# Objects accelerate and fall at the same rate except...

…for air resistance (I have often heard people say); sure that’s easy to understand - a feather falls much slower (in air) than a steel pellet of the same mass.

But I’ve never heard anyone mention buoyancy as another complicating factor and yet a factor it must be, mustn’t it? objects that are immersed in a fluid (in this case air) will experience a degree of upthrust related to the difference between their own weight and the weight of air that they displace…

That’s because boyancy is an implicit part of air resistance.

The General Question that I have somehow failed to frame properly is:

Is that right or am I talking out of my arse?

JS Princeton: I don’t think it’s quite the same; it isn’t air resistance that makes a helium balloon rise.

I’ll take a whack at thinking through what I think you’re asking. For an object to be positively bouyant in air it must displace a volume of air whose weight is greater than that of the bouyant object. For the object to be neutrally buoyant, its wieght must equal that of the volume of air it displaces.

Obviously, if you compare the the acceleration of two identically shaped objects, one of which is filled with normal temperature and pressure air while the other is filled with something like helium, enough so that it is positively or neutrally buoyant, the air-filled object’s going to fall to the ground long before the buoyant object, which may never.

So, are you thinking of comparing two objects’ descent where both are negatively buoyant, but one is almost neutrally buoyant, and the other is significantly negatively buoyant?

Here’s my WAG: For most objects, buyancy effects (in air) are really small.

As I recall, buyancy forces are proportional to the mass of the air displaced by the object.

According to this site – http://www.grc.nasa.gov/WWW/K-12/BGP/PAT/Fuel_and_Air2_act.htm
– the density of air is 1.22 kg/m^3 at sea level.

As I recall from High School chemistry, the density of water is approximately 1g/cm^3 = 1,000 kg/m^3.

So, assuming that a feather is roughly the density of water (feel free to correct me!!) , the buyancy forces would be pretty minimal compared to air resistance.

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Not quite. Air resistance increases with the square of the velocity. Buoyancy simply causes a decrease in the apparent weight of an object.

Buoyancy is also quite negligable since air typically is about 400 g/m[sup]3[/sup].

“except for Air resistance” is a somewhat inaccurate shorthand for “in a vacuum”.

If you want to pile on the caveats, it’s probably “objects in a gravitational field will accelerate at the same rate unless acted on by an outside force”.

And, of course, there’s no buoyancy in a vacuum.

Truth has a good expansion on my quick shot. Basically, when you have a light object, the buoyancy (spelling, for me!) does play a nontrivial role in how it behaves. It is considered as one of the terms of the air resitance. It is ignored for most objects because of the low density of air, but the obvious example where it cannot be ignored is hot-air balloons falling to the ground. They build up what’s normally deemed “air resistance” in physics texts due to its velocity cross-sectional area, but the real resistance due to air is also due to the buoyant force on the balloon (which has not much to do with the other term).

And indeed, normal air resistance goes like the cross-sectional area of the object, as JS mentioned, whereas buoyancy goes pretty obviously as the volume of the object instead (i.e. if you have two objects with identical masses but with one taking up twice as much volume as the other, the effect of buoyancy will be twice as big on one as on the other).

Yes, that’s exactly it; or simply that one body is less negatively buoyant than the other.

Well, you get air resistance no matter if you go UP or DOWN. A major contribution is due to the increased pressure you feel that is the result of an increased velocity. It doesn’t matter which direction the velocity is as long as the air is everywhere. If you want to take into consideration all the effects of air, you need to start dealing with fluid dynamics.

In general air resistance for falling objects is noted for objects that are so much more dense than air that buoyancy doesn’t matter. If it does matter, it’s simply another term to consider.

Quite; I imagine that if we’re talking about the descent of a lead cannonball and a steel one, air resistance is almost irrelevant and buoyancy is such a small factor as to be almost impossible to measure.

Or, to use real men’s units, 0.002377 slugs per cubic foot.

Yeah, I took aerodynamics classes in the US.