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Conservation of energy/mass is the result of a symmetry called time shift symmetry, and if this symmetry is broken energy/mass will no longer be conserved. It is far from obvious that time shift symmetry would be preserved if closed timelike curves were possible, so you can't use conservation of energy as an argument that time travel is impossible.


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Because in the second scenario you described, the exhaust gases from the rocket fly off at high speed into space. This is where the extra energy goes. A better alternative to get circular motion of the satellite with the earth removed, would be a second satellite, connected to the first satellite with a long cable. If, for example, both satelittes have the ...


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Considering 'space-time', rather than space and time, time is essentially just a 4th axis along which we can move (generally at a rate of one second per second in the positive direction); the other three being the familiar x, y and z Sending something backwards through time (if possible) would not involve destroying energy in the present and creating it ...


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The above statement is not correct. First of all, you need to work against the force of friction while climbing stairs.So the energy is not entirely converted to PE.Rather a portion of it is dissipated. Secondly, even if we leave out friction, the basic flaw of the statement lies in the part: " the energy is converted to PE within system only. The person ...


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Can matter be created in a pure vacuum (with no energy)? It's a subtle question. Firstly, how do we know whether there is energy? But even if there were energy if it was a minimum of energy then you wouldn't be able to use it to make things, and the energy minimum would be considered a good vacuum. But can you make particles? If they just appeared ...


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I was not able to convince him that this propulsion drive cannot work due to conservation of momentum. Am I wrong about that? No, you are not wrong. It's clear that the engine cannot work because of momentum conservation. It's basically just a fixed double pendulum. Why should there be any positive momentum in any direction after one full circle? ...


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Historically, conservation of energy may have been discovered by Julius Robert Mayer in 1842. When he was a youngster he tried to build a water wheel that drove an Archimedean screw to lift water back up to the top of the wheel and keep it turning. He found this to be impossible. The lesson stayed with him 'til later in life he became a doctor and studied ...


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You are correct that global energy isn't conserved. But it is actually worse than that. Since energy is frame dependent and there isn't necessarily a global frame, then there isn't even an objective number called total energy that can change from moment to moment. So there just isn't a thing called total energy. And energy isn't free, to get some energy ...


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There is a reason physics starts with kinematics, description of motion and evolution is what it is about and once you throw in the causes you get dynamics, which is everything. It is not obvious that energy is secondary at all. And I dispute it. How can you tell you have something? Because it interacts in certain ways (dynamics) or it has the capacity to ...


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Technically, the energy of a system is conserved. This is a subtle, but important, distinction from the energy being constant. Conservation is different from constancy in that energy can move in and out of a system and can change forms, but it is neither created nor destroyed. An expanded formula would look like this: ...


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then the created pions will be at rest correct? Well, they will be at rest in the Center of Momentum frame. But that is not the frame of reference that your problem is stated in. Momentum is conserved, which tells you that you have written the pion four-vectors incorrectly.


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Most time machines seem to require having exotic matter which has negative energy density, so perhaps you can send back some negative energy and some positive energy. Creating mass isn't an issue, mass isn't conserved and really that's because the mass of a system isn't the sum of the masses of the parts. And there are other options. For instance, if you ...


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Given the persistence of this kind of thing, maybe determining the misconceptions underlying it are not so easy to determine and resolve. [Given that we're talking about physics students, I guess it's fair to them to sort this out rather than ignore as one might otherwise.] For my money, I'd ask whether within each part of the mechanism Newton's Third Law ...


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Part of your problem comes from thinking that the potential energy is somehow located in or a property of the person alone. And the way the subject is usually introduced could easily lead you to think that, but it's not right. The potential energy is a property of the person-Earth system. In fact all potential energies are properties of systems of ...


1

Initially your ball has some energy ($2J$) and some momentum ($2Ns$). And the wall has some energy ($0J$) and some momentum ($0Ns$). And there is some internal energy, $U=U_0,$ the thing that heat increases. Afterwards the ball has some energy ($0J$) and some momentum ($0Ns$). And the wall has some energy ($0J$) and some momentum ($2Ns$). And there is some ...


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Timaeus has given the full technical answer: the kinetic energy of the wall itself changes a tiny bit. Since kinetic energy scales as $v^2$, this is totally negligible in the first case (where the wall starts with $v = 0$) but actually significant in the second case (where the wall starts with $v = 2$), and that's where the missing energy goes. Luckily, in ...


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To find the minimum velocity at the bottom-most point, we find the minimum velocity at the uppermost point. This minimum velocity is the one such that the centripetal force is equal to the force of gravity. Any lower and gravity will pull the object down and out of the loop, any higher and a faster velocity would be required to generate it (thus, not a ...


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As one of the comments mentions, it is simpler to consider a linear case. Dropping a body of mass $m$ on one moving with mass $M$ and velocity $v$ is essentially considered the instantaneous transformation $M \to M + m$. Momentum must be conserved in the collision, but the mass of the system effectively increases, producing a smaller kinetic energy: $$ ...


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Energy is conserved, but if you ignore some kinds of energy then it will look like it isn't conserved. You can imagine a really big disk with some radial pointing two by fours attached at the one o'clock, two o'clock etcetera positions then attach springs to each two by four with the spring pointing in the clockwise/counter-clockwise directions. Add a nice ...



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