Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
How do we cool exactly as sweat evaporates from our skins? We all know that when our sweat evaporates to the air we feel colder, but since this process is a latent heat transfer our body temperature will not change, then if our body temperature is constant how do we cool down?
| To expand slightly upon Farcher's answer:
At any air temperature at which it is a liquid, water molecules will be striving to evaporate from that body of liquid at a rate which depends on the ambient temperature (higher means faster) and on the relative humidity (i.e., moisture content) of the air at that temperature (... | {
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Is there an exact constant value for the speed of light in a vacuum distorted by a gravitational wave? In a vacuum, construct a cylinder of photons arranged as follows:
A 'measuring apparatus' computes the speed of light as 299,792,458 m/s.
However, suppose the vacuum is distorted by a gravitational wave
The 'measuri... |
Question, can any 'measuring apparatus' truly compute the constant speed of light
since the underlying geodesics can never be fully known?
To start with although the velocity of light in vacuum and the velocity of photons in vacuum as far as our measurements and theories go have the same value, light is composed out ... | {
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What causes the difference in magnetic permeability between materials? Why do some materials (like iron) have greater magnetic permeability than others (like aluminum)? We don't need to consider negative permeability here.
Is it that more of the atoms have electrons that polarize their spin and some atoms don't polar... | The point is that spins are interacting with each other as well as with the external field. Plus, they get disturbed by the statistical motion of the particles. That is the reason for example, why ferromagnetism breaks down above a certain temperature. Furthermore, due to the Pauli principle, spins tend to pair with re... | {
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Computing the partition function from a Metropolis Monte Carlo sample I must be missing something. I could not find an answer in similar posts.
Suppose I have an energy $E(x)$ and have sampled many points, $\{x_1, x_2, ..., x_N\}$ through a Metropolis Monte Carlo simulation. If the space is high enough dimension such t... | Metropolis Monte Carlo is a method for calculating averages, like
$$
\langle f(x)\rangle = \frac{\int f(x)p(x)dx}{\int p(x)dx}.
$$
One cannot however calculate the normalization constant, $Z=\int p(x)dx$. In physics this is usually not a problem, since the partition function is not a measurable quantity - it is a conve... | {
"language": "en",
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Is there a Maximum Data Density of a Physical Volume? Is there an established or proven relationship concerning how much data can fit in a given volume of space / spacetime?
| The limit you want is the https://en.m.wikipedia.org/wiki/Bekenstein_bound bekenstien limit. This limit states that the amount of information a given volume can contain is proportional to the surface area of that volume. Specifically it is 1 bit of information for every 4 plank areas.
Note that because the limit is a ... | {
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Why do outermost particles on a rotating rigid body gain more kinetic energy? This is something which I know from my $9^{th}$ standard that on a rigid body rotating about a fixed axis , the velocity of the outermost particle is the maximum and it should be true so that the rigid body stays in one piece but I really don... | In reality there will be some bending of the rod like this
There is a tension in the rod that provides the centripetal force that make the particles move in a circle. The tension will vary along the rod, and so will the angles...
The resultant force on a particle, acting perpendicular to the rod, depends on component... | {
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Gravitational wave and 1st law of thermodynamics Introduction:
A prediction of the general relativity is that any moving mass produces fluctuation in the space-time fabric, commonly referred as Gravitational-Wave.
This prediction was recently confirmed by the LIGO experiment.
The generation of such gravitational waves ... |
any moving object having a mass would create gravitational waves
This is not true in general. At the lowest order, the rate of energy lost as gravitational waves is proportional to the third time derivative of the quadrupole moment tensor of the system. For example, a mass moving at constant velocity will not radiate... | {
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Equations for implementing a 2D FDTD plane wave incident at an oblique angle with Bloch periodic boundary conditions I am interested in modeling a periodic device via 2D Finite Difference Time Domain method (FDTD), in order to calculate the reflection and transmission from a single-frequency plane wave incident at a va... | I found the answer - the intensity should be calculated as the y-value (i.e. the direction of power flow) of the Poynting Vector: $\qquad S_y = E_zH_x - E_xH_z$
For TE ($H_z=0$): $\quad S_y = E_zH_x$
For TM ($E_z=0$): $\quad S_y = -E_xH_z$
Since the $E$ and $H$ fields in the Yee grid are staggered in time by half a ti... | {
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How they work: dehumidifier vs air conditioner From what I understand both dehumidifiers and air conditioners do the same thing. They blow air onto cooled pipes. This means that dehumidifiers must cool the air and air conditioners must dehumidify as well. So what is the difference in operation between them? How do thei... | the mass flow rate of air through a dehumidifier is typically low, to furnish the longest time possible for heat transfer from the cold coils to the air. This means that the compressor rating of a dehumidifier is also low, meaning that its capacity as a refrigeration device will be relatively low.
the mass flow rate of... | {
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Is this a Dirac delta function in disguise?
Consider a typical detector equivalent circuit, where the detector can be seen as an ideal current generator $I(t)$. Since $I = I_C + I_R$ (currents through the capacitor and resistor), $I_R R=V$ and $\frac{I_C}{C}=\frac{dV}{dt}$, the equation of the circuit is:
$$\frac{dV}{... | *
*Yes, OP has essentially constructed a one-sided Dirac delta distribution
$$\delta_{[0,\infty[}(x)~=~\lim_{\varepsilon\searrow 0} \frac{1}{\varepsilon} e^{-x/\varepsilon}$$ on the positive half line $[0,\infty[$ via a generalized function, so that
$$\int_{[0,\infty[} \mathrm{d}x~\delta_{[0,\infty[}(x)~f(x)~=~f(0) $$... | {
"language": "en",
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True or False: energy is conserved in all collisions Using introductory physics, how would you answer this question? (I have a disagreement with my instructor and I’m curious to hear your input)
One of us says true because the question doesn’t specify “kinetic energy,” or a “system” and all energy is always conserved. ... | If this is a school/test question, the "correct" answer to put down on the test is whatever the teacher said in that particular class. That's what they're going to be expecting, and looking for, as the test is to test you on how well you've done in their course. If they are taking the idea that at this stage, the only ... | {
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Result of Davisson Germer experiment if electrons only exhibited particle nature The occurrence of minima and maxima in Davisson-Germer experiment confirm the wave nature of electrons.
Let us assume that the electrons do not posses any wave nature, and they only possess particle nature. In such case, how would the resu... | If the electron has classical particle nature then one would expect phenomena like
*
*Coulomb or Rutherford Scattering
*Bremsstrahlung
But to observe these the setup should be such that to reduce other possibilities. But you would expect any possibility that is allowed by the interaction of charge particles with ... | {
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If I throw a ball into a quarter of a circular tube, what will be the final direction of the ball?
