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Experimental Estimation of Gravitational Acceleration Using Manual Free Fall Measurements
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Abstract
Hand-timed free-fall experiments are a standard way for students to estimate the gravitational acceleration g, but it is often unclear whether the resulting errors come from air resistance or from the person operating the stopwatch. We dropped three everyday objects (an eraser in three orientations, a pencil sharpener, and a pencil in two orientations) from heights of 0.3 m and 1.0 m, with four hand-timed trials per configuration, and extracted g by inverting the exact solution of the quadratic-drag equation of motion. Air drag raises the extracted value of g by only 0.05–1.45% (mean 0.37%), a correction well described by the simple estimate kh/3, where k is the drag parameter. By contrast, the fall times of different configurations dropped from the same height differ by 25 ms (RMS), although drag predicts agreement within 0.7%. Using this observed scatter as the timing uncertainty, the inverse-variance weighted mean of all twelve configurations is g = 10.29 ± 0.42 m/s2, 5% (1.2σ) above the local reference value gtheo = 9.802 m/s2. The measured times are, on average, 16 ± 7 ms shorter than those expected for free fall, consistent with a systematic early stop of the stopwatch; this offset explains why the 0.3 m drops overestimate g by 24% on average and the 1.0 m drops by 8%. We conclude that, for household objects dropped from about a metre, drag corrections are unnecessary and the accuracy of hand-timed free fall is limited by systematic timing bias, which is best addressed by measuring at several heights and fitting fall time against √(2h).
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Experimental Estimation of Gravitational Acceleration Using Manual Free Fall Measurements. (2026). International Journal of Engineering, Science and Environment (IJESE), 1(2). https://ijese.in/journal/article/view/48
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