Question

The average density of Earth is \(5.52 \mathrm{~g} / \mathrm{cm}^{3}\). What is its density in (a) \(\mathrm{kg} / \mathrm{m}^{3} ;\) (b) \(\mathrm{lb} / \mathrm{ft}^{3}\) ?

Short answer

The density of Earth is 5520 kg/m³ and 344.61 lb/ft³.

Step-by-step solution

- Understand the Given Data

The given average density of Earth is 5.52 g/cm³. This needs to be converted into two different units: kg/m³ and lb/ft³.

- Convert g/cm³ to kg/m³

First, we convert 5.52 g/cm³ to kg/m³. We know that 1 g/cm³ = 1000 kg/m³. Therefore, we multiply the given density by 1000:odensity = 5.52 g/cm³ × 1000 (kg/m³ per g/cm³) = 5520 kg/m³.

- Convert g/cm³ to lb/ft³

Next, we convert 5.52 g/cm³ to lb/ft³. Using the conversion 1 g/cm³ = 62.428 lb/ft³, we multiply the given density by 62.428:density = 5.52 g/cm³ × 62.428 (lb/ft³ per g/cm³) ≈ 344.61 lb/ft³.

Key concepts

unit conversion

In science and engineering, unit conversion is essential because it allows us to express measurements in different units. These conversions are necessary when working with various engineering applications and scientific data.
Unit conversion involves knowing the relationship between different units and applying this relationship through multiplication or division.

• In our problem, we are converting the Earth's density from g/cm³ to kg/m³ and lb/ft³.
• 1 g/cm³ can be converted to kg/m³ by recognizing that there are 1000 g in a kg and 1,000,000 cm³ in a m³. So, 1 g/cm³ equals 1000 kg/m³.
• For converting g/cm³ to lb/ft³, we use the conversion factor 1 g/cm³ = 62.428 lb/ft³.

Understanding these relationships and conversion factors is critical in making accurate and meaningful conversions.

density calculation

Density is a fundamental concept in physics and engineering, describing how much mass is contained in a given volume. It is generally expressed as mass per unit volume: \(\rho = \frac{m}{V}\), where \(\rho\) is density, \(m\) is mass, and \(V\) is volume.
In our exercise, we use the given density of the Earth in g/cm³ and convert it to different units of measurement.

• A crucial step is understanding the conversion factors between these units.
• First, we converted the density from g/cm³ to kg/m³: 5.52 g/cm³ × 1000 kg/m³ per g/cm³ = 5520 kg/m³.
• Next, we converted the density into lb/ft³ using the factor 1 g/cm³ = 62.428 lb/ft³: 5.52 g/cm³ × 62.428 lb/ft³ per g/cm³ ≈ 344.61 lb/ft³.

These density conversions help in comparing and using the density value in multiple settings and units.

measurement units

Measurement units are standardized quantities used to specify the size, length, or amount of something. Understanding different measurement units and their conversions is essential in science and daily life.
Commonly used density units in our problem include:

• g/cm³ (grams per cubic centimeter) - used for small objects and in scientific settings.
• kg/m³ (kilograms per cubic meter) - more common in engineering and for larger scales.
• lb/ft³ (pounds per cubic foot) - often used in the U.S. customary system for practical applications.

Knowing how to convert between these units helps in avoiding errors in measurement and ensuring consistent results across various applications.