He density of aluminum is 2.70g/cm3 .Part AWhat is its density in pounds per cubic inch (lb/in3)?
The Correct Answer and Explanation is :
To convert the density of aluminum from grams per cubic centimeter (g/cm³) to pounds per cubic inch (lb/in³), we need to understand the relationship between these units.
Conversion Factors
- Grams to Pounds: There are approximately 453.592 grams in a pound.
- Cubic Centimeters to Cubic Inches: There are approximately 16.387 cubic centimeters in a cubic inch.
Steps for Conversion
- Convert grams to pounds:
[
\text{Density in lb/in}^3 = \text{Density in g/cm}^3 \times \frac{1 \text{ lb}}{453.592 \text{ g}}
] - Convert cm³ to in³:
[
\text{Density in lb/in}^3 = \text{Density in g/cm}^3 \times \frac{1 \text{ in}^3}{16.387 \text{ cm}^3}
]
Combining these two steps, the overall conversion factor from g/cm³ to lb/in³ can be expressed as:
[
\text{Density in lb/in}^3 = \text{Density in g/cm}^3 \times \frac{1 \text{ lb}}{453.592 \text{ g}} \times \frac{1 \text{ in}^3}{16.387 \text{ cm}^3}
]
Substituting the values:
[
\text{Density in lb/in}^3 = 2.70 \times \frac{1}{453.592} \times \frac{1}{16.387}
]
Calculating this gives:
[
\text{Density in lb/in}^3 = 2.70 \times \frac{1}{453.592} \times \frac{1}{16.387} \approx 0.098
]
Result
Thus, the density of aluminum is approximately 0.098 lb/in³.
Explanation
The density of a material indicates how much mass is contained in a given volume. In engineering and manufacturing, understanding the density of materials like aluminum is crucial, as it affects material selection, weight calculations, and structural integrity. Aluminum is valued for its low density, making it an ideal choice for applications where weight savings are important, such as in aerospace and automotive industries. The conversion of units ensures that professionals can communicate and calculate specifications accurately across different measurement systems, particularly when working with international teams or in global markets. By knowing the density in lb/in³, engineers can better assess the performance of aluminum in various applications, including load-bearing designs and material optimization.