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Re: timing data for falling objects



At 08:52 -0700 07/06/2002, John Mallinckrodt wrote:

I'm pretty skeptical of this. Basketballs interact viscously with air
up to speeds best measured in millimeters per second. Above that,
the dominant interaction is via dynamic drag. If one uses Stokes law
(which is appropriate for spherical objects subject to viscous drag
and the resulting linear velocity-dependence) to analyze the terminal
motion of a basketball one finds that the implied viscosity of air is

viscosity = weight/(6*Pi*radius*v_terminal)

Assuming a weight of 10 N, a radius of 15 cm, and a terminal speed of
20 m/s, this gives a viscosity around 2 poise, roughly 10,000 times
the measured viscosity of air. This is far too large an error to be
able to attribute to my admittedly armchair speculations about the
input values.

On the other hand, assuming a dynamic drag force (and the resulting
quadratic velocity-dependence) one finds that the implied drag
coefficient is

drag coefficient = 2*weight/(Pi*density of air*radius^2*v_terminal^2)

Since the density of air is around 1.3 kg/m^3, this gives a drag
coefficient of around 0.5 as one would expect.

You're right, John. Sloppy writing on my part. I meant to say drag
coefficient, but it was late and I wasn't thinking very clearly.

Hugh
--

Hugh Haskell
<mailto://haskell@ncssm.edu>
<mailto://hhaskell@mindspring.com>

(919) 467-7610

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