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[Phys-L] Re: A "simple" physics problem?



Here's a simple physics problem that I'm having a bit of difficulty
answering. I would appreciate an answer together with your
reasoning:

An ice cube containing small pieces of lead shot is floating
in a cup of warm water. What will happen to the water level
as the ice cube melts?

Of course, the answer is the same as that for the more standard "a
chunk of metal in a boat is thrown overboard" problem--the water
level drops once the lead is no longer "floated" by the ice cube.
But this version may offer a more enlightening way of understanding
that answer.

For the most part, AS the ice cube melts, NOTHING happens to the
level of the water. The melted ice, which previously DISPLACED its
weight in water simply BECOMES its weight in water. But, at some
particular instant, enough ice has melted so that the lead shot
suddenly drops from the ice cube. The remaining ice, relieved of its
weighty burden, quickly pops upward as a result of the (now) excess
buoyant force. The water level drops as surrounding water rushes in
to fill the void.

The same effect happens in the boat example, but the action of the
anthropomorphic agent serves as a minor and unnecessary distraction.

John Mallinckrodt
Cal Poly Pomona
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