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



On 04/22/2009 11:00 AM, chuck britton wrote:
This has been one of my favorite 'discussion topics' when ....

It is one of my all-time favorite topics. It is one of my
oldest memories of my father. We were driving home from
somewhere, on a long, deserted road. I was 5 or 6.

The MOST important thing is to have a rousing discussion of what will
happen and WHY.

Yeah. He asked me to predict what the balloon would do if
he applied the brakes. Then he did the experiment, again
and again.

I was wildly impressed. We had a long discussion, including
the role of the air.

I'm not sure he mentioned the equivalence principle.

I remember one particular student who was bound for MIT and had had
ALL the 'advanced' physics and math courses.
He could argue convincingly for EITHER result and was really quite
unable to come up with the 'basic' force diagram that would convince
the other (less advanced) students.

He's done well at MIT but STILL may not be able convince anyone of
the right answer.

Well, I never attended MIT ... but in accordance with the phys-l
tradition of micro-analyzing seemingly simple problems, let me
point out that there *are* two "right answers".

a) Let's assume everybody knows the steady-state response. You apply
an acceleration, wait until things settle down, and look at the
steady-state result.

b) But what about the transient response? What happens if you very
*suddenly* apply the acceleration at t=0? The balloon won't even
find out about it for a while. Relative to the newly-accelerated
reference frame, the balloon simply must accelerate in the opposite
direction for a while.

On a quiz, or in any other non-interactive situation, when you
ask this question, if you want the steady-state answer be sure
you explicitly ask for the steady-state answer! It drives students
nuts when a question has two different physically-correct answers.

So, what's the next step? The right way to proceed is not to start
a holy war over which of these results is correct; the right way is
to figure out the _timescale_ "tau". If we apply the acceleration
suddenly and then wait a time long compared to tau, we should see
the steady-state result emerge in the limit. Or, better, ramp up
the acceleration gradually over a time long compared to tau.


So I'll let y'all have at it: What's your estimate of tau? How long
before we observe a steady acceleration in the canonical direction?
What physics determines tau?