Not a Viable Source of Alternative Energy

Back when I was playing with a strong magnet dropping through a coil of wire I wondered how much energy I could extract from the dropped magnet and if I could do anything with it. The coil I was using was at least 15 cm in diameter, which means that I wasn’t capturing all of the flux lines from the magnet — the field of a dipole drops off as 1/r^3, so a smaller diameter would be much better and the slowing of the magnet could be noticeable, as we’ve seen before with someone dropping a magnet down a copper tube.

Since I’m a physicist, I wanted to quantify this. I didn’t have a copper tube handy, but I do have a roll of aluminum foil which is on a roll with an inner diameter of about 3.8 cm (1.5 in), which is a reasonably tight fit for my strong magnet. I set up my slow-motion camera and my ipod in stopwatch mode to double-check the timing (yes, it was shooting at a rate of 210 frames per second)

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I exported the video to individual frames to make it easier to analyze, and counted frames. The free drop takes about 0.25 seconds, give or take (it’s hard to tell exactly which frame represents release) and I estimate the distance as being about 32 cm (a foot-long roll = 30 cm, with the start just above and stop just below). The drop through the aluminum foil roll takes about 0.38 seconds. The freefall drop is easy to analyze: v = gt, and to double-check for g, just rearrange the familiar kinematics equation and solve. The drop time implies a speed of about 2.45 m/s at the exit. For g we get 10.2 m/s^2, so my little experiment seems good to 10% or better.

For the drop through the tube, we don’t know exactly what’s going on. There’s a damping force that varies with speed and eventually we would expect the magnet to reach terminal velocity. To get an estimate, though, let’s first assume it’s a uniformly lower acceleration. That would give us a value of 4.4 m/s^2 for the acceleration and an exit speed of 1.67 m/s. If we assume it hits terminal speed immediately then the speed would be 0.84 m/s. The truth is somewhere in the middle. There are probably several ways I could test this further, but the ones I can think of either require dropping the magnet from a distance above the tube, and it’s a tight fit, so it probably means lots of trials before I got lucky and got the magnet to drop in, or using a longer tube. I know aluminum foil comes in different lengths, but I only have the one. Since I want an idea of the energy extracted, let’s use the worst case value of 1.67 m/s.

I found the mass of the magnet using a small electronic scale and a plastic cup to keep the magnet away from the metal pan (where it might also be attracted to the interior or the case and mess up the measurement) and subtracted the mass of the cup. 60 grams.

Which means the magnet lost about 0.1 Joules of kinetic energy in the foil, in less than 0.38 seconds, or an average power of just over a quarter of a Watt, in that worst-case scenario. The best-case is 50% higher. And this is using aluminum — copper will give is a better result. Recall that Faraday’s law is
\(V = -frac{dphi}{dt}\)
Copper’s resistivity is about 2/3 of aluminum’s, so a given potential will drive about 50% more current and boost the resistive force owing to the larger field from the additional current. In other words, we can expect copper to be more efficient at converting the mechanical energy to electrical. It will more closely approximate the terminal-speed-quickly scenario, and it should have a smaller terminal speed.

What I want to do in the near future is wind a coil on one of these cardboard tubes and see if I can light up a little light bulb.

Using Tiny Nets

How do you catch atoms? In very tiny traps

Trapping atoms is near and dear to my heart, regardless of whether you do it for sport or food or to knit the tiny pelts into a shawl. So it’s disappointing to find conceptual holes in an article on the subject.

Traps for neutral atoms come in three different flavors. One is called an optical molasses trap, where the Doppler shift is used to turn the atom’s translational motion into light, which prevents atoms from flying away from the trap.

In short, no. Optical molasses uses radiation pressure to slow atoms down — atoms scatter photons and slow down, much like throwing pong-pong balls at a a bowling ball will slow it down. “turn the atom’s translational motion into light” is somewhere between awkward wording and flat-out wrong. The rest is OK up until this part

If I use three pairs of laser beams all facing a cloud of atoms, then no matter what direction the atoms are moving, they always get driven back to the place where the laser beams meet.

