 Dealing with Density MathBitsNotebook.com Terms of Use   Contact Person: Donna Roberts The term "density" basically refers to the degree to which something is filled or occupied. The term can actually be described in a variety of ways, with reference to specific areas of study. This page is going to concentrate on the two interpretations shown below. 1. In physics, density is the mass per unit volume. 2. Density is the quantity of something per unit measure (unit length, area, or volume).

 Definition 1: Volumetric Density
Density is a measure of how much mass
is located within a specific volume of space. The formula is easy to remember, if you remember the labeling for density. The "cubic" units (volume) are on the bottom and a form of mass (weight) is on the top. Density is not necessarily associated with "size".
Small objects with a large mass can have a high density (ball bearings, gold bars).
Large objects with small mass can have a low density (sheets of balsa wood, hot air balloons).

 I M P O R T A N T     C O N C E P T !!!!

The density of an object determines whether it will float or sink in another substance.
This concept is a common place phenomena and a popular scenario for questions.

• An object will float if it is less dense than the liquid it is placed in (a boat floating in water).
• An object will sink if it is more dense than the liquid it is placed in (a rock sinks in water).
• If two liquids do not mix, the less dense liquid will float on top of the denser liquid (oil floats on water).

Water has a density of 1.0 g/cm3.
(one gram per cubic centimeter)
Every one gram of water takes up one cubic centimeter of space.

Objects that have a density greater than 1.0 g/cm3 will sink in water.
Objects that have a density less than 1.0 g/cm3 will float in water.  Are "mass" and "weight" the same thing? Not really! An object has mass. Its mass never changes, but its weight may change. If you take the object to the moon, its mass will remain the same, but it will weigh less. Weight is a force associated with the pull of gravity.

Since we are working on Earth, where the gravitational pull is pretty stable, we tend to think of mass and weight as being the same.  In everyday use, since all objects on Earth (at a gravitational force of 1G) have the same mass and weight, "weight" is often used to describe both concepts. Prior to the 20th century, even technical journals failed to distinguish between mass and weight, erring on the side of weight as the general term.

 Technically, grams, kilograms, pounds, ounce, etc are units of measure of mass. The unit of measure for weight is the Newton, the unit of force. But, since you probably do not state your body weight in Newtons, you can see how we are still using weight and mass as the same concept (at least on Earth). The pounds you see on the scales are technically an estimate of your mass, and not a measure of weight. Confused? No need to worry. Since our problems will be dealing with objects on the Earth's surface, we will still be using words like "grams" or "pounds" to measure both mass and weight. You should, however, keep in mind that mass and weight are technically different concepts which may come into play in certain situations.  Definition 2: Area Density
Density is the quantity of something
per unit measure (unit length, area, or volume).

Population Density: The term "population density" fits this second definition of density. Population density is population (of animals, fish, people, plants, insects, etc) divided by total land area (or water volume). Notice how, in this "density" situation, you may be working with square units instead of cubic units.

For people, population density is the number of people per unit of area (square miles or square kilometers).

For example, the world's population is approximately 7 billion people with the Earth's total area (land and water) being 197 million square miles. The worldwide human population density is approximately 35 people per square mile. If only "land" is considered (58 million square miles), the population density increases to 120 people per square mile.

To solve these problems, look to the final label: "people per square mile" which can be written "people/square mile" and is obtained by dividing the number of people by the number of square miles.

Quantity Density: Density questions need not deal only with living organisms.

For example, the size air conditioner that is purchased for a room depends upon the volume of air space being cooled, or BTUs per cubic foot of air space.

Again, to solve these problems, look to the final label: "BTUs per cubic foot of air space" which can be written "BTUs/cubic foot of air space" and is obtained by dividing the number of BTUs by the cubic foot of air space. 