# UM-StL Physics 111e FasTrack Modeling Exercise

Newsflashes:

• 05apr28 -- Our "live-remote" spacetime explorer platform in deep space is on-line.
• 02sep10 -- Recent results toward "fielding a laboratory" for these experiments on the web.
• Imagine the airtrack experiment illustrated in the figure below, in which a spring is compressed by distance x0, and then the first glider is released. The time interval between gate-pair A is measured using map-clocks (tA) and a traveling-clock (tauA). The first glider then collides with and sticks to a 2nd glider. The time interval between gate-pair B is measured using map-clocks (tB) and the traveling clock on the first glider (tauB).

Data for this experiment for various values of spring compression distance x0 are found in the table below. The experiment was done twice, once with a rather flexible spring, and the other with an extremely tight spring (resulting in much higher glider speeds). In each case, the gate separations (xA and xB) are 1 foot or 0.305 meters. The data contain some errors in the measured times, although we've been careful to eliminate systematic errors, and to keep the random variations in measurement of the same time-interval at or about the 1 percent level.

This data provides clues to some of the natural rules of motion that we'll be exploring in this course. Rather than tell you what others (including Aristotle, Galileo, Newton, and Einstein) have proposed doing with such data, modeling workshop physics traditionally asks: "What patterns do YOU see in the data".

One starting point might be to plot the data in various ways, to see if any simple (or even unexpected) relationships emerge. For example, in the case of the flexible spring data set, does the relationship between map-times (t) and traveling-clock times (tau) seem reasonable, taking into account the expected random errors in the measuring process? Is the relationship between spring compression (x0) and the map-clock interval in traversing gate-set A (tA) reasonable? How about the difference between the map-clock times for gate-set A (tA) and gate-set B (tB)?

Another question to ask: What concepts might be useful for cashing in on the insight from this experiment? Galileo in the 1500's might have said velocity, or even acceleration, would be helpful. Newton in the 1600's might have suggested using the concept of force, or momentum. Maxwell might have suggested considering energy. Einstein in 1906 might have agreed about energy and momentum, and stressed the importance of specifying the frame of reference when measuring both positions and times. What do you think? There are likely better ways of understanding it than anyone has come up with yet!

If, after you've considered the above questions on your own, you are curious how others might have responded, you might like to entertain a guess about the kinds of reasoning Galileo Galilei would have applied to the data, if confronted with it in 16th century Italy. At risk of locking yourself into one particular way of thinking, then, click here.

UM-StL Physics and Astronomy, P. Fraundorf (c) 2000
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