Density
Which weighs more, a ton of feathers or a ton of bricks? This old riddle plays with the distinction between mass and density. A ton is a ton, of course; but bricks have much greater density than feathers, so we are tempted to think of them as heavier.
Density, as you will see, is an important characteristic of substances. It is crucial, for example, in determining whether an object sinks or floats in a fluid. Density is the mass per unit volume of a substance or object.
In equation form, density is defined as
Example:
Calculating the Mass of a Reservoir From Its Volume
A reservoir has a surface area of and an average depth of . What mass of water is held behind the dam?
Solution:
Solving equation
for gives
The volume of the reservoir is its surface area times its average depth :
The density of water is .
Substituting and into the expression for mass gives