Re: free fall data

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

Here are free fall data I took from the DSON017 movie which came on the
same CD-ROM as VideoPoint. Called "Vertical Ball Toss" it was recorded
at 30 fps. There are 29 frames but only the 2nd half, the ball on the 
way down is analysed here. "Insignificant" digits were used to avoid 
additional rounding errors (in that sense digits are very significant).

  time(s)   dist(m) speed(m/s) g(m/s^2)

  0.36666   0.000                     AVERAGES
  0.40000   0.015     0.450
  0.43333   0.047     0.960     15.30          As you can see, the
  0.46666   0.088     1.230      8.10   11.1   values of g fluctuate
  0.50000   0.140     1.560      9.00          between 5.4 and 18.7
  0.53333   0.198     1.740      5.40
  0.56666   0.271     2.190     13.50   10.8   The mean acceleration is
  0.60000   0.359     2.640     13.50          10.66 (or 10.08 if 15.3
  0.63333   0.453     2.820      5.40          and 18.72 are ignored).
  0.66666   0.557     3.120      9.00    9.6   
  0.70000   0.677     3.600     14.40          The mean is very good
  0.73333   0.897     3.900      9.00          but the constancy of g
  0.76666   0.948     4.224      9.72    9.3   is not demonstrated. I
  0.80000   1.099     4.530      9.18          the most simple way of
  0.83333   1.265     5.001     14.13          calculating v and g.
  0.86666   1.437     5.157      4.68    12.5
  0.90000   1.630     5.781     18.72          Even averages of 3 values
                                               fluctuate by more than 5%
  time(s) dist(m) speed(m/s)   accel(m/s^2)    

The velocity versus time data are very linear, as Bob Carlson said, even
when my glasses are on. His way of handling data in a class are very close
to what I will do this week in the algebra-based College Physics. First 
each of my six groups will be fillmed dropping the ball. Then data will 
be analysed on the big TV sceen without digitizing (I can digitize on 
my audio-visual Mac at home but not at school). A big piece of wood, with 
equidistant lines painted, will be placed behind to obtain distances.
A digitized movie of one experiment will be analysed in class later.

Yes, Bob, knowing that this is a teacher-to-teacher exchange I do address 
issues which are not necessarilly appropriate for all students. The 
question about side-wise filming is one of them; I hope somebody will 
reply. I think that the error analysis through simulations on the 
spreadsheet is worth doing. Start with ideal time-distance data and you 
insert an additional column in which distances are smeared by as much as 
you wish. Then you calculate v and g from smeared data. In my version of 
Excel the formula for uniform smearing would be =B10*(1+0.05*RAND()). This 
is for smearing in the range between 0.95 and 1.05 of B10. (Non-unifirm 
smearing can also be imposed. I did not try them but I see that statistical 
functions, such as POISSON and NORMDIST, are availble in Excel). I like 
the idea of illustrating propagation of errors on the spreadseet.
                                                         Ludwik Kowalski
P.S.
    I agree with Bob Carlson who wrote (On Sun, 14 Sep 1997):

> Those of us that have analyzed real experimental data may have a different
> perspective as to what looks linear. Video analysis is an experimental tool,
> not a computer game. As such, the data is real. Video files are just large
> (visual) data base recordings of position versus time. They are not created
> animations produced to fit physical laws. ... When using video analysis as 
> an experimental tool, experimental design is just as important as with any 
> other experimental method. Done correctly, this approach gives comparable 
> results to other timing methods including spark timers, smart pulleys, and 
> sonic rangers.