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Re: Air resistance



On Thu, 11 Dec 1997, LUDWIK KOWALSKI wrote:

I am showing the falling coffee filter data from one of our good-
looking set, T8. Again the sampling rate was 40 per second and averaging
was 15. The total mass (3 filters and Al disk) was 13 grams; no significant
buoyancy complication in this case. Please analyse the data "your way" and
find the "best fit" values of b and n (assuming R=b*v^n), where R is the
air resistance force.

This data is clearly inferior to the basketball data as would probably be
expected given the susceptibility of coffee filters to instibilities and
air drafts. There are very obvious deviations of 5 to 10 mm in d from
that which would be predicted by *any* kind of simple force law.

Nevertheless, assuming a power law drag force with a constant background
acceleration of 9.8 m/s^2, I get a minimum chi^2 at about n = .44 (b =
m*3.6 = .047 in SI units) and an implied uncertainty of about 6 or 7 mm in
d. Given that level of uncertainty, the 95% confidence limits on n are
something like -.3 < n < 1.3.

On the other hand I can't get a significantly better fit to this data than
I get when I simply assume a constant acceleration of 4.42 m/s.

Suffice it to say, I'd be very cautious about trying to say anything very
meaningful on the basis of this data set.

John
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A. John Mallinckrodt http://www.intranet.csupomona.edu/~ajm
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