# Gravity independant of mass?

## Main Question or Discussion Point

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.

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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 accleration of g under earth's gravity.

Thanks, I fully understand now.

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?

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.