Did Galileo Really Drop Balls from the Leaning Tower of Pisa?

[smt22]

Following text:

"Galileo Galilei is supposedly the first one to prove that the speed of a falling
object is independent of its mass. He did this by demonstrating that a 100 pound
cannonball and a one pound ball dropped at the same time from the Leaning
Tower of Pisa reached the ground at the same time. The acceleration of gravity
is therefore independent of mass."

I have never really understood why it hits the floor at the same time. When I look at the formula F = mg, I would say the force of gravity is greater for the 100 pound ball, so why does it not fall faster? Let's also assume that it's performed in vacuum.

 

[flatmaster]

you've got that equation right.

F=mg

With F Being the force of gravity on the object. However, the 100 pound ball is harder to accelerrate than the 1 pound ball. That can be expressed as

F=ma

Where F is the force on the object, and a is the acceleration of the object. All you must do is set these forces equal to each other.

mg=ma

divide by m.

g=a.

So any object, neglecting air resistance will fall with an acceleration of g under Earth's gravity.

 

[smt22]

Thanks, I fully understand now.

 

[Raap]

But considering air resistance, shouldn't the cannonball in Galileo's story reach the ground first? Did they modify the story or wasn't it noticeable?

 

[Varnick]

It probably wasn't noticeable, but as far as I know the "Leaning Tower of Pisa Stories" are entirely fictitious, and the experiments were actually performed using angled ramps to the same effect, but reducing the impact of air resistance.