Assuming energy is conserved of course, no friction and similar mass. looking at this as a collision I know the mass relation plays a part, but how? Also how is having 1/4 of a circle is different from 1/5 or 1/3?
edit: ... | The thing that will simplify calculation is the assumption that the cross-sectional diameter of the tube is equal to that of the ball. Because then, at the exit point, the horizontal velocity of the ball must be equal to the horizontal velocity of the tube. Why? Because then, at any point of its journey, the ball will ... | {
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Inclined Stationary Bike Why would it make you work harder if you incline a stationary exercise bike? What's the physics involved? Assuming all other factors remain constant and only the incline changes, why would you burn more calories?
| When tilting the bike machine, you are adding an additional gradient that you must now ride against. This increases the amount of power your body needs to output to maintain the same speed.
It might seem counterintuitive, but remember that the floor underneath the exercise bike keeps moving, while the incline remains,... | {
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Strange behavior from non-zero origin in relativity This is from Purcell's E&M book, appendix G.
I take the photo in (a) as a given. In frame F, the letter E is stationary, and in frame F', the letter L is stationary. This assumes that $\beta = \sqrt3/2$, $\gamma = 2$, and that at the start in both frames ($t=0$ and $... | In both cases, we are given the position of the origin of one frame in the other frame. So, if we can work out where the origin of one frame was in the other frame at the start, we can work out the time.
In case (a), we know that because of length contraction, the position of the origin on $F'$ in $F$ is $x = 0$, since... | {
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Proof of form of 4D rotation matrices I am considering rotations in 4D space. We use $x, y, z, w$ as coordinates in a Cartesian basis. I have found sources that give a parameterization of the rotation matrices as
\begin{align}
&R_{yz}(\theta) =
\begin{pmatrix}
1&0&0&0\\0&\cos\theta&-\sin\theta&0\\0&\sin\th... | Rotation matrices are orthogonal matrices, i.e., $$R^{-1}=R^T.$$
An orthogonal n-by-n matrix has $n(n-1)/2$ independent parameters (see here for an elegant proof), which in our case is 6 parameters. Linear algebra tells us that a 6-component vector can be represented in terms of 6 linearly independent vectors. The rest... | {
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Does gravity get stronger the higher up you are on a mountain? So I saw this article stating that gravity is stronger on the top on the mountain due to there being more mass under you however I have read some questions other people have asked and most of the responses state that the mass is concentrated at the middle o... | Probably not by itself.
The gravitational acceleration of a spherically symmetric body is given by:
$$
g = \frac{GM}{r^2}
$$
where $r$ is the distance from the center. Assuming the uniform density, this would be:
$$
g = \frac{4\pi}3\frac{G\rho R_0^3}{r^2}
$$
where $R_0$ is the radius of the body. When standing on the s... | {
"language": "en",
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Integration of tensor to find potential I have question given as:
$$\partial_k \varphi = -(C_k+ D_{jk}r_j)$$
where $C_k \,\&\, D_{jk}$ are constants and $D_{jk}$ is symmetric and traceless. I have to find $\varphi$.
I am getting : $\varphi = A -C_kr_k - D_{jk}r_jr_{k}$
but answer is: $\varphi = A -C_mr_m - \frac12 D_{s... | I think your answer and the official answer are basically the same but they used the fact that the tensor D is symmetric and there is on additional little problem in your solution. Let me start from the beginning:
\begin{equation}
\partial_{k}\phi=-D_{jk}r_{j}
\end{equation}
this expression can be written as:
\begin{eq... | {
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Why does $dG < 0$ imply that processes involving chemical reactions are spontaneous? Here is a short proof/derivation of why $dG < 0$ implies that a process is spontaneous (for constant temperature and pressure):
But this derivation assumes that only mechanical work is done on the system. If the process involves chemi... |
But this derivation assumes that only mechanical work is done on the system.
The derivation does assume that the only form of work done is PV work. You object that this assumption is invalid if chemical changes occur. But chemical changes are not "work", so this assumption does not undermine the conclusion.
Your expr... | {
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Can a conductor be uniformly charged if charges tend to reside on the surface? As per the title, I'm thinking if it is possible to have a conducting metallic solid sphere with uniform charge distribution if the charges in a conductor tend to distribute themselves on the surface of the conductor.
| No, that is not possible. This can be shown by applying the following equations at any point inside the conductor:
$$-\frac{\partial\rho}{\partial t} = \nabla\cdot\mathbf{J} \\ \mathbf{J}=\sigma\mathbf{E} \\ \nabla\cdot\mathbf{E}=\frac{\rho}{\epsilon_0}$$
so that
$$\frac{\partial\rho}{\partial t} = -\frac{\sigma}{\epsi... | {
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Why does twisting a cork make it easier to remove from a bottle? When we want to remove a cork from a bottle first we turn the cork. Turning in one direction makes it easier to remove in the axial direction.
Does anyone know something more about this?
| tl;dr– Twisting the inside of a cork can compress it, making it easier to remove. The same method is used with foam earplugs.
Twisting makes the cork smaller.
Materials tend to get compressed when twisted internally.
Examples:
*
*Foam earplugs.Foam earplugs are basically the same thing as corks, in that they're st... | {
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Why can't a third charge steal some potential energy from a system of two charges? Suppose three positive point charges are situated at the vertices of an equilateral triangle (as shown in fig). We can calculate the potential energy of this system which is
$$U_{total}= U_{AB}+U_{BC}+U_{AC}$$
Now with two charges fixed... | The reason is the linearity of the Maxwell equations. Each charge feels the sum of the electric fields of the other two. Therefore the work to remove C to infinity is the sum of the work required due the field of A and of B. The work due to A does not depend on the presence of B and vice versa.
| {
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How to make a warp bubble moving? In answer to this question it is stated that:
In summary, warp drives move because they already move, or else they need to propel, and their movement is not related to spacetime expansion or contraction.
This means that firstly a warp bubble had to be accelerated at some speed. The s... | I don’t think @JS4137’s answer is quite complete. The warp bubble moves because its (fictional exotic) mass moves. The energy-momentum tensor of the alcubierre drive has forward-pointing momentum on the inside of the torus and backward-pointing momentum on the outside of the torus. I’ve seen someone elsewhere on a foru... | {
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Least action principle universality, why does it work? For example, hen working with general relativity, one sees that Einstein equations can be derived from an action principle via the Einstein-Hilbert action. This occurs too in classical mechanics, optics, electrodynamics,...
Even in modified theories of gravity, or ... |
In summary, what is the precise theoretical argument of why the
principle of least action works in complete diferent scenarios?
It is possible to derive a theory from a Lagrangian and the theory is not right, in the sense that it doesn't fit some experiments. Example: Nordstrom theory of gravitation.
So, I don't thin... | {
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Why do we feel weightlessness in water but not on land? When we draw a Newtonian free body diagram of a man standing still on land, we draw force g and the reaction force. In water when floating still, we still have force g but we also have the reaction force and buoyant force. We are not accelerating in either case. S... | Dale's answer is an excellent breakdown, but there is still an important component missing.
