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The way I like to understand this is in terms of generators of translation. A well known result from classical mechanics (see Goldstein) is that momentum is a generator of translation in the canonical coordinate conjugate to that momentum. For example, linear momentum generates space translations, and angular momentum generates rotations. In Hamiltonian ...


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Yes, at the fundamental level all energy terms are normally either kinetic or potential energy. The only demonstration of this that I know of requires a tool called the Lagrangian, which you might not be familiar with. But maybe you can at least get a flavor of how it goes. The Lagrangian, very briefly, is a particularly useful way to represent all the ...


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Yes. For example, consider the harmonic oscillator potential $V(x)$, where the ground state has energy $\hbar \omega / 2$. Then the ground state of the potential $V(x) - \hbar \omega / 2$ has zero energy. This works because in quantum mechanics, like in classical mechanics, absolute energies don't matter. You can always add or subtract constants. ...


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When you work "fairly hard", your body can produce about 200 W of power - enough for two incandescent bulbs. Top athletes can produce more - in short bursts. Your body is roughly 25% efficient in converting "calories" (which are actually kilo calories) to Joules - meaning that if you work out hard enough to burn 600 kcal per hour, then you actually produced ...


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A (kilo)calorie is a unit of energy, while a watt is a unit of power, which describes the rate at which energy is expended. So a 100W bulb is using 100 joules a second. A kcal is about 4184 joules, so a 100W bulb takes about 42 seconds to consume (really: convert into light and heat) a kcal. The joule is the SI (derived) unit of energy. Units of energy ...


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An average person uses approx. 1500-2500kcal/day. Since one kcal equals 4148J in SI units, that's between 6.2-10.4MJ per day. A day has 86400 seconds, which brings us to an average power consumption of 72-120W... about as much as a light bulb. :-) Physical exercise varies between light (300kcal/h) at an additional 350W to very strenuous at probably six ...


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Saying that a body possesses heat energy is as absurd as saying it possesses work! that is work and heat are merely names given for energy transfers. when you heat an object and say heat energy is transferred, we mean that the molecules in the heated object are becoming more jiggly(vibrations) that is their kinetic energy is increasing. that is what is meant ...


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but still we have momentum telling us that both blocks must rise to the same height That's not true here. In the first case where the bullet is embedded, the final velocity of the bullet and the block must be identical. Since initial momentum of the two shots were the same, then the final momentum will be the same as well. Because they are connected, ...


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De-exictation is the process of transitioning from a high energy state to a lower energy state; the photon emitted has energy equal to the difference in the energy of the two states. If we're tacitly assuming that we started with a system in the ground (i.e. lowest energy) state, then something had to put the electron into the higher energy state before we ...


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It is just understanding the system: closed or open. A closed system doesn't interact with the environment, hence there is no change in pressure and volume. In other words, no external work is done on the system neither by the system. In the second case, there is pressure change due to interaction with environmental, hence work is done by the system or on ...


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I found the answer. the d(PV) is the work done to push new mass in the system


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Gravity fluctuations will always cause vibrations in atoms and molecules limiting the lowest temperature obtainable. Closer to the mass source, the stronger the gravity field. As stated by Asaf earlier, evaporative cooling will lower the temperature only so far. Adding a magnetic field may temporarily increase temperature by increasing vibrations in the ...


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The walls do not really matter that much here. I would say that the only points that matter to understand that quote are: The confining potential is conservative so that $K+U = constant$ The confining potential is virtually flat $U = 0$ almost everywhere inside the box (say 99% of the box) except very close to the walls These two conditions are enough to ...


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Here's an image of the 'particle in a box' model: At the endpoints, you can see that there is an infinite potential outside the boundary of the box and zero potential inside. The unrealistic assumption in this model is that every time the particle reaches the boundary, an infinite force repels it to keep it in the box.


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A 40W incandescent light bulb has a luminous efficiency of 1.9%. That means only 1.9%, or 0.76W, of the energy consumed by the bulb ends up as visible light. LED bulbs have an efficiency of around 10% - the efficiency depends on the design and can be as high as 15% or as low as 8%. So a 6W LED bulb will produce between 0.9 and 0.48W of visible light. The ...


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You're mixing power needs with luminous effects. According to the advert you posted, that LED bulb consumes 6W (power) to get a luminous flux of 500 lumens (lumen is a photometric unit, like candela or lux): https://en.wikipedia.org/wiki/Luminous_flux On the other hand, an incandescent bulb would need to consume 40W (power) to get the same luminous flux. ...


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The advertising suggests that the new 6W bulb generates as much light as a 40W incandescent light used to. Most of the energy in an incandescent light bulb is converted into infrared radiation that we can't see or it's at the red end of the spectrum where the human eye is not very sensitive. This is a typical incandescent spectrum and you can see how ...


