Energy conservation Definition and 432 Threads

Please see the derivation below that, if the metric is time-independent, then the integral over a sufficiently large 4D spacetime region of ##T^0_{\,0} \sqrt{-g}## is independent of time, where ##T^{\mu\nu}## is the energy-momentum tensor of a relevant collection of matter-energy fields. Thus, I...

Assume that this is a case where by sheer coincidence, two sources of coherent single-frequency EM wave pulses with equal duration are both fired in opposing directions, with both carrying the same frequency and amplitude and orientation. These two waves meet head-on while moving in opposing...

So I do realise that this problem involves energy, I still wrote equations for forces acting on each block. I will assume coefficient of friction to be ##μ## for convenience. For block 1: ##F - kx - μm_1g = m_1a## For block 2: ##kx= μm_2g## I then wrote an energy equation assuming a velocity...

Hi, reading Feynman's lectures on section 10-5 I came up with a question. He claims that electromagnetic fields have momentum. He gives an example of two charges A and B in a electromagnetic field. When the charge A is suddenly moved (as I understand by an external force w.r.t. the "A + B"...

I'm trying to make a very basic physics engine. So far I've got a variety of small things worked out but I've been driving myself crazy trying to work out collisions. From one sense I get I can use momentum and impulse to determine the velocity of an object after a fully elastic collision (no...

Hi, soppose we have a resistor at a given temperature T connected through a diode to a cell battery. The voltage accross the resistor due to thermal noise should charge the cell converting termal energy into chemical energy without limits. Does the above process violate the second law of...

Hello, Stephen Hawking's book The Future of The Universe says that matter would have to exceed the minimum speed of 5 times the speed of light to exit a black hole. This means that the matter would have to be transferred to Energy using E=MC^2 but all energy is limited by the speed of light...

Hello all, I'm new here … interesting discussions. My question is: When an electron "jumps" from a higher energy level to a lower one, a photon is emitted. Is it correct to say that it is the electron that emits the photon? Or when an electron aligns in a magnetic field, a photon is either...

Through mechanics, potential energy is released by the controlled falling of a suspended mass. At an idling condition, a one tonne mass is allowed to slowly fall. The pushing force of that mass is used to maintain a set rpm of a flywheel. The flywheel shaft drives an electric generator. At a...

Dear PFer's, this is a problem I have been struggling with for years. Is energy conserved (not in a statistical sense) in QM? The so-called collapse of the wavefunction, occurring during a measurement process, is incompatible with energy conservation - at least in the general case. A starting...

With given information in the problem I can't decide which direction balls will go after collision. I assumed they will go in opposite directions. I know that is not a full solution, but I can't come up with anything else. From conservation of energy we have...

For this problem, How can energy be conserved if the bit highlighted in orange is true?Many thanks!

When a coin is dropped from a certain height and collides with a glass surface, is the majority of the potential energy converted to sound or heat? And how would one determine this as I only hear the sound and cannot measure the significant change in temperature?

I was wondering why energy of capacitor does not equal change in kinetic energy PLUS change in potential energy where potential energy is the change in the potential energy of the charges. I believe that should be so because energy conservation = change in kinetic energy plus change in potential...

I have successfully completed parts A, and B, however, I am confused on Part C. Here was my attempt and the answer key's attempt: My attempt: Since I correctly knew the speed after the collision, and the gravitational potential energy after the collision if I set h=0 at when it was at rest...

Please help me to understand which ans is correct. To determine the ##P2##. $$ h_{LM}\ne 0 $$ Method 1： $$dP=\frac{\partial P}{\partial x}dx+\frac{\partial P}{\partial y}dy+\frac{\partial P}{\partial z}dz$$$$\phantom{\rule{0ex}{0ex}}\rho \overset\rightharpoonup{a}=-\triangledown p+\rho...

I wrote some potentials but they were wrong. I used the cm of all fluid parts and I used the radius which is $$ \sqrt S/ \pi $$ .

I found this article* about the behavior of quasar outflows in cosmology and how they can create a magnetic field. In section 2.1.4., the authors say that when a quasar produces a "wave" or an outflow, the material will be emitted with energy coming from both the quasar itself and the Hubble...

krotovs solution is based on energy conservation. My question is that why the solution didn't consider inductors energy? the question: The solution:

Hi, I completely failed this homework. I mean I think I know what happen, but I don't know how to show it mathematically. The energy lost by the wave is used to oscillate the electrons inside the conductor. Thus, the electrons acts like some damped driven oscillators. I guess I have to find...

Sean Carroll has an article (https://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/) where he explains that matter can gain energy from spacetime expansion. At the end of the article, he says: In general relativity spacetime can give energy to matter, or absorb it from...

this is an easy problem but would it be possible to consider car-car system. What I did on paper was carsystem and because they have the same properties(mass en speed) multiply by ##2## solution for car-car-earth system I assume is the following if it is possible? solution for car-car: law or...

For reference:

Is there any approach in any books out there, where we consider that in universe exists only one field, let it be called the Unified Field (UF), in which all of the known fields (gravitational, EM field, quark field, gluon field, lepton field, Higgs Field, e.t.c.) are just components (pretty...

This is the catapult. At equalibrium the spring is 0.09 meters in length. When its fully stretched out its 0.225 meters long and I place a rock (0.205 kg) close to where my finger is on the catapult. The catapult starts with this much energy because 1/2 * k * x^2 90.54 is the spring constant...

