PHYSICS 22 LABORATORY
E4: Archimedes’ Principle
Spring 07
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OBJECTIVES: To determine the density of various solids and liquids
Reading:
Introduction: Recall that the mass of a body, m, is related to its density r and volume V by
Eq(1)
rSolid is the mass density so it has units of kg/m3.
(Continued next page)
When underneath the liquid, the object displaces (or replaces) a volume V of water. What force must the remaining liquid have exerted on this volume of water before the object was immersed? This same force, the buoyant force, must be exerted on this volume when it is occupied by the object. Archimedes told us that this buoyant force B is equal to the weight of the water displaced by the object:
Eq(2)
From Equations (1) and (2) and setting the y-components of the forces acting on the body equal to zero:
Eq(3)
Solving for the volume of the body:
Eq(4)
Remember that if you try to measure the force T using a balance, the balance reads T/g, because it gives a mass not a force.
Having determined the volume of the object, we can find the mass density from
Eq(5)
Apparatus:
Procedure:
1. Use the Vernier calipers and balance to determine the density of the regular mass you are using.
2. Use Archimedes’ Principle to determine the density of this object.
3. Use Archimedes’ Principle to determine the density of your irregular object.
Measurements: Record measurements here. Make sure they are labeled.
Analysis:
1. Calculate the percent error between your measurements in 1 and 2, above.
2. Using the table of densities below, determine metal in your sample for your regular and irregular masses. Calculate the percent difference between your measured value and the tabulated value.
3. Use the precision of your measuring devices (calipers, balance) to estimate the errors in the densities you calculated parts 1-3 of the procedures above. Remember, for addition and subtraction, errors add, for multiplication and division relative errors add.
4. Do the tabulated values lie within the range of errors you estimated in 3 above?
Conclusions:
Material / Density (g/cm3)Aluminum / 2.699
Brass, yellow (7% Cu, 30% Zn) / 8.56
Copper / 8.89
Gold / 19.33
Iron / 7.85
Steel / 7.79
Lead / 11.00
Magnesium / 1.741
Nickel / 8.75
Osmium / 22.5
Potassium / 0.87
From CRC Handbook of Chemistry and Physics