Re: [Phys-l] balloon floating in air in car

[curtis osterhoudt <flutzpah@yahoo.com>]

Yeees... but not quite. A sound wave in an ideal gas will not have exerted a net force in either direction on the balloon, after it has passed. If the gas is non-ideal (thus allowing for relaxation processes), things also depend on the size of the balloon compared to the wavelength of the sound around it, and its relative compressibility (density is already assumed less than the surrounding gas' in this problem). In fact, one can trap particles at sound nodes or antinodes or _not_at_all_ depending on the combinations of these physical parameters. 

   So: we have the further complications that the car would have to have within it a non-ideal gas (air is just fine), allowing for relaxation processes within it. Additionally, these processes have to be fast enough (helped, I'm sure, by roughness in the car's interior, so that the "little whorls with lesser whorls" can develop), and the car's acceleration has to be applied (by the back windshield?) for a long enough time that the pressure waves can sweep the length of the car several times and build up to a net gradient from back to front. Assume further that the gas in the balloon is less dense, AND that its compressibility is not such that (density_balloon x compressibility_balloon) = (density_air x compressibility_air). If that were NOT the case, the specific impedance across the balloon/air interface would be matched, and pressure waves can't see a difference between the balloon and the air. 
  
   It makes for a fantastic back-of-the-envelope question, but linear acoustics just ain't going to cut it. To run the full gamut, perhaps to get good estimates of, say, the angle of the balloon's string relative to the vertical, requires a remarkable amount of calculational trickery. If a student can pull it off, I'd be pretty impressed.

   Once they figure that out, ask them: OK, you have a hot-air balloon floating in the air. A series of wind gusts come along (they're basically pressure gradients). Based on the balloon-floating-in-air-in-car question, which way does the hot air balloon move?


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Down with categorical imperative!
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________________________________
From: "Quist, Oren" <Oren.Quist@SDSTATE.EDU>
To: Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu>
Sent: Saturday, April 25, 2009 9:07:39 AM
Subject: Re: [Phys-l] balloon floating in air in car

A little disappointing that no one seems willing to pick up on this as there is some good physics involved.

The accelerating car would set up a pressure wave in the air.  The time to affect the balloon would be proporsional to the car's interior dimension divided by the speed of the pressure wave (speed of sound).

________________________________________
From: phys-l-bounces@carnot.physics.buffalo.edu [phys-l-bounces@carnot.physics.buffalo.edu] On Behalf Of John Denker [jsd@av8n.com]
Sent: Friday, April 24, 2009 1:55 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] balloon floating in air in car

On 04/22/2009 02:28 PM, Quist, Oren wrote:
> I would venture that the tau depends upon the speed of sound in the
> air in the car.

Indeed it does.  That is a good place to start.

As the next step, to convert the speed of sound (c) to a time (tau),
we need a distance.  A physically-relevant distance.  Options
include:
-- Multiply c by the mean-free-path of the air molecules?
-- Multiply c by the diameter of the balloon?
-- Multiply c by the size of the car interior?
-- Bring in some other physics?


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