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By Noether's theorem, there is a conserved quantity (a number) associated with every continuous symmetry of a physical system. Energy is by definition the conserved quantity associated with time translation invariance (i.e. that it doesn't matter whether we perform an experiment today or tomorrow, given that all circumstances are the same). In this sense, it ...


12

Yes the effect is real, potentially at least, but no it's not measurable. As an aside, the redshift of light by its gravitational interaction with (homogeneous and isotropic) dust is exactly what the FLRW metric predicts, but this clearly isn't what the question means. The gravitational field of a beam of light is calculated in the paper On the ...


9

The source of gravity is not mass, but stress-energy-momentum, so you are correct that the energy converted in this process already has gravity and that that gravity is only rearranged The change in the gravitational field needs time to propagate, though, and this does indeed happen at the speed of light.


8

To add to Dirk Bruere's answer. As I describe in detail in this answer here, the accountant's idea of a budget is a good analogy: the budget seems "abstract" but the law of conservation of energy is experimentally proven and in this way energy is very "real": a system fulfilling conservation of energy behaves in a way that is measurably very different from ...


8

Steam is caused when water vapor condenses. This is caused by the air having too much water vapor for it to hold. When you have a lot of heat under the pan, the air above the pan is quite hot and can hold a lot of water. The water evaporating from the pan disperses into the atmosphere and doesn't condense. When you turn off the heat, the pan and food ...


7

Noether's theorem states that to every continuous symmetry of a physical system there is an associated, conserved quantity. The conserved quantity associated with time translation invariance (i.e. it doesn't matter if you perform an experiment now or tomorrow, provided you set it up the same way) is what we call energy. Therefore, somewhat tautologically, ...


6

The momentum operator $P$ in the infinite well can be defined as a self-adjoint operator by infinitely many ways with respect to the boundary conditions by: $$P_\theta=-i\hbar\frac{d}{dx}\\ \mathcal{D}(P_\theta)=\left\{\psi\in \mathcal{H}^1[0,a]:\psi(a)=e^{i\theta}\psi(0)\right\},$$ where $\mathcal{H}^1[0,a]$ is the Sobolev space, on the interval $[0,a]$. In ...


5

Heat Drag is the same thing as air resistance. It's a form of friction. Friction turns some of the kinetic energy of a moving object into heat; drag does the same thing, thus slowing a falling object down. When an object slows down due to friction, it heats up (and some of the heat dissipates to the surroundings). The same principle applies here: There will ...


5

To add to HDE 226868's correct answer "heat": Even the ram drag component, arising when the parachute losslessly exchanges momentum with the relatively moving air and thus feels a Ram Pressure (see Wikipedia article of this name, and also my footnote), ends up as heat because the air eddies and currents airising from ram effect (see my footnote) then ...


4

But the question here is that if anything doesn't exist in this universe, then how can the same thing be used to do something that exist? Most people have no trouble understanding numbers, but they don't exist in the universe - we define them. Numbers are the first abstraction most people learn, and I'd be very surprised if you couldn't abstract a group of ...


3

The branch of physics that studies these problems is called "thermodynamics", and it is a very successful theory as it describes most bulk matter behavior and can be used in engineering and other projects reliably. In thermodynamics matter is composed of molecules modeled as classical particles with some collective properties that are defined by ...


3

We don't know! If we were to observe a situation where energy conservation did not appear to work, that would be a major puzzle. As you say, either we would have to discover some alternative contribution to the energy that we had been neglecting, or we would have to give up on energy conservation. A priori it is not obvious which one of those two resolutions ...


3

Thus, work is done on the car, right? No, the car does (positive) work on whatever is stopping it. Alternatively, you could say that negative work is done on the car, but still, the meaning is the same: the car loses energy and something else gains that energy. What that something else is, and what type of energy it gains, depends entirely on how the ...


3

Some quick scribbling suggests that caloric intake for a $70\;{\rm kg}$ human over the course of $50\;{\rm yr}$ at $2500\;{\rm Cal}$ per day is enough to accelerate that person to almost $75,000\;{\rm m}/{\rm s}$. Escape velocity from Earth is about $11,000\;{\rm m}/{\rm s}$, so even with a reasonable hit for inefficiency (about $2\%$ energy efficiency is ...


3

The total energy of the universe is a vexed issue since different commentators have different views about what the concept means. See the question Total energy of the Universe for a sampling of the various viewpoints. If you Google for zero energy universe you'll find several papers purporting to show that the total energy is zero. However since their ...


