in coordinate and momentum spaces as mentioned for example in Sakurai book. Does the discrete symmetries such as parity and time reversal symmetry of a given Hamiltonian changes when we change from coordinate representation and vice-vers... |
See for example this question or the answers to this question, neither of which seem to say exactly why the system Hamiltonian eigenstates (and not some other complete basis) are used. It is presumably something that baffles every person learning elementary statistical physics for the first time: why are the "accessibl... |
In Galilean dynamics, we do not have just one Euclidean 3-space $E_3$, as an arena for the actions of the physical world evolving with time, we have a different $E_3$ for each moment in time, with no natural identification between these various $E_3$s.
Sect 17.2, Chapter Space Time of Road to Reality
This paragraph c... |
So in my understanding, the RWA allows us to neglect terms that go as $e^{i(\omega+\omega_0)t}$ in an interaction Hamiltonian because if $\omega+\omega_0>>\omega_r$ where $\omega_r$ is the resonance frequency of the relevant interaction then the terms that oscillate with that high frequency tend to average out to zero ... |
I know that scientists debate if the universe is infinite, but for the purposes of this question let’s assume that the universe is finite and has a boundary. When a new black hole forms does the diameter of the universe contract slightly, since part of the space-time that makes up the universe gets folded up into the b... |
What is the restriction on the norm of the operator $L_k$ in the Lindblad master equation $\dot{\rho} = \sum_k L_k \rho L_k^\dagger + \frac{1}{2}\left\{ L_k^\dagger L_k, \rho\right\}$? Although there doesn't seem to be a specific reference that addresses this question, $L_k$ must be a bounded operator. Is it typical to... |
I am studying the spontaneously broken global non-Abelian symmetry. Suppose we have an $SU(2)$ doublet of bosons $\Phi = (\phi^+, \phi^0)^T$, with Lagrangian density
$$
\mathcal L = (\partial_\mu\Phi^\dagger)(\partial^\mu\Phi)+\mu^2\Phi^\dagger\Phi-\frac{\lambda}{4}(\Phi^\dagger\Phi)^2
$$
This theory has $SU(2)\times U... |
The parallactic angle is defined as that angle between a vector pointing toward the northern celestial pole and a vector pointing toward the northern hemisphere observer's zenith. I know the formula but how is it derived?
|
I have question about the inner product of the material derivative.
$$\frac{D\mathbf{v}}{Dt}=\frac{d\mathbf{v}}{dt}+\mathbf{v}\cdot\nabla\mathbf{v}.$$
How can you calculate the second term inner product?
$$\mathbf{v}\cdot\nabla\mathbf{v}=\begin{bmatrix}v_1\\v_2\\v_3\end{bmatrix}\begin{bmatrix}a_{11} & \cdots & a_{13} \... |
The "interpretation" of spin superposition is that a particle can be both spin "up" and spin "down" along some direction $ \vec r $ simultaneously. But what does this actually mean, since by ordinary vector addition, these two opposite vectors would cancel out to give a net result along of zero along $ \vec r $ ?
|
Is there an equation that gives you how the normal force is distributed? In particular, I am considering a basic example with a rectangular object at rest on an inclined plane. I think the biggest part of the normal force is applied at a distance down the incline from the center of mass of the object equal to the coeff... |
In the fourth edition of Introduction to Electrodynamics, a scenario is described in example 5.3 where a rectangular loop of wire supporting a mass $m$ hangs vertically with one end in a uniform magnetic field $B$, which points into the page. A current runs through the loop of wire that initially keeps the loop suspen... |
Assume a Hamiltonian $H$ with $N$ orthonormal eigenstates $\{\vert n\rangle\}$ of energies $\epsilon_n$. One can define a density of states,
\begin{align}
\rho(E)&=\mathrm{tr}\,\hat{\delta}(E-\hat{H})\\
&=\sum_{n=1}^{N}\langle n\vert\hat{\delta}(E-\hat{H}\vert n\rangle\\
&=\sum_{n=1}^N \delta(E-\epsilon_n).
