Optimizing acceleration measurements using a single photogate

Abstract

Measuring the acceleration of a glider on a slightly inclined air track is a typical activity in different experiments in didactic Physics laboratories. In this paper, we discuss acceleration measurements derived directly from the quantity $\Delta v / \Delta t $, testing its reproducibility with several time sensors (photogates). Using a standard lab equipment we show that acceleration measurements using two photogates strongly depend on the photogates used and even on the distance between them, what can frustrate the goals of the experiment. The technical aspects behind that unexpected behavior can be partially overcome by working with a single photogate in a method where the glider is launched uphill and its speed is measured in the ascending and the descending motion. Using this alternative approach we were able to reduce discrepancies by a factor of 6, down to less than 1\%. For both methods, the systematic errors between photogates surpass the statistical uncertainties for each photogate. Finally, we show that these discrepancies can be explained by an offset of the order of 1 ms in time measurements.