Density
Density is a fundamental property of matter that indicates how concentrated the mass is within a specific volume. It is calculated as the ratio of an object's mass to its volume, expressed using the formula: $$ d = \frac{m}{V}$$ where \( d \) represents density, \( m \) denotes mass, and \( V \) stands for volume.
In the International System of Units (SI), density is measured in kilograms per cubic meter (kg/m³).
However, it's also common to express density in grams per cubic centimeter (g/cm³), especially in practical or scientific contexts.
Converting these units is straightforward: 1 g/cm³ is equivalent to 1000 kg/m³.
Conversion Example: If we need to determine what a density of 1 kg/m³ equals in g/cm³, we can do a simple conversion. Knowing that 1 kg/m³ is equivalent to 0.001 g/cm³, it quickly becomes clear that a density of 1 kg/m³ corresponds to 0.001 g/cm³.
Calculating Mass and Volume
Using the density formula, you can also derive other useful information:
If you know an object’s density (\( d \)) and volume (\( V \)), you can calculate its mass (\( m \)):
$$ m = d \times V $$
So, given the same volume, the denser the material, the greater its mass will be.
On the other hand, if you know the mass and density, you can find the volume:
$$ V = \frac{m}{d} $$
These relationships help solve many practical problems, such as estimating the weight of an object if you know its volume or determining how much space a certain mass of a material will occupy.
Density of Common Substances
To better illustrate density, here are a few examples:
- Water, one of the most common substances, has a density of 1000 kg/m³ (or 1 g/cm³). This means that one cubic meter of water weighs 1000 kg, equivalent to one metric ton.
- Helium, used in balloons, has a very low density of about 0.179 kg/m³, making it perfect for lifting balloons.
- Air, the substance we breathe daily, has a density of roughly 1.29 kg/m³. This low density explains why it is both invisible and light.
- Gold, one of the densest and most valuable metals, has a density of 19,300 kg/m³. This high density explains why even a small quantity of gold can be very heavy.
Understanding density helps explain everyday phenomena, such as why objects float: an object will float if its density is lower than that of the liquid it is placed in.
Exercises
