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15

If you could take from orbital energy, then it would decrease, until at some point in the future it would zero. Hence, it can't be perpetual.


10

We already harvest energy from the Moon. It causes the tides and stress and strain and motion throughout the Earth. As a result, the Moon keeps getting farther away. (And it causes some heating in the Earth). The Moon at one time had a spin that was not locked to the Earth, and the tidal bulges in the Moon's shape caused by the Earth generated heat in the ...


8

First, the energy expectation value of the superposition state you have written down is $$ \left(\frac{n_1 + n_2}{2} + \frac{1}{2}\right)\hbar\omega $$ and one might naively conclude that therefore the energy of the state lies in between the energy of its constituents. This naive concept doesn't work, though - the "energy" of a state that is not an energy ...


5

You could harvest lots of energy from the moon but not an infinite amount. Taking orbital energy from the moon will cause its orbit to decay with time. This offers its own problems. The closer the moon got to Earth, the more extreme tides would become on Earth with potentially destructive consequences. And, in the end, if you continued to take energy ...


3

It is difficult to see how. Most comets and asteroids would encounter the Earth on a crossing orbit and the encounter velocity would be roughly the vector sum of the Earth's velocity around the Sun (of order 30 km/s) and the individual velocity of the rogue object. The individual velocity will vary from $\pm 30$ km/s for objects at a similar distance to the ...


3

Conservation of energy is still fine the following sense: For any region, the energy at a later time is equal to the energy at the current time, plus the net flow of energy in and out of the region during the interval of time. And the energy in question includes the rest energy of bodies, their kinetic energy, their thermal energy, etc. Anything except ...


2

There are macroscopic forces that admit no description in terms of a potential, for example, any friction force proportional to the velocity of a moving object as path-dependent integral, and is hence non-conservative. But we know the macroscopic description is not the fundamental description. In terms of the interaction of the constituents of matter, all ...


2

Where did the energy you spent go? You gained knowledge about the equation I gave. I'll try a different approach before this question is closed or migrated elsewhere. In the context of your question, the answer must be know (heh... no). Consider the case that you expend all the energy calculating incorrectly. Knowledge is, at least, justified ...


2

Yes, absolutely. Potential energy is not a measurable physical quantity. What can be measured are differences in potential energy. So, if you compare the potential energies of a given mass at the Earth's surface and $100 \, \mathrm{m}$ above the surface, you cannot choose their difference, because that is governed by the laws of physics. However, you can ...


2

Dark energy is not negative energy. It causes a repulsion because of its unusual equation of state, which causes it to behave as if it has a negative pressure. There is some discussion of this in the answers to Have negative pressures any physical meaning? and possibly also 'Negative pressure' counteracting gravity?. When general relativists talk ...


2

Quoting Sean Carrol's article linked by Симон Тыран, which makes the case for energy not being conserved: Having said all that, it would be irresponsible of me not to mention that plenty of experts in cosmology or GR would not put it in these terms. We all agree on the science; there are just divergent views on what words to attach to the science. In ...


2

I'd say part of the answer must be that whatever dynamic variable you use, like Enstrophy, Vorticity, their potential analogues, etc. those are always 'filtered' fields. Filtered in the sense, that you start with the velocity field $\vec v = \sum u_i \vec e_i$ that has full information over the dynamics and then apply some operators (integration and ...


2

In the case of an explosion, before the explosion the momentum of the bomb is zero, so according to law of conservation of momentum, the momentum after explosion should also be zero. So, momentum of the bomb before collision = momentum of the bomb after collision. As for sound and light energy, I think that it is the chemical energy of the bomb that is ...


2

Introductory physics problems often limit the momentum economy to the motion of large particles or fragments (collisions and explosions) for simplicity of calculations. In reality, the momentum transferred to any surrounding gas (air) should ideally be part of the conservation. These introductory problems are constructed so that compression waves and huge ...


2

If the particle is in an eigenstate of the Hamiltonian, you will get the same energy eigenvalue every time. We know that energy is conserved because the Hamiltonian obviously commutes with itself. The only time it is not conserved is if the Hamiltonian depends explicitly on time.


