Re: free fall data

[John Gastineau <gastineau@mindspring.com>]

At 05:46 PM 9/14/97 EDT, Ludwik wrote:

> But my goal is to "discover" that acceleration remains constant.
> In that situation the step-wise approach is unavoidable. Ideally, the
> final result should be a horizontal a=f(t) line for all intervals.

As you discovered with your spreadsheet experiment, it takes an
exceedingly high level of precision in the position measurements to obtain
a horizontal acceleration vs. time graph. The old spark timer lab that
many of us used to teach had terrible acceleration graphs too. I used to
have my students fit a parabola to the position data, a line to the
velocity data, and then calculate acceleration values carefully so as to
not average dependent data. The uncertainty on the acceleration grew
steadily worse going from the position to the acceleration data. Lesson
learned: work with the least processed data feasible. 

How is realizing that a parabola fits the position data extremely well
different from "discovering" that the acceleration vs time graph is
constant? Only constant acceleration yields a parabolic position graph.
It's just a very hard experiment to get a really constant acceleration
graph. You'd have to work too hard to do it in an intro physics course. 

I partially take that back--if you use photogates and MBL, you can get
amazingly uniform acceleration graphs. I'm sitting here at my desk this
sunny day, trying hard to avoid working on a lab manual, so I pulled out a
CBL system and quickly obtained these data:

t (s)		v (m/s)        a (m/s^2)
0.0206		1.21359	
0.05711	1.5713		9.797589701
0.086464	1.8594		9.814676024
0.111775	2.107037	9.783769902
0.13439	2.325581	9.663674552
0.155025	2.52908	9.861836685


Note that I don't start with position, as the photogate gives you
velocities most directly. Position is obtained by integration. 

The first two columns are just the raw numbers spit out by the calculator,
and the last column I calculated with delta (v)/ delta (t), ie, successive
differences. Very simple-minded analysis, no cleverness with using
non-adjacent velocities.  

And, the numbers ain't bad, since the timing is done to the microsecond or
so.

Having said that, note that I'm NOT a fan of photogates; I think that most
students don't understand the numbers. To confirm my suspicion I've pulled
a nasty trick a few times while leading teacher workshops. I set up the
software so all you get is the raw data--the raw times, in milliseconds,
from a picket fence photogate experiment. It takes most teachers a minimum
of an hour to do the analysis. If teachers don't get it, neither do the
students. 

I'd much rather use World in Motion or similar video products and use a
real-world video, warts and imprecision and all, than use a photogate.
Just realize that the precision is not as high as you might like. 

JEG


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John E. Gastineau      gastineau@mindspring.com               KC8IEW
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