LECTURE                                             DENSITY

In this lecture you will learn:

Archimedes of Syracuse
Born: 287 BC in Syracuse, Sicily
Died: 212 BC in Syracuse, Sicily
The problem.  King Hieron II gave a goldsmith a weight of gold  to make a crown.  The crown weighed the same as the gold, but he wanted to know if it was pure gold, or a gold and silver combination.

They weigh the same, but the crown is irregular and cannot be measured to see if it is the same size. 

<--are these equal?-->
"The most widely known anecdote about Archimedes tells of how he invented a method for determining the volume of an object with an irregular shape. According to Vitruvius, a new crown in the shape of a laurel wreath had been made for King Hiero II, and Archimedes was asked to determine whether it was of solid gold, or whether silver had been added by a dishonest goldsmith.[13] Archimedes had to solve the problem without damaging the crown, so he could not melt it down into a regularly shaped body in order to calculate its density. While taking a bath, he noticed that the level of the water in the tub rose as he got in, and realized that this effect could be used to determine the volume of the crown. For practical purposes water is incompressible,[14] so the submerged crown would displace an amount of water equal to its own volume. By dividing the weight of the crown by the volume of water displaced, the density of the crown could be obtained. This density would be lower than that of gold if cheaper and less dense metals had been added. Archimedes then took to the streets naked, so excited by his discovery that he had forgotten to dress, crying "Eureka!" (Greek: "??????!," meaning "I have found it!")[15]"

"For Isaac Newton, this matter consisted of “solid, massy, hard, impenetrable, movable,” ultimate particles (“atoms”), which were discrete, localized, indivisible bodies."[1]


Mass is always "positive" attraction.  "The mass of an object is a fundamental property of the object.  Definitions of mass often seem circular because it is such a fundamental quantity that it is hard to define in terms of something else."  Consider that matter has mass and that is what attracts other mass and it comes together to create stars and planets, etc.  Two balls suspended in space (they have no weight at all) will gradually be attracted to each other. 
The weight of an object is the force of gravity on the object and may be defined as the mass times the acceleration of gravity, 
w = mg

Take a look at the two boxes below. Each box has the same volume. 
If each ball has the same mass, which box would weigh more? Why?

density is a function of how closely molecules are packed
to calculate the density  the mass (in grams) is divided by the volume (in cubic centimeters)

cite: http://www.nyu.edu/pages/mathmol/textbook/density.html

GOLD and SILVER have different densities so the same weight of material has different volumes and different volumes displace different amounts of water.

the HIGHER the density, the SMALLER the volume of water is displaced. HIGH/SMALL
the LOWER the density, the GREATER the volume of water is displaced. LOW/GREAT

density of gold    19.32g/cm3 (grams per cubic centimeter)
density of silver   10.5 g/cm3

remember that the WEIGHT of the crown = the WEIGHT of the gold given to the goldsmith
193.2 gms of gold will displace   10.0 cm3 of water (193.2g/cm3 divided by 19.3g)

HOWEVER, IF the crown displaces MORE than 10 cm3 of water... means it is NOT pure gold
193.2 gms of silver will displace 18.4 cm3 of water (193.2g divided by 10.5g)

water is 1 gram = 1 ml = 1 cubic centimeter is a STANDARD

– least dense, hydrogen gas, with a density of 0.000089 grams per cubic centimeter 
the element osmium is 22 grams per cubic centimeter, is only slightly more dense than gold or platinum.

–  A cubic foot of gold is 1200 pounds !!!!
= three steel oil drums filled with water. 

Now you know why robbers stealing gold SHOULD look like they are getting a hernia trying to move it!

density of gold    19.32g/cm3
density of lead     11.3 gm/cm3
density of silver   10.5 g/cm3
density of water    1gm/cm3
density of wood    0.5 gm/cm3.