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Exerting a force and providing energy are quite different things. In particular, to provide energy to a body the force needs to perform work, that is, it needs to move the object in the direction that the force acts in. In the case of the Moon, the movement is circular and perpendicular to the gravitational force, so there is no inwards / outwards motion.* ...

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A battery connected to a capacitor is an RC circuit in the limit $R \to 0$ (i.e., there is no resistor and the resistance of the wire is negligible). One might think that the energy loss is zero in this limit, but this is not the case. For an RC circuit with a battery and an initially (i.e., at $t=0$) uncharged capacitor, we have Q(t) = CV ...

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The process of inverse Compton scattering does exactly this. A photon can interact with a relativistic (ie. hot) electron, absorbs some of its energy, and emerges from the interaction with a higher frequency and energy. This has the effect of cooling the electrons. Roughly speaking, the new frequency is related to the original frequency by $\nu \sim \gamma^2 ... 3 The vector potential of an oscillating dipole (using the usual electric dipole approximation) can be written as $$\vec{A} =\frac{\mu_0 I_0 l}{4\pi r} \cos \omega(t-r/c)\ \hat{z},$$ where the dipole is of length$l$, with a current$I_0 \cos \omega t$and$\hat{z}$is a unit vector along the z-axis of the dipole. Using the Lorenz gauge one can then ... 3 Can we write for example$\frac{dE}{dt}=\frac{\partial E}{ \partial t}$? Try writing an expression for$W(t_2)$and$W(t_1)$and subtracting them and then dividing the result by$t_2-t_1.$If you then push the parts with the fields inside a common integral then will you see something that looks like$\partial/\partial t$? Don't ever let symbols ... 3 Conservation laws are intimately connected with symmetries. This was proved by a mathematician called Emmy Noether in 1915 and is called (not unreasonably) Noether's theorem. The only assumption required is that the system can be described with Lagrangian mechanics. In particular conservation of energy is related to a symmetry called time shift symmetry. ... 3 You are looking at a specific application of a more general formula $$v_q^2-v_{oq}^2=2a_q(q-q_o),$$ where$q$is the coordinate direction, the$v$terms are velocity components along the$q$axis,$a_q$is the constant acceleration component along the$q$axis, and$q$and$q_o$are the positions along the$q$axis, which match, respectively with$v_q$... 3 The following diagram and explanation from Cornell University's page A Brief Introduction to Particle Physics may be of help: (Note, as correctly mentioned by @HDE in the comments, the term 'mini Big Bang' is a bit misleading, but the main point remains as @Jon Custer mentioned in the comments: The mass gets converted into energy. And energy can be ... 3 At the moment we don't know what dark energy is so we formulate hypotheses and compare them to the experimental data. The two most popular hypotheses are: dark energy is due to a cosmological constant dark energy is a scalar field referred to as quintessence and both of these have the property that the total energy inside a volume of space increases as ... 3 Is it carried away as momentum imparted on the [product] atom? Is it carried away in neutrinos? Is it carried away as gamma rays? All of these can happen, and in general nuclear reactions will output their energy via a combination of these. The specific combination, of course, depends on the specific reaction. Also, if neutrinos are massless, can ... 3 You can actually infer the difference of the approaches just by looking at their names. A vector has direction and an energy (a scalar quantity) does not. Therefore, when you are trying to figure out scalar quantities such as distance and speed, you may find energy method more advantageous; when you look for velocity, acceleration, you have to use vector ... 2 As you say, light is composed of quanta, and they are called photons. They are elementary particles and they have energy h*nu . They can be generated by changing charges and magnetic fields, by the atomic transitions from excited energy levels. For an observer at rest with respect to the atoms (or accelerating charges) emitting the photons the energy they ... 2 "Matter can never be destroyed, so what happens to those particles? Do they just disappear? Where does the mass go?" It's not true that "matter can never be destroyed". According to classical understanding, yes, mass was always conserved and was never destroyed. But that's not entirely correct. The meaning of the well known equation$E=mc^2$is that energy ... 2 What happens to a particle and antiparticle that collide? The 511keV/c² electron is typically converted into a 511keV photon, and the 511keV/c² positron is converted into another 511keV photon. However it needn't be a 1:1 conversion. Check out positronium where you can read that the triplet state's leading decay is to three gammas. That's three photons, ... 2 It does not matter that there is no external force acting on the system. The kinetic energy comes from the man running on the boat. He is turning the chemical energy in his muscles into kinetic energy. If we have an isolated system (i.e. one with no external forces and where nothing leaves or enters the system), we require energy to be conserved within that ... 1 You need to distinguish between real and virtual gravitons. A gravitational wave can in principle be represented as a superposition or real gravitons, just as an electromagnetic wave can be represented as a superposition of real photons. A gravitational wave carries energy, just as an electromagnetic wave does, so if a system is generating gravitational ... 1 An ideal capacitor never "dissipates" energy, it merely stores it. The amount of energy stored in a capacitor is given by the formula you mentioned:$U = \frac{1}{2}CV^2$. In the case of the LC circuit, the energy stored in the capacitor moves into the inductor in form of magnetic field energy and then goes back and forth from them. In the case of an ideal ... 1 What evidence is there for additional dark energy coming into existence when space increases? None. As I understand since cosmological constant is a 'constant' - increasing the space must generate additional dark energy that fills that space That's what people say. But we have no evidence whatsoever of anything wherein conservation of energy does ... 1 Normally, an isolated system means that no energy, momentum or angular momentum enters of leaves the system. These quantities are conserved for the system. The best way to answer the question of whether isolated or not is to imagine a boundary around the system and ask: does any energy, momentum or angular momentum pass through it? OR: are there only ... 1 You should get over your fear of Bernoulli because it is useful in a number of different situations. Besides you will find that the conservation of (total) energy will simply revert to the Bernoulli equation (which is a statement of the conservation of mechanical energy) under most practical assumptions (as you have found out). It is not difficult to ... 1 The gravitational potential energy is the energy stored in the gravitationnal field not in the masses them selves, the energy$E = mc^2\$ is the mass-energy equivalence (at rest), think of it as energy has mass, most of the matter mass is due to the quark-gluon plasma energy and contributions from higgs mechanism,the more energetic particle the more massive, ...

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