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Archimedes’ Principle and Applications
Objectives:
Upon successful completion of this exercise you will have .
..
1. .
.. utilized Archimedes’ principle to determine the density and specific gravity of a
variety of substances.
2. .
.. utilized Archimedes’ principle to determine the density and volume of an
irregularly shaped object and then through extrapolation methods determine the
amount of mass removed to create the irregular shaped object.
3. .
.. determined the mass density of an unknown liquid.
Theory:
The average mass density,
m
, of an object is defined as the mass, M, of the object
divided by its volume, V, or
m
= M/V
[1]
The average weight density,
w
, is defined as the weight , W (equals M*g), of an
object divided by its volume, or
W
= W/V = Mg/V =
m
g,
[2]
where g is the acceleration of gravity.
The specific gravity, s.g., of a material is
defined as the ratio of the density of the material to the density of water.
Thus,
s.g. = density of material/density of water
Note that specific gravity is a unitless quantity which depends only on the material.
The density of water is approximately 1.00x10
3
kg/m
3
in the SI system of units.
Archimedes’ principle states that an object partially or wholly immersed in a fluid
will be buoyed up by a force equal to the weight of the fluid displaced by the object.
From equation [2] the weight of the object is
W = (
m
g)V
[3]
Thus, according to Archimedes’ principle, the buoyant force, F
B
, on an object
submerged in a liquid
F
B
= weight of liquid displaced = (
m
)
liq
gV,
[4]
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 Spring '08
 Staff
 Physics, Gravity

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