Do all things fall at the same rate?

[xxbluejay21]

Ok, first of all, I'm in college, I'm not stupid, I've taken physics, so I'm not a total noob, but I have some questions that I came across when I was doing a lab in my calculus class.

 

If a baseball and a ping pong ball are dropped at the same place on earth, with no air resistance, they will fall at the same speed and land at the same time. This is what I disagree with/am confused about.

 

They fall at the same speed because of the earth's gravitational constant (the earth pulls everything equally) no matter what the size/shape/mass of the object is. This is only for earth. On the moon, the gravity is different, thus the constant and the acceleration would be different, correct?

 

Well doesn't everything that has a mass have gravity? And isn't the amount of gravity something has proportional to how much mass it has?

 

Say an apple falls from 100 feet. It will land in a specific amount of time. Say an orange is dropped also from a 100 feet. It will land in the same amount of time. But say there is an object that is the size of an orange but has the mass of the sun, thus has the gravitational pull of the sun. If that was "dropped" from a hundred feet from the earth, would it hit at the same time as the orange and apple did? Wouldn't it not, since the earth is pulling on it but it is also pulling on the earth with a tremendous amount of force?

 

Now back to the fact that everything with mass has gravity. The baseball and the ping pong ball have different masses, thus different amounts of gravity, and although this difference is negligible because the earth's mass/gravity is like a billion times bigger/stronger than the objects', wouldn't the objects fall at SLIGHTLY different times because of the fact that they have different masses? The earth pulls on all objects the same, but the objects don't pull back with the same force.

 

That is what I thought. Please give me your input.

[DJBruce]

I personally think the easiest way to think about this is by looking at the math. So by Newton's Law of Universal Gravitation for a two bodies of mass [math]m_{1}[/math] and [math]m_{2}[/math] the force between the two bodies is:

[math]F_{12}=F_{21}=\frac{Gm_{1}m_{2}}{r^{2}}[/math]

So if you consider want to see how fast a body would fall you would say:

[math]v_{1}=v_{0}+at=v_{0}+\frac{F}{m_{1}}t=v_{0}+\frac{\frac{Gm_{1}m_{2}}{r^{2}}}{m_{1}}=\frac{Gm_{2}}{r^{2}}t+v_{0}[/math] so we see that regardless of the mass of the object falling the acceleration is independent of the mass of the falling body. This is because although a large body, like the sun has a much larger force acting on it because of its large mass it needs a bigger force to move it.

 

Also it is key to note that Newton's Law is reciprocal in that it states the force of gravity is equal in magnitude for both objects. Think Newtons third law ie: equal and opposite forces. So this means that the force of gravity exerted by the sun on the Earth is the same as the force exerted by the Earth on the Sun.

 

Hope this helps.

Edited May 26, 2011 by DJBruce

[DrRocket]

Ok, first of all, I'm in college, I'm not stupid, I've taken physics, so I'm not a total noob, but I have some questions that I came across when I was doing a lab in my calculus class.

 

If a baseball and a ping pong ball are dropped at the same place on earth, with no air resistance, they will fall at the same speed and land at the same time. This is what I disagree with/am confused about.

 

They fall at the same speed because of the earth's gravitational constant (the earth pulls everything equally) no matter what the size/shape/mass of the object is. This is only for earth. On the moon, the gravity is different, thus the constant and the acceleration would be different, correct?

 

Well doesn't everything that has a mass have gravity? And isn't the amount of gravity something has proportional to how much mass it has?

 

Say an apple falls from 100 feet. It will land in a specific amount of time. Say an orange is dropped also from a 100 feet. It will land in the same amount of time. But say there is an object that is the size of an orange but has the mass of the sun, thus has the gravitational pull of the sun. If that was "dropped" from a hundred feet from the earth, would it hit at the same time as the orange and apple did? Wouldn't it not, since the earth is pulling on it but it is also pulling on the earth with a tremendous amount of force?

 

Now back to the fact that everything with mass has gravity. The baseball and the ping pong ball have different masses, thus different amounts of gravity, and although this difference is negligible because the earth's mass/gravity is like a billion times bigger/stronger than the objects', wouldn't the objects fall at SLIGHTLY different times because of the fact that they have different masses? The earth pulls on all objects the same, but the objects don't pull back with the same force.

 

That is what I thought. Please give me your input.

 

 

Short answeer -- The gravitational force exerted on a body is proportional to its mass, but the resulting acceleration is inversely proportional to its mass and the net result is that the acceleration is independent of the mass. This is basically what DJBruce told you.

 

Longer answer -- The short answer works so long as the mass of the object is sufficiently small relative to the Earth that the movement of the Earth can be neglected. In reality you have a two-body problem, and both bodies accelerate towards their combined center-of-mass according to Newton's law of universal gravitation. A somewhat heavier body will approach the Earth very slightly more rapidly than a light body. A really really heavy body will move the Earth with appreciable acceleration and then things are very different from everyday experience. If the orange were the mass of the sun, it would appear to an outside observer that the orange was fixed and the Earth moved.