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PHYSICS 23 LABORATORY
Sections L03, L05 and L09
O4s: Archimedes’ Principle
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OBJECTIVES: To determine the density of various solids and liquids
Introduction: Recall that the mass of a body, m, is related to its density  and volume V
by
m   SolidV
Eq(1)
Solid is the mass density so it has units of kg/m3.
(Continued next page)
T
B
Liquid
mg
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:
B   LiquidVg  mLiquid displaced g
Eq(2)
From Equations (1) and (2) and setting the y-components of the forces acting on the body
equal to zero:
B  mg  T  W  T   Liquid gV
Eq(3)
Solving for the volume of the body:
VARCHIMEDES 

W T
Liquid
g

m T / g

Liquid
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
 Solid  Vm
Eq(5)
Apparatus
Procedure:
1. Use the Vernier calipers and balance to make the measurements needed to
calculate the density of the regular mass you are using.
2. Use Archimedes’ Principle to make the measurements needed to calculate the
density of the regular object.
3. Use Archimedes’ Principle to make the measurements needed to calculate the
density of your irregular object.
Measurements: Record measurements here. Make sure they are labeled.
Analysis:
1. Calculate the density using your measurements of the dimensions and mass of
your regular object.
2. Calculate the density of your regular object using Archimedes’ Principle.
3. Calculate the percent difference between your calculated densities in 1 and 2,
above.
4. Calculate the density of your irregular object using Archimedes’ Principle.
5. Using the table of densities below, determine metal in your sample for your
regular and irregular masses. Calculate the percent difference between your
measured values and the tabulated value.
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