# Tag Info

62

The work you need to do (to insert the log) against the pressure of the fluid at that depth is equal to the work done by the fluid to get the log up to the height you desire. If you consider a log of volume $V$ and a tank of depth $h$, the pressure at that depth would be $\rho gh$, where $\rho$ is the density of the fluid, and $g$ the acceleration due to ...

50

[5/3 - Extended the answer, made some corrections, and responded to John Duffield's comment] This is actually the paradox that led Einstein to General Relativity. Consider a special case: An electron and positron are at the Earth's surface. Bring them together and they annihilate, creating gamma rays (which is very energetic light). The gamma rays travel up ...

39

Not if the laws of physics (particularly the laws of gravity) are as we understand them. In general relativity, there are a set of equations, called the Einstein field equations, that relate the curvature of space (roughly speaking, how much gravity there is) to how energy and momentum are distributed in space and time. To be consistent, these equations ...

31

Can we create an amount of energy at a point in space and destroy an equal amount of energy at another point in space, with both the processes occurring simultaneously? This will not violate energy conservation, as the total energy in the universe is constant. So is it possible? If you learn about Einstein's Special Relativity, you'll discover that the ...

31

Do black holes violate the first law of thermodynamics? No. See Wikipedia re the first law of thermodynamics: "The first law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic systems. The law of conservation of energy states that the total energy of an isolated system is constant; energy can be transformed ...

21

The short answer to your question is that the statements that "virtual particles need not conserve energy" and "intermediate components of Feynman diagrams need not be on the mass shell" are equivalent statements, but from two different historical perspectives. The concept of a virtual particle was introduced into physics in the mid-1920s while the ...

20

Your guess at the solution to this paradox is correct. "Pumping energy up" to the space station, regardless of the method you choose, would require an input of at least the amount of energy you would gain in kinetic energy on the way down. This is just a variation on the impossible perpetual motion machine concept. In practice, you would not only not gain ...

17

I believe, the answer is a small but quantifiable, yes, there is a non flat road configuration that would lead to better gas mileage between any two points at the same height. I have numerically solved for such an optimal path. I believe I can give a nice explanation of why that is, but it will take some work, so bear with me. Granted, you can only expect ...

15

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.

14

Ever since Newton and the use of mathematics in physics, physics can be defined as a discipline where nature is modeled by mathematics. One should have clear in mind what nature means and what mathematics is. Nature we know by measurements and observations. Mathematics is a self consistent discipline with axioms, theorems and statements having absolute ...

13

I'm neither an expert on QFT, nor do I have a very deep knowledge of how the ideas developed - so this is at best a partial answer. I always thought that your first guess is what they actually meant: A virtual particle is an "off-shell"-particle, which means that it does not obey the usual momentum equation equation. Now people tend to interpret this as the ...

11

Very little of the energy from a rocket engine ever goes to the kinetic energy of the rocket. The only way you get perfect conversion to KE of the rocket is when the propellant is directed in the opposite direction of motion and when the ejection velocity is exactly equal to the speed of the rocket. In that case, the propellant winds up containing 0 kinetic ...

11

What does this small change means in form of Rotational Kinetic Energy? There's a problem with your calculation: You assumed a constant value for the Earth's moment of inertia. The Moon and Sun raise tides on the Earth itself. These Earth tides result in subtle changes in the Earth's moment of inertia. The signature of these tides can easily be seen in ...

11

First, the energy expectation value of the superposition state you have written down is $$\left(\frac{n_1 + n_2}{2} + \frac{1}{2}\right)\hbar\omega$$ and one might naively conclude that therefore the energy of the state lies in between the energy of its constituents. This naive concept doesn't work, though - the "energy" of a state that is not an energy ...

8

Update: According to this paper, "On the Interpretation of the Redshift in a Static Gravitational Field", the answer I give below is a common but misleading interpretation. The classical phenomenon of the redshift of light in a static gravitational potential, usually called the gravitational redshift, is described in the literature essentially in ...

8

The mass of a free neutron is 939.566 MeV/c$^2$ (almost 1 GeV/c$^2$, so that's probably where your instructor got the "1" value), and the mass of a free proton is 938.272 MeV/c$^2$. A free neutron will decay into a free proton, free electron ($\beta^-$), and an anti-neutrino, $\bar{\nu}$. The mass of the electron is 0.511 MeV/c$^2$, and of the ...

8

Let's say that the rocket is traveling in the $y$-direction at some velocity $v$, which may or may not be non-zero. A force - in this case, thrust provided by the engine - is applied perpendicular to the direction of motion, in the $x$-direction. This force produces an acceleration, which causes the rocket to move. Therefore, the force is not applied at a 90 ...

7

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.* ...

7

Even if the laser had perfectly reflecting, i.e. lossless, mirrors at either end of the cavity, and both ends were sealed so no light could escape it would still require a continual power input. That's because excited atoms/molecules can decay by mechanisms that don't involve a photon e.g. collisional de-excitation. The lost energy goes into heating up the ...

6

Virtual particles are not real. Though sounding like a tautology, it is an important one - they are not actual states in the asymptotic Hilbert spaces of a quantum field theory, where particles usually live. They are a name given to internal lines of Feynman diagrams, which, in turn, are mere computational tools in a perturbative approach to QFT. Nothing in ...

6

Your question asks why the "current quark masses" [see http://pdg.lbl.gov/2011/download/rpp-2010-booklet.pdf at page 21] of the quarks that make up a proton don't add up to the mass of the proton. The problem is that, for the light quarks, the "current quark masses" are very different from the "constituent quark masses" [see wikipedia]. "Constituent quark ...

6

It is not true that in all fusion and fission processes the mass of the products is less than the mass of the reactants. This is only valid for exothermic reactions. The change of mass is due to the change in the binding energy of the nucleons (note that the change in binding energy is in the order of 1 MeV, while the mass of the nucleons is around 940 ...

6

When a radioactive element decays, part of its mass is converted to energy - no obvious need for antimatter anywhere. Instead, the energy is released because the binding energy of the sum of the fragments might be higher than that of the parent nucleus. However, to fully convert matter to energy you do need the antiparticle. Otherwise, you run into ...

6

I think one simplifying way of thinking about this idea is in terms of causality. That is, here we see a case where two things must be intrinsically linked. The energy being destroyed and the energy being created must have some mediator and they must always at the same time. The problem, however, is that if they must be causally related, there must be some ...

6

When you put the log inside (from the side) you need to place the water from the log position somewhere else. The relevant "somewhere" is at the surface of the tank, so you have to lift the water there (it takes a lot of energy to get a log-equal volume of water to the roof level). The surface is now higher than before (the log-equal volume divided by the ...

6

You are making the mistake of thinking that photons are energy while massive particles are not. Photons are just a particle, albeit a massless one. There are other massless particles, for example gluons, and indeed at energies above the electroweak phase transition all fundamental particles are massless. So the distinction you are making between photons and ...

6

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 ...

5

Energy kinematics I have this question, because typically problems that can be solve using conservation of energy or just energy-related principles, can usually be solved sing kinematic equations. Yep. In fact, there are two profound pieces of math, Hamiltonian and Lagrangian dynamics, which say that you can use energies to derive the actual kinematic ...

5

Just to expand on Hritik's great answer with a little more physical insight: Energy as a "stuff", friction in this picture. Very often we can define a scalar field (a smoothly-varying set of numbers, one for each point of the space) which describes everything about a pattern of forces. We call this the "potential energy" field. It is useful because a ...

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