FastTrack Modeling: Possible comments on the data by Galileo Galilei

Caution: This might lock you into a way of thinking, so consider the problem independently before you give close consideration to the kinds of reasoning that Galileo might have used. For much more "Galilean reasoning", this time in "dialogs" actually written by him, take a look at Galileo Galilei's Dialog Concerning the Two Chief World Systems (1632, translated by Stillman Drake, UC Press, 1962), for example. You can also find some of this on the web (especially if you can read italian). Some context on Galileo, and related images, may be found here.

Galileo Galilei

Flexible spring case: It looks like the speed after launch (xa/ta) is proportional to the compression of the spring x0. Hence doubling the spring compression doubles the resulting rate of motion. This is unlike the motion of falling, where (as my experiments on the tower at Pisa suggest) to double the final speed one needs to quadruple the heiqht of fall. Also note that the speed after collision (xb/tb) is always half that before collision (xa/ta). Thus in this case the "rate of motion" halves when the "amount of substance" doubles. Aristotelians here in Italy have long preferred to ignore such subtle effects, claiming that the rate of motion is simply proportional to the effort expended maintaining that motion.

Tight spring case: The observations above beqin to fail for the largest compressions in this series. This part of the experiment is quite beyond my experience, since none of the pendulum-based timers I've made come close to measuring time intervals as small as 1/1,000,000,000 of a second. Hence I'm not sure what to make of this behavior.

Others

How might have Isaac Newton, Albert Einstein, Aristotle, and others responded to the task of conceptualizing the same data set? If you have some ideas about this, let us know. If you really want to bias your perceptions (hopefully after you've given your own brain a chance to wrestle with ways to make sense of the data), speculation on inputs from a couple of other celebrities may be found here.