Notably: why is the experience so different from lying on a highly contouring mattress in air? Proprioception and the ability to move freely in the vertical direction (as Marco pointed out) are part of it, but there's another fa... | {
"language": "en",
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Can the fish topple the bowl? A man is standing inside a train compartment. He then hits one side wall of the compartment with his hand (or you can assume he kicks the wall with his leg). Will the compartment begin to move? I don't think so. (If it happens, there will be no need of fuel.)
I mentioned this incident as ... | If you consider no energy loss from the system in the first part i.e the man in the train.
The man doesn't need to kick the train to make it move.
Even if the man walks inside the train, the train will move so as to keep the coordinates of center of mass to be same since there is no external force acting on the system.... | {
"language": "en",
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When two molecules collide, does it produce a sound? When we are in an empty room with no one around, we don't hear any sound, but there are billions of atoms and molecules that are colliding at the same instant.
So my question is, when two molecules collide, does it produce a sound?
| A sound wave is a synchronised movement of millions and millions of atoms or molecules. The random collisions of atoms or molecules are not synchronised and do not produce a sound wave.
A sound wave is like a stadium wave in a large sports stadium. You only get a wave if people move in a synchronised way, each person s... | {
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Can we observe an event that occurs more than 13.7 billion light years away? In Kurzgesagt's latest video about the largest black holes, the narrator says that two black holes have been observed orbiting each other at a distance of 17 billion light years from Earth. So light must take at least take 17 billion years to ... | The easiest way to think about this (and without going into cosmology concepts such as the Hubble horizon) is that when the light was emitted, the black hole was not 17 billion light years away from Earth. They were closer. They are 17 billion light years away now because the universe has expanded while the light was t... | {
"language": "en",
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What are the conditions for magnetic field and electric fields to be closed? Assume we have a statement:
The electric field $E$ cannot form closed loops
I am trying to prove/disprove this claim.
The conditions for a closed loop is:
$$\oint_CE\cdot dl=0$$
Using stokes theorem:
$$\iint_S(\nabla\times E)\cdot\hat n\;dS=... | There’s definitely some confusion here - if a field line forms a closed loop, then by definition the electric field is tangential to the loop at every point of the loop, which means that $\oint \mathbf E\cdot d\mathbf r\neq 0$.
In a conservative field, closed loop integrals of that type always vanish; as a result, if a... | {
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How can a twin travelling astronaut paradox be resolved? This is a variant of the twin paradox. But having each of the twin astronauts take off in opposite directions and returning to meet such that all aspects of acceleration and velocity are the same. Both should observe the other’s clock being slow for the whole tri... |
Both should observe the other’s clock being slow for the whole trip
This is the part you have got wrong.
In twin A's frame, twin B would age slower during the 1st half of twin A's journey
In twin A's frame, twin B would also age slower during the 2nd half (return half) of twin A's journey.
But that does not mean that... | {
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'Multiplication' of Spinors I am struggling to understand what is meant when spin eigenstates are 'multiplied' together. For example, Brandsen and Joachain's Quantum Mechanics says that there are four spin eigenfunctions for a two particle system:
$$ \alpha(1)\alpha(2), \alpha(1)\beta(2), \beta(1)\alpha(2), \beta(1)\be... | He means the tensor product. In quantum mechanics, when one handles two systems in different Hilbert spaces, $\mathcal{H}_1$ and $\mathcal{H}_2$, the joint state that considers the two systems lives in $\mathcal{H}_1\otimes\mathcal{H}_2$. So, if you have two spin states $|\alpha(1)\rangle\in\mathcal{H}_1$ and $|\alpha(... | {
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Why is "work done/time taken" correct over "force × velocity" as a definition of power? (A level) I came across a multiple choice A level past paper question (CIE June 04 paper 1 Q15) asking to choose which of the following defined power:
15 What is the expression used to define power?
(A) $\frac{\text{energy input}}{... | Velocity and force are both vectors (in this case, a number each for forward, left and up). The standard ways to multiply vectors are $F \cdot v$, which yields a scalar, the cross product, $F \times v$, which yields a vector and an outer product, $F \otimes v$, which yields a matrix.
This site on A levels covers vector... | {
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"answer_id": 7
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How do geodesics explain two identical balls thrown up at the different speeds? As stated in the title, two identical balls, both thrown directly upward, but at different speeds. The slower ball will reverse direction at a lower height than the faster ball. But the curvature of spacetime that they are passing through... | You have already got some good answers.
But I would like to add some more concrete and visual explanations
for convincing you. This can be done with Newtonian mechanics and
elementary geometry only, but without the advanced mathematics
usually used in general relativity.
Here is a table with some trajectories of balls
... | {
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"source": "stackexchange",
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Gauss Law: Electric Flux and relation with Charge What does the Gauss law specifically say? I know that $$\text{Electric Flux}=\frac{\text{Total Charge contained}}{\epsilon}$$
But while reading on the method of curvilinear square, there is a line:
The total charge contained by the conductor is equal tothe flux emanat... | It's just a question of units.
Gauss' law in SI units is as you have written it. In SI units, $\epsilon_0=8.8542\times 10^{-12} F m^{-1}$. In cgs & Gaussian units, $\epsilon_0=1$, and is unitless. Your source is probably using one of the latter systems.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Angular momentum of rolling sphere confusion I was reading about the angular momentum of rigid bodies, and I cam across the following problem.
Imagine a solid sphere is rolling down over an inclined plane without slipping, and I was trying to find the angular momentum of this body.
I found the following formula : $L = ... | The confusion arises because the $r$ in $I\omega=\frac{2}{5}mvr$ is the distance to the center of the rolling sphere. The $r$ in the second term $mvr$ is the distance to some fixed origin about which the total angular momentum is defined.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/658894",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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A bob being at equilibrium at every position In this video, at 1:39 it had been said that the bob is at equilibrium at every position of the path it traverses and therefore balanced the forces? It didn't make any sense to me. How can it be at equilibrium at all the positions of it's path? How are they even able to bala... | If the bob were swinging, the only equilibrium point would be at the bottom of the swing where the acceleration is zero. In this video, the bob is held nearly stationary at each angle θ by the external force F.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/659073",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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About the "worst prediction in all of physics": the cosmological problem Physicist Sabine Hossenfelder on YouTube just recently posted a video about vacuum energy, the cosmological constant and the "worst prediction" in physics. The worst prediction in physics refers in this case to the enormous discrepancy of a factor... | The status is that the prediction must be wrong and that this is an unsolved problem of QFT.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/659313",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
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Stress developed in a Hoop due to rotation
In the given question with constant angular velocity. It asks us to find longitudinal stress at each of the positions. Now I'm not even sure what longitudinal stress is but here is what I tried as A is the farthest it will have the highest Radius and hence highest centripetal... | Hint: It depends on how much mass it outside the 'radius of rotation'.
For example at B and C, there is tension there, as a centripetal force is needed to make the half circle (green) between B and C rotate. You would need to integrate $\delta m \times \omega^2r$ for each mass element in the green section, where $r$... | {
"language": "en",
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Why does piercing plastic film lid before microwaving help?
