ARCHIMEDES' PRINCIPLE
PRELAB
PURPOSE
To determine the specific gravity of several different solids and of a liquid by means of Archimedes' principle.
EQUIPMENTpan balance, 5 cylindrical samples, sample rock, string, vernier calipers, water, ethylene glycol mixture (automobile coolant) or glycerol, beaker, graduated cylinder.
RELEVANT EQUATIONS
Volume of Cylinder:
Density:
Specific Gravity:
DISCUSSION
Archimedes' principle states that an object immersed in a fluid is buoyed up by a force equal to the weight of the displaced fluid. The volume of the displaced fluid is equal to the volume of the immersed portion of the object. Therefore, the apparent loss in weight of an immersed object is equal to the weight of an equal volume of the fluid. If the fluid used is water, then Archimedes' principle provides a convenient method of determining the density of solids that are more dense than water as well as the density of other liquids. We can conveniently compare the density of an object made of any substance to that of water by taking the ratio robj/rwater, which is called the Specific Gravity of the substance. Specific gravity is the ratio of the density of a substance to the density of water. It may be obtained by comparing the weight of the substance to the weight of an equal volume of water.
If a solid object more dense than
water is weighed in air, the weight Wo = robj
g V, where V
is its volume and g is the acceleration of gravity. If the object
is then weighed while it is totally immersed in water, then its immersed
weight W1 =
Wo
— B, where B is the buoyant force. Archimedes’
Principle states that
B = weight of water displaced,and so
we have: B = rwater
g V. Therefore W1
= robj
g V — rwater
g V. The specific
gravity of the object SGobj
, is:
But, the denominator is: rwater g V = (Wo - W1):