[ExI] mythbusters follow-on

spike at rainier66.com spike at rainier66.com
Thu Dec 23 02:54:00 UTC 2021

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From: spike at rainier66.com <spike at rainier66.com>
…

Earlier I wrote about a video where some yahoos were firing baseballs to M1.5 and hitting stuff.  That really got my wheels spinning.

At about 9:23, the instant where the baseball strikes the jar of donut sprinkles, you can see a flash of light:

>…What does a Gong Sound Like when Hit with a 1189mph Baseball? - Smarter Every Day 267 - YouTube <https://www.youtube.com/watch?v=at-xZA5U1ps>

I viewed that a dozen times trying to figure out what reaction would cause that flash, and I think I have the answer.

Regardless of how small a time slice one takes, momentum is conserved over that time interval and energy is conserved over that time interval.  Those two principles lead to the discovery of shock waves and hydrodynamic compression waves, even without a baseball cannon.  (It would be tragic indeed to miss out on the baseball cannon just because we calculated what would happen.)  Dividing time into small increments makes it a lot easier to estimate all the stuff that happened during that interval.

For Yanks among us, do recognize that these calculations are a loooot easier if you go over into metric.  We can do a lot of it in our heads, not even scrounging an envelope to do BOTECs, for we know since we were kids that the flash of lightning is followed by thunder, about 5 seconds per mile of distance.  We all know that because we dang well remember stuff we were told when we were in first grade (too bad about all the cool stuff we learned in college (which doesn’t stick nearly as well.))  The beauty of metric: speed of sound about 5 seconds per mile so about 3 seconds per kilometer so about 300 meters per second so 300 millimeters per millisecond so about 0.3 millimeters per microsecond.  (Isn’t that simple?  (a prole can do that in her head (no need to mess up a perfectly good scrap envelope.)))

The baseball is going M1.5, so we can round to about half a millimeter per microsecond.  Half a millimeter is easy to envision, that’s the thickness of one of those leads in the clicky mechanical pencils (or about the thickness of a strand of uncooked angel hair pasta (depending on where the hair sample is taken from the angel (but I digress.)))

Impact to impact plus one microsecond.  Using the principles of conservation of momentum and conservation of energy, we can estimate the thickness of the zone which knows about the impact is about a millimeter in thickness.  Reasoning: the speed of sound in the medium (the donut sprinkles) plus the velocity of the baseball and I might be missing some other important factors, but it occurred to me why that flash is visible on the video at 9.23, which is… if one takes the volume of that spherical shell the size of a baseball about a millimeter thick, we see that all the kinetic energy dissipated by the ball over that microsecond is in that spherical shell.  That conservation of energy requirement predicts the temperature of the donut sprinkles and the air that is also in that shell must get to a coupla thousand Kelvin until that shell gets thick enough to contain all that energy.  Result of stuff at a coupla thousand Kelvin: a flash of light.

One last insight please: after the impact we can focus on any single donut sprinkle and see that it shatters into a jillion pieces as the shock wave passes over it and accelerates it faster than it can hold itself together.  The energy in a shock wave is proportional to its area (again because of conservation of momentum and conservation of energy) so we can watch what happens to the sprinkles about 80 microseconds after impact, run the clock backwards, estimate the size of the impact-affected zone, and we realize that those sprinkles must have been shattered into bits small enough that a bunch of chemical bonds in the sugar were mechanically broken.  All that energy goes somewhere too.  Result: flash!

One of many things for which I am deeply grateful is that I was born late enough in history to witness in super slow motion a baseball travelling over a thousand miles an hour strike a jar of donut sprinkles.  Decades from now on my deathbed or freezebed, I will have a satisfied smile on my face from having witnessed that.

spike

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