1

The equation you wrote $$ H|\psi\rangle=E|\psi\rangle $$ is the time-independent Schrödinger equation for an energy eigenstate. I.e., the state you are considering is already an eigenstate of the Hamiltonian with energy $E$. Therefore, as mentioned in the other answer, its time evolution is a simple phase factor, and you will always measure $E$ if you keep ...


1

If energy is conserved, how so that a measurement of the energy of a state, such as $$ \psi = N (\phi_1 + \phi_2), $$ could result in two different energies? I think your question is easiest to tackle with the consistent histories interpretation of QM (though you'll reach similar conclusions with any other interpretation). We must remember that energy can ...


1

The wires don't perform work because the direction of motion of the log is always perpendicular to the wires. If the wires don't stretch, then the motion of the log is circular with each wire as the radius of that circle. Therefore, the motion is perpendicular to the tension force. The formula for work $W = F\Delta x \cos \theta$ is zero for $\theta = 90^o$. ...


1

The first law of thermodynamics (through conservation of energy) precludes that there can ever be an infinite energy source. However one must consider infinity as theoretical. We humans might consider an energy source that could power the whole of our society for a million years infinite, but on a cosmic timescale it is merely a dot on a very, very long ...


1

The answer was in fact covered by the Curious Mind, but for you to see the process how the potential energy transforms into kinetic, here is an elementary elaboration. The equation of motion in the gravitation field says that $ \ (1) \ h_0 - h = \int _0^t v(t) \ \text d t $ Multiplying this equation by $mg$ which is constant $ \ (2) \ E_P(0) - E_{P}(t) = ...


1

I think you could possibly engineer such a collision between two bodies in horseshoe orbits. The minimum mutual speed between the two bodies depends on their mass difference, with a limit that approaches zero speed if the bodies are the same mass. I haven't tried very hard to do this, but it's the only possible way around the escape-velocity argument put ...


1

The relationship between the density $\rho$ of some quantity $Q$ and its flux $\mathbf j$ is always in the form of a continuity equation, $$ \frac{\partial \rho}{\partial t}+\nabla\cdot\mathbf j=S, $$ where $S$ is a source term for $Q$, equal to the amount of $Q$ that appears per unit volume per unit time at each position. If $Q$ is conserved and you've ...


1

When you walk up a hill, pushing a bicycle or not, you increase your potential energy by spending chemical energy. One of the reasons you need to eat is to ingest fuel, so to speak, that allows you to spend energy on doing your daily tasks. For example, your body can metabolize sugar (most notably glucose) by oxidizing it, which frees energy that you then ...


1

Suppose you raise your book to a height. Here as you said the potential energy of book will increase. now what happens if I let the book go down? The potential energy will now convert into kinetic energy and hence the potential energy of the book will decrease. Now what If I stop the book in the midway by catching it before it touches the ground? When ...


1

Your thought experiment stumbles upon an important idea in electrodynamics which is quite counter-intuitive.The EM field produced as radiation due to the charge in fact produces a reaction force on the charge itself. This is known as the Abraham–Lorentz force which is proportional to rate of change of acceleration of the charge. In SI units it is given by, ...


1

When they say "Do not ignore electric force", they mean that there is both a magnetic and an electric force on the electron/positron, and you should not forget the electric force. In other words, you are asked to compute, for the $\vec v_+$, $q_+$ of the positron, the effect on the electron of its $\vec E$ and $\vec B$ field. Fortunately, 5 keV (kinetic ...


1

Long story short: conservation of energy only holds locally where you can assume a static spacetime. On large scales the expansion of the universe gets relevant, so energy is said not to be conserved universally since the amount of dark energy per volume stays the same while the volume increases, see Sean Carroll's article, from which I quote: The famous ...


1

Whether energy is or isn't conserved in an expanding universe is a somewhat vexed issue. On the one hand you have an experienced physicist claiming that energy is conserved, and on the other hand you have an experienced physicist claiming that energy is not conserved. The problem is that accounting for energy in general relativity is a complicated business. ...


1

It all depends on where you have set your coordinate system. If it is on the earths surface then yes but if you set it say on the sun then no.


1

Law of conservation of energy states that the energy can neither be created nor destroyed but can be transformed from one form to another. Let us now prove that the above law holds good in the case of a freely falling body. Let a body of mass 'm' placed at a height 'h' above the ground, start falling down from rest. In this case we have to show that the ...



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