I've done this many times: buy food in a plastic box covered by a very thin plastic film. The instructions say simply:
*
*stab the film with a fork, several times
*microwave it
*eat it
I was very skeptical about the first step, because the fork makes suc... | The holes allow the steam created to be released gradually.
If they were not put in there would be a possibility of a sudden messy explosion, or someone getting burned by a sudden release of steam when they opened the lid.
Why your food didn't seems as hot might need more 'experiments' to decide.
Microwave ovens create... | {
"language": "en",
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Relativistic doppler shift When rearranging the doppler shift equation in terms of wavelength to get in terms of $\beta$ we get:
$\beta = \cfrac{(\lambda_{source})^2-(\lambda_{obs})^2}{(\lambda_{source})^2 + (\lambda_{obs})^2}$.
My question is since $\beta>0$ when the observed wavelength is greater than the source e.g.... | Note that for the longitudinal Doppler shift
\begin{equation}
\left.
\beta\boldsymbol{=}
\begin{cases}
\dfrac{v}{c}\boldsymbol{>}0\,,\quad \texttt{if observer moves away from the source}\vphantom{\dfrac{a}{\dfrac{a}{b}}}\\
\dfrac{v}{c}\boldsymbol{<}0\,,\quad \texttt{if observer moves towards the source}
\end{cases}
\ri... | {
"language": "en",
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Thin film interference equation confusion For thin film interferences, why is that when you have two phase changes, the equations you use for constructive and destructive interferences are switched?
| In the first phase change, you get a phase difference of, $$Δϕ=π$$ and so you get destructive interference. When you get the second phase change, you get another additional phase difference $$Δϕ=π$$ which is the same as no phase difference, or $$Δϕ=0$$
In other words, you will find that the two waves emerge in phase. ... | {
"language": "en",
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A bowling ball on an infinitely long track We knew that a after a bowling ball is threw out with a certain velocity to a non smooth track, it first rolls and skids as the translational velocity (decelerates due to friction) of the center of mass is greater than tangential velocity of the point of contact of ball with t... | There are two forces causing a real rolling ball to lose energy. One is friction with the air. The other results from the slight deformation of the two surfaces at the point of contact. The ball is effectively rolling “uphill”.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Car A has higher power, but car B has higher torque. Which one would win in a straight drag race? Suppose we have 2 cars with different specifications.
Car A has a higher power specification but a lower torque specification.
Car B has a higher torque specification but a lower power specification.
Suppose they enter a... | Torque is a fetish for solving the transmission non-idealities.
The power wins the race. But it is not the maximal power of the engine, it is the average power output of the engine for a given type of competition.
One can easilly find a truck or even a tractor with a mind-boggling (from a racng cart viewpoint) engine t... | {
"language": "en",
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"source": "stackexchange",
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Rest frame of perfect fluid I learned that dust is a collection of particles at rest with repect to each other. Thus the four velocity field $U^\mu$ of dust will be a constant and it is easy to think of what the rest frame of dust means. It is simply the frame that every individual particle is at rest and is applicabl... | In the rest frame, $U^0 = 1$. So $T^{\mu \nu} = \rho$.
If you view the dust from another frame, the individual components will change, but the magnitude will not.
| {
"language": "en",
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Quantum properties of long wavelength electromagnetic radiation How could we have known that Electromagnetic radiation is quantized if we only knew about long wavelength radiation? What are the 'quantum' properties shown by long wavelength electromagnetic radiation?
| It is difficult to answer by keeping the what-if approach of the original question. It is difficult to imagine the technological development necessary for an experimental investigation of QED at low frequencies without the accompanying understanding of the high-frequency regime.
However, it is exciting to note that man... | {
"language": "en",
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Are energy and work the same thing? When revising formulas the other day I came across something:
Energy = power × time
If we substitute power we get
Energy = work/time × time
The time cancels out. So is work equal to energy?
|
This image represent how we earn money and spend also.
With physical example we understand better than a theoretical example.
Money is like energy we earn this by work . Work and energy has same unit but how different is clearly shown in figure .
Work is just a way to transfer energy , as work is just a way to get mon... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/661101",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "13",
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Can an ideal dipole experience an electric force? It is known that electric force a charged body is given as $\vec{F} = q \vec{E}$ given that $\vec{E}$ is uniform. Now, for an ideal dipole, what would we take as the charge for calculating the force exerted on it by an external electric field?
| The electric force on a dipole is $\mathbf F=(p \cdot \boldsymbol \nabla ) \mathbf E$, where $p$ is the dipole moment, $\mathbf E$ is the electric field, and $\boldsymbol \nabla$ is the gradient operator.
Note that this force goes to zero for a uniform field (as mentioned in another answer). Note also that there will b... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Rigorous proof that a net force of zero guarantees zero linear acceleration in rigid bodies I've never found a rigorous proof of this fact.
The center of mass' acceleration is not necessarily the linear acceleration, specially if the body is attached to a pin or another geometric constrain, then the center of mass spin... |
The center of mass' acceleration is not necessarily the linear acceleration
This is your problem. An object that is not point-like does not have a single linear acceleration, rather each point on the object has its own linear acceleration given by
$$\vec a_P = \vec a_0 + \dot{\vec\omega} \times (\vec r_P - \vec r_0) ... | {
"language": "en",
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Does magnetic attraction power of magnet decay over time? I probably have a common question to start with. Does the magnetic attraction power of a permanent magnet for example, decay over time, if the magnet is actively used to attract stuffs and perform some work? Then I have couple of followup questions based on the ... | In physics, “work” $W = \int \mathrm d\vec x \cdot \vec F$ is only done when the displacement $\mathrm d\vec x$ is nonzero. If the weight doesn’t move, no work is done.
Most people have a permanent magnet that’s been on their refrigerator for a year. The energy cost is the same as keeping it on the shelf.
In a ferroma... | {
"language": "en",
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Is superconductor just a perfect conductor or anything more than that? If I had a hypothetical perfect conductor having infinite conductivity and I cool it below a certain temperature, will it be a superconductor? If not, then how can we distinguish between the two using the experimental and theoretical methods?
