[meteorite-list] Fall Times: Theory

From: Sterling K. Webb <kelly_at_meteoritecentral.com>
Date: Thu Apr 22 10:22:34 2004
Message-ID: <3EE1487C.B8AE1F49_at_bhil.com>

Hi, All,

    Watching this thread go by, really glad somebody pointed out
that the 32 foot per second figure is really 32 foot per second
per second, or an acceleration, not a velocity. Kinda hoped my
buddy Gallileo would jump up on the List and explain what that
means but I guess he's fiddling with that telescope thingy today,
so...

    OK, you're holding a rock, and the rock is just standing
there, then you let go of it. One second later, it's moving at a
velocity of 32 feet per second. Since it started out at a
velocity of zero and ended up one second later at a velocity of
32 feet per second, it's averaged 16 feet per second for one
second: it's fallen 16 feet.

---------------------------------------------------------------------------------------

 Time Start-of-second Speed End-of-second Speed Fell
this second Total
---------------------------------------------------------------------------------------

  1 0 32
16 16
  2 32 64
48 64
  3 64 96
80 144
  4 96 128
112 256

    And so on. Hey!!! There's a pattern here. The total distance
of the fall is:

            (Number of seconds) ^ 2 x Acceleration
            ______________________________________

                               2

    So, if the distance is time*squared times acceleration
divided by two, then we can move all those terms around to find
that the time for a fall from a given distance is: the square
root of (twice the distance divided by acceleration).

    So, the example given of taking 6 or 7 minutes to fall 63,360
feet is a little off. The fall time for 63,360 feet is 63.93
seconds, or just over a minute.

    You may remember that one witness to Park Forest estimated
the time between the "flash" and the "boom" at "about two
minutes." Since sound travels at under 1100 feet per second,
that's an altitude of about 125,000 feet, or a fall time of 88.39
seconds. Notice that even though we doubled the altitude, the
fall time didn't double. Acceleration is just like compound
interest. Remember that the next time you think about jumping out
of a transcontinental airliner in the stratosphere (fall time
about 45 seconds)!

    OK, OK, it's a real world and there's real air resistance and
at a certain point air resistance may prevent the chunk from
gaining any more velocity and if I jump out of an airliner in the
stratosphere and flap my overcoat open to the wind, I'll stablize
at about 90 mph, but if I dive head first, I'll be going 135 mph
when I hit Kansas.

    First, the source of the fragments may have stagnated (lost
most of its velocity) before it breaks up and the gravity fall
begins, but this may not always be the case, so there may be an
initial velocity to account for.

    Second, the bigger the fragment the faster it will fall,
since mass goes up by the cube and surface area only goes up by
the square, so the fragments sort themselves by mass. (That's why
the big chunks land at the far end of the strewnfield.) The
smaller the fragment, the slower its "terminal velocity" against
air resistance.

    If we throw you down a 1000 foot mine shaft, there'll be this
dopplered scream, then strawberry jam at the bottom. If we throw
your cat down a 1000 foot mine shaft, there'll be this (higher
pitched) dopplered scream, then a cat with a broken ankle at the
bottom. If we throw a mouse down a 1000 foot mine shaft, there'll
be no scream at all, then a dazed but perfectly healthy mouse at
the bottom, saying, "What the hell was that all about?!"


Sterling K. Webb

(Disclaimer: I am not responsible for those
who attempt to duplicate this experimental
procedure with either persons or cats.
Mice at your own [and mouse's] risk.)
Received on Fri 06 Jun 2003 10:05:49 PM PDT