I don't know.
But it occurs to me that conservation of energy might be a problem. The only cases of spiral orbits I can think of immediately involve some change of orbital energy--drag from viscous forces, emission of gravitational waves or absorption of electromagnetic energy as in a cyclotron.
Not that's obvious to me. But it might be worth trying to narrow the range of possibilities first. Are you sure that spiral orbits are possible? Are there stable closed orbits in the Kerr metric? If so, it might be worth starting from one of those and trying to perturb it. ( Perhaps replace r...
It might help if you told us a bit more about your set-up. What sort of quantities of water, in what sort of vessels? (Other things being equal, water evaporates faster from a shallow open pool than from a deep tank.) What are your heat sources?
The vapour-pressure of water increases much more than linearly with in creasing temperature. But vapour pressure isn't the only factor that determines the evaporation rate. In general air flowing over a water surface (or bubbled through water) will cause faster evaporation than still air (the...
Unweighted, the arithmetic mean is always >= geometric mean, so I suspect your weights may have to have a sum > 1. Think what happens if one of the numbers you're averaging is zero.
How about this: For large n, sin(π/n) is approximately π/n, so the series is approximately πΣ(1/π) which is known to diverge.
With alternating signs, the series approximates πΣ( (1/n) - 1/(n+1) ) which approaches π.ln(2). Actually I think I find it more persuasive to group pairs of successive...
It can't do that simultaneously, if that's what you're thinking. The body's angular momentum is represented by a vector--and that direction of that vector is the axis about which it rotates. The axis may not coincide with any of the coordinate axes, but it is a single axis.
For elementary particles, the magnetic momentum depends on the angular momentum and the mass, though not necessarily in a simple way. For similar particles the magnetic moment increases with the angular momentum*. For particles of the same spin, the magnetic moment is roughly inversely...
Doing two separations with half a gallon of water in each should be more effective than a single separation with one gallon (and three separations would be more effective still). That principle would help you use less water.
I just looked at Tinkham's page 40 on the web; he says he's "solving the skin depth problem", as though it's an understood procedure, presumably with standard assumptions and approximations. And he's talking about good conductors the whole time; so I think "general" here simply means both real...
I still suspect it's semantic. As far as I can tell a real, frequency-dependent skin-depth implies a good conductor. How does Tinkham set up the problem?
Perhaps the way to think about this question is to imagine the hypothetical well with one sub-band as a kind of "bucket" that would have been filled with electrons to a "depth" of 50 meV. (This seems to explain why the occupancy is expressed in meV.) How would you picture the real well in those...
As I understand it, the total energy is the fermi energy you have the equation for, plus the potential energy referred to some chosen zero level. I think it might be useful to draw an energy-level diagram comparing the assumed quantum well with one sub-band and the real well with two sub-bands.
Actually you can. As DrClaude says the frequency corresponds to ℏ ω / k.
Maybe think of it this way. We have an energy E that could be the energy of a photon with frequency ν, where hν = E. So we could just agree to talk about the frequency, knowing that if necessary we could always convert...
It's not exactly clear but this probably means that the decay rate was still appreciable after 40 days, so you can rule out a half-life that is much less than that.
I think I'd approach it this way. Assume the source is reasonably pure and macroscopic--say a few grams. Pick a credible mass number, and estimate the number of alpha emitters in the source. Compare that number to the number of decays, at the specified rate, in one second, an hour, a day, 40...
Good questions. To which I would add: What is the mass of the source and its atomic weight, or equivalently the number of gram-moles it contains? A flux of 3.5x10^6 particles per second is one thing if it's coming from a 5 kg source, and something else if it's produced by 1 mg.
Reference...
I don't know if you'd find it helpful, but I like to start from Newton's law for this type of problem.
Net Force = Mass x Acceleration.
You've found the acceleration. The mass is 100/g kg.
The net force is the applied force less the frictional force = 40 - 100.μ N (where μ is the frictional...