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[Phys-L] Re: Nuclear Potato Cannon



Perhaps it is not worth the time to think very much about some of the
crazy stuff you find on blogs (and even in news media), but assuming
this blogger is correct that a large piece of metal "disappeared" in
1/160 second or less, this is not difficult to figure out.

The piece of metal was going too fast to register on the film because of
underexposure. If you have been involved in photography you know the
latitude of the film is one or two f-stops, and once you under or
overexposed by two or more f stops you begin to "lose things." To make
matters worse, high-speed cameras generally underexpose the film and
require "push processing."

Suppose an object has a dimension of one foot in the direction it is
moving. If it is moving 1000 ft/s when a photograph is taken, no
portion of the object exposes any portion of the film for longer than
1/1000 second. If the normal exposure for the film was about 1/160
second, then a one-foot object moving 1000 ft/s receives an exposure
that is about 1/6 of the proper exposure. That's more than two f-stops
underexposure and the object may not expose the film, especially if it
is a dark-colored object.

If the object fragments, the dimensions of the pieces are smaller, and
the exposure for any piece is much less than if the whole piece moved
together. Additionally, it would not be impossible for the fragments to
exceed 1000 ft/s by a factor of two or more. (The muzzle velocity of a
gun often exceeds 1000 ft/s and can be near 3000 ft/s.) Most likely the
top of the container fragmented (that's why it was never found) and the
fragments moved too fast to expose the film (that why it seems to
disappear in the photos). In this case "too fast" does not mean the
fragments traveled the full film frame in less than 1/160 second.
Rather it means each fragment traveled its own length in a time that is
perhaps as slow as 1/4 to perhaps as fast as 1/32 (2 stops to 5 stops)
of the normal exposure for the film.

Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu
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