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Re: Test question /Reality Strikes!



At 10:04 PM 6/4/2003 -0400, you wrote:
Perhaps it is mixing apples and oranges to take a difference between a
volume and a mass, as Brian suggests, but we are indeed talking about
water displacement aren't we? The reality is that when I went to school
we still defined 1 cm^3 of water as 1 gram and also as 1 ml. That is,
they were equivalent by definition. Having one foot in chemistry as
well as one foot in physics, I can tell you that chemists still
interchange the three at will even though today water gets as dense as 1
g/ml only at 3.98 Celsius, and water never gets as dense as 1 g/cm^3.

Yes... I could have said "...the difference between the cup's mass and
THE MASS OF THE WATER DISPLACED BY the cup's material volume." I guess
I didn't think I was outside the box on that one. If we're getting that
picky about our assumptions, then I guess we also need to bring
temperature into the problem.


Michael D. Edmiston, Ph.D.


I'm afraid that the revised text that Michael offers above suffers
a similar defect, in my view. When we are talking about water
levels in a fixed container, the topic of interest is the volume of
the liquid, augmented by the volume of any items sunk in it ,
and by the water volume displaced by items floating on it,
as they affect the overall surface level.
Mass not being of the essence, but rather volume, may I
counter-offer this rendition?
" ...the volume of the sunken cup, reduced by the volume of water
formerly displaced by the cup's weight when it was floating empty."

You will see that this formulation also eliminates the word "difference"
which offers no clue as to which volume is acting in a given direction
(i.e. a positive volume raising the water level) and which volume is acting
in the reverse direction.

When applied to Herb's sunken plastic cup which is more dense than water,
we find a volume of heavy plastic is reduced by a bigger
(water displacement) volume. The end result being a negative volume to add
to the positive displacement volumes of the two floating blocks, when a
dense cup sinks.

Sincerely

Brian (Persnickety?) Whatcott