Experiment of The Month
The MU Physics Department does not claim that we invented these labs. Actually, the origin of these labs are currently unknown to us. Our labs do not have written instructions. In keeping with this spirit, the description given here will be brief and general. The intent is that each performance of the lab will be unique; in each nature will reveal a slightly different face to the observer.
In this month's lab we estimate the average diameter of a family of marbles by measuring the probability that a "shooter" marble will hit one of a family of marbles lined up about a meter away. We have two different authors this month, and the variation in the two versions of the lab are interesting. This kind of flexibility is one of the strengths of the Millersville physics laboratory program. It allows labs to evolve and improve, without being welded to a standard procedure.
Dr. Dooley presents a rather empirical approach, with limited analysis, concluding on an experimental basis that the uncertainty in the value for the diameter falls when the shooter marble is rolled a large number of times. The uncertainty falls roughly as one divided by the square root of the number of trials.
Dr. Nolan not only performs an equivalent experiment, but also develops the mathematical theory, based on the binomial probability distribution, which predicts the "one over square root of N" dependence of the uncertainty. This version shows that the observed behavior is the consequence of reasnoable ideas about the probability of hitting a marble, and is more satisfying to the analytically inclined.