A more convenient method to predict gravitational acceleration (g) using smartphone’s proximity sensor in a simple pendulum experiment

Abstract

The application of smartphones in physics learning is inevitable because of the advanced technology installed in them. The simple pendulum is a classical topic in physics relating to gravitational acceleration. Smartphones are equipped with a proximity sensor that can record the period of an oscillating pendulum. A method to determine gravitational acceleration (g) using a smartphone proximity sensor in a simple pendulum experiment was presented in this study. This proposed method is more convenient and straightforward because it does not require additional equipment apart from string and bob. Furthermore, the simplicity of this method is assisted by software used that is able to display directly the results of period measurement that subsequently were applied to calculate the gravitational acceleration (g). The string length was varied to analyze the consistency of measurement results. The calculated g values were compared to the local gravity value and produced a relative error with a range of 0.11%–0.54%. The reported g value combined with uncertainty propagation was 9.75 ± 0.02 ms−2.

Pendulum with a large bob

“…Equation ( 1) presents a linear relationship between T 2 and I/mD with a constant gradient of 4π 2 /g. For a uniform sphere of radius R suspended by a massless string of length L as shown in figure 1(b), D = L + R. By the parallel-axis theorem, I = I cm + mD 2 , where I cm is the moment of inertia about the axis through the centre of mass and perpendicular to the plane. If the object is treated as a simple pendulum, I cm = 0, giving…”

“…One of the authors (WK) set a challenge for a group of students learning oscillatory motion: they were to calculate the local gravitational acceleration g based on the oscillation period of a bob suspended by a string. Everyone agreed that we could apply the formula for the period of a simple pendulum to a small-sized bob [1,2]. On the other hand, the students' approaches diverged when they were told to use larger objects.…”

Improved Accuracy in Determining the Acceleration Due to Gravity in Free Fall Experiments Using Smartphones and Mechanical Switches

“…Building upon these advancements, Fontana, Yeung, and Hall in 2020 advocated for the utilization of the ticker tape timer method to not only ascertain gravitational acceleration but also account for the effects of friction [24]. Another popular technique for measuring g in the classroom is the pendulum [25][26][27][28][29]. Both of these techniques are popular because they are both directly influenced by the gravitational acceleration and they offer straightforward and accessible ways to measure the acceleration due to gravity in a classroom setting.…”

“…This is a key driver behind the widespread adoption of photogate timers in educational laboratory settings. In contemporary contexts, smartphones equipped with a plethora of sensors offer a versatile platform for accurate time measurement and data acquisition, as documented in recent literature [20][21][22][23][26][27][28][29][30]. A compelling alternative to conventional stopwatch and photogate methods emerges through the utilization of readily accessible smartphones equipped with sound-recording capabilities.…”