Re: Air resistance

[LUDWIK KOWALSKI <KOWALSKIL@alpha.montclair.edu>]

> Date: Wed, 10 Dec 1997 15:22:06 -0600
From:"JACK L. URETSKY <JLU@hep.anl.gov>
Subject: Re: Air resistance

> I don't understand the data.  Look at the values from 1.600 s on. The
> space increments, with two exceptions, increase from increment to
> increment by .05.  The two exceptions tell me that the position 
> measurements are uncertain in their last place, and the velocity 
> differences are unccertain in their first significant digit.  The 
> accelerations are not good to more than 1 signifigant digit, and the 
> differences are garrbage.

That is precisely why averaging is essential. You should have seen the
data at the averaging of 3 to appreciate how much improvement is due
to averaging.

Assuming the limit of accuracy is one lambda (0.0085 meters for the 
ultrasound at 40 kHz) the designers of the instrument probably decided to 
truncate data (number of bits in the ADC unit) to that level, more or less. 
This limitation is corrected through avearging. I am only guessing. The 
technology was borrowed from the auto-focusing cameras where high accuracy
is not needed.

And the whole point of this discussion is to understand the limitation of 
the instrument that so many of us are now using. The data are not totally 
wrong; they show that the values of a are slightly less than g and decrease 
monotonically, as one would expect. For the folling coffee filters one may 
actually see how a terminal v is reached asymptotically for given m. Have 
you used ultrasonic detectors, Jack? They would be great for the Socratic 
dialogues classes you were describing before. Tell us more about your
experience with teaching through discussions (rather than through pure
lecturing ?)
                                                    Ludwik Kowalski