Experiment 09

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:
 



 

                                                                         (1)
We can also measure the specific gravity of another fluid with density rfluid by then weighing the same object in that fluid. If the object’s weight immersed in the fluid is W2 , then W2 = Worfluid g V. The specific gravity of the fluid is:


But, the denominator is: rwater g V = (Wo - W1):

                                                                                 (2)