Re: Superman

From: Darren Dunham (ddunham_at_redwood.taos.com)
Date: 10/12/04 

Date: Tue, 12 Oct 2004 18:17:38 GMT

David Lee <davidlee_malvern@dont.use.this.bit.hotmail.com> wrote:
> Darren Dunham wrote in-line...(so I'm staying at the top)

> You haven't the first clue about Archimedes principle! There is absolutely
> NO loss of mass implied in my argument - your problem is that you have
> entirely ignored the difference in density between brine and fresh
> water.

Yes, I've completely ignored it. I don't see how it makes any
difference.

> The average density of surface seawater is about 1027 kg per cubic metre.
> Consider an iceberg with a mass of 1 metric tonne (1000kg).

Check.

> This will displace 1 tonne of seawater - a volume of 0.974 cubic
> metres.

Check.

> If we remove this iceberg from the ocean then the ocean's effective
> volume will be reduced by just this amount. Now imagine we melt the
> iceberg - it will produce a volume of water of exactly 1 cubic metre.

Right.

> If this water is returned to the ocean

Will it "this water" mix with the ocean water or not?

> then there will be a net INCREASE in volume of 0.026
> cubic metres.

No. If it doesn't mix with the ocean water, being less dense it will
float, only displacing 1 ton of water (same as the iceberg did). It
can't displace more unless somthing pushes it underwater.

If it does mix with the ocean water then it becomes denser, so it takes
up less volume, still displacing the same amount (but no longer
"floating").

> Of course these numbers are a simplification since the density of seawater
> varies with salinity and temperature and brine is not an ideal solution so
> the volumes will not add linearly. However the principal is sound - melting
> an iceberg will cause a small increase in the sea level.

Nope.

> A similar, counter-intuitive, argument is the answer to the question: A boat
> is floating on a pond. In the boat is a large rock. If the rock is thrown
> into the water, what will happen to the level of the water in the pond?
> 'Common-sense' suggests that the water level will rise whereas in actual
> fact it will fall.

It will fall because the rock is now supported not by the water, but by
the ground underneath. If fresh water were denser, you could consider
the same argument for the iceberg. The (unmixed) fresh water would sink
to the bottom and be supported by the ground, not by displacement. But
that's not the argument here. 

-- 
Darren Dunham                                           ddunham@taos.com
Senior Technical Consultant         TAOS            http://www.taos.com/
Got some Dr Pepper?                           San Francisco, CA bay area
         < This line left intentionally blank to confuse you. >

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