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Re: [Phys-l] Space Balloon

Since you, a heavy sinking object, move backward in the bus, the balloon, a light rising in the air object will move forward. In this case if the balloon were loose, it would travel forward for the reason you move backward, and would rise because of the static differential vertical force on it.

cheers
Joseph J. Bellina, Jr. Ph.D.
Professor of Physics
Saint Mary's College
Notre Dame, IN 46556

On Feb 20, 2007, at 6:17 PM, paul giusti wrote:

I seem to have missed a few threads, but reading through this email, i seem
to feel the urge to think out loud in the hope that my confusion can be
clarified!

Firstly, in relation to this "equivalence principal", i cannot see how it
could be stated that if the spacecraft/car accelerates toward the "front",
then the balloon would also move to the "front".
The reason for my confusion on this one is that if the vehicle is moving
forward, the balloon should not travel in the same direction- it should
travel in the opposite direction- towards the "back".

If you stood in a bus and the bus accelerated forward, you are going to move
in the opposite direction. No?

Secondly, if it is a helium balloon, would it not travel upwards?




From: John Denker <jsd@av8n.com>
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Subject: Re: [Phys-l] Space Balloon
Date: Tue, 20 Feb 2007 17:54:58 -0500
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On 02/19/2007 10:43 PM, thecraftyphantom@australia.edu wrote:

On Earth a helium filled balloon rises because of bouyancy. How would
the
same helium filled ballon move in a spacecraft

That's tricky.

An even simpler-to-state question that is just as tricky
to answer concerns the behavior of a helium balloon in
a car, when the car is subject to various accelerations
(notably sudden speeding up or slowing down).

Students wrestle with this one. They don't always predict
the right answer. They can /test/ their predictions in a
car rather more cheaply than in a spacecraft.

I believe the "car" version captures most of the
interesting physics, because the string on the balloon
nulls out the vertical forces and accelerations,
leaving the other two directions free, to first order.
So I guess 2/3rds of the physics is the same :-).

=================================

This is really quite a tricky question, and there is more than
one right answer ... or more than one part to the right answer.

Sometimes I think that there should be a large sign on the wall
of the HS physics classroom saying "in this course we do not
use accelerated reference frames". But there are some problems
that practically beg to be analyzed in an accelerated frame, and
this is one of them. (Merry-go-round / centrifuge problems are
another.) If the students have heard even the cartooniest description
of general relativity, they know that gravity is locally equivalent
to an accelerated reference frame, and it's hard to criticize
them for taking such an approach. I reeeeally don't like situations
where a student who uses a little bit of initiative or a little bit
of sophistication gets marked wrong.

The analysis using the equivalence principle is a one-liner: If
the vehicle (spacecraft *or* car) is accelerating toward the "front",
the balloon will float to the "front" just like it would in any other
accelerational field, including the terrestrial gravitational field.

The equivalence principle is such a grand idea -- and this is such a
clear demonstration thereof -- that wild horses couldn't drag me
away from this approach.

My father set up the demonstration for my brother and me when we were
about 8 years old, so by the time I got to high school I had no
doubt about the macroscopically-correct answer.

===================================
.........HOWEVER........!!!!!!!!

In high school, I felt in my bones that the answer given above was
not the whole story.

The argument I made to myself went like this: Sure, the balloon had
buoyancy ... but it still had mass, and by the laws of inertia it
should /initially/ move to the "back" in the accelerated reference
frame, just like everything else.

Back then I wasn't able to quantify that idea. Nowadays I could
make an argument about timescales, d(acceleration)/d(t), the
speed of sound, and the size of the balloon ... but not back then.
Still I knew in my bones that it had to go to the back, at least
a little bit, initially.

I kept my mouth shut about this, because I knew that (at that school
at least) there was always One Right Answer, and looking at things
from a different direction was not appreciated.

I was in college before I learned that d(acceleration)/d(t) had a
name: It's called /jerk/.

I'm not suggesting that you need to discuss non-steady accelerations
in high school ... but I am suggesting that if the student claims
that a /sudden/ acceleration causes everything to move to the back,
he's not wrong. Also, if you want to get picky about it, a
/large enough/ acceleration will cause everything to move to the
back.

Bottom line: It's a tricky bit of physics. The equivalence- principle
argument is simple, profound, elegant, and practical ... but it is not
the whole story.
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