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The point of this demonstration is that the beaker, the water in it, and the object each have a particular mass but we do not always observe these masses directly. These masses are initially seen as weights on the two balances (except for a slight effect due to the buoyancy of air).
When the object is suspended in the water, a portion of its weight is transferred from the upper balance to the lower balance. The precise amount of weight transferred is the weight of water displaced by the object.
When the object rests on the bottom of the beaker, its weight is completely supported by the lower balance.
Since we know that the weight
readings on the two balances are coupled, there is no need to use both
of them - either will be sufficient.
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The Specific
Gravity (Specific Gravity is the ratio of
the density of a substance to the density of water at the same temperature
and pressure) of an object may be determined
with the lower balance, observing the change in weight as the object is
suspended in the water (W1, the
weight of water displaced by the object),
then as the object is dropped to rest on the bottom of the beaker (W2,
the weight of the object). The ratio
of these two weights gives the Specific Gravity
of
the object:
Specific Gravity = W2/W1.
W1
= 201.00 - 200.00 = 1.00 g
W2
= 210.00 - 200.00 = 10.00 g
Sp. Gr. = 10.00/1.00 = 10.00
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The specific gravity of an object
may also be determined with the upper balance. A solid sample is
weighed first in air (W1'),
then suspended in water (W2').
The difference between these weights is the weight of water displaced,
and the specific gravity may be estimated as:
Sp. Gr. = W1'/(W1'
- W2')
W1'
= 10.00
W2'
= 9.00
W1'
- W2'
= 1.00
Sp. Gr. = 10.00/1.00 = 10.00
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The upper balance is generally used to determine the
densities of liquids. A glass plummet is weighed first suspended
in air (W1)
then suspended in water (W2).
The volume of the plummet is calculated from the difference in these weights
and the difference in densities between water (DW)
and air (DA):
V = (W1
- W2)/(DW
- DA).
The plummet is then weighed
in a fluid of unknown density (W3),
and the density of this fluid (DF)
is calculated:
DF = DA
+ (W1
- W3)/V
or
DF
= DW
+ (W2 - W3)/V.
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This last calculation corrects
for the buoyancy effect of air, which is neglected in the previous two
calculations. This correction is necessary in very precise calculations,
as in determining the density to within 0.01%.
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Archimedes
and the Golden Crown