Originally Posted by
ANCPER
What's the world coming to
when pilots don't know the basics of physics?
Indeed. What you're missing though, is that you are the one who doesn't know the basics of physics.
It is astonishing that you continue to insist that you're correct when it has been demonstrated quite thoroughly that you are wrong.
And TINSTAAFL, this is directed at you also, as you too seem determined to continue posting your incorrect understanding of this.
There have been several very detailed explanation of *why* a more dense object will fall faster through the atmosphere than will less a dense dense object of the same dimensions. Your example of an empty container falling at the same terminal velocity is, quite simply, wrong. It has been repeatedly explained in this thread *why* it is wrong, with detailed discussions of the forces involved. Instead of simply repeating the claim that they fall at the same speed, without offering proof, why don't you *explain* why you think the explanations are incorrect?
Serious question? If you wish to be taken seriously, why aren't you explaining your case instead of just contradicting the explanations which have been given? Merely repeating your contradiction makes you appear as John Cleese in Monty Python's argument sketch.
Additionally, a number of posters have cited a very compelling example which makes it abundantly obvious that you are wrong, yet, you pretend that you haven't even noticed. Again, consider the example of two balloons, one inflated with air, and one filled to the same dimensions with water, or concrete, or whatever dense material . Drop them both from the same height. They do not fall at the same rate. Everyone realizes this, except, apparently, you. The air filled balloon is identical to the "empty container" you claim will fall at the same rate as one filled with concrete. In fact it *is* by any definition a container (Not technically empty, as it is filled with air, but so too is the "empty" container in your post actually filled with air)
So how can an "empty" (air filled) container fall at the same speed as the same container filled with concrete (as you claim) when it is obvious to all that an air filled balloon does not fall at the same rate as one filled with concrete?
That, by the way, is not merely a rhetorical question. I actually would like to see your answer. You have a very simple, obvious, very easily understood example that shows without any question that you are wrong, and somehow you rationalize that away. I am truly interested to hear your explanation for how or why you disregard this.
If the fact that it the balloon is filled with air is confusing you let's consider a different form of the same example. A feather. No doubt you have seen feathers falling, and noted that they fall rather slowly. Now lets suppose that a jeweler had very carefully crafted a replica of that same feather from gold. The form of the feather is identical on a microscopic level, it is the same dimensions, the same thickness, the shaft is the same dimensions, as are the barbs, and the barbules between them, everything is duplicated to the same dimensions, except that it is made of solid gold instead of ... well whatever it is feathers are made of.
With me so far? OK, I think that everyone will agree that the real feather will fall decidedly slower than the gold feather, right? Is that not a pretty conclusive demonstration that , all else being equal, the speed of a falling object through air is *not* independent of it's mass ? If you believe that it is not, explain *why* not. If you can't explain *why* not, than that's likely an indication that you're mistaken.
While you are mulling over your explanation of the previous obvious flaws in your claim, you might consider the following:
NASA webpage on Terminal Velocity
and
Wikipedia Article on Terminal velocity
Both of these pages contain an equation for calculating an object's terminal velocity (and both pages describe how that equation is derived) the equations are the same equation in slightly different formats. The NASA page puts the equation in a format that can be shown using only ASCI text and no special formatting (such as fractions, radical signs, or greek letters) but mathematically the equations are identical.
Now here's the point which demonstrates quite conclusively that you're wrong. Both equations contain a term for mass, which can *only* mean that terminal velocity *is* in fact affected by mass. If terminal velocity was (as you erroneously claim) independent of mass, mass would not be included as a variable in the equation for calculating it. But, it is included, so it must affect the velocity*. Now, I suspect that you're getting ready to say; “ But the NASA equation uses “weight” which is not the same as mass” True, in the context of physics, weight is not the same as mass. In physics, “weight” is the force of gravity on an object. And weight is equal to gravity times mass (g*m ) so where the NASA equation has W, it really means g*m so the first term in parentheses (2 *W) becomes (2*g*m) which you will note is the same as the upper term beneath the radical in the Wikipedia Equation: 2gm The asterisks in the NASA equation denote multiplication, while the multiplication is implied in the Wikipedia equation, so 2*g*m is just a different way of writing: 2gm. Bottom line, the equations are identical, and they both contain mass as a variable.
This leaves us with this:
Your (fallacious) opinion:
Originally Posted by
ANCPER
the only determinate when it comes to how fast an object will fall is the area of the object and therefore the drag(resistance) it will produce, mass does not come into it.
NASA's “opinion”:
Originally Posted by NASA
Terminal Velocity = sqrt ( (2 * g* mass ) / (Cd * r * A)
Just as a suggestion, if you find that your understanding of the physics of falling bodies differs significantly from NASA's, it's probably time to consider that you are mistaken.
All the preceding can be summarized neatly in two questions:
How do you resolve you claim that mass doesn't affect the velocity of a object falling through air, when a balloon filled with air and a balloon filled with concrete obviously and unquestionably fall at different speeds?
If Mass doesn't affect the speed of a falling body, why does NASA, one of the worlds foremost organizations for the study of aerodynamics and ballistics, say that it does?
Serious questions. Response expected. Lack of response will indicate a tacit admission of being mistaken.
* if anyone is having difficulty following this reasoning, all you have to do is make some simple calculations of terminal velocity using those equations and the same values for all terms, but different values for mass. The calculated terminal velocity will be different.
Try it with the following terms to keep it simple:
Drag Coefficient (Cd in NASA's equation) = 1
Area(A in NASA's equation) = 1 (square meter)
Gravity (g) = 9.8 (meters/sec/sec)
Rho ("r" in NASA's equation) = 1.3 (kg per cubic meter sea level standard temp at pressure )
Mass = 1 (kg)
Don't worry about the units, just plug the numbers into the equation and see what you come up with.
Now do it again, using all the same numbers except you use 10 kg for mass instead of 1kg. Notice that the calculated terminal velocity is different? the point here is that you can't include a quantity in an equation and not have it affect the result. That means the terminal velocity of an object is dependent on mass. QED.