More than 400 years ago Galileo Galilei (1564-1642), of which we have all heard for his great achievements, laid the foundations of physics.
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Based on experimentation, he was the first to determine, in a body that falls freely, the proportionality between the distance traveled and the square of the time it uses in said path. Despite the lack of measuring instruments and in a time marked by the inquisition in which ideas could cost him his life.
Galileo determines in his investigations, that all objects fall with a constant acceleration and that this is independent of the mass. He determined that air resistance is the reason why light objects take longer to fall than heavy objects, which are less affected by that resistance.
This publication shows one of the simplest ways to obtain the value of the acceleration of gravity with time measurement instruments, with which at the time Galileo did not count and whose results do not differ from those obtained by him.
The particular case of a uniformly accelerated movement is analyzed to determine the value of the acceleration of gravity.
A body in free fall moves in a vertical straight line with a constant acceleration, which is known as gravity. This acceleration is the cause that the speed increases uniformly while falling freely.
The equation that governs this movement is given by:
From experimental data of height vs. time of a metallic sphere in free fall, we will determine the value of the acceleration of gravity.
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The equipment used consists of a sphere subject to a sensor, once released, the sensor activates the chronometer. The impact of the metallic sphere on the small platform stops the clock, recording the transit time of the metallic sphere, which is displayed on the equipment.
The methodology used consists to vary the height and record the different times of fall of the sphere for each position. To minimize the error, three time values were tabulated for each height, which once obtained were averaged (Figure 3).
If you do not have this type of sensors, you can use a timer to measure the fall times in the different positions. By this method the readings of the times will be less precise, increasing the error, however it is a valid procedure to obtain the value of gravity.
With the obtained data a graphical representation was obtained that shows the relation between the heights and the square of the average times of fall of the sphere.
The graphic representation shows that
The result obtained represents the value of gravity in the laboratory.
Percentage error:
theoretical value of gravity = 9.81m/s2
Error% = 100x (theoretical value - experimental value) / theoretical value
Error% = 100x (9.8846 - 9.81) / 9.81
Error% = 0.76
The result obtained validates the value of the acceleration of gravity used at present.
The value of gravity plays an important role in different areas of physics and engineering. In astronomy, geology, oil exploration, the calibration of instruments such as scales, the correct measurement of gravity is of vital importance.
Systems like the simple pendulum also allow to obtain in a simple way the value of the acceleration of gravity.
Currently there are systems available on the Internet, which allow knowing the value of gravity anywhere in the world with an accuracy of 6 decimals. This system was created in Germany's metrology institute and is known as SIS (Schwere-Informationssystem).
It is truly impressive the contributions that, to the scientific knowledge, Galileo’s work left.
The honor made to his legacy is known, in one of the most transcendental events of history, when on the trip to the moon in 1971 Commander David Scott drops a hammer and a falcon feather to demonstrate, in the absence of resistance of the air, that what was predicted by Galileo was true.
Finally, I invite you to watch two impressive videos referring to the predictions of Galileo, taken from YouTube.
REFERENCES
- Physics for Science and Engineering Volume I, Fishbane, Gasiorowicz, Thornton. Editorial Prentice Hall
- https://www.tendencias21.net/Ya-se-puede-medir-la-gravedad-exacta-de-cualquier-lugar-del-mundo-desde-casa_a1609.html.
- http://www.academia.edu/11063207/Aportaciones_a_la_f%C3%ADsica_de_Galileo_Galilei
- https://www.xataka.com/espacio/la-historia-de-la-pluma-y-el-martillo-que-un-astronauta-dejo-caer-en-la-luna-en-homenaje-a-galileo.