Density and Archimedes' Principle Page Page has been visited times since March 21,2000

__Introduction__

Tradition tells us that the king was suspicious about the purity of the gold in his crown and
asked
Archimedes to find a way to determine if it was the real thing. Solving the problem seemed to be
impossible because in those days (3rd century B.C.) nothing was known about chemical analysis.
One
day Archimedes was thinking about the problem while taking a bath. As he lay floating in the
bathtub
he thought about his "weightless" body. Suddenly he realized that all bodies "lose" a little weight
when placed in water, and the bigger their volume, the more weight they lose. He realized that
the
*density* of a metal can be found from its *weight* and its *weight loss
in water*. The weight of the King's
crown and its *apparent loss of weight in water* would tell him if it were made out of
pure gold.
Archimedes shouted "Eureka!" (I have found it!) and rushed out into the street naked to announce
that he had solved the problem. Today the effect he observed is called Archimedes' Principle.

__Objective__

To determine the density of an object by two different methods and to compare the results.

__Procedure__

__Method 1: Determination of density by direct measurement of
volume.__

The object you have is a cube of metal. The volume of a cube can be found from the formula
V=a^{3},
where a is the length of one edge in centimeters. The mass of the cube can be found by weighing
it.
Then the density can be determined by dividing the mass by the volume.

a. Weigh your cube on the electronic scale. Record your mass below.

b. Measure the edge of the cube in centimeters with your plastic ruler. Record the length
below.

b. Calculate the volume. Record the volume below.

d. Calculate the density. Record the density below.

__DATA__

Mass of object: m_{1} = ______________ g

Length of edge of object = _____________ centimeters

Volume of object: V = edge x edge x edge = ______________ cubic centimeters (cc)

D = mass/volume = ____________ grams per cubic centimeter (cc)

(mass divided by volume)

**Method 2: Archimedes' Principle**

Archimedes' Principle says that the apparent weight of an object immersed in a liquid
decreases by
an amount equal to the weight of the volume of the liquid that it displaces. Since 1 mL of water
has
a mass almost exactly equal to 1g, if the object is immersed in water, the difference between the
two
masses (in grams) will equal (almost exactly) the volume (in mL) of the object weighed. Knowing
the mass and the volume of an object allows us to calculate the density.

a. Record m_{1} below from the value on the previous page.

b. Set up balance arm hooked to wooden block and paper clip on other end.

c. Hang your cube on the paper clip.

d. Read the mass on the scale. This is m_{2}. Don't worry if it is different from
m_{1}.

e. Fill the beaker with water up to within one inch of the top rim.

f. Immerse your cube in the water, being careful not to let it touch the walls or bottom.

g. Read the mass on the scale. This is m_{3}. Record m_{3} below.

h. Subtract m_{2} from m_{3} and record the difference.

i. Calculate the density: divide m_{1} by the difference m_{2} -
m_{3}.

**DATA**

Mass of your object (m_{1} from the previous page): m_{1} =
______________ g

Electronic scale reading with object hanging on balance arm in the air: m_{2} =
__________ g

Electronic scale reading with object on balance arm immersed in water: m_{3} =
__________ g

Difference in mass of your object: m_{2} - m_{3} = _____________ g

Density of your object:

m_{1}

D = ---------- ________________ grams per cc

m_{2} - m_{3}

Questions:

1. How do the two densities compare?

2. Why is Archimedes' Principle so important and well remembered if there is another
perfectly good
way (method 1) of measuring density?

__Materials Required__

5 Electronic lab scales (capacity 1200 g, ±0.1g)

5 250 mL beakers

30 metal objects -- all cubes, including lead!!

30 plastic metric rulers

5 wooden meter sticks

5 metal fulcrums

10 metal hangers

5 laboratory electronic calculators, placed in on benches as follows from left to right: 1,1,2,2

Box of regular size paper clips

5 special wooden blocks with hooks to be placed on electronic balances as counter weights.