A bowling ball has more weight than a racquet ball.
Agreed.
Which should have some effect according to your idea of displacement.
True, it does (both calculably and in reality demonstrably).
But, If you go to your roof and released both from the same height at the same time, they would hit the ground at exactly the same time.
I am saying that they don't, but that the difference between when one hits the ground and the other one is very small. If you increased the distance, or increased your measurement precision, you would see the difference.
The "all things fall at the same rate" is a rule of thumb which is perfectly adequate for most cases we experience, but is not strictly speaking true. It would arguably be true if "perfect vacuum" were attainable - but even then not in the standard worldview (that you likely have) because there would still be the varying gravitational attraction of varying masses to consider/factor in.
We have a math formula for determining the speed at which objects will fall and the "weight" of the object is not represented anywhere in the math formula.
That's not quite right, but yes - the oversimplification taught to many students is just an acceleration and time. That is assuming there is no buoyant force, drag, etc. to consider - which is of course, untrue.
The fact that the math can still accurately tell you how fast something will fall without this concept being represented anywhere in the formula ought to tell you that you've misidentified the source of this force.
That is a mistake in your logic. It just means the variance in weight is not a major factor in the speed of the falling (assuming an over simplified "perfect vacuum" etc). Besides, what we are discussing is the the relationship of the weight to the weight of the media it displaces, which unquestionably is the cause of falling. That is in archemides' principle - so it is in "the equation".
The equations say it is, and it isn't hard to understand why it's true either. Things do not fall the same rate in the presence of air / through any media (unless they are identical). The oversimplified equations you are talking about are not correct when air (or any media, including low pressure air - aka "vacuum" - is present). They are just "correct enough" for everyday use in some cases.
If all things are equal except the object's weight, they hit the ground at the same time. This is not something you can deny.
How about a glider airplane which is empty and one which is filled with lead. The media itself has a significant impact, especially when the shape causes drag / increased collision with it. A simpler analogy/demonstration would be an empty plastic bottle, and one which is filled with rocks dropped into water (air behaves as a fluid as well).
Ohh you mean if you throw them out of helicopter at 30,000 feet they might land at different times?
I'm saying that they do fall at different times, and this becomes easier to observe when the height they fall from is greater. The media is not null, the buoyant force is not null. They may be small - but they are always non zero.
See the problem with that it becomes impossible to do a controlled experiment
We aren't talking about experiments - we are merely talking about observations. It is certainly possible to observe dropping things out of a helicopter or - better yet - from a weather balloon. Dropping things off a roof is also not an experiment, nor "controlled" - not that it really matters.
you're introducing countless variables that will change the result.
The variables are always there, in reality. The variables i am specifically talking about are drag and buoyancy. They are never (and can never) be zero. This necessarily means that only identical objects can fall perfectly identically and through perfectly identical/uniform media.
In order for science to work you need to isolate the experiment as much as possible
Agreed, but we aren't in any way discussing an experiment. We are merely discussing observation/phenomena. Experiments are horses of an entirely different color.
Lemme guess, "They don't remove ALLLL the air.... They leave behind 0.0000001% of the air in a vaccum"....
Correct, and that is the reason that the buoyant and drag forces (among others) are never and can never be 0 - but i agree that the asymptote points reasonably clearly to the conclusion that if there could be no matter - things would fall at the same rate. All of this is irrelevant though, because the rate of fall isn't at issue - it is the reason for falling which is. The reason for falling remains the exact same in both the open air and in the vacuum chamber; the weight of the object is greater than the weight of the media displaced.
But the point is they are still falling
Exactly.
That's a problem for a model that relies on the premise that it's the surrounding air causing objects to fall.
We are not discussing a model. We are discussing the reason for falling, and more specifically how archemides' principle explains, describes, and can be used to experimentally validate that cause.
We haven't been doing any experiments, nor discussing any. It is very important that you understand that. Experiment has a rigorous and inflexible definition in science, and its colloquial/incorrect usage is an attack on science. We are only talking about observations.
and have air resistance be the only variable?
I'm following so far; we are only observing air resistance.
If the sheet of paper falls slower than the brick of paper, then you've just proven yet again, that "weight" doesn't matter and the variable that effects air resistance is shape....
Once again, the weight of the page alone is not the reason the page falls. The page falls because its weight is greater than that of the media it displaces. This is true in both shape configurations. The acceleration profile is, however, most influenced by the media and the object's interaction with that media - but this, once again, is not the cause of falling. Drag and buoyant force both play large rolls.
Again, all this shows is that the weight isn't what most largely influences the acceleration profile. That is NOT the same thing as showing that it isn't involved, or furthermore - and the point - that the cause of falling isn't as archimedes describes.
Air can't simultaneously be the thing that's creating the force that makes you fall
No one said it was! As i keep saying, and archimedes formalized more than 2 millennia ago - it is the interplay/relationship between the weight of the object and the weight of the surrounding media which causes falling.