\end{align}... |
A probability density function (PDF) is a function whose integral value corresponds to a probability range. Considering the PDF f(x), where x is a continuous variable over the domain $0$ to $\infty$, I know that:
\begin{equation}
f(x)dx
\end{equation}
corresponds to the probability that of finding something between the... |
According to Einstein's theory of relativity
Time slows for a individual who moves at the speed of light and time goes backward if the individual is faster than the speed of light.
So , is it that for light. Time slows down.
|
Let's say I have a capacitor defined by two perfectly conducting plates of area x by z separated by some distance y. If my understanding is correct, the Poisson equation describing the charge density of the region between the plates is given by: $$\nabla^2 V=-\frac{\rho}{\epsilon}$$
Where $V$ is the electric potential,... |
A piece of ice is floating in a glass of water. There is a small ironic ball inside the piece of ice.
If the ice completely melts, the ball will be released into the water. Then will there be any change in the water level?
|
Imagine placing a compound lens (two convex lenses, +150 mm and +75 mm focal lengths separated by 3 mm) between a light source and a screen. In the lab, I adjusted the position of the compound lens so that when it is closer to the screen, an in-focus reduced sized image forms on the screen. I then positioned the compou... |
I am curious whether there is a sense in which each of the EPR particles is in an eigenstate of some observable.
Consider a pair of EPR particles 1 and 2, of which combined state is given by
$|\Psi\rangle_{12} = \frac{1}{\sqrt{2}}(|A\rangle_{1}|A\rangle_{2}+|B\rangle_{1}|B\rangle_{2})$.
From this one gets a reduced den... |
Consider this soy sauce bottle:
The cap has two holes that are directly opposite to one another. Covering one hole, I find the soy sauce almost doesn't pour at all.
However, consider a bottle with a single hole. Wouldn't the contents easily pour out? A teapot has a single hole and it pours easily.
It seems there's a c... |
I'm looking for a 1+1D (1 time + 1 space dimension) paper model of the current $\Lambda$CDM cosmological model; if possible, one which somehow respects the scales of geodesic spacelike distances at constant cosmological times, and which shows light cones.
What I'm looking for is something like this picture on the Wikip... |
Any thing that has mass decays with some decay width, similarly if I want to explain redshift by considering massive photon, how much should be the mass?
Is it less than today's upper limit.
EDIT
Solution of wave equation
$\square \phi =0 $ gives a wave that doesn't disperse over time.
But wave solution of the form $(\... |
Zeilinger showed experimentally that increasing temperature of $\rm C_{70}$ buckyballs causes the interference pattern in the double slit experiment to smear out increasingly.In other words the interaction of the photons radiated away with the environment causes decoherence of the quantum system, see https://www.oeaw.a... |
I know from the angular spectrum method that given a field $U$ with a wavelength $\lambda$, we can decompose it with Fourier transform.
\begin{equation}
U(x, y,0) = \int \int {\tilde{U}_0(f_x,f_y)} e^{2 \pi i (f_x x + f_y y)} d f_x d f_y
\end{equation}
And propagate it along a distance $z$
\begin{equation}
U(x, y, z... |
We know that an indicator diagram can be drawn for an quasi static process only. An fast process in which there is no sufficient time for the exchange of heat can consider to be adiabatic. Can i draw an indicator diagram for it?
|
Imagine you have a cup of height $h$ which is filled with water up to $f\cdot h$, where $f\in(0,1)$. Let's say $f=\frac{2}{3}$ so it is easier to understand. Then suppose you have a straw of length $l>h$. What would be the minimum force needed for water to rise (also supposing there is an atmospheric pressure $p_0$)? I... |
The Heisenberg uncertainty principle arises from the description of matter as being represented as a wave packets, and hence its fourier decomposition having a range of multiple wave numbers in its creation, giving rise to a range of momentum associated with a specific wave packet.
