Gravity independant of mass?

In summary, Galileo Galilei proved that the speed of a falling object is independent of its mass 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. This is due to the acceleration of gravity being independent of mass. However, when considering air resistance, the cannonball may have reached the ground first, but this was not noticeable in the experiment performed by Galileo.
  • #1
2
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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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  • #2
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.
 
  • #3
Thanks, I fully understand now.
 
  • #4
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?
 
  • #5
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.
 

1. How does gravity act independently of mass?

Gravity is a fundamental force of attraction between two objects with mass. It is independent of the mass of the objects and acts equally on all objects, regardless of their mass. This means that all objects will experience the same acceleration due to gravity regardless of their mass, as long as they are in the same location.

2. What evidence supports the idea of gravity being independent of mass?

One of the main pieces of evidence is the experiment conducted by Galileo in which he dropped objects of different mass from the Leaning Tower of Pisa. He observed that all objects, regardless of their mass, fell at the same rate, providing evidence that gravity acts independently of mass.

3. Can gravity affect objects with no mass?

No, gravity only affects objects with mass. Objects without mass, such as photons, do not experience the force of gravity. This is because mass is a necessary component for the interaction of gravity.

4. How does the theory of general relativity explain gravity independent of mass?

The theory of general relativity explains gravity as the curvature of space-time caused by the presence of mass. This means that all objects with mass create a curvature in space-time, and this curvature affects the motion of other objects with mass, regardless of their size or mass.

5. Does gravity act differently on different planets?

Yes, the strength of gravity can vary on different planets due to their different masses and sizes. However, the way gravity acts independently of mass remains the same on all planets, as long as they have mass. This means that objects of different masses will still experience the same acceleration due to gravity on different planets.

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