I only... | Indeed, zero resistivity(infinite conductivity) is not taken as the true definition of superconductivity. The fundamental proof of a superconductor is the demonstration of Meissner effect. Thus, a superconductor is not just a perfect conductor having infinite conductivity but also a perfect diamagnet that exhibits Meis... | {
"language": "en",
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Equation of capacitance of a capacitor Imagine the two terminal of a parallel-plate capacitor are connected to the two terminal of a battery with electric potential difference $V$. If the capacitance of the capacitor is $C$, and the area of each plate is $A$, then how can I express the charge stored on each plate ($\pm... | You have the formula in the question: $Q=CV$ (which holds for any capacitor, not just one with a parallel plate). There is no way to include any additional dependence on the plates' area $A$, because once you know $C$, and $V$, $Q$ is already completely determined. So, when written as a function of $C$, $V$, and $A$... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Basics of centripetal force Suppose an object is moving in a circular path. We know that the net force that is working on that object is the centripetal force towards the center. But the object should have gone closer towards the center in that case due to the radially inward force working on it, but it doesn't. Why do... | Another way of analyzing the situation: imagine an object moving counterclockise at a velocity of $1$, starting at the point $(1,0)$ at time $0$. If it continues moving in a straight line, then at time $t$ it will be at point $(1,t)$, a distance of $\sqrt{1+t^2}$. The Taylor series for that is $1+\frac{t^2}2-\frac{t^4}... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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What is the correct entropy density of the cosmic vacuum? Which of the following two arguments is correct?
(1) The total entropy of the cosmic vacuum should be the same as the entropy of the cosmological horizon (with radius $R$). The horizon entropy $S$ is given by the black hole entropy $A/4$ (in Planck units); the t... | Let us evolve the Universe in both arguments to a de Sitter end-point so the 'horizon' is then the future cosmic event horizon in both cases. What is then clearly the same in both arguments is that the entropy is:
\begin{equation}\tag{A}
\ S=S_{Bulk}=S_{dS}\sim \frac{E}{T_{dS}}
\end{equation}
Also, $T_{dS}\approx 2.4\... | {
"language": "en",
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When two balls collide with each other (not head on), will linear momentum still be conserved if there were friction between the balls?
As shown in this figure, where the surfaces of the two balls A and B are not smooth. Therefore, when they collide there will be frictions.
My question is that since we derived the con... | At the time where the collision occurs, you have this situation.
writing the EOM's you obtain
$$m_1\dot v_1 =f_\mu\\
m_2\dot v_2=-f_\mu\\
I_{o1}\,\dot \omega_1=f_\mu\,\rho_1\\
I_{o2}\,\dot \omega_2=-f_\mu\,\rho_2
$$
multiply with $~dt~$ and integrating :
$$m_1\left(v_{1f}-v_{1i}\right) =\int f_\mu\,dt=dp\\
m_2\left... | {
"language": "en",
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Why did mirror-image life not evolve? Mirror life is a hypothetical form of life with mirror-reflected molecular building blocks. For instance, a mirror virus RNA would be constructed with left-handed sugars.
Why do we see absolutely no mirror life? Would we expect extraterrestrial life to perhaps be mirrored? If we mo... | Chirality of life may need antimatters world. I am no expert in biology. In physics, time need to be inverse I believe for antimatters to exist. There is a need for separation between. Other than black holes, it might be impossible for antimatters or chiral life to exist, if life have same issue. Chirality deals more t... | {
"language": "en",
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Free space motion I was going through Kleppner and got this interesting doubt. At page 138 there is an article named rocket in free space.So if there is no external force. The fuel can expand rapidly or slowly without affecting final velocity of rocket. Or we can say the velocity of rocket change by same amount whether... | I believe that the rocket can burn the fuel "slowly" or "quickly", but cannot burn the fuel "instantaneously". Whereas on the flatcar, all the people can jump at once.
The rocket acceleration is assuming that the fuel burn is a continuous process that you can divide as finely as you want. The burn of some small fuel ... | {
"language": "en",
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Why don't electrons tunnel out of atoms? The overlap of a free electron wavefunction and a bound electron wavefunction is nonzero. So why don't electrons slowly bleed out of atoms? If any wavefunction enters a free particle state it will just escape!
| The electrons do not tunnel out of atoms, because they are in a potential well with energies below those of the energies of the continuous spectrum. Thinking of tunneling obscures here the basic intuition of energy conservation that we have from classical physics.
The situation is quite different in radiactive nuclei, ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/662672",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is it possible to create a magnetic environment where it pushes and pulls at the same time, making the target “levitate”? To better understand why I ask this, the backstory is I’m getting more and more annoyed by rolling office chairs rotating, hitting my ankles, hard to switch directions when wheels having ~90 degrees... | I believe I have heard that there is a train in Japan which is supported by magnetic levitation, but that would be for linear motion, and might require a significant amount of power.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/663742",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Light from Maxwell's equations According to Maxwell's equations, an accelerating electron emits light. My question is, does Maxwell's equations explain the emission of all electromagnetic waves in the universe including, say, light emitted from a bulb?
Is this view of light emission from Maxwell's equations any differe... | When we say that an accelerating electron emits light we are considering an electron as a classical particle, whereas when we talk about an electron jumping between the states in an atom, we are considering electron as a quantum particle. Thus, it would be incorrect to treat this as two different mechanisms of emission... | {
"language": "en",
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Question concerning Feynman lectures volume 3 chapter 7-2 I am currently reading The Feynman lectures on physics volume 3. In chapter 7-2 (7.9) Feynman said the amplitudes of a moving particle are given by the equation $e^{-(i/\hbar)(W_pt-p\cdot x)}$. Where $W_p$ is the energy of the particle over and above its rest en... | Feynman is considering a particle with a definite momentum $p$.
*
*From solving the eigenvalue problem for the momentum operator $\hat{p}=-i\frac{\partial}{\partial x}$, we know that the wavefunction of a momentum eigenstate with a given momentum $p$ is given by $e^{ipx}$ up to normalization.
*We also know that an ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/664030",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How do I determine the exact distance from Jupiter to the Sun on a specific date? I've recently needed to determine exactly how far Jupiter was from the Sun on April 25th 2018, when a Hubble image of Jupiter was taken.
I'm a beginner in physics and Google searches lead me nowhere. I wouldn’t mind calculating it, but I ... | Try Stellarium. It takes a download, but it's free. You can set the location of your telescope to the Sun, and then check the distance to Jupiter.
| {
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"url": "https://physics.stackexchange.com/questions/664138",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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How to calculate the total energy from a given wavefunction? For a given wavefunction, $\Psi(x,t)$ of a system, how one can calculate the total energy?
For example, the wavefunction for a particle of mass $m$ moving in a certain potential $U(x)$ is given by: (where $A$, $L$, $E$ are real constants.)
$$\Psi(x,t)=\left\{... | The wave function of the form
$$
\Psi(x,t) = \psi_0(x) e^{-i\frac{Et}{\hbar}}
$$
corresponds to the stationary state of a system with energy $E$. This fact implies that $\psi_0(x)$ is an eigenfunction of the Hamiltonian operator:
$$
-\frac{\hbar^2}{2m}\psi_0''(x) + U(x)\psi_0(x) = E\psi_0(x).
$$
Knowlege of $\psi_0(x)$... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Using Maxwell's equations to find $\mathbf{B}$ The $\mathbf{E}$ component of an electromagnetic wave in free space is:
$$\mathbf{E}(x, t) = E_0 \cos{(kx-\omega t)} \hat{\bf y}$$
How do I find the corresponding $\mathbf{B}$ component using one of Maxwell's equations (in differential form)?
