Re: timing data for falling objects

[John Mallinckrodt <ajm@CSUPOMONA.EDU>]

Hugh wrote:

> ... it seems to me that what Robert is looking for ... is data from
> a free-falling object that covers enough time to show the effects of
> air resistance, perhaps even terminal velocity. I suspect that it
> might be difficult to come by, ...

I have to agree with Hugh here.  If the purpose is to determine the
velocity-dependence of the drag force--as I suspect it is--it will be
difficult to come by data that is accurate enough.  There was a
thread on this in December 1997 that may be reviewed at

 http://lists.nau.edu/cgi-bin/wa?A1=ind9712&L=phys-l&D=0#95

(BTW, the review is made needlessly difficult due to the fact that
various contributors used the subject headings "air resistance", "Air
resistance", and "Air Resistance" which are all considered to be
different threads by the archiving software.)

On the other hand if one *assumes* a particular velocity dependence,
it is relatively easy to extract other parameters.  You do need to be
careful, however, not to make the wrong assumption. For instance,
Hugh went on to say

> ... how about generating some [data] of your own, by videotaping
> an object (a basketball, say, being dropped from the top of a four-
> or five-story building.) We did that a few years ago and it was
> clearly enough to show the effects of air resistance (but not
> terminal velocity). It was enough that we could get data on the
> coefficient of viscosity of the air.

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.

John
--
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