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Re: Swartz letter in AJP (work-energy theorem)



Carl says that he is off traveling for a few days. But I know where he has
gone: He has taken a senior group of Academy midshipmen to safeguard the
secret new warship USS Widget from the endangering Hurricane Frances. (I
have no idea how the term midshipman came about -- middle of the
ship?) They are going to the North Atlantic. I am not supposed to tell
anyone about the USS Widget but....

It is designed to travel on _top_ of the Arctic ice rather than as a
submarine. The hull is made of flubonium (Now please don't repeat that to
anyone) and is very smooth. The ship is propelled by jet engines. When
Carl reaches the Arctic ice the ship will just ramp itself up and glide
along atop it until she reaches port. The ship is headed for Thule,
Greenland.

This information is blue top secret -- that is two steps above top
secret (This is the government for you; how could anything be two steps
above top) -- so don't pass any of this along to foreign country
people. It is sternly classified because the ship is still
experimental. The problem that is faced is to reduce the frictional force
as it is propelled along the ice.

The hull is smooth but there are still some crags and fissures all over the
hull surface. It is also true that the ice is not perfectly smooth; there
are bumps and farcles throughout. Also flubonium, although it is fairly
adiabatic, is not perfectly so.

Thus, as the USS Widget is jet propelled across the Arctic ice, WORK is
done on the ship -- and by the ship. Ice farcles crash into the hull crags
and do WORK. And hull crags do WORK on the ice farcles. This while
flubonium atoms are jostling about and some of them reach the hull surface
and even though they are chemically bound to the hull and do not dissolve,
some do impact water molecules and do WORK on them. At the same time those
water molecules collide with hull atoms and do WORK on them. All this time
the jet engines propel the ship and do WORK on the ship. Then of course
there is the air but this is getting silly so this consideration and other
weirdness will be omitted from the following calculations.

As the ship approaches Thule, Carl and the Middies will calculate the
various components of work done. -- They set aside for the nonce the
calculations for the work done BY the ship.

They calculate the net WORK done ON the ship and the point at which they
should extinguish the jets so that they can safely just glide up to the
Thule Navy pier and stop. But note that the work done by the ice farcles
on the hull crags is a bit complicated. Sometimes the impinging force
attacks a flubonium atom directly and jostles it individually and thus does
WORK on the atom. Sometimes a farcle will lift the hull a bit and do WORK
effectively on the entire ship and sometimes the farcle can't make up its
mind and seems to does WORK both ways. But ever since the efforts of my
ancestor John Paul Jones, the Navy is used to complications and can
calculate the result with the secret electronics carried by the USS Widget.

Note that NOTHING moves across the hull surface. NOTHING is
transferred. NOTHING flows. WORK is done and the ship stops.

Yes also WORK is done on the ice and ocean and Earth. The rotation of the
Earth is altered. But then the rotation of the Earth was altered when the
ship left Annapolis and stopping at Thule just makes up for this.

These aberrations are left as a trivial exercise for the Middies.

However, Tom Young is visiting Thule and asks why they didn't use
Tom's invention of energy to make the calculations. There is both the
bulk forward KE of the ship and the internal energy to deal with.

The Middies say that of course they used the concept of energy. But only
the macro horizontal KE was needed. The ice was colder than the ship so
the flubonium atoms did net work ON the ice molecules. But the net force
associated with this work was not horizontal. The ice farcles did work on
the flubonium atoms, but again the net force associated with this work was
not horizontal. So they need only consider the macro forward KE of the
ship and the WORK done by the ice farcles to hinder this motion. They
don't now yet whether the ship will get hotter or colder on the trip, but
they say it doesn't matter. Unless of course the ship overheats and melts.

But the Middies insist that any computed energy is an invention and not
real, that it is not a substance, that it is not fluid-like, that it does
not move between anything, that it is not transferred, that it does not
flow anywhere.

And I am sure that Carl and the Middies will admirably safeguard the USS
Widget and bring her back to Annapolis after the storm. Besides the crew
and the highly advanced secret apparatus aboard the ship have weakened the
storm already.

Well, sort of anyway.

Jim


Jim Green
mailto:JMGreen@sisna.com
http://users.sisna.com/jmgreen