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PURPOSE

To determine the specific gravity of several different solids and of a liquid by means of Archimedes' principle.

EQUIPMENT  pan balance, cylindrical samples, sample rock, vernier calipers, water, ethylene glycol mixture (automobile coolant), beaker, graduated cylinder.

RELEVANT EQUATIONS

DISCUSSION

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.

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 just equal to the volume of the immersed portion of the object. Therefore, the apparent loss in weight of an immersed object is just 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 more dense than water and 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 ρ_obj /ρ_water, which is called the Specific Gravity of the substance.

If a solid object more dense than water is weighed in air, the weight W_o = ρ_obj g V, where V is its volume and g is the acceleration due to gravity. If the object is then weighed while it is totally immersed in water, then its immersed weight W₁ = W_o - B, where B is the buoyant force. Archimedes‘ Principle states that B = the weight of water displaced, and so we have: B = ρ_water g V. Therefore W₁ = ρ_obj g V - ρ_water g V. The specific gravity of the object SG_obj is:

We can also measure the specific gravity of another fluid with density ρ_fluid by then weighing the same object in that fluid. If the object's weight immersed in the fluid is W₂, then W₂ = W_o - ρ_fluid g V. The specific gravity of the fluid is:

But, the denominator is   ρ_water g V = (W_o - W₁), so

(2)