Understanding density is crucial for solving various problems related to materials such as water, saltwater, blood, air, oil, and wood. Density is defined as mass per unit volume, and it is commonly expressed in several units. For instance, freshwater has a density of 1000 kilograms per cubic meter (kg/m³), which means that a volume of 1 cubic meter of freshwater has a mass of 1000 kilograms. This can also be expressed as 1 kilogram per liter (kg/L) or 1 gram per cubic centimeter (g/cm³). The conversion between these units is essential for calculations, especially when dealing with different substances.
For example, saltwater has a density of approximately 1030 kg/m³, which can be converted to 1.03 kg/L or 1.03 g/cm³. Similarly, whole blood has a density of about 1060 kg/m³. The conversions rely on two key factors: 1 cm³ = 1 mL and 1 m³ = 1000 L. These relationships allow for seamless transitions between different units of measurement.
When considering air at sea level, its density is significantly lower at about 1.2 kg/m³, which is approximately 800 times less dense than water. This lower density explains why we can move freely through air. Other materials like oil and wood typically have densities around 800 kg/m³, making them less dense than freshwater.
To illustrate the application of density in problem-solving, consider a scenario where you have 500 mL of a liquid with a density of 2.2 g/cm³. To find the mass, you can use the formula for density, which states that density (ρ) equals mass (m) divided by volume (V): ρ = m/V. Rearranging this gives m = ρ × V. Here, the volume is 500 mL, which is equivalent to 500 cm³ (since 1 mL = 1 cm³).
Substituting the values, you get:
m = 2.2 g/cm³ × 500 cm³ = 1100 g
To convert grams to kilograms (the SI unit), divide by 1000, resulting in 1.1 kg. To find the weight (w), use the equation w = mg, where g is the acceleration due to gravity, approximately 10 m/s² for simplification. Thus, the weight is:
w = 1.1 kg × 10 m/s² = 11 N
This example demonstrates how to apply density concepts and unit conversions to solve real-world problems effectively.
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