It can't be both
I don't see why you think this, but in any case - no one is claiming it is. You seem to be misunderstanding. Hopefully the above has cleared that up.
Air resistance doesn't prove gravity,
Obviously! Who said it did? If you think it was me, please provide quotes so i can better understand what made you come to this conclusion.
but it certainly disproves your model.
We are not discussing a model. We are discussing the cause of falling (or trying to, anyway).
This is also proven by a parachute slowing your descent despite making your weight heavier, not lighter.
You are still getting distracted. We are talking about archimedes principle and the cause of falling. The fact that things don't all fall the same speed is a tangent that is only helping you to lose focus (also, weren't you arguing the opposite a second ago?!)
Agreed.
True, it does (both calculably and in reality demonstrably).
I am saying that they don't, but that the difference between when one hits the ground and the other one is very small. If you increased the distance, or increased your measurement precision, you would see the difference.
The "all things fall at the same rate" is a rule of thumb which is perfectly adequate for most cases we experience, but is not strictly speaking true. It would arguably be true if "perfect vacuum" were attainable - but even then not in the standard worldview (that you likely have) because there would still be the varying gravitational attraction of varying masses to consider/factor in.
That's not quite right, but yes - the oversimplification taught to many students is just an acceleration and time. That is assuming there is no buoyant force, drag, etc. to consider - which is of course, untrue.
That is a mistake in your logic. It just means the variance in weight is not a major factor in the speed of the falling (assuming an over simplified "perfect vacuum" etc). Besides, what we are discussing is the the relationship of the weight to the weight of the media it displaces, which unquestionably is the cause of falling. That is in archemides' principle - so it is in "the equation".
The equations say it is, and it isn't hard to understand why it's true either. Things do not fall the same rate in the presence of air / through any media (unless they are identical). The oversimplified equations you are talking about are not correct when air (or any media, including low pressure air - aka "vacuum" - is present). They are just "correct enough" for everyday use in some cases.
How about a glider airplane which is empty and one which is filled with lead. The media itself has a significant impact, especially when the shape causes drag / increased collision with it. A simpler analogy/demonstration would be an empty plastic bottle, and one which is filled with rocks dropped into water (air behaves as a fluid as well).
I'm saying that they do fall at different times, and this becomes easier to observe when the height they fall from is greater. The media is not null, the buoyant force is not null. They may be small - but they are always non zero.
We aren't talking about experiments - we are merely talking about observations. It is certainly possible to observe dropping things out of a helicopter or - better yet - from a weather balloon. Dropping things off a roof is also not an experiment, nor "controlled" - not that it really matters.
The variables are always there, in reality. The variables i am specifically talking about are drag and buoyancy. They are never (and can never) be zero. This necessarily means that only identical objects can fall perfectly identically and through perfectly identical/uniform media.
Agreed, but we aren't in any way discussing an experiment. We are merely discussing observation/phenomena. Experiments are horses of an entirely different color.
Correct, and that is the reason that the buoyant and drag forces (among others) are never and can never be 0 - but i agree that the asymptote points reasonably clearly to the conclusion that if there could be no matter - things would fall at the same rate. All of this is irrelevant though, because the rate of fall isn't at issue - it is the reason for falling which is. The reason for falling remains the exact same in both the open air and in the vacuum chamber; the weight of the object is greater than the weight of the media displaced.
Exactly.
We are not discussing a model. We are discussing the reason for falling, and more specifically how archemides' principle explains, describes, and can be used to experimentally validate that cause.
We haven't been doing any experiments, nor discussing any. It is very important that you understand that. Experiment has a rigorous and inflexible definition in science, and its colloquial/incorrect usage is an attack on science. We are only talking about observations.
I'm following so far; we are only observing air resistance.
Once again, the weight of the page alone is not the reason the page falls. The page falls because its weight is greater than that of the media it displaces. This is true in both shape configurations. The acceleration profile is, however, most influenced by the media and the object's interaction with that media - but this, once again, is not the cause of falling. Drag and buoyant force both play large rolls.
Again, all this shows is that the weight isn't what most largely influences the acceleration profile. That is NOT the same thing as showing that it isn't involved, or furthermore - and the point - that the cause of falling isn't as archimedes describes.
No one said it was! As i keep saying, and archimedes formalized more than 2 millennia ago - it is the interplay/relationship between the weight of the object and the weight of the surrounding media which causes falling.
I don't see why you think this, but in any case - no one is claiming it is. You seem to be misunderstanding. Hopefully the above has cleared that up.
Obviously! Who said it did? If you think it was me, please provide quotes so i can better understand what made you come to this conclusion.
We are not discussing a model. We are discussing the cause of falling (or trying to, anyway).
You are still getting distracted. We are talking about archimedes principle and the cause of falling. The fact that things don't all fall the same speed is a tangent that is only helping you to lose focus (also, weren't you arguing the opposite a second ago?!)