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10

Some energy densities for easily compactified substances: Purely electric storage: electric field in a capacitor, 0.000 36 MJ/kg electric field in a supercapacitor, up to 0.004 2 MJ/kg 1 T magnetic field has energy density $\frac{1}{2\mu_0}B^2 = 0.4\,\mathrm{MJ/m^3} $, estimate mass for superconducting magnet enclosure to decide where to put this on the ...


9

As you say, the power produced per cubic metre of the Sun's core is surprisingly low. This is because proton-proton fusion is a very slow process, as has been discussed hereabouts before. The core is so hot because conduction of heat through the core is slow. The average speed with which a photon escapes the core is the astonishingly low value of about ...


8

The expectation value of energy is something else than the energy in a particular experiment. With your choice of the initial states, the photons emitted (negative difference) or absorbed (positive difference) will have energies either $$ E_1-E_0 \text{ or } E_2-E_0 \text{ or } E_1-E_5 \text{ or } E_2-E_5 $$ If each of the four transitions were equally ...


7

It's the water itself that forms the lens. Lenses work via refraction. The refractive index of water is about 1.333, which is different from the refractive index of air (about 1.0), so rays of light bend at the junction of the air and the water.


7

Is it possible the: is ke meaning kinetic energy? I ask because the equation for the de Broglie wavelength of a non-relativistic particle is: $$ \lambda = \frac{h}{\sqrt{2m_0 KE}} $$ where $KE$ is the particle's kinetic energy.


7

If you take an isolated hydrogen atom then the electron sits in well defined atomic orbitals that are eigenfunctions of the Schrodinger equation. This is a stable system that doesn't change with time. If you now introduce an oscillating electromagnetic field (i.e. light) then this changes the potential term in the Schrodinger equation and the hydrogen ...


5

Just think about it. The wavelength is the inverse of the frequency, so the shorter the wavelength, the higher the frequency. Photons in the visible electromagnetic spectrum are generated by an oscillation of charge currents. Consequently, because these oscillations are proportional to the frequency of the light wave, more oscillations yield a higher energy. ...


4

The Higgs gives mass to other fields because it couples to them, producing terms in the QFT Lagrangian that look like what you ordinarily would call a mass term, without us having ever to write down an explicit mass term. Thus, the Higgs "gives rise" to the field/particle species property "mass", since it allows us to get massive theories without having to ...


4

While people normally quote Newton's Second law as $\vec F = m \vec a$, it is better written as $$ \vec F = \frac{d\vec p}{dt} $$ Force is a rate of change in momentum. This means that the average force applied when an object undergoes some discrete change in its momentum is $$ F_{\text{avg}} = \frac{\Delta p }{\Delta t} $$ The change in your momentum ...


4

The energy is conserved but it becomes "lumpy"- more in some places (directions), less in others. Total over all directions is the same.


3

The work done by a force $\mathbf{F}_1$ when a particle travels a path $\gamma : [a,b]\subset \mathbb{R} \to \mathbb{R}^3$ is defined by $$W(\mathbf{F}_1, \gamma) = \int_\gamma \mathbf{F}_1 = \int_a^b \mathbf{F}_1(\gamma(t)) \cdot \gamma'(t) dt$$ I wrote that way just as a way to make clear that the work depends both on the path and on the force. If ...


3

A few thoughts to help you on your way. When an elevator is moving, you have to do work against gravity. You are changing the potential energy of the system. The faster the elevator moves, the more work per unit time is needed (because power = work times velocity). If you are changing the velocity of an object, you are changing its kinetic energy: if it's ...


3

As far as dimensional analysis goes, temperature and energy are separate and independent physical dimensions. However, there is a more or less unique way to translate temperatures into energies and vice-versa, which is by means of Boltzmann's constant $$k_\text{B}=1.380×10^{−23}\:\text{J}/\text K.$$ Any given temperature $T$ has an associated ...


3

Let us assume that once the bubble is created, the physics is essentially no different from what is responsible for the work making an Helium balloon rise in the air i.e. you have a macroscopic/mesoscopic object which has a density smaller than that of the fluid surrounding it. Now, we all know that in a static fluid under gravity, pressure is decreasing ...


3

Newton's law does predict the bending of light. However it predicts a value that is a factor of two smaller than actually observed. The Newtonian equation for gravity produces a force: $$ F = \frac{GMm}{r^2} $$ so the acceleration of the smaller mass, $m$, is: $$ a = \frac{F}{m} = \frac{GM}{r^2}\frac{m}{m} $$ If the particle is massless then $m/m = 0/0$ ...