Since as I understand it, the de Brog... |
In the derivation of results for an ideal gas, it is common to calculate the classical partition function for a single particle in a box. This can be done using the Boltzmann factor and integrating over phase space.
$$
Z_1 =\int e^{-\beta E(\{\vec{p},\vec{q}\} )} \frac{d^3p d^3r}{(2\pi\hbar)^3}
$$
$$
Z_1 = V \left( \sq... |
Since Schwarzchild Metric is a vacuum solution (hence won't work inside earth), what metric do we use to describe gravity inside earth? What are the conditions to derive it?
|
First consider the classical case, the simplest optical resonant cavity is a rectangular cavity whose surface is an ideal conductor. The field inside the cavity can be described by Maxwell Equations.
The field is:
$$E_x=A_1\cos\left(\frac{m\pi x}{L_1}\right)\sin\left(\frac{n\pi x}{L_2}\right)\sin\left(\frac{p\pi x}{L_3... |
As given in the picture, the scene is magnified billions of times. Now I am ignoring the force of attractions between q2,q6,q3,q7. Will there be force of attractions between q1 and q2? And suppose the number of negative charges tends to infinity? Will the force vanish?
————>*EDIT * *Can we can draw a field line betwee... |
On the usual quantum-mechanical Hilbert space, the operators q and p commute to a constant: [q,p]=i.
I'm looking for an elementary example of some Hilbert space for which 3 operators, r, q, and p, commute as follows: [q,p]=i, [p,r]=i, and [r,q]=i.
|
The topology for the lowest order $γγh$ interaction in the Standard Model is given by
where we have an intermediate top quark loop. I am confused with the charge conservation at each vertex. Since both the photon and Higgs boson are neutral, and the top quark has a charge of $(3/2)e$, I think we will need a top quark ... |
For my master thesis I am researching the heating and cooling down of a system with oil as thermal energy storage. I'll explain what and how I calculated what I have before I form my question:
I have the temperature wrt time when heating up and cooling down. I can calculate how much heat is added to the system with the... |
There are some metal oxides that are said to be extrinsic n-type and p-type semiconductors without having been doped. For example, $\mathrm{In_2O_3}$, $\mathrm{SnO_2}$ and $\mathrm{ZnO}$ are said to be n-type semiconductors, while $\mathrm{NiO}$, $\mathrm{Co_3O_4}$, $\mathrm{CuO}$ or $\mathrm{Cr_2O_3}$ are p-type semic... |
Helicity: projection of spin onto motion. Since neutrinos are massive, I can always move to a reference frame where their motion is towards the opposite direction, meaning I should reverse their helicity. Yet it's said "neutrinos can only be left-handed"; so how do you deal with this change of reference frames?
Is the ... |
I am teaching myself about open quantum systems and I am confused by the following statement on the wikipedia page about open quantum systems:
"The fact that every quantum system has some degree of openness also means that no quantum system can ever be in a pure state. A pure state is unitary equivalent to a zero-tempe... |
What is the maximum range of a shell projected across horizontal
ground from a gun with an initial speed of 300 m s-1? What will its
speed be at the highest point of its trajectory? (Ignore air
resistance.)
The questoin above, i have tried but can't get it. The answers are 9000 m; 212 m s-1. Im confused as the quest... |
In this article
https://arxiv.org/abs/1912.09634
in equation (33), the authors propose a periodic screened Coulomb potential that is just of the form
$$ V(r) = \sum_{\gamma \in \mathbb{Z}^2} \delta(r - \gamma_1 L_1 - \gamma_2 L_2)$$
where $L_1,L_2$ are two lattice vectors.
I wonder if there is a canonical more smoothe... |
Now I'm studying the phase transition of the many-body system as a school degree.
What I'm curious that, I found the meaning of quantum impurity system is : One particle interacts with an ensemble system.
