The Relationship Between Mass, Volume & Density

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Mass, volume and density are three of an object’s most basic properties. Mass is how heavy something is, volume tells you how big it is, and density is mass divided by volume. Although mass and volume are properties you deal with every day, the idea of density is a little less obvious and takes careful thought. However, once you get the hang of it, density is very useful.

TL;DR (Too Long; Didn't Read)

Volume is the size of an object, and mass is its weight. To get density, divide mass by volume. For example, a lead brick, 5 cm x 2 cm x 10 cm, weighs 1,134 g. The brick’s volume is 5 x 2 x 10 = 100 cubic cm. Divide 1,134 by 100 to get the density of lead, 11.34 grams per cubic cm.

Mass: a Mystery?

Mass is not completely understood, so it is defined in two very different ways: Inertial mass measures how strongly an object resists acceleration, while gravitational mass measures how strongly an object attracts other things to itself. It isn’t clear why these two different types of mass are the same, but experiments confirm that they are. Strictly speaking, a scale measures weight, but you can usually think of weight and mass as the same thing.

Space and Volume

Volume measures the spatial size of an object. Although the formula used to calculate volume depends on its shape and can be complicated, you can think of it generally as width times height times length. Measuring an object's volume can sometimes be easier than calculating it. Putting it into a large container of water and measuring the rise in water level can quickly find the volume, no matter what shape it is.

Divide for Density

Density is calculated by dividing an object’s mass by its volume. Density is less intuitive than mass or volume, but if you have ever picked up an object and found it much lighter or heavier than you expected, that’s because its density is not what you thought. Density usually can’t be measured directly and must be calculated after mass and volume have been determined. Density is sometimes used to describe other quantities divided by volume, such as energy density.

Density as a Constant

Scientists and engineers frequently use density, as it is useful for calculating an object’s properties and identifying the materials an object is made of. The densities of thousands of substances, including metals, plastics and more, are well-known. At room temperature and pressure, the density of a given substance is almost always constant--an iron nail and an iron boat anchor both have the same density though they are very different things. After calculating an object’s density, a scientist can look the value up in a table and in many cases accurately determine what the object is made of.

Archimedes’ Great Discovery

One of the most famous examples of calculating density is the story of Archimedes and the golden crown. A king had asked Archimedes to determine if his new crown was made of pure gold, but without damaging it in any way. Archimedes realized that by submerging the crown in water, he could determine its volume and therefore its density. This way, he proved that the crown was not pure gold, but had cheaper metals in it.

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