Question

The density of polypropylene, a plastic commonly used to make bottle caps, yogurt containers, and carpeting, is \(0.55 \mathrm{oz} / \mathrm{in}^{3} .\) Calculate the density in units of \(\mathrm{g} / \mathrm{cm}^{3}\).

Short answer

0.951 g/cm³

Step-by-step solution

Understand Conversion Factors

To convert the density from ounces per cubic inch to grams per cubic centimeter, you need to know the conversion factors: 1 ounce = 28.3495 grams, and 1 inch = 2.54 centimeters. Since the density is given in cubic units of inches and we want it in cubic units of centimeters, we'll also need the conversion for cubic inches to cubic centimeters.

Convert Ounces to Grams

Start by converting the density from ounces to grams. Since the density is 0.55 ounces per cubic inch, we use the factor 1 ounce = 28.3495 grams. The calculation is:\[ 0.55 ext{ oz} imes 28.3495 ext{ g/oz} = 15.592225 ext{ grams} \]

Convert Cubic Inches to Cubic Centimeters

Next, we need to convert the volume from cubic inches to cubic centimeters. Since 1 inch = 2.54 centimeters, we have:\[ 1 ext{ cubic inch} = (2.54 ext{ cm})^3 = 16.387064 ext{ cubic centimeters} \]

Calculate the Density in \\(\text{g/cm}^3\\)

Now, we combine our conversions to find the density in grams per cubic centimeter. Using the calculations from the previous steps:\[ \frac{15.592225 ext{ grams}}{16.387064 ext{ cm}^3} \approx 0.951 ext{ g/cm}^3 \]

Finalizing the Result

The density of polypropylene when converted from ounces per cubic inch to grams per cubic centimeter is approximately 0.951 g/cm³.

Key concepts

Polypropylene Density

Polypropylene is a versatile type of plastic commonly seen in everyday items such as bottle caps, yogurt containers, and even carpets. A critical feature that defines polypropylene is its density which is measured to be about 0.55 ounces per cubic inch. Density is a property that indicates how much mass of a substance is contained in a given volume. For polypropylene, understanding its density helps manufacturers determine its suitability for specific applications based on weight and space efficiency. In the engineering and manufacturing sectors, having precise knowledge of a material's density is crucial for design and production processes. This knowledge ensures the final products hold the correct attributes expected by consumers.

Unit Conversion

Unit conversion is the process of changing a measurement from one unit to another. This becomes particularly important when dealing with measurements in different systems, like converting from the imperial system to the metric system or vice versa. The exercise we are examining requires converting density from ounces per cubic inch to grams per cubic centimeter. To do this, two conversion steps are needed:

• Convert mass from ounces to grams. Given: 1 ounce = 28.3495 grams.
• Convert volume from cubic inches to cubic centimeters. Given: 1 inch = 2.54 centimeters.

Within unit conversion, always ensure that conversion factors are accurately applied to maintain measurement precision. An error can lead to incorrect interpretations of the data that could be costly in practice.

Metric System Conversion

The metric system is a universal system for measurement, used mainly outside of the United States for its simplicity and consistency, thanks to its base ten structure. When engaging in metric system conversion, particularly in scientific or international contexts, you smoothly consolidate measurements from one system to a global standard. For example, when calculating the density of polypropylene in grams per cubic centimeter, these conversions are vital to produce an accurate result in a widely understood metric. Here’s how it applies:

• Convert the mass measured in ounces to grams (base unit for mass in metric).
• Convert cubic inches to cubic centimeters (base unit for volume in metric).

These steps not only help standardize the results but also facilitate clearer communication of the properties of materials in scientific and industrial settings. Understanding these conversions and implementing them correctly is key to effective data presentation and application in problem-solving scenarios.