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18

MSalters already said "yes". I would like to expand on that by computing the change. Let's take a 10 kg cannon ball, made of lead. Heat capacity of 0.16 J/g/K means that in dropping from 1000 K to 100 K it has lost $10000\cdot 900 \cdot 0.16 \approx 1.4 MJ$. This corresponds (by $E=mc^2$) to a mass of $1.6 \cdot 10^{-11} kg$ or one part in $6\cdot 10^{11}$. ...


16

Of course, it does, since: $$\frac{\partial E}{\partial t} = \frac{\partial }{\partial t} \left(m \cdot c^2 \right) $$ Very little, though


11

The idea of partitioning energy into different forms like "mechanical energy" or "chemical energy" and such is actually arbitrary. More or less by definition, energy is that which is conserved unter time translations by Noether's theorem. If what you call "mechanical energy" has changed, then there is another term in the Noetherian energy that has changed ...


6

Consider the case in which we shoot an electron up in the stratosphere, it travels up to a certain height and then it stops when its KE = 0. We say, according to that principle, that lost energy is stored as PE. This has been experimentally verified of course, as in falling back it gains the kinetic energy it lost going up. The concept of potential ...


2

The answer to this question depends on your assumption about the continuity of the "metric", the descriptor of the gravitational field. Case 1: Assume that the metric can be discontinuous. In this case the gravitational potential increases abruptly as one crosses the wormhole's throat. It seems that an object entering the lower mouth (A) and immediately ...


2

Would the mass of burnt firewood be equal to the mass of firewood before burning? You won't get a good answer by simply looking at the "burnt firewood". The combustion is using oxygen from the air, and it is creating carbon dioxide and many volatilized materials that will disperse in the air. But we can imagine combustion happening in a box that is ...


2

Yes. The photons play a vital role in balancing out the momentum and kinetic energy.


2

Disclaimer: I'm not a GR expert, but this is how this question has been explained to me by other physicists before. If I got something wrong, please correct me. The traveler does indeed not have to exert as much work to leave the gravity well via the wormhole compared to the normal route. They are not repelled from mouth A nor attracted to mouth B by any ...


2

I think this answer is very hard to answer exactly, since it is not so easy to perform the necessary calculations in the framework of general relativity. It is quite easy to start with curved spacetime that represents a traversable wormhole and investigate, how the matter must be distributed to cause the curvature and investigate what by what forces does it ...


2

However, isn't any closed loop on a PV diagram reversible? The arrows can simply be drawn in the reverse way to create a refrigerator. If any closed loop is reversible then why does the specific Carnot engine (a specific loop) have the highest efficiency? This was exactly the question I asked myself ten years ago :-) The problem is that often students ...


1

You assume that the angular momentum of the right hand rod will be zero after the rods have separated, but this is not so. Consider this diagram showing the rods before and after: Angular momentum is always measured about some reference point. Any reference point can be used, but for convenience I've chosen the centre of mass of the two rods and I've ...


1

The idea of circular orbits with fixed energies for the hydrogen atom's electron is outdated. As was mentioned in the commentary, once you deal with the Atom at the quantum level, there is no fixed radius to a given orbital. Orbitals become probability distributions - for the shapes just put "Orbitals" in a google image search. As you will see, there is ...


1

In Zero-Energy Model, negative energy associated with Gravity counterbalances positive energy associated with matter, photons, etc. So, No, Big Bang wasn't cold. You are just looking at partial picture (you just ignored Gravity). This is what Zero-Energy Model says: With traditional Big Bang model (which doesn't contain Inflation), the universe started out ...


1

In the standard homogeneous cosmological models the total energy in an expanding volume is zero. This is true for positive, negative or zero curvature and it must take into account the gravitational energy (which is negative), dark energy, matter and heat. Since the gravitational energy is negative the heat can be positive and increasing as you go back ...


