Re: Air resistance

[Vern Lindberg <vwlsps@ritvax.isc.rit.edu>]

Ludwig,
	>         Please help to decide between the two positions taken:
	>
	>1)  The data shown below demonstrated that n is between 1.6 and 2.4
	>2)  The data shown below demonstrated that n is between 0.2 and 5.0

Fascinating discussion, great ideas for experiments, but neither position
below satisfies me.  I believe that the data show little more than that the
object is falling but not in free fall.

My concerns:  You give 16 data points and then use velocity data that uses
15 point averaging.  If I want to really check the results I rely on the
actual raw data--namely the time and position.  This means that I casn only
generate 2 velocities with 15 point averaging.

What does MacMotion really mean by averaging?  Do they do a least squares
fit to 15 points or what?

Plotting position versus time in Excel resuilts in a curved line--some
acceleration is obvious.  A second order polynomial fit to the data gives
d = 4.7454 t^2 - 11.495 t + 7.3998, suggesting a constant acceleration of
9.49 m/s^2, as noted earlier by John.

More meaningful data for me would involve complete data for a broader time
range extending from close to the initial drop until close to terminal
velocity.


John,
 Precisely what are you fitting?  d versus t?  With what function?  Did you
integrate to get d-t formula for different resistance functions or what?

> The data were collected with the Vernier motion detector at the rate
> of 40 samples per second, averaging=15. The first 4 colums are output
> from the Mac Motion software. ...
>
>      t(s)         d(m)         v(m/s)        a(m/s^2)         R(N)
>
>     1.400        0.608         1.773           9.63
>     1.425        0.655         2.013           9.65
>     1.450        0.708         2.254           9.65
>     1.475        0.768         2.494           9.64           0.09
>     1.500        0.835         2.734           9.60           0.11
>     1.525        0.904         2.975           9.61           0.10
>     1.550        0.983         3.215           9.59           0.12
>     1.575        1.066         3.454           9.54           0.14
>     1.600        1.155         3.691           9.48           0.18
>     1.625        1.251         3.927           9.44           0.20
>     1.650        1.352         4.162           9.38           0.23
>     1.675        1.458         4.395           9.33           0.26
>     1.700        1.573         4.632           9.31           0.27
>     1.725        1.692         4.865           9.33
>     1.750        1.816         5.035           7.83
>     1.775        1.945         4.971           1.27