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This question appears to be a pseudo-duplicate on the Skeptics exchange, as pointed out by @CraigGidney. The highlights of the comments here and answer there appear to be that: 1) Yes, one could potentially accrue some electricity from soil. 2) No, it would not (ever) be sufficient to charge an iPhone, let alone 3 times. 3) In the comments here, "there ...


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The temperature limit for laser cooling is not related to gravity but to the always-present momentum kick during absoprtion/emission of photons. Ultracold atom experiments typically use laser cooling at an initial stage and afterwards evaporative cooling is used to reach the lowest temperatures. In evaporative cooling the most energetic atoms are discarded ...


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EDIT: The question has been edited (to yet a more obscure form). Here I am replying to the original formulation: Is it possible to calculate the kinetic energy of a body if only its speed is given? Yes ... if the speed is $c$ (the speed of light). In the case of massless particles (think: photon) in the vacuum, what you'd call kinetic energy is ...


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The potential energy is the ability to perform work in the way that... potential energy $U$ is converted into kinetic $K$ energy during the fall. The kinetic energy implies a speed $v$ and thus causes a momentum $p=mv$. On impact this momentum is reduced drastically causing a force $F=dp/dt$. Is the impact-surface displaced by x, then the work $W=Fx$ has ...


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Not at all clear what you mean by "the energy of a star". A ten solar mass star that explodes as a core collapse (type II) supernova releases about $10^{46}$ J, mostly in the form of neutrinos. By comparison, the total rest mass energy of the star is around $2\times 10^{48}$ J. Another comparison would be how much energy a star releases during its ...


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To my understanding, work is done on object A when object B is applying a force on object A, causing object A to displace. Work is done whenever a force displaces an object. Since energy is the ability to do work, what work does a moving object do, due to its kinetic energy? A moving object might not do any work at all. Imagine an empty ...


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The work the ball that you kick does is the ball going against air-resistance and changing its velocity.


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This is a really good question. What you are wondering about is why, when the cross section is constant, the Bernoulli equation doesn't predict free fall. It doesn't have anything to do with viscosity if the fluid is considered inviscid. The reason that the Bernoulli equation cannot be extended to the case of constant cross section is that the usual form ...


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This got me thinking though, what would happen if the cross section does not change, and you have vertical flow of fluid in some pipe with an obvious change in elevation, but then had both the entrance and exit at atmospheric pressure. The energy equation, which is supposed to remain constant for a continuous fluid without losses, would have a differing ...


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Firstly, given a differentiable Lagrangian $L(q,\dot{q},t)$, we can always form the Lagrangian energy function $$\tag{1} h ~:=~\sum_ip_i \dot{q}^i-L ,\qquad p_i ~:=~\frac{\partial L }{\partial \dot{q}^i }. $$ Secondly, make the assumption that $$\tag{2} \text{The Lagrangian } L=L(q,\dot{q}) \text{ has no }{\it explicit} \text{ time dependence.} $$ ...


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Utilising Black Holes as a potential energy source Have I got a surprise for you! I'm aware of the Penrose process and the basic physics behind that. Be wary of Penrose. He has a habit of appealing to Einstein's authority then flatly contradicting the guy. And then he'll tell you about the parallel antiverse and other fairy tales: Also, I ...


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Great question. Black holes are some of the brightest objects in the universe. While we think they require the Blandford-Znajek (BZ) mechanisms to produce things like Relativistic Jets, the bulk of the light (emission) they produce is just the efficient thermalization of gravitational energy when material falls into (`accretes' onto) them. The simplest way ...


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What you are assuming is that the heat capacity remains constant as the temperature changes which is not completely accurate. For example for water, to raise the temperature of water from 15C to 16C requires 4.1855 J whereas to raise one gram from 72C to 73C requires 4.192 J. Not exactly the same. See engineering toolbox for data.


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It is difficult to climb another flight of stairs after climbing ten. I would be exhausted. But nevertheless, the additional potential energy needed to get one level higher is just the same. If it was different, there is an experiment you could do: Take the other person into the elevator of a large building. Go up to some level but don't let them see which ...


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Internal energy is a measure of the amount of kinetic and potential energy possessed by particles in a body and is measured in Joules. Heat energy on the other hand only concerns transfer of internal energy from a hotter body to a colder body.


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I think the error occurs where you state : Now because we found that both disks have the same amount of kinetic energy (and the same mass), that means that they have the same translational speed. (In fact, my professor also did a demo of this in class and we observed that they did have the same speed). The two discs have the same total KE but ...


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There are a lot of subtle considerations involved in precise measurements and calculations of luminous intensity. This article gives an taste of the subject: https://en.wikipedia.org/wiki/Candela If what you want is an answer in watts per square meter, you are going to have to either settle for an estimate based on typical properties of halogen bulbs or ...