For optical molasses, this isn’t true — it’s a dissipative or damping force, which is very strong (hence the use of molasses — near resonance the accelerations can be hundreds of g’s), but there is nothing that pushes the atoms to a particular place. Atoms will random walk— very slowly — until they leak out, like a drunken frat boy in a field, wearing heavy boots. Now, you can get the atoms to tend to collect at a point with the addition of a quadrupole magnetic field and the appropriate polarization of your light, because there is a restoring force that depends on the field strength. This is now a drunken frat boy with heavy boots and the center of the field is a low spot. That’s called a Magneto-Optic Trap, or MOT. (Which, of course is “TOM” backwards, so it’s ridiculously easy to remember). In very rough numbers, a MOT will confine an order of magnitude or so more atoms than a molasses, at least in my experience with a few species of alkali atoms. The atoms in a MOT want to be both slow and at the zero point of the field, whereas in a molasses they just want to be slow. But there’s a cost — the atoms in a MOT tend to be hotter, so if you are going for cold atoms what you can do is trap your atoms in a MOT and the turn the magnetic field off. The cloud expands since there’s no longer a restoring force but it does so slowly because you still have a molasses. I did a video of this a few summers back, though the system is not optimized to give the nice expansion into molasses (the price of getting to play with it)

The big drawback of this trap is that it puts atoms into an excited state. From there they have many options, only one of which involves emitting the absorbed photon—atoms that don’t choose this path escape the trap. Furthermore, the excited state destroys a BEC (remember, all the atoms need to be in the same state to form a BEC), so the trap must be switched off at some point in the preparation process and cannot be used to manipulate the BEC.

Atoms in a molasses are neither dense nor cool enough to form a BEC, so this is a bit of a non-sequitur. There’s no BEC to manipulate. Typically the next step is to load the atoms into a magnetic trap, which the article explains next, and do evaporative cooling — you change the shape of the trap to let the most energetic ones out, which lowers the temperature, similar to evaporation.

Next up is the dipole force trap.

Take an atom sitting just to the right of the center of the laser beam. As photons pass through the electron cloud of this atom they are deflected—those on the left-hand side are deflected to the right, while those on the right are deflected to the left.

Another instance of ummmm, no. The author is likely confusing the explanation of forces on macroscopic spheres (as in optical tweezers) for the atomic response. This indeed explains what happens to a polystyrene sphere, but an atom? The light used is of order a micron in wavelength, which is orders of magnitude larger than the atom itself. So there is no way for a photon to go through one side or the other. What’s going on here is that the intense light has an electric field, and because the light has an intensity gradient, there is a gradient of the electric field. This induces an electric dipole in the atom, which gives rise to a force in the direction of the gradient — the atom is pushed toward the region of highest intensity. There’s no dissipation here, though, so no cooling is going on. Once again, you typically cool the atoms first and then load them into the trap.

Plasmonics, the last section, is not something I’m “up” on, so I can’t really critique anything, but given the rest of the article, there’s a decent chance of a large conceptual gaffe in it.

FFS is Probably not "Fox Fails Science"

FFS: Fox Fails Physics

In short — and we’ll describe it in more detail below — their “expert” argues that the 1st law of thermodynamics and Le Chatelier’s Principle explain why carbon dioxide can’t cause global warming. This is not only wrong, this is high school physics-level wrong. Either the FOX folks are incredibly stupid, or stunningly sociopathic. I’m guessing both.

Short version of this (and many other anti-AGW arguments) is that if they are right, then insulation of any type can’t possibly work. Congratulations, you’ve just proved that wearing a coat in winter is pointless. Surrender your coat.

Got Milk?

Protip: add a few drops of milk to water to make lasers show up better. You want particulates to scatter the light, and little globules of fat do just fine.

Here you can see total internal reflection of the laser off of the surface of the water. The structure of the beam is probably because I didn’t stir the water, so the milk was only mixing due to the residual motion of it and the water. You can see it’s settled a bit at the bottom.

Oh Buoyancy!

Via Zapperz

A man who obviously has a “girth” larger than the inner radius of a floating inner tube, appears to have gone through it unscathed, both for him and the inner tube.

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The inner diameter of the tube is around a meter (I’m guessing this guy is bigger than a 40-in waist). If the tube part is 10 cm across, that’s about 8L of volume being submerged, displacing 8L of water, exerting ~80N of buoyancy force, or more than 17 pounds. Another way to look at it is if you filled the tube with water it would weigh that much. Is it reasonable that the man’s “spare tire” would hold that up? In addition to the malleability of flab, water is a pretty decent lubricant.

A Water Bridge in Air

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ArXiv pdf

[T]he floating water bridge remains stable without breaking for big aspect ratios and unbent by gravity due to the effect of the induced polarization forces at the interface, generating normal stresses that counteract not only capillary forces but also gravity.