Using measurement uncertainties to detect incomplete assumptions about theory in an experiment with rolling marbles

Abstract

In this lab activity, carbon copy paper is used to record the horizontal distance a marble flies off a table after rolling down an incline. The minimal scatter of the dots visually shows the high precision—i.e. the small uncertainty—of the measurements to students. The theoretical prediction of this distance will be too big if students forget to include rotational energy in the energy balance when they calculate the marble’s speed at the bottom of the incline. This results in a discrepancy between the predicted horizontal distance and the measurement result. The precision of the experiment and the absence of overlap with the theoretical prediction is evidence that the prediction has to be wrong. Including rotational energy and taking a 10% energy loss due to friction into account, makes the measurement result overlap with the theoretical prediction, bringing them into agreement. Thus, measurement uncertainties guide the process of comparing the measurement result with the prediction: overlap between the theory-based prediction and the measurement result indicates agreement, whereas no overlap implies discrepancy. The lab activity presented here is an activity where measurement uncertainties are used in a meaningful, indispensable manner. The experimental result is evidence that forces students to rethink their assumptions, in this case about the conservation of energy. This leads to the revision of their calculation, emphasizing the necessity to include rotational energy and friction. Without it, the highly precise measurement result is in disagreement with the theoretical prediction. A procedure such as this—comparing empirical data with theory—is an authentic and common practice in science and should thus find its way into the physics classroom; but it cannot be done without an analysis of measurement uncertainties.