Date: Tue, 24 Jun 2003 21:46:25 -0400 (EDT)
From: "Keith F. Lynch" <kfl at KeithLynch.net>
To: WSFA members <WSFAlist at KeithLynch.net>
Subject: [WSFA] Re: bees on the wing
Reply-To: WSFA members <WSFAlist at keithlynch.net>

Ron Kean wrote:

> Introducing a balloon filled with helium would displace air from
> inside the cargo compartment if the cargo compartment were not
> airtight, ...

I've never heard of a truck whose cargo compartment was airtight.
But ok...

> Assume the cargo compartment is rigid and airtight, and that it
> already contains a tank of compressed helium, an empty rubber
> balloon, a small weight, string to tie the weight to the balloon,
> and a lab assistant.  Now, all the truck's contents are sitting on
> the floor of the cargo compartment and the truck and its contents
> together weigh a certain amount, on the truck scale.

> The lab assistant fills the balloon with helium and ties off
> the balloon's neck, but does not yet attach the small weight to
> the balloon.  The balloon floats up to the ceiling of the cargo
> compartment, pressing upwards on the ceiling.  From that, it would
> seem the truck would now weigh less on the scale, but the truck and
> cargo have exactly the same mass as before, so from that it would
> seem the truck should weigh the same as before.

The truck weighs the same as before.  The air in the truck is slightly
denser than it was before some of the space it had been taking up was
occupied by the helium balloon instead.  The denser air presses down
on the floor proportionately more than before.  It also presses up on
the ceiling proportionately more than before, but since the ratio is
constant, the difference is positive.  And is, of course, equal to the
weight of the air in the (airtight) truck, which is constant (ignoring
variations in gravity, e.g. from the moon being overhead vs. on the
horizon, and also ignoring variations in buoyancy due to differences
in the external air pressure, temperature, and humidity).

> Next, the lab assistant ties the weight to the balloon, and the
> balloon buoyancy just balances the weight, leaving the balloon and
> weight floating in the middle of the compartment.

The truck weighs the same as before.  The balloon is no longer pushing
up on the ceiling, but the weight is no longer pushing down on the
floor.  And you postulate that they're equal.

> If, in the two cases outlined above involving a helium balloon, the
> truck and cargo still weigh the same as before, why would that be?

How could they not?  Mass in a closed system is conserved.

(Yes it is.  If you set off an H-bomb in this rigid airtight truck,
and were careful to let none of the energy escape, it would still
weigh exactly the same.)
--
Keith F. Lynch - kfl at keithlynch.net - http://keithlynch.net/
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