Problem 16 - Applied Physics

Question

If \(108 \mathrm{in}^{3}\) of ammonia gas weighs \(0.00301 \mathrm{lb}\), what is its weight density?

Step-by-Step Solution

Answer

The weight density of the ammonia gas is approximately 0.00002787 lb/in³.

Step 1: Understand the Problem

We are given that 108 cubic inches of ammonia gas weighs 0.00301 lb. We are asked to find the weight density, which is the weight of the substance per unit volume.

Step 2: Write the Formula for Weight Density

Weight density is calculated by dividing the weight by the volume. The formula is:\[\text{Weight Density} = \frac{\text{Weight}}{\text{Volume}}\]

Step 3: Substitute Given Values into the Formula

We know the weight is 0.00301 lb and the volume is 108 in³. Substitute these values into the formula:\[\text{Weight Density} = \frac{0.00301}{108}\]

Step