Density is a fundamental physical property that describes the relationship between an object’s mass and the space it occupies, known as its volume. A brick and a piece of foam of the exact same size will have vastly different densities because the brick contains significantly more matter in that volume. Determining this value is a straightforward process that requires two measurements and a simple calculation, making it a valuable tool for scientific analysis.
Determining the Necessary Components
The calculation of an object’s density requires accurately measuring its mass and its volume. Mass is the quantity of matter an object contains and is typically measured using a balance or a precise scale. The standard units for this measurement are commonly grams (g) or kilograms (kg). This measurement must be taken first, providing the numerator for the density calculation.
Measuring an object’s volume can be done using one of two methods, depending on its physical form. For objects with regular, geometric shapes, such as a cube, cylinder, or rectangular prism, volume is calculated by measuring the object’s dimensions. For a simple rectangular solid, this involves measuring the length, width, and height with a ruler and multiplying the three values together to get the volume (V = l × w × h). The resulting volume will be expressed in cubic units, such as cubic centimeters (\(\text{cm}^3\)).
For irregularly shaped objects, the water displacement method must be employed. This involves submerging the object in a measured amount of liquid. One must first fill a graduated container, such as a graduated cylinder, with enough water to fully cover the object and record this initial volume (\(\text{V}_1\)). The object is then gently lowered into the water, ensuring it is completely submerged.
The presence of the object causes the water level to rise, and the new volume (\(\text{V}_2\)) is recorded. The volume of the object itself is equal to the difference between the final and initial water volumes (\(\text{V}_2 – \text{V}_1\)). Importantly, one milliliter (mL) of water is equivalent to one cubic centimeter (\(\text{cm}^3\)) of volume, providing a direct conversion for the result.
Calculating and Expressing Density
Once the object’s mass and volume have been accurately determined, the final step is to calculate its density. Density (\(\text{D}\) or \(\rho\)) is defined as the mass (\(\text{m}\)) divided by the volume (\(\text{V}\)), expressed as \(\text{D} = \text{m}/\text{V}\). Performing this division yields the object’s density value. For example, if an object has a mass of 150 grams and a volume of 50 cubic centimeters, its density is 3 grams per cubic centimeter.
The resulting density is expressed as a combined unit of mass per unit volume. The most common units for solids and liquids are grams per cubic centimeter (\(\text{g}/\text{cm}^3\)) or grams per milliliter (\(\text{g}/\text{mL}\)). The standard SI unit is kilograms per cubic meter (\(\text{kg}/\text{m}^3\)). The choice of unit depends on the scale of the measurement.
Practical Application of Density Values
The density value obtained from the calculation is a characteristic property of a substance. It can be used to identify unknown materials by comparing the calculated density to established density tables. For instance, if a sample has a density of \(19.3 \text{ g}/\text{cm}^3\), it suggests the material is gold, as this value is constant for pure gold regardless of the sample’s size.
Beyond identification, density determines how an object will behave when placed in a fluid, such as water or air, a concept known as buoyancy. An object will float if its density is less than the density of the surrounding fluid. Conversely, an object will sink if its density is greater than the fluid’s density. This principle explains why a dense steel ship can float—its overall volume includes a large amount of air, making the ship’s average density less than that of water.
Understanding density is applied across numerous real-world situations, from engineering to environmental science. Builders rely on the known densities of materials like steel and concrete to ensure structural stability in construction. In the shipping industry, cargo density is a consideration for safe loading, and the principle is used to design ships and submarines to ensure they float or sink as intended.