Hi! I want to start with saying that I'm not an expert on these type of problems, but I will be gratefull for some calarifications. I've heard that there's nothing in psysics that says that time travel is impossible. I want to make a case with the time traveling battery. Could be any mass with...

The transition probability -- the probability that a particle which started out in the state ##\psi_a## will be found, at time ##t##, in the state ##\psi_b## -- is $$P_{a \to b} = \frac{|V_{ab}|}{\hbar^2} \frac{sin^2[(\omega_0 - \omega)t/2]}{(\omega_0 - \omega^2}.$$ (Griffiths, Introduction...

As my current studies have proven conservation of energy is a universal law. How is it possible for two entangled particles to be equally or similarly affected when a force or energy is applied to a single member of the entangled pair? The production of such a pair would be invaluable to...

Hi all, My question is about Doppler redshifts, but I'm going to mention cosmological redshifts first because I'm a lay person as far as cosmology's concerned (I'm an amateur astronomer and did a few introductory astrophysics/cosmology courses at university, but my degree focus was planetary...

Is energy really not conserved in a constantly expanding universe?

A bullet with mass m, velocity v perfectly elastically, vertically collide with one end of a rod on a slippery plane and the bullet stops moving after the collision. Find the mass of the stick M the bullet stops moving after an elastic collision, so all energy is transformed to the rod. There...

I've tried establishing a systems of equations with -(1/2)kx^2+mpgx+(1/2)mpvp^2=0, but this leads to an annoying quadratic that when solved does not give one of the listed answers. My thought was that the spring's potential energy is going to be equal to the gravitational potential energy and...

It is known that constructive interference in one place must be compensated for by destructive interference in another. Take a simple Fabry Perot resonator for example. The interference occurring at both sides of the first mirror (assuming one incident electric field) compensate each other out...

The total amount of energy is still a conserved quantity, even in an expanding universe based on a positive and constant energy density, and even under the rapid exponential expansion during inflation, total amount of energy is conserved. For how this works, see this lecture by Alan Guth, the...

While I am working through proving the homework statement, I encountered a problem. The problem is as follows: From the energy equation above, one can see that the minimum value of ##p## is ##m_T##. However, how does one explain why when ##p=m_T##, ##\sqrt{m^2_B+m^2_T}>m_A##?

Also, I have heard from physicists that vacuum energy fluctuation (creation and destruction of virtual particles) violates energy conservation. The reason, they justify, is based on uncertainty principle (energy-time form of uncertainty principle), energy can exist and disappear for a very short...

The ##I_i## are the intensity of the rays, in other words energy per surface units per radians by seconds. The d##\Omega## are the solid angles The equation p75 isis what I don't understand. I suppose that each side represent the energy going and out of the surface dS but I don't understand...

Hi all. I'm trying to prove energy conservation in a (maybe) uncommon way. I know there are different ways to do this, but it is asked me to prove it this way and I'm stucked at the end of the proof. I'm considering ##N## bodies moving in a gravitational potential, such that the energy is ##E =...

I solved this problem easily using Newton's second law, but I had problems trying to use mechanical energy conservation to solve it. How I solved using Newton's second law: ##\text{(part of the rope that is on the left)}\, m_1=x\rho g,\, \text{(part of the rope that is on the right)}\...

I've come to a grinding halt with this and I can't see a way forward. Can someone please take a look at what I've done so far and let me know if what I have done is OK and then if it is, give me a hint on how to proceed. First up, Is ## u \cdot \nabla \cdot T = u_\alpha...

This is very much, a ... what's wrong with this approach... Consider a large mass with no atmosphere, i.e. the moon. On it, construct a tower of arbitrary height. On the tower build an energy to mass machine, to convert energy to mass via E=mc^2. Once the mass is created, drop it from the...

I'm looking at Schutz 7.4 where first he obtains the following expression for a geodesic: $$ m \frac {dp_\beta} {d\tau} = \frac 1 2 g_{\nu\alpha,\beta } p^\nu p^\alpha $$ This means that if all the components of ##g_{\nu\alpha }## are constant for a given ##\beta##, then ##p_\beta## is also...

I am learning about capillary action of water. As water moves up paper. How is that not violating energy conservation as it is going against the force of gravity. This obviously can't be infinite energy.

Hello! I need some help with this problem. I've solved most of it, but I need some help with the Hamiltonian. I will run through the problem as I've solved it, but it's the Hamiltonian at the end that gives me trouble. To find the Lagrangian, start by finding the x- and y-positions of the...

Hi PF! I don't understand the sentence: on one side says the energy is preserved, and, at the end, the total energy of the system will change if ##W## or ##Q## is added: ##\Delta{U}=Q+W##. Greetings!

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I am not sure if i can explain my question properly. I am studying the Generators section in the magnetism chapter. As i mentioned the statement "The rate at which work is done is exactly equal to the rate at which energy is dissipated in the resistance". When the term dissipated is used does it...

I thought I'd calculate how much heat was required to melt the Iron Throne, and then multiply that by the number of flame-gushes during the sack of Kings Landing, to get a total amount of energy expended. Then I'd convert that to calories and use the average number of calories per goat to...

In b). Since the force T is perpendicular to the trajectory of the mass m, T does not perform any work on m, therefore the translational mechanical energy is conserved, from which I deduce that the initial speed is equal to the final speed, moreover, the speed is constant. Now, when analyzing...