Falling paper sheets to investigate aerodynamic drag

Many physics education papers have tackled the issue of effectively introducing aerodynamic drag (“drag”, henceforth) by analyzing the motion of falling objects in diverse scenarios. However, to the best of our knowledge, no works have taken into consideration the relationship between the falling time and the cross-sectional area of a constant-mass object dropped from a fixed height as the crosssectional area is changed, even though this approach might represent a further perspective to the understanding of a considerable number of common physical phenomena: from the flight of a flying squirrel up to the reentry of a spacecraft. In this paper we propose an educational activity based on the falling-time vs cross-sectional-area relationship to investigate the effects of drag on constant-mass not-point-like falling objects. The starting point – taking inspiration from an experimental activity proposed in another paper – is measuring the falling times of different kinds of paper sheets, dropped from a fixed height, as the sheet area is progressively halved. By plotting the falling-time vs sheet-area curve, the gradual overlapping of all the curves should be observed as the sheet areas tend to zero. Hence, students could graphically extrapolate an estimate of the falling time when areas are assumed to be zero and compare it to the theoretical value obtained using the kinematics formula. Finally, the constancy of the gravitational acceleration regardless of the mass of the object when drag is negligible might be inferred.