I assume that I must use one o... | You can integrate the first equation in time to obtain:
\begin{align}
\int \nabla\times\mathbf{E} dt = \mathbf{B}(t) - \mathbf{B}(0)
\end{align}
If if you have already an expression for $\mathbf{E}(t)$, you can just substitute it into the above equation and you'll obtain an expression for $\mathbf{B}(t)$.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/664392",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What class of spacetimes has an associated temperature? It is very well known that the Schwarzschild metric carries a temperature inversely proportional to the mass. Is there a much wider class of spacetimes that has temperatures associated with it? What properties a spacetime must have to carry temperature?
| The "temperature" of the Schwarzschild metric is not exactly a temperature. If Hawking radiation is exactly thermal then the unitarity of quantum mechanics will be violated. There is growing consensus that quantum gravity is unitary and information is conserved. To preserve unitarity the radiation emitted cannot be unc... | {
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Are there integrals in physics that do not involve a rate of change? In physics, whenever I see the expression
$$\int_a^b f(x) \ \text{d}x$$
for some function $f(x)$, I read this as
$$\int_a^b \frac{\text{d}F(x)}{\text{d}x} \text{d}x$$
where $F(x)$ is the antiderivative of $f(x)$. In other words, I consider every Riema... | If the integrals $f$ is continuous, then the Fundamental Theorem of Calculus states that $f$ has an antiderivative.
| {
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Damped harmonic motion initial conditions I was reading Halliday's section on Damped Simple Harmonic Motion, which stated that this equation:
$$-b\dot{x} - kx = m \ddot{x}$$
Is the differential equation that dictates the displacement of the object, and $b$ is the damping constant of the system.
The author claims that t... | This is an algebraic trap...
You are assuming that xm always is the maximum amplitude of the movement. That is wrong.
Let's look at this equation:
$$a =- \omega x $$
$$x = Acos(\omega t) + Bsin(\omega t)$$
or to mimic your expression:
$$x = x_mcos(\omega t + \phi)$$
If the initial amplitude, is x0:
$$A = x_mcos(\phi)$$... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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When a car accelerates relative to earth, why can't we say earth accelerates relative to car? When a car moves away from a standstill, why do we say that the car has accelerated? Isn't it equally correct to say that the earth has accelerated in the reference frame of the car? What breaks the symmetry here? Do the force... | From a physics perspective, everything you say is correct. But human language is considerably more subjective and messy when it comes to definitions.
It's not that we can't say that the Earth accelerates in this scenario, it's that we don't say it because we don't observe it.
Even if we did observe it, we tend to say t... | {
"language": "en",
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Why do individual helium atoms rise? Balloons full of helium rise because the buoyant force is great than the gravitational force and the buoyant force is due to a pressure difference between the top and bottom of a ballon but why exactly does a individual helium atom rise?
| One thing to remember is the speed that the gas molecules travel is inversely related to the molecular mass. For example the average molecular speed is
v = (8kT/(pi*m))^0.5
[I don't know how to do math text]
Therefore the very light helium atom will have a higher average speed than nitrogen or oxygen. In a gravity fie... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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What does it mean that uncertainty can be calculated by the "smallest division on a scale"? I have been reading everywhere a little bit to understand the concept of uncertainty but I cannot understand exactly how to find the uncertainty value. On this explanation it says that the uncertainty can be calculated by the "s... | The smallest possible division on a scale will allow you to establish the uncertainty in a measurement. If you are using a ruler or voltmeter etc., then the maximum error you get when you read off a measurement will be $\pm$ one half of the smallest division.
If for example you are using a ruler, and each of the smalle... | {
"language": "en",
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Is it possible to create light only from a changing current in a wire? A changing current in a wire creates an electromagnetic field. Light can be considered an electromagnetic wave, so my question is: would it be theoretically possible to create visible light by inducing a current in a wire with a frequency inside the... | Well, yes; in a sense, that's what a mirror reflection is, an example of
light created by the motion of electrons in the silver or aluminum metal
as a response to the incident light. The outgoing light is, in a very real sense, newly
created by the electrons' motions, rather than being the exact same
light that impin... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/665489",
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Fire caused by friction with water Friction causes heat and heat causes fire, but could something catch in fire because of friction with a high speed water stream?
If so, what material would it be and how fast would the water speed need to be flowing?
| Regardless of the heat source, a material will not ignite unless it reaches, at a minimum, its Self-Ignition Temperature (SIT). In addition to reaching this temperature you need to have the proper mixture of fuel and oxygen for ignition to occur. Finally, for self-sustained combustion sufficient heat must be maintained... | {
"language": "en",
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Can I measure my velocity in a spaceship by measuring how much two static charges attract? We know that parallel current in two parallel wires causes them to attract. The explanation is that moving charges generate attractive magnetic fields.
https://youtube.com/watch?v=43AeuDvWc0k
If I have two charged pith balls in a... |
If I have two charged pith balls in a space ship, then they should attract more the faster the space ship travels.
The electric repulsion between the balls is always larger than the magnetic attraction, so they repel less the faster the ship travels.
The rate at which they repel as a function of the speed of the ship... | {
"language": "en",
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Conflicting intuitions about free fall So I just started studying physics recently, and I came up with a question that I'm not sure how to solve, and I think it may be because of some fundamental misunderstanding. I don't want anyone to answer the problem, I'm just providing it for context.
The problem: Let's say a man... | From the work/kinetic-energy theorem, the falling guy has to do enough work to counter his kinetic energy when he gets to the box. This leads to the equation
$W=\frac{1}{2}mv^2$
Using conservation of energy and assuming that the guy started falling from rest, it is seen that
$mgh=\frac{1}{2}mv^2$
where $h$ is his sta... | {
"language": "en",
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Are scattering experiments probabilistic in quantum mechanics? Suppose we have a electron that will scatter into an atom. When the electron is far way of the atom long before the scattering the system is represented by the state $\left|\psi_\text{in}\right\rangle$ . After the scattering the system will be in the s... | The pre-scattering state vector $|\psi(0)\rangle\equiv |\psi_{in}\rangle$ evolves into the post-scattering state vector $|\psi(T)\rangle \equiv |\psi_{out}\rangle$ deterministically, via the unitary propagator $U(T)$. The outcomes of measurements performed on the post-scattering state, however, are non-deterministic a... | {
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Newtonian mechanics vs. Pressure in Flight Which one is better to describe lift of a plane wing:
Newton's third law of motion:
(The wing applies a force on air and the air applies an equal and opposite force on wing - which causes lift.)
OR
Pressure:
(The force that is created from the higher pressure region to the l... | The first one is correct.
The second one (the way the diagram says it anyway) is incorrect and a very common misconception, or at best misleading and rather thin.
