Re: The air track experiment

[Ludwik Kowalski <KowalskiL@MAIL.MONTCLAIR.EDU>]

JACK L. URETSKY wrote:

> ......  It is my private opinion that Galileo "cooked" his
> results - go for it, inquisition! ...

A very satisfactory linear relation between v and t is usually
obtained, using Vernier or Pasco equipment, when a cart
rolls along a tilted table. As soon that the linearity of v(t) is
accepted the constancy of a(t) follows from the definition
of acceleration.

Yes, some amount of "cooking" is involved in saying that
(v-v0) is proportional to t (rather that, to t raised to the
power of 1.02, for example) but this is only a matter of
experimental errors. Galileo did not have instruments we
use and in his case there were "more cooking".

Suppose you are experimenting with a ball rolling along an
inclined track (for example two broom sticks). The angle
of inclination is 10 degrees or less and your track is two
meters long. The clock is a pendulum whose period is 0.3
seconds. How large deviation of b from 1.000, in the
(v-v0)=B*t^b relation, would be expected? Probably
not too much, but not as little as 1%.

To illustrate "creative cooking" (extraction of truth by
intuition, logical extrapolations, etc.) I would use Kepler
rather than Galileo. There were an article on this subject
in TPT, at least two years ago. Newton data, allowing
to discover the 1/r^2 relation, were also quite shaky.

Ludwik Kowalski
Department of Mathematical Sciences
Montclair State University.