1

I suspect you are meant to treat the collisions between spheres 1 and 2 and between spheres 2 and 3 as separate collisions. Solve 1 and 2 first. There will always be a solution where 1 continues with unchanged speed - reject this solution, it would mean that 1 passed through 2 without colliding at all. Then, take your solution for the velocity of 2 and solve ...


1

The other answers are great. I decided to plot it, however, because it's nice visualizing these things. Since your biggest doubt is about kinetic energy, be sure to pay attention to the last graph. SYSTEM. Motorcycle going to the left, truck going to the right, bound by an elastic rope ten meters long ($k=100\frac{\mathrm N}{\mathrm m}$). Masses and speeds ...


1

In canonical quantization one constructs the Hamiltonian formalism. Energy conservation is therefore manifest (since Hamiltonian is time-independent and commutes with itself). Quantum-mechanically, the Hamiltonian of the system can be expressed via particle creation-annihilation operators. So, the total energy of the field is also the total energy of all ...


1

The law of the conservation of mass was superceded by the more general law of conservation of energy when it was realized that mass and energy were equivalent. Anyway, you are correct. The mass of the combustion products will always be less than the mass of the original materials. The difference being equivalent to the energy produced.


1

I think this solves everything, it is slightly adapted from the wikipedia. "The closely related concept of matter conservation was found to hold good in chemistry to such high approximation that it failed only for the high energies treated by the later refinements of relativity theory, but otherwise remains useful and sufficiently accurate for most chemical ...


1

so the total torque relative to the center is zero and the revolving speed stays constant at $\omega_1$ This is not possible. When the two forces are unequal, there is a net force on the disk which means its center of mass will decelerate. The net angular momentum of the system (disk plus arm) remains constant - because there is no net torque on the ...


1

This question is very similar to mine, but does not consider gravitational wells aside from the wormhole itself. Actually I think that question does consider a gravitational well that exists in the surrounding space. What seems to me to be different about your question is that you're asking about the forces exerted on objects as they move around ...


1

Posting another view on the already nice answers. Conservation of (mass-)energy is a principle in physics. Feynman used to say, (Feynman lectures on physics) that when various processes are studied, one finds that energy is not conserved, but then looks under the carpet or in waste bin and finds another form of energy which when taken into account makes the ...


1

Let $S$ and $S'$ be the two inertial frame and $S'$ moving with a constant velocity v w.r.t. $S$ frame. Now a force $F$ acting on the particle at point $A$ and displace it to the point $B$. If the position x-coordinates of A point and B point in $S'$ frame are $(x_1',x_2')$ and in $S$ frame are $(x_1,x_2)$ then at any time $t$, $x_1=x_1'+vt$ and ...


1

I had prepared this answer for a question that was made duplicate, so here it comes, because I found an instructive MIT video. (the second link) This answer is for electromagnetic waves mainly Have a look at this video to get an intuition how interference appears photon by photon in a two slit experiment. It comes because the probability distribution for ...


1

Even burning in a closed container would result in a loss of mass via the electromagnetic radiation emitted (i.e. visible light and infrared), and as stated, it would be immeasurably small.


1

It would appear evident that its KE has been drained out by g and definitely destroyed. Is this correct? This is from a different perspective than the other answers and is not so much an answer as an extended comment on the above quoted question. It occurs to me that creation and destruction are, in some sense, absolute. In your thought experiment, ...


1

The covariant formulation of EM is precisely this. The formulation as a gauge theory also does this. ($c = 1$ in the following) Given the $E$- and $B$-fields as spatial three-vectors in some frame, we construct the antisymmetric field strength tensor as (roman indices are spatial indices, summation over repeated indices implied) $$ F^{0i} := E^i \; ...


1

The kinetic energy of the center of masses of the two colliding bodies may increase if their internal structure changes, i.e. if at least one of the bodies were in an excited state, and the conservation laws of energy and momentum allow the exceeding energy to transform into kinetic energy.



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