3

It is possible to capture positrons (antiparticle of electron) in a magnetically confined plasma - the repulsive forces get very large unless you do something to equalize the charge. The energy density that could be achieved is stunning. This was the principal plot line behind Dan Brown's "Angels and Demons" - this plasma (made at CERN, that den of mad ...


3

Since the photon reflects, its momentum changes: $p_{ph}'=-p_{ph}$. But total momentum of the system is conserved: $p_m+p_{ph}=p_m'+p_{ph}'$. Thus, the mirror will change its momentum. But, if the mirror has large mass, then it'll get very small energy from the collision. For zero-mass particle (photon) falling onto the mirror with mass $m_2$, the energy of ...


2

Your requirement that the measurement be made with equipment available in a kitchen is a severe constraint as I can't think of any way of measuring the electrical power supplied. If it's impossible to measure the electrical power in then the only other approach is to measure the thermal power out - i.e. measure the heat produced by the appliance. Given that ...


2

The collapse of the wavefunction is not a real physical process. It's a feature of a particular interpretation of quantum mechanics, the Copenhagen interpretation (CI). Other interpretations, such as the many-worlds interpretation (MWI), don't have such a collapse. The different interpretations make the same predictions about all observables, and therefore ...


2

When a bubble is rising up, water is filling up the space behind it. The work done by the bubble rising up is exactly same as the water coming down to fill the space behind it, but with a -ve sign. So the total energy will remain constant.


2

Photons coming from changes in the energy level of an electron in a bound state ( atom,molecule,lattice) come in discrete energy slices. emission spectrum of iron Photons coming from the radiation emitted by accelerating or decelerating charged particles are coming in a continuum spectrum. Bremsstrahlung radiation Spectrum of the X-rays emitted ...


2

There are several things in play here. A photon emitted as a result of a transition of electrons between two well defined orbitals in principle has a well defined state However, the uncertainty principle limits how well that state can be known. You have shown yourself familiar with the energy-time formulation of the uncertainty principle; a transition ...


2

The question is what do we need the matter content of the universe for. As I understand it, in the usual case we want to find the conserved quantity associated with a certain conserved current gained by the projection of the energy-momentum tensor into a Killing vector, as for example in the paper by Abott and Deser. The requirement of asymptotical ...


2

You may define a conserved total stress-energy tensor (matter + gravitation). The main problem is that a conserved total stress-energy tensor is not covariant, and that a covariant stress-energy tensor is not conserved. Said differently, $\nabla^\mu T_{\mu\nu}=0$, which is a covariant equation, does not represent a conservation law, while $\partial^\mu( ...


2

If the bell is still vibrating when you let air inside it, then the answer is yes. If the bell was damped just before the door is opened, then the answer is no. Sound is transmitted through compression / decompression waves (pressure waves) in a medium (e.g. air, water, wall). This necessitates contact of the vibrating source of sound with such a medium. ...


2

As for the helicopter problem, theoretically, arbitrarily low power can be sufficient to float a load, if you push down a lot of air with very low speed. However, you need longer and lighter (and maybe wider) blades for that, so the problem you'll have to solve is that of structural strength. Let me note that recently a muscle-driven helicopter ...


2

You have a rather precise power meter in your home, which is a "gift" of the electrical power company. Turn off every other load that is connected to that power meter and do your measurement. Alternatively, you can invest $20 in an electronic power meter that is available online and in many stores.


2

The easiest way would be to use an energy monitor device (the most popular one seems to be the Kill-A-Watt but there are others). They simply plug into the wall and then you plug your appliance into it. It displays instantaneous voltage, current, power, power factor, etc. and can keep total energy over time. Another option would be to buy an electric ...


1

There is no way one can answer this question without further requirements. In practice, engineering considerations will put wireless charging of vehicles probably somewhere between the 20kHz and 150kHz range (unless the regulator permits a higher frequency). Why 20kHz? Because all wireless charging solutions will involve the generation of some amount of ...


1

The notion of kinetic energy is ill-defined in the spacetimes where you have a time-dependent cosmological expansion. If you somehow attached two galaxies to each other with a spring, however, the expansion of the universe would do "work" against that spring, as there would be a force requied to keep the proper distance of the two galaxies fixed. At ...



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