Galileo
Calculation of the g value by free fall analysis
Autor:
Título 4
Learning objectives :
This activity allows students to experimentally determine the value of the acceleration of gravity by analyzing a free fall. It reproduces Galileo's historical approach with modern tools.
Concepts covered
Free fall; Acceleration of gravity; Laws of Galilee; Potential energy conversion; Interpreting acceleration graphs
What students will do :
The student drops their smartphone (protected by a pillow) from a known height and records linear acceleration data during the fall. By identifying the start and end of the fall on the acceleration graph and measuring the elapsed time the student can calculate g using the relationship between height and time in a free fall.
What is required :
Smartphone with the FizziQ application; A soft pillow to hold the smartphone; Tape measure to measure the height of fall; FizziQ experience notebook
Scientific background :
Galileo revolutionized physics in the 17th century by discovering that, contrary to Aristotelian beliefs, all bodies fall with the same acceleration regardless of their mass. For a fall without initial speed, the relationship between height h and time t is given by: h = ½gt². This equation allows us to calculate g by precisely measuring h and t. The smartphone's accelerometer measures linear acceleration on three axes. During free fall, in the absence of air resistance, the device should measure zero acceleration on all axes (state of weightlessness), but this value is difficult to observe in practice. To determine g, it is more reliable to identify the start and end of the drop on the graph: the start corresponds to the moment when the acceleration drops suddenly (when the smartphone is dropped), and the end to the moment of an acceleration peak (impact on the pillow). The time elapsed between these two events corresponds to the fall duration. Knowing the height h and the duration t, we calculate g = 2h/t². The main sources of error include: air resistance (which becomes significant beyond 1-2 meters of drop), inaccuracy in height measurement, and human reaction time if triggered manually. Carrying out several tests allows you to improve the precision by calculating the average. This simple experiment reproduces Galileo's conceptual approach with modern tools and perfectly illustrates the transition from a physical observation to a quantitative law.