OTOOP...Re: SC - cups

[david friedman]

At 9:00 AM -0400 9/18/98, Phil & Susan Troy wrote:

>Wait! I've got it! Some government agencies maintain laboratories deep
>underground to protect them from nuclear attack. Maybe the cup of water was
>weighed in one so deep that its greater proximity to the earth's core caused
>it to weigh more, just as it might weigh less, say, at the top of Mount
>Everest?

I'm afraid you have it backwards. A sphere of uniform density acts, for
purposes of gravity, like a point mass at its center--but only if you are
outside the sphere. A spherical shell, seen from inside, produces no
gravitational effect--attractions from opposite sides just cancel. So if
you are beneath the surface of the earth, the part above you doesn't count,
only the part below. The farther down you go, the closer you are to the
center--but the lower the total mass contained by the relevant sphere
(under you). The volume of a sphere goes as the cube of the radius. So as
you go deeper, gravitational attraction increases by the square of the
radius because you are closer to the center, but decreases by the cube of
the radius because there is less mass under you, so on net it
decreases--reaching zero at the center of the earth (as is obvious from
symmetry considerations).

Maybe the people who use "a pint's a pound the world around" don't care
about errors as small as six percent. Maybe they're right.

David/Cariadoc
http://www.best.com/~ddfr/


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