Sorry for being a bit tardy in getting back to this. Thanks to all for
risking your necks playing. :-)
The self-selected sample of the Class of 2001 appeared to be far brighter
than the self-selected sample of the Class of 1993. At least this time
there was no ENGINEER looking up constants from handbooks on alloys to
answer the penny-problem. :-)
Rather than describing what happen then, I'll just give the ONE post
which recapped what happened in 1993. Note that the "general solution"
covered the case (not 24 bottles) of the Phyco-plonk as a special case
of the general solution.
------------------ reproduced in full from the BHD ----------------------
Date: Fri, 12 Nov 1993 09:54:00 EST
Sender: Scuba diving discussion list <[log in to unmask]>
From: "Reef Fish (Large Nassau Grouper)" <RFLNG>
Subject: Re: pennies (reference)
Gentlemen, the PROBLEM in question was solved by Diane in a few minutes.
Done. Finished. Explained. 50 or so posts by others later without any
added substance ... excuse me for an imitation of Diane's "dive babe" call:
A A R R R R R R R G G G G G G G G G G H H H !!!!!
Let me recap, and hope to save others 50 future posts on the same problem
using different constants from handbooks on different alloys, fluid, etc.
What I attempted to do two days ago was to show that a MUCH MORE GENERAL
problem was completely solved too, using Diane's argument (without her
numbers), by minding only the relative magnitures of two numbers X and Y
that you don't need (for the problems in question) to know the exact values
nor to refer to handbooks for them. To no avail. Recap:
> Date: Tue, 9 Nov 1993 08:29:43 -0500
> From: [log in to unmask]
>
> A penny sits balanced on-edge on a floating piece of wood in a
> glass of water. A puff of wind sends it falling off the wood into
> the water. When everything settles, has the level of the water in
> the glass risen, fallen, or stayed the same?
Let me diagram the problem as follows: Note that the ONLY relevant info
is that the penny is on a FLOATING (with penny) piece of wood, and we can
safely assume that the penny SINKS in water, when dropped there.
: :: :
: :: <-- penny on-:edge
: .........::........ :
:......: wood floating :........: <-- water level
: :.................: :
: :
: water :
: : <-- glass container
:.................................:
It's a CUTE, but EASY problem, if you understand Archimede's Principle.
I received Diane's posted solution 16 minutes later, which took Diane
probably less than 30 secs. to solve: (Congrats. Diane. And she duly
received her NED award later :-)
> Date: Tue, 9 Nov 1993 08:46:07 -0600
> From: Diane Palme x2617 <[log in to unmask]>
: ... lucid narrative deleted ... :
> H2O volume (mass of penny) > > H20 volume (volume of penny)
>
> therefore, the water level goes *DOWN*]]] Cool]
> Am I right? Am I, am I, huh? Do I get a certificate?
Of course you're, Diane. And THAT should have been the end of THAT Problem.
SOLVED. Correct reason given. ...
Then, SEEMINGLY relevant, but in actuality irrelevant questions began to
surface ... first the density of copper:
>>Surely the density of copper is 2.8g/cm^3?
followed by the composition of penny, zinc/copper/alloy ? ... and Diane
(bless her heart) produced the SAME correct argument she did a few hours
(after about 10 irrelevant posts by others) earlier, by using NUMBERS,
from an engineering handbook. Prompted by her remark to Rob:
> Rob, we weren't flaming you or anything, it's just that we engineering
types
> are rather particular about the numbers. :) To prove it, let's actually
DO
> the numbers ...
and the dreaded thought (by me) that we may have another 50 more posts (by
others) dealing with constants of other metals, alloys, salt water, fresh
water, etc., using handbook numbers that are ENTIRELY UNNECESSARY, I merely
substituted a couple of Diane's numbers by X and Y, and in so doing,
simplified Diane's solution by noting that it solved a much more general
problem at the same time.
> Date: Tue, 9 Nov 1993 15:59:00 EST
> From: "Reef Fish (Large Nassau Grouper)" <RFLNG>
: ... details of high school math. deleted ... :
> volume of water displaced due to mass of penny: X*Z/Y (a)
> volume of water displaced due to volume of penny: Z (b)
> Clearly, (a) > (b) whenever X > Y. (c)
Now follow this carefully ... the handbook NUMBERS are absolutely
unnecessary.
They waste one's time looking them up; waste one's time doing the 5th-grade
arithmetic in (a); and they waste space. Once you understood the essence of
the problem, you can do the general solution WITHOUT ANY NUMBERS OR ALGEBRA:
: :: :
: :: <-- ANY solid:object
: .........::........ :
:......:ANY floating block........: <-- fluid level
: :.................: :
: :
: ANY fluid :
: : <-- any container
:.................................:
Examples of solid: coins/metals of any composition, size, or shape ...
Examples of fluid: salt/fresh water at fluid state; any beverage ...
Examples of block: wood, metal with air space that makes it float (as a
a boat); ANY block that floats on the fluid with the solid on top.
Make hollow block with lead or gold or uranium if you wish ...
Now watch carefully the general solution to the general problem:
If the solid object SINKS in the fluid (when off the floating block),
^^^^^
(that's all my X > Y means: density of solid > density of fluid)
(DENSITY OF COIN > DENSITY OF WATER)
THE FLUID LEVEL FALLS!
(WATER)
I think this is another reason why we should stick to DIVING discussions
sprinkled with HUMOR for diversion. Some readers ALWAYS seem to get
bogged down on this physics stuff, however trivial it may be.
Cech Claude G <[log in to unmask]> reflects:
> It occurs to me this morning that the penny problem illustrates the
> danger of relying too heavily on common cents. :-!
I'll drink to that, on a floating block I'm sitting, over a pool of fluid
(beer). To test if you FINALLY understood what's going on, you may try this
Exercise OFF THE NET (PLEzzzzzzzz): As you drink the fluid (beer) from the
beer-pool while sitting on the block which is floating on that same beer
pool, will the beer-level (in the pool) rise, fall, or stay the same? :-)
-- Bob.
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