VisionLearning: Adapted from Martha Marie Day, Ed.D., Anthony Carpi, Ph.D.
Key Concepts

Density
Density is a physical property of matter that is defined as the ratio of an object's
mass to its volume.

Archimedes is credited with being one of the first people to consider density as a
property of matter.

An object's ability to sink or float is determined by its density compared to the
density of the liquid.
Sometime around 250 BC, the Greek mathematician Archimedes was given the task
of figuring out is some of the gold in his King’s crown was replaced with silver.
Archimedes thought about the problem while relaxing in a bath. As he got into the
pool, he saw that water spilled over the sides of the pool. This was a big observation
for Archimedes. He realized that the amount of water that spilled was equal in volume
to the space that his body occupied. In other words, he figured out how to measure
volume. This fact gave him a way to figure out if the King’s crown was mixed silver
and gold or a pure gold crown. Because a given amount of silver takes up more space
than an equal amount of gold, Archimedes placed the King’s crown and a pure gold
crown of equal mass in two tubs of water. He found that more water spilled over the
sides of the tub when the King’s crown was dropped in. It turned out that the King’s
crown was NOT made of pure gold! Legend has it that Archimedes was so excited about
his discovery that he ran naked through the streets of Sicily shouting "Eureka! Eureka!"
(the Greek word for "I have found it!").
Archimedes used the concept of density to show that the King’s crown was not
made of gold. Density is a physical property of matter that shows a relationship of
mass to volume. The more mass an object contains in a given space, the denser it is.
Since different substances have different densities, density measurements are a
useful means for identifying substances. For example, have you ever heard the joke
“what weighs more, a ton of brick or a ton of feathers?”
VisionLearning: Adapted from Martha Marie Day, Ed.D., Anthony Carpi, Ph.D.
Figure 1: Bricks and feathers.
Of course, they both weigh the same, they have the same mass of 1,000
kilograms (one metric ton). However, a metric ton of feathers will have a volume of
almost 400 million cm3 (about the size of four tractor trailer trucks), while a metric ton
of bricks will occupy only one-half million cm3 (about the size of a big-screen TV). The
bricks are denser than the feathers because their mass is packed into a smaller
volume. This relationship between the mass and volume of a substance is what defines
the physical property of density:
Density = Mass/Volume
Density is an intensive property of matter that is defined as the ratio of an
object's mass to its volume. Mass is the amount of matter contained in an object and
is commonly measured in units of grams (g). Volume is the amount of space taken up
by a quantity of matter and is commonly expressed in cubic centimeters (cm3) or in
milliliters (ml) (1 cm3 = 1 ml). Therefore, common units used to express density are
grams per milliliters (g/ml) and grams per cubic centimeter (g/cm3).
Let's look at an example. A typical brick has a mass of 2,268 g and occupies a volume
of 1,230 cm3. The density of the brick is therefore:
2,268 g
÷
1,230 cm3
=
1.84 g/cm3
Density can sometimes be confused with weight. The reason is if you look at
two objects of equal-volume, the denser of the two objects will be heavier.
Remember, though, that it is the relationship between mass and volume that
determines density and not volume or mass alone. Look at the table below for
examples of the densities of common substances.
VisionLearning: Adapted from Martha Marie Day, Ed.D., Anthony Carpi, Ph.D.
Density of Some Common
Substances
Substance
Density
(g/cm3)
Air
0.0013
Feathers
0.0025
Wood(Oak)
0.6 - 0.9
Ice
0.92
Water
1.00
Bricks
1.84
Aluminum
2.70
Steel
7.80
Silver
10.50
Gold
19.30
Figure 2: Densities of common substances.
Buoyancy and Density
When Archimedes stepped into his bathing pool, not only did he realize that
water spilled over the edges, but he also observed something that we all notice when
we go swimming – he felt lighter. The ability of an object to "float" when it is placed in
a fluid is called buoyant force, and is related to density. If an object is less dense
VisionLearning: Adapted from Martha Marie Day, Ed.D., Anthony Carpi, Ph.D.
than the fluid in which it is placed, it will float. If it is more dense than the fluid, it will
sink.
Density explains why some objects float on water while others sink. For example,
wood floats on water because it is less dense; steel, by comparison, sinks because it is
denser than water. You might ask, how can large steel cruise ships stay afloat? Large
ships have a tremendous amount of space in them that is filled with air. Steel is
denser than water, but air is less dense. Metal ships can float because their total
density is less than that of the water that they float on. When the metal hull of a ship
is breached, like when the Titanic struck an iceberg, water rushes in and replaces the
air in the ship’s hull. As a result, the total density of the ship changes and causes the
ship to sink.
This concept of changing density is also used in another type of ship, a
submarine. A submarine has a volume that does not change, but it can change its
mass by taking in water into its tanks. When water is taken in to the tanks, the mass
of the submarine increases. The increase in mass causes the submarine to sink. When
water is released from the tanks the ships density decreases allowing it to rise to the
surface.
The concept of density also explains another common phenomenon. Have you
ever noticed what happens to a bottle of oil and vinegar salad dressing when it is
allowed to sit still after it has been shaken? The oil will rise to the top and the vinegar
will settle to the bottom of the bottle. This happens because oil is less dense than
vinegar. When materials of different densities are put in contact with one another, their
densities will determine how they order themselves. This phenomenon, where
materials layer themselves according to their density, is called superposition.
Another factor that can affect the density of a material is temperature. Many
materials expand when they are heated. Because a material that expands will take up a
larger volume, its density will decrease. This fact most commonly occurs with gases
and some liquids and explains how hot air balloons work. When the air inside of a
balloon is heated it expands and its density decreases. The balloon thus gains positive
buoyancy with respect to the colder air surrounding it and it floats into the sky.