3

Have a look at the answers to Why does holding something up cost energy while no work is being done?. Gripping things takes energy not because a constant, stationary force does any work but because of the way muscles work. A stationary force doesn't do any work so no energy can be harvested from it. The best you could do is capture the heat given off from ...


3

Fat can't just completely be changed to energy, there need to be chemical reactions in the body as the body metabolizes the fat. Some energy in released by the metabolism. By 1933, Tainter and Cutting discovered that dinitrophenol causes cells in the body to waste energy. So, yes, the energy of fat can be extracted without mechanical excercise. ...


2

(Summary: In this post I argue that you need at least an energy of $m v_1^2(1-\cos(\theta))$ in the idealized kinematics situation to deflect an asteroid of mass $m$ and velocity $v_1$ by an angle $\theta$ using rockets, without changing the magnitude of $v_1$.) Energy isn't the be-all and end-all of motion. The problem is that momentum also has to be ...


2

Each electron has a fixed charge of $-1.602\times10^{-19}\,\mbox{C}$ (where (C stands for coulombs). If you gather $6.24\times10^{18}$ electrons, the total charge will be \begin{align*} \mbox{Total charge} &= \mbox{Charge per electron}\times\mbox{Number of electrons}\\ &= ...


2

The logic is simple: a body loses energy because opposing forces cancels themselves out. if you want to move in a direction +x against an opposing force -x the net balance must be in the direction +x. The logic is the one that rules the composition of forces or vector addition If $F_2 > F_1 = -18 N$ then the body will move, accelerate in the -x ...


2

Let's make a concrete example with numbers: Suppose that $v_a = 6m/s$ and $v_b = 0 \rightarrow E_k = 0.5 * 6^2 = 18, p_a = 1 * 6 = 6, v_{cm} = p/M = 2$ . According to the conservation of energy and momentum: Kinetic energy and momentum are conserved only in a perfect elastic collision, if the bodies stick together the collision is inelastic an ...


2

To turn thermal energy into useful work completely one would need a thermal bath at the temperature of absolute zero. This is explicitly forbidden by the third law of thermodynamics. The best one can do is given by the efficiency of the (theoretical) Carnot cycle: http://en.wikipedia.org/wiki/Carnot_cycle. Th efficiency of the Carnot cycle only depends on ...


2

I agree with CuriousOne that the example is more confusing than helpful, but this is the way I would explain it. Suppose you take a spring, place it on the ground then compress it. If you now suddenly let go of the spring it will rebound and bounce upwards off the ground: The spring clearly has work done on it because its kinetic energy increases and ...


2

To escape Earth, you'd need to be alive for (see this) $$ \frac{1}{365 E} \left(\frac{GMm}{R}\right) \ \mbox{years} \approx 1 \ \mbox{year}, $$ where $E \approx 2000 \times 1000 \times 4 \ J = 8 \times 10^6 \ J$ is the average daily energy intake (couldn't find a good source for a worldwide average), $G \approx 7 \times 10^{-11} \ m^3 kg^{-1} s^{-2}$ is the ...


2

If there was no friction, your breaks couldn't clamp down on your rotors to slow the car, and the car's tires couldn't "stick" to the pavement. Your engine is generating energy, and it does cause pressure in the braking system. That braking system, triggered by you and your foot (and assisted by the car) converts that motion to heat through friction between ...


2

If I eliminate the associated Kinetic Energy of the car, where does this energy go? While conservation of energy dictates that the energy due to the car's motion must be conserved, it does not say how. An old-style braking system converts that kinetic energy into heat. A more modern regenerative braking system converts that kinetic energy into a ...


2

You can't overtake so you have to stop acting on the throttle and lose 20mph with the engine brake alone waiting for an opening. When it's clear, you accelerate a lot to get back to cruise speed; then repeat the situation several times. Why is it inefficient? Presumably this occurred at highway speeds, where hurry up and slow down is very inefficient. ...


2

A general answer which is not of any particular use is that electrical energy, and the forms in which we store it, are typically very low entropy systems. The lower the entropy the more they "want" to dissipate and the harder it is to stop that tendency to turn into (ultimately) heat. Same way that it is a lot easier to store water that is 10 degC above ...


2

Carbon has no melting point at ordinary atmospheric pressures (around $0.1\,\mathrm{MPa}$)- it will sublime directly into gaseous form. Below pressures of around $10\,\mathrm{MPa}$, there is no way that carbon could exist as a liquid.


2

It is Nature's bookkeeping to balance the accounts. The same with all conserved quantities.



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