Re: free fall data

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

I did find a source with information on videotape formats. In the 1993 
book "Mastering the World of Quicktime" Jerry Borrell writes (p 64):

"VHS tape generates 200 lines of resolution and Hi8 provides 400 lines;
other formats produce even higher resolutions. ... S-VHS has a signal
with 420 lines." 

Wouldn't this be a strong indication that the 480 pixels resolution along 
the vertical frame is illusionary when a VHS camcorder is used? A clicking
error of one pixel vertically is likely to be relatively larger (factor 
of 640/200) than an error of one pixel horizontally, for the same 
displacement.

What limits the horizontal resolution of an analog image from a camcorder? 
Is the horizontal VHS resolution good enough to benefit from the 640-pixels 
of a common digitizing system? I suspect that filming sidewise may help to
improve data. This would be true only when all other erros, such as paralax, 
etc. are much smaller than pixel errors. Strong zooming, to cover as many 
pixels as possible, is equivalent to filming from a short distance. It may 
be associated with sizable paralax errors. 
............................................................................
Another subtopic:
The best way to determine g, as accurately as possible, is to measure time 
and displacement from the beginning to the end of the fall. The experiment 
must be repeated and the average g used as our best number. This is a very 
reasonable approach when WE ALREADY KNOW that g=const. Subdivisions of the 
total time into short subintervals is necessary only when the goal of an 
experiment is TO DEMONSTRATE that g is constant.

In that context the time subintervals must be as short as practically
possible. The accuracy is sacrificed to get better information about g(t).
(You can call this the incertainty principle, if you wish.) In my opinion 
the use of consecutive subintervals has one advantage. Suppose the data 
are y1, y2, y3, y4, etc. and that a small error was made in y2. This makes 
(y2-y1) a little smaller than it really is. But (y3-y2) is automatically 
larger by the same amount. (I am assuming that errors in y1 and y3 are 
negligible.) Thus a slightly larger v12 is followed by a slightly smaller 
v23. This self-correcting tendency is probably present in other ways of 
defining subintervals but it would be less obvious to students.

Averaging over the data points separated by long subintervals may lead
to wrong shapes of v(t) and g(t), even when data are very accurate. You 
may come to a conclusion that g is constant when cyclic fluctuations of 
v are present. This observation was triggered by the message below. It is 
clear to me that the author was assuming that g is constant and his goal 
was to find the most accurate single value of g. He would not use the 
method if he suspected that rapid fluctuations of v may be present.
So perhaps I am being too picky this time. 
                                                     Ludwik Kowalski
.......................................................................
> I avoid noise in the free fall data by having the students use 16
> positions evenly spaced in time.  The key point is that *no* position
> gets used more than once.  I ask them to calculate the average velocity
> between the 1st and 9th point, the 2nd and 10th point, etc. to the 8 and
> 16th points.  This means they only get 8 velocities, BUT THEY ARE
> INDEPENDENT, AND ARE OVER LONG DISTANCES-SO SMALL POSITION ERRORS ARE'T
> FATAL.