In my mind, it's better to say there exist higher and lower pressure regions BECAUSE of the force of the wings on the air. They are two sides of the same co... | {
"language": "en",
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How can work done be equal and opposite when the forces are unequal and object travels the same distance Let's suppose we have a spring fixed to a wall, attached to a block and nothing is said about the forces acting on the block or spring. It's known that if the block is displaced in the positive direction, the work ... | Two possibilities: (1) The block is moving as it starts compressing the spring. The spring does negative work on the block and removes its kinetic energy, and the block does positive work on the spring, giving it potential energy. (2) The block starts at rest and is pushed by an external force. The force does positiv... | {
"language": "en",
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What does a magnetic monopole field "look like"? If magnetic monopoles exist, they are predicted to have large charges--or equivalently, a large coupling constant, which means that perturbative models don't converge.
While I get that that makes it very difficult to calculate things like the binding energy of monopolium... | The magnetic monopole acts exactly like an electric monopole. In magnetostatics, the equation of interest
($\mu_0=1$):
$$\nabla \cdot \vec{B} = \rho$$
where $\rho$ is the magnetic charge density, has a solution:
$$\vec{B} = \frac{1}{4\pi}\frac{q}{r^2}$$
for point particles, i.e: $\rho = \delta(r)$, and $q$ is the magne... | {
"language": "en",
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Is it just a co-incidence that the interference pattern of light can both be explained using a classical wave and using a probability function? Approach 1-Light can be thought of as a vector electric field wave. To explain the interference pattern, one can just add the electric fields like vectors and calculate the int... | Maxwell's equations in vacuum are equivalent to a massless relativistic wave equation for the four vector potential. This wave equation produces a wave function, which has to be interpreted in a probabilistic way. It describes, simply put, the average number of photons that you can expect in a certain location. The obs... | {
"language": "en",
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Does the frequency of light have any effect on gravitational lensing? General relativity considers gravity as the curvature of space-time instead of a force. Therefore, what is bent around an astronomical object is the space-time itself. The light just follows the path as regular.
In classical physics however, I think ... | *
*Resorting to classical physics would result in no bending of light as light as no mass.
*But as you pointed out distorted spacetime curvature results in light travelling a bent path which is gravitational lensing.
*Splitting light by gravity is called Rainbow gravity theory, which is highly controversial..
I thi... | {
"language": "en",
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How much work is done to maintain vertical position (hovering) of a drone? Ignoring all losses in the efficiency of the means to lift the drone, this would reduce down to resolving the key elements of the equation involving a) the acceleration of gravity and 2) the time, and 3) the mass. So this is really just a math p... | If you ignore all losses due to inefficiency then the work for hovering is 0.
A drone is horribly inefficient. To make things hover efficiently you can use a superconductor and a magnetic field which requires 0 energy. There are also gyro-stabilized magnets that waste very little energy hovering.
Here is a picture of a... | {
"language": "en",
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What is the difference between amplitude and phase angle for a pendulum? I understand the definition in terms a plain trigonometric function, such as $A\cos(\omega t+\phi)$. The amplitude is half of the distance between peak and bottom, and the phase angle* is how the function shifts horizontally.
However, I am having ... | Look at a solution of the (linearized) equation of motion for the pendulum,
$$\theta(t)=A\cos\left(\sqrt{\frac{g}{l}}t+\varphi\right).$$
The amplitude $|A|$ is the maximum value of $\theta$; the angle varies between $-|A|$ and $|A|$ in the course of each period of length $T=2\pi\sqrt{l/g}$.
The phase angle $\varphi$ te... | {
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Hamiltonian Field Theory in Peskin & Schroeder In Section 2.2 of their QFT textbook, Peskin & Schroeder introduce the Lagrangian and Hamiltonian field theories of a classical scalar field. While defining the action $S[\phi]$ and deriving the Euler-Lagrange equation for the classical scalar field $\phi$, the classical s... | When you transform from the Lagrangian to the Hamiltonian picture, you necessarily must choose a particular foliation of spacetime -- that is, you must single out a particular time direction, and consider surfaces of constant time. One simple way to understand this is that while the Lagrangian is a Lorentz scalar, the ... | {
"language": "en",
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Do I have to apply more force than gravity to lift my leg above the ground? How much force do I do apply when I lift my leg above the ground? The same amount as gravity does on my leg (mg)? Or MORE than it (greater than mg)? If the displacement from the ground to my lifted leg is h meters, then what's the work done? mg... | Because your leg began at rest, moved for a time $\Delta t$ and ended at rest, the average force it felt was
$$ \langle F \rangle = \frac{\Delta p}{\Delta t} = 0 $$
meaning on average your force was equal and opposite to gravity.
However, when you accelerated upward you acted with more force than gravity, and when you ... | {
"language": "en",
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Transitions in Ising lattice gauge theories in 3+1 dimensions What is known about the character of the transition (apart from the self-duality of the model and its self-dual point marking the transition point) in the Z2 lattice gauge theory in 3+1 dimensions?
| The latest result on the model is by Malin Forsström:
"Decay of correlations in finite Abelian lattice gauge theories"
which applies to finite Abelian gauge groups and in particular $\mathbb{Z}/2\mathbb{Z}$. It proves exponential decay of two point functions in some regime with regards to the coupling ($\beta\ge 0.4$ i... | {
"language": "en",
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How to increase the current in a lemon battery? I tried to make the classic lemon battery today and ran into a bit of trouble.
I used 4 large tennis ball sized lemons with copper and zinc galvanized nails for electrodes.
I connected the 4 lemons in series and a voltmeter gave a reading of 3.5 V so I'm confident that my... | The current-producing character of a battery is in general set by the surface area of its electrodes. Try using 1/2" wide strips of copper and zinc metal instead of nails, and remember: throw away the lemons when done!
| {
"language": "en",
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Water in a glass Consider water in a glass and glass is held in hand. Hand is steady. Surface of water will be flat.
Now if the hand is given angular motion in a horizontal plane (w.r.t. floor) i.e. glass is moved along an arc of horizontal circle, surface of water will not be flat.
But the same glass of water when it ... | You are correct in that the surface of the Earth is not an inertial frame of reference (strictly speaking). Objects at the Earth's surface are indeed subject to inertial effects. For example Coriolis force, centrifugal force etc.
But because the earth's rotation is very slow and the earth is very large, for small-scale... | {
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What exactly robustness of a solution mean? One usually comes across many research papers that talk about robustness, but since I have never been introduced to this term formally in my education, I am not sure what distinguishes a robust solution/condition from a non-robust one.
Is the idea of robustness connected to s... | Essentially it means that if you make small changes in the input parameters you get small changes in the output values. That is there is roughly bounded by a linear or polynomial relation and is not exponentially related. In the latter case, we say the solution blows up. In the former case we say it is robust and as on... | {
"language": "en",
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Do electromagnetic waves contain electrons? I understand that EM waves are oscillating electric and magnetic fields. But doesn't this mean that the wave itself contains charged particles that generate the fields?
| The canonical answer is no: the electromagnetic field is itself a kind of matter, distinct from what we usually percieve as matter in terms of particles, such as electrons, protons, etc.