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In general relativity, the field equation relates the metric (through the associated curvature tensor) to the stress energy tensor $T^{\mu\nu}$. This can be interpreted as a flux of energy and momentum in spacetime (i.e. integrating $T^{\mu\nu}$ over a spacetime hypersurface, like a three dimensional hypersurface of constant time, tells you the rate at which ...


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$V$ and $N$ are independent variables. If $F$ is identically zero, there can be no work, neither by expansion nor by chemical potential. So $Φ$ and $G$ must be zero, respectively.


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You can't. The theoretical upper limit for the efficiency $\eta$ of a "classical heat engine" (an IC engine falls into this category) is that of the Carnot cycle: $$\eta = 1-\frac{T_C}{T_H}$$ $100\%$ efficiency corresponds to $\eta=1$. $T_H$ and $T_C$ are the temperatures (in ${\rm K}$ or other absolute units) of the hot and cold reservoirs of the heat ...


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A non conservative force is generally anything that is affected by friction or air resistance. The amount of energy lost is distance dependent because the further the path traveled, the more an object is affected by these forces. Conservative forces are displacement dependent, meaning they depend only on an initial and final position, and that all the ...


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The simplest example for a non-conservative force is frictional force. For example, to move an object from point A to point B on the table we would require say $10$ J of energy, now to put it back to point A, we would need same $10$ J of energy. Practically nothing observable has changed, but we've performed $20$ J of work, which went to overcome frictional ...


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@Prayas Agrawal No I'm not missing that - I'm just explaining the original error. Of course the total work = the KE. In fact since the floor is frictionless, the disc remains stationary and just spins since the force has no line of action through the CoM. In the case of friction the force of the weight of the disc provides a torque on the ground via the ...


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"As we can see from the picture, both disks have the same force being applied to them and they also go the same distance d→" This is the erroneous assumption - the 2 discs do not go the same distance. Some of the distance that the rope is pulled will rotate disc 2 as it unravels. As a result the liner distance is less and the balance of work goes into ...


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You cannot simplify the effects of EM radiation on biological systems to simply $E=hf$ because different materials absorb or transmit different frequencies preferentially. $E=hf$ tells us the energy per photon, but it doesn't tell us how much is absorbed by any particular type of cell. It also doesn't tell us the intensity of the radiation (energy per ...


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While you are correct saying disk 2 has rotational kinetic energy, you are missing that no matter the situation, since ground is frictionless, the work done be external force(F, in this case), is same in both cases. Thus by work energy theorem, $$Work=change in KE$$.Thus since work in case 1 equals work in case 2 thus both disk have same kinetic energies.


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When connected to the centre of mass of disc 1 the force causes an acceleration of the centre of mass and the work done by the force is $Fd$ where $d$ is the displacement of the centre of mass and the force $F$. The translational kinetic energy of the disc increases by an amount $Fd$. When the force acts on the rim of disc 2 the centre of mass of the disc ...


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The mass of a ball is scalar. Its potential energy is stored in its position in a gravitation field. A dipole has its potential energy in its orientation with regards to an external field. It can do work by exerting torque when orienting along the field.


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Does this mean that without any external force the kinetic energy of any thing can be increased? No, of course not. Just because there is no torque that doesn't mean that there isn't a force. In this particular case, you have an inwards radial force that is performing work by countering and exceeding the centrifugal force. This work is what causes the ...


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The electrical power delivered by a battery is $\mathcal{E} I$ where $\mathcal{E}$ is the emf of the cell and $I$ is the current passing through the cell. This "input" power originates from a chemical reaction within the battery. The electrical power dissipated in an external circuit connected to the terminals of the battery is $VI$ where $V$ is the ...


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You've discovered the virial theorem. The virial theorem tells us that for a bound system where the potential energy $V$ is given by an equation: $$ V(r) \propto r^{-n} $$ The average kinetic energy $T$ and average potential energy $U$ are related by: $$ 2T = -nU $$ For the electrostatic force $V(r) \propto r^{-1}$ so $n = 1$ and: $$ 2T = -U \tag{1} $$ ...


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This is true for central potential problems. Because in that case, both potential energy and kinetic energy are in (1/r) terms. Also, Potential energy is negative and its magnitude is twice that of Kinetic energy . Thus we conclude that only the mathematics of this problem allows it to be expressed as the formula u proposed and it is general for any central ...


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Well, contrary to what Lemon said, internal energy is sum of ALL energy of constituting particles related to their DISORDERED motion only. To prove my statement, look out for the derivation of formula for internal energy for an IDEAL gas, and the derivation for value of C(molar heat capacity at constant volume) henceforth. Now coming to your question, since ...



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