The Pisa Balls Experiment

                                                            Material required:
 1) Two balls of different masses.
2) Thermacol sheet with two holes of the same diameter as the balls
3) A cardboard sheet of the same dimensions as the thermacol sheet.
4) A sound analyzing software (Audacity)

                                                                    

Procedure:
1) Take the cardboard sheet in your hands put the thermacol sheet on top of it.
2) Then place both the balls in the holes
3) Then pull the cardboard sheet swiftly so that both the balls fall at the same time.

4) Place an audio receptor between the falling position of both the balls and connect it to a computer and save the sound wave we obtain when the balls hit the ground.

The sound wave in Audacity clearly showed that both the balls hit the ground at the same time. In the sound wave below, the first spike is when both the balls hit the ground.

The proof with calculation:

First of all, we know that the only force pulling the objects down (acting on the objects) is their weight ( W representing the vector weight of the object).

We know that a force is represented as:

In this case, weight is a force with the vector gravity as acceleration.

the only force acting on free-falling objects is W.
Thus:

From this, we could say that the time taken for the objects to hit the ground is the same since they have the same acceleration.

Mathematical Demonstration of the fact that the time of descent of a free-falling object does not depend on its mass:

By integrating acceleration, we get the velocity of the object:

We are interested in knowing when the ball hits the ground i.e. when the Y coordinate of the position vector OM is equal to zero.
To find t, we do :

By this, we conclude by saying that the time of descent of a free-falling object depends on the initial height and the gravity but not on its mass.