Ether
The modern view mentioned above was not always generally accepted: there have been many attempts to model electromagnetic waves... | {
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Spin angular momentum? An electron spins around its axis and magnetic field is produced. It can spin either in clockwise $\left(\frac{1}{2}\right)$ or in counterclockwise $\left(\frac{-1}{2}\right)$ direction.
The spin angular momentum is given by $S=\sqrt{s\left( s+1\right) }\cdot \dfrac{h}{2\pi }$.
If $s$ is $\frac{1... | You are confusing the square of the spin vector
($\vec{S}^2$) with its 3 vector components ($S_x, S_y, S_z$).
The square of the spin $\vec{S}^2$ always has the value $s(s+1)\hbar^2$, which is positive.
And the electron has $s=\frac 12$ (no negative sign).
The components $S_x$, $S_y$ and $S_z$ each have two possible val... | {
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How to simplify this complex circuit? I am new to circuit solving and I tried to simplify this circuit, but I am unable to do so. I can't figure out which resistances are in series and which resistances are in parallel.
Do I have to use star-delta conversion here or the circuit can be solved without conversion?
I just ... | First combine resistors $R_B$ and $R_C$ as parallel resistors forming resistor $R_{B//C}$.
Next perform a $\Delta-Y$ transform on resistors $R_A$, $R_E$ and $R_{B//C}$. All three of these resistors share a common node; consider the node of resistor $R_A$ that is not the common node to be node $1$, the node of resistor ... | {
"language": "en",
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Explaining the phrase "as viewed by A, clock $\mathfrak B$ appears to be ticking faster than clock $\mathfrak C$" In writings concerning time dilation and GPS (incl. on PSE) one can find statements such as
When viewed from the surface of the Earth, the clocks on the satellites appear to be ticking faster than identica... | The main principle in relativity theory is that anyone will see physical processes in their local vicinity proceeding like normal. Any time you have to observe something far away, the rate of those processes may be different from the far away perspective, because of relative motion or gravitational fields (which are a ... | {
"language": "en",
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Why do rain drops fall with a constant velocity? While reading my physics book. I came across a line that says that:
Rain drop falls with a constant velocity because the weight(which is the force of gravity acting on body) of the drop is balanced by the sum of the buoyant force and force due to friction(or viscosity ... | Apart from the other answers which provide a physical explanation, perhaps a mathematical proof might convince you:
$$\sum \vec F = 0 \rightarrow m \vec a = 0$$
$$m\frac{\text{d} \vec v}{\text{dt}} = 0 \rightarrow \text{d} \vec v = 0.\text{d}t $$
$$\int_{v_i}^{v_f}\text{d}\vec v = \int_{t_i}^{t_f}0.\text{d}t$$
$$\Delt... | {
"language": "en",
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What does the back EMF graph of a DC motor look like? Shouldn't it be oscillating like the output voltage of an AC generator? From what I understand, the net emf of a DC motor is made of its supply emf and back emf. The supply emf is constant, whilst the back emf depends on how fast the coil is spinning.
Initially, the... | Assume a dc motor with no resistance and no friction.
The speed of the coil which reach a maximum when the applied emf is equal to the back emf and in this condition no current is drawn from the power supply.
This is not unreasonable because the coil is rotating and constant speed ie its rotational kinetic energy is no... | {
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How is Newton's third law working here? I understand that if I were, for example, to throw a bowling ball in outer space then the ball would move away from me by the force I generated. But the ball would also exert a force on me in the opposite direction and move me away in the opposite direction of the bowling ball.
I... | When the gas is inside a container the molecules (red) are hitting all sides and exerting a force in all directions (due to Newton's 3rd law), first diagram.
When gas is allowed to escape, second diagram, the molecules are still hitting the wall at B and exerting a force, but no longer hitting the wall at A. This cau... | {
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Why does light have multiple frequencies? The wavelength of visible light ranges from 750 - 400 nm, and so do the corresponding frequencies. However, a photon only has one frequency, given by $E =h\nu$, at a given time, and it can’t be changed unless the photon gets energy from somewhere, which isn’t possible in the va... | Once it is emitted, the wavelength of a photon does not change (if we ignore cosmological redshift due to the expansion of space). But different photons can be emitted with different wavelengths.
| {
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Watching Kerr Ring Singularity Can you see light from ring singularity from inside the Cauchy Horizon? In between 2 horizons space and time coordinate swaps places, so the inside region lies at the future. But after crossing Cauchy time starts behaving normally, so light from the ringulaty should be visible to an obser... | If you want a representation of what an observer can actually see "inside" a black hole (hint: it is probably more complicated than you think!), your options are very limited!
A good place to start with is Andrew Hamilton's Home Page. Unfortunately he has not been able to provide the software for you to reproduce his... | {
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What particles are thought to have existed before Inflation? What fundamental particles do most Grand Unified and Inflationary theories predict existed before the Inflationary period? Basically, what do we expect the family of particles existing during the Grand Unification epoch to look like? It is my understanding th... | In one sense, all types of fundamental particles (certainly everything in the Standard model, plus probably more besides, depending on which variety of GUT you prefer) existed in the grand unification epoch, since the energy density/temperature was so high that particle/anti-particle pairs of all types could be created... | {
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Why do strangeness producing reactions have a small cross section? My professor told me that kaon producing reactions have a small cross section compared to other nucleon collision reactions. The reason for that is the production of a strange quark but he didn't elaborate further on why this actually is the case. I rem... |
I remember reading that reactions that involve quarks of different generations have lower probability of occuring but they mentioned this in the context of the weak interaction.
Flavor changing goes through the weak interaction.
Does the same still hold in reactions where kaons are produced via the strong interactio... | {
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Do accelerating masses generate gravitational waves? The accelerating charge can radiate electromagnetic waves, then, can the accelerating masses radiate gravitational waves?
| Yes. The prime example of generating gravitational waves are two bodies orbiting around each other, for example the Hulse-Taylor binary, which was the first indirect discovery of gravitational waves in 1974 and lead to a Nobel Prize in 1993. (Keep in mind, that even if a body orbits on a perfect circle, there is accele... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 1
} |
Units in Bohr's model of an atom In the Bohr model the values of the orbital kinetic moment and of the allowed
radii are quantized according to :
$$mv_nr_n = n \hbar, \, r_n = \frac{n^2 \hbar^2}{me^2}$$
By combining the two, i get : $$v_n = \frac{e^2}{n \hbar} = [ C^2 s^{-1}kg^{-1}m^{-2}]$$
Now, dimensional analysis gi... | from the fact that the potential energy in the model is $(-e^2/r)$ you can get that $[e]=[({\rm Energy} \cdot {\rm distance})^{1/2}]$ so $[e^2/\hbar] = [({\rm Energy}\cdot {\rm distance})/({\rm Energy}\cdot{\rm time})] = [v]$ and all checks out. This is $[e]$ in cgs units.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/670373",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
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