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Re: help with air friction?



To answer John's question directly, I do the more complex modelling BECAUSE
the primary focus of the lab is the use of spreadsheets to model physical
phenomenon rather than the air-resistance per se.

Rick

-----Original Message-----
From: John Mallinckrodt <ajmallinckro@CSUPomona.Edu>
ToDate: Thursday, November 20, 1997 11:39 AM
Subject: Re: help with air friction?


On Thu, 20 Nov 1997, Richard W. Tarara wrote:

I then have students model the process using spreadsheets with the drag
coefficient calculated from .5rhoCA: rho = density of the medium, C the
geometric factor (.5 for a sphere) and A the cross sectional area. Yes,
this is cheating somewhat since this IS the factor for v^2 dependence, but
I
have them model the air resistance force as a v^n dependence and have them
start with n = 1. Their data clearly doesn't fit this (so small
corrections
in 'b' aren't critical--the units from above don't really work). For n =
2
they get really very good fits. We don't consider buoyancy but then the
data are not that precise.

Rick,

I wonder why you don't just skip the theoretical coefficient business at
first and simply have them determine whether the approach to terminal
speed is better modeled by a linear or quadratic speed dependence. For
linear dependence you simply write

drag coefficient = weight/terminal speed

and for quadratic dependence

drag coefficient = weight/(terminal speed) ^2

Since you, presumably, have a good idea of both the weight and the
terminal velocity this is straightforward. You could also look at other
power law dependences in the same manner if you chose to.

Because quadratic drag always gives smaller drag forces for a given
terminal speed and for speeds less than the terminal speed, the approach
to terminal speed is quicker. This difference might be difficult to
notice depending on how good your data is, however. If you are able to
establish that quadratic drag is the better model, you can then point out
that the drag coeficient is well approximated by the standard ".5rhoCA"
formula with C some number "on the order of 1."

John
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