Captain Kangaroo was before my time, but Mystery Science Theater once recreated a signature gag of the beloved children's show in which Tom and Crow tricked Joel into saying "ping pong ball," upon which a seemingly endless stream of ping pong balls began to shower down on him. Jocularity ensued. I still don't understand the point, although I noticed a similar ritual marks the conclusion of our presidential primaries, albeit balloons rather than ping pong balls fall from the ceiling of the convention center once a candidate has been selected. If that's not a compelling argument against democracy, I don't know what is.
In some cultures it might be considered impolite to ask what one of these stories has to do with the other. Not so here at LabKitty, where all things are connected even though the thread may appear tenuous to the casual observer. A butterfly flaps its wings in Beijing and Ashton Kutcher gets to bang Demi Moore as the saying goes, or at least it did in the first edition of Strogatz, before the editors at Westview Press got a big ole stick up their butt.
Impulse is the thread today, and not the kind that makes LabKitty write on the blog after whiskey. We imagine a U235 nucleus on the launch pad with a grain of sand strapped to it. When the nucleus pops the grain of sand is launched skyward. How high? we ask. The conservation of energy gives us a handy answer. At t-zero, the grain gets a bolus of kinetic energy. At max altitude, the grain is (momentarily) not moving (before it starts to fall back to earth) and so all of that kinetic energy has been converted into potential energy, mgh. Given the mass, m, and gravitational constant, g, we can solve for the height, h, if we know how much kinetic energy the grain launched with. For simplicity we will assume all of the fission energy is converted into kinetic energy, which, yes, is unrealistic, but so is ignoring drag and assuming g is constant. The idealized problem is all I can handle, which now that I think about it also sums up my views on dating.
Looking up the energy released by one fission of U235 in my copy of The Los Alamos Primer (everybody wave to the nice NSA person now putting LabKitty on a watch list), I find a figure of 200 MeV.
The potential energy formula is mgh. Mass is in kilograms, g is 9.8 m/s^2, and h is in meters, which gives energy in kg•(m/s)^2 otherwise known as a joule (J). We need to convert MeV to joules. That particular alchemy does not appear in Unit Converter -- although "ergs" and "btus" do (seriously, Apple? F'ing hippies) -- but after some Wiki sleuthing I discover 1 eV = 1.6E-19 J. Ergo, 1 MeV = 1.6E-13 J so 200 MeV = 3.2E-11 J.
Next, we need the mass of a grain of sand. You may be interested (or not) to learn that sand is not merely coarse and rough and irritating and gets everywhere, it also has a real actual engineering definition: rock particulate matter between 1/16 mm and 2 mm in diameter. Smaller is silt, larger is gravel. The categories were apparently inspired by their turgid hydraulic properties: silt remains in suspension, sand tumbles, and gravel sinks. Very small rocks float.
Mass is volume times density. Sand can be anything, but the familiar kind, the beach kind, the kind that got all up in Amadala's metal bikini and supplied Anakin a merciful double entendre which was probably something like I am pleased we have made intercourse until the suits at Paramount took Lucas aside and explained you can't say that in a PG and not expect the merchandizing to take a hit, that kind of sand is quartz. The density of quartz is 2.65 g/cc.
Long story short: pick a diameter in the middle of the sand range, assume a spherical grain, plug in 2.65 g/cc and we get a mass of about 1 milligram. Plugging 1 mg into our formula for potential energy gives an altitude attained by a grain of sand strapped to one fissioning U235 nucleus of 3.2E-11 J / [ (0.001E-03 kg)(9.8 m/s^2) ] = 3.2E-06 m or about 3 microns.
It seems to me this is stretching the definition of a "visible" jump but I don't write the textbooks.
Suppose, now, we repeat this exercise with a ping pong ball (PPB). We've already done the heavy lifting (no pun intended) -- all we have to do is substitute the mass of a PPB for that of a grain of sand. The mass of a regulation PPB (which is a thing, believe it or not, I guess until the Wii achieves full market penetration of the lingering communist nations) is 2.7 g, or 2700 times more massive than a grain of sand. This gives a maximum ping pong ball altitude of 3 / 2700 microns or about 12 angstroms.
Most unimpressive. However, if we consider the energy supplied by 5 kg of U235 (all we have to do is multiply by a factor of 21.3 Avagadro numbers) we get 7E14 meters, which is about half than the width of the observable universe. I suppose there is a lesson here regarding extrapolation.
If you think this is all toys in the attic mad, of course it is. But it is more. In a documented application of the LabKitty Nuclear Ping Pong Ball Metric (tm), observers at the 1957 Plumbbob nuclear test were combing through the post-shot wreckage and discovered a 2000 lb steel pressure plate that had heretofore been bolted to the end of a pipe was missing. That in itself was not notable, for a great number of things typically go missing after a nuclear test (an entire island went missing after the Mike shot in 1952). More to the point, a hardened camera fortuitously captured the plate being blown off the pipe during the blast. Analysis of the film suggested the plate was launched at about 66 km/s. Escape velocity at sea level is about 11 km/s. The first man made object to be launched into space was not Sputnik, but quite possibly a steel plate blown off the end of a pressure pipe during the Plumbbob nuclear test.
I think about that steel plate from time to time, wondering where it has gotten off to, charred and mangled drifting across the silent firmament forever. Escape velocity for 58 years gets you roughly as far into space as Voyager 1, which is currently at the edge of our solar system. Captain Kangaroo is also traveling through space; in the 60 years since the first episode was broadcast his message has traveled 60 light years which puts it roughly right in the middle of Nowhere Interesting, although it passed the red dwarf Proxima Centauri around the time of the first Kennedy/Nixon debate. In another 400 years, it will reach the Pleiades. If there are aliens -- and there had better be -- they will in all likelihood encounter Captain Kangaroo long before the steel plate. Indeed, the aliens will likely encounter all of broadcast TV before encountering the steel plate. (The aliens won't get cable fare like Game of Thrones or Spartacus: Gods of the Arena, which is unfortunate. I suppose they'll have to buy a bootleg DVD off the back of a truck down in the garment district like the rest of us.)
Thusly drawn to Earth by this siren call, I wonder what the aliens will make of our Cold War era society. The welcoming countenance of Captain Kangaroo, suffering outrageous slings and arrows of the treacherous Mr. Moose on the one hand, and a steel plate stamped BLOW OFF COCK, slightly radioactive, on the other.
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