Determining the normal acceleration (of the Earth)

Based on Galileo Galilei’s thought experiments (Discorsi) and alleged experiments on the Leaning Tower of Pisa, we determined the acceleration of gravity g. I suggested three possibilities to the students, and they came up with a fourth idea themselves.

Here is a sketch:

Possibility 1)

Drop a bar of chocolate with a standard weight of 100 g from the height of your own body, on average 1.70 m, and measure the time it takes to fall. The acceleration is calculated using the distance-time law s = g/2 t² + vt + a, i.e. for initial acceleration a = 0 and initial velocity v=0:

g = 2 s/t²

The result of an experiment with a person with s = 1.99 m is approximately g = 10 m/s².

Possibility 2)

The Earth has a moon with an orbital period of approximately 30 days. From the law of gravity, we get g = G * M/ r², and Kepler’s third law tells us that T²/ r³ = constant, so r = ( T²/ constant )1/3, i.e.

g = G * M * constant1/3

T2/3

The constant comes from Newton’s law of gravity, which eliminates the mass of the Earth M.

Option 3)

Experiments with a test specimen on an inclined plane that is tilted at varying angles. The students carried out this experiment. The air cushion track (friction-free) was tilted by 10, 30, 60 and 90° and the time taken for a car to travel along the track was measured each time when it was simply released at the top.

Determination of gravitational acceleration according to Galileo (Discorsi)