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density and specific gravity

updated fri 13 aug 99


Terry Hagiwara on thu 12 aug 99

I just can't help making a few comments about the density and units.
Dimensionality and units are the first things you teach in Phys 101.
Actually, they should be taught earlier in high school.

Specfic gravity is practically the same as density, number-wise.

Density is defined as the mass in unit volume, and has the DIMENSION of
[Mass]/[Volume]=[Mass]/[Length]^3. Its UNIT is g/cm^3 if the mass is
measured in gramm and the length is measured in cm. The unit can be lb/ft^3
if the mass is measured in lb and the length in foot.

The specific gravity as I understand is defined as [Weight]/[Volume]. The
source of confusion is that the weight, that is the gravitational force on
the mass, is measured using also the same UNIT name as gramm and lb and so
on. One pound of weight is actually the strength of gravitational force on
one pound of mass on Earth. The earth's gravitation varies depending where
you are. It's weaker (slightly) up in high mountains or on the Equator, for
instance. One gramm of mass is one gramm anywhere anytime. One gramm of
weight gets lighter at the top of Mt.Everest and heavier at the North Pole.
But the difference is minute, numberwise.

The first thing we (have to) teach in physics 101 is that one compares (or
equates) two quantities of the same DIMENSION, and use the same UNIT when to
compare. For instance we compare the volume of a bucket with that of
another. To see which is larger, we compare the both in the same UNIT,
whether it is cubic ft or cubic meter. If not in the same UNIT, one has to
be converted to the other. One cannot compare (or equate) two quantities of
different DIMENSION. We don't compare nor equate the volume of a bucket to
the weight of the bucket.

terry hagiwara