Is quantum dissipative system can be one of the Quantum impurity systems?
|
I am currently working on the article "Non-Invertible Global Symmetries and Completeness of the Spectrum" (arXiv:2104.07036), and in section 5.1 the author approaches the $O(2)$ gauge theory. In order to do this he says that the group has a $1$ dim irrep of determinant, and othe $2_q$ irrep related to the charge conjug... |
Thermal velocity of electrons is in order of $10^{6}$ m/s. For electric field $E$ of magnitude 1 V/m, acceleration on electron would be in order of $10^{11}$ m/s^2. This acceleration should dominate thermal speed and drive all electrons in direction opposite to field with very great speeds. But drift speed of electrons... |
When you want to calculate the potential at the surface of the sphere, you can just use kq/r, r being the radius of the sphere. Can someone explain why?
|
The Problem
Suppose I have an open window with an area $A$, and a uniform wind source (a fan) pointing towards the window, positioned at a distance $s$ away from the window.
At the exit of the fan, let the velocity of the air be, uniformly, equal to $u$. How can one calculate the average velocity $v$ across the window?... |
I wonder whether the source $J$ in QFT can make one to quantize the field when the system is in the excursion to the minimum. Precisely, I want to know that following process makes sence.
Suppose, I have a real scalar $\phi^4$ theory, which originally has
$\mathbb{Z}_2$ symmetry but it is spontaneously broken. So, whe... |
In a circuit containing resistors, the current remains the same throughout. This can be verified by Ohm's Law. But by the expression $I = q/t$, the charges passing through the resistor reduces per second. Then how the value of current remains same all over?
|
Say there's an object, a rectangular prism, that becomes electrically charged and then stuck on a wall using the electrostatic attraction between the object and the wall. The object and wall are pretty strong, rigid, and flat. The torque created with the vertical unalignment of the friction and weight forces means ther... |
In a closed box in inertial motion a ball bounces up and down vertically. Apart from this movement, the ball is motionless relative to the box. The trajectory of the ball seen by a stationary observer will be tilted toward the front, not vertical.
Next, we do the same experiment but with a photon. The photon is directe... |
I will get right to the question; for readers unfamiliar with its genesis, I append a background section below.
I want to know how testable the prediction is that the water in a rotating bucket would experience a centrifugal pseudo force in the closest approximation to empty space we have access to (i.e., as far away f... |
I have taken some measurements of refractive index (refractometer (commercial Brix meter), nD20 i.e. 20 degrees C and 589 nm) and density of sucrose/water mixtures and also of ethanol/water mixtures.
For non-mixtures, the Lorentz-Lorenz equation predicts:
$$ \frac{n^2-1}{n^2+2} = \frac{\alpha}{3\epsilon_0} \frac{N_A}{... |
I have two objects that collide with some velocities and mass. About each of them, I know the radius, the velocity before and after the collision, the mass, and the position. I wish to calculate their angular velocities as a result of their collision.
The collision is elastic, and friction is assumed. Everything is als... |
In Lagrangian mechanics, once we define $q$ which is about the position, then we automatically get $\dot q$ such that the data $(q,\dot q)$ uniquely determines the state of the system.
But in Hamiltonian mechanics, $p$ and $q$ are somehow independent. From my understanding, even if $(A,B)$ determines the state of a sys... |
The below are definitions for Helmholtz and Gibbs energies
$$F=U-TS$$
$$G=U+PV-TS$$
I am confused about whether $T$ and $P$ refer to the temperature and pressure of a system or reservoir. Some sources mention that $T$ and $P$ are the temperature and pressure of the reservoir, not system while others mention the opposit... |
We have a spring of spring constant $k$. If we apply force $F$ on the spring,it elongates. The restoring of by hooked law $kx$ also develops on spring. Then a time will come when $kx=F$ i.e equilibrium position is obtained. But according to Newtons 3rd law, if we apply force $F$ on th3 spring,the spring will also pull ... |
I am starting field theory and have questions regarding what I learned about tensor/Einstein notation. I made up my own problem where I am deriving things backwards to practice tensor notation and manipulation.
Starting with the Lagrangian
$L = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu}$,
where $F_{\mu\nu} = \partial_{\mu}A_{\n... |
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