Gravitational Acceleration Measurement at Three Locations in Muaro Jambi through Free Fall Experiments

Quantitative Analysis and Uncertainty

Abstract

This study examines the relationship between fall height (h) and the square of the fall time (t²) and estimates the local gravitational acceleration (g) at three locations in Muaro Jambi (Mendalo, Sungai Duren, Muaro Pijoan). The experiment was conducted by dropping a spherical ball from three heights (0.80 m; 1.00 m; 1.50 m) and recording the fall time repeatedly using a digital stopwatch. A graphical analysis of h versus t² was applied using linear regression without an intercept (regression through the origin) so that g = 2·slope. The results show a consistent quadratic pattern (h ∝ t²), but the numerical estimate of g deviates from the theoretical value (≈ 9.81 m/s²). The causes of the deviation are analyzed and are dominated by uncertainty in the time measurement (human response to the stopwatch) as well as contributions from air resistance and height measurement errors. Due to the limited number of height points (n = 3) and the use of manual time measurement, these results are insufficient to assess small geographic variations in g. This study recommends the use of automatic timing sensors (e.g. Phyphox, mechanical switch), variations in object diameter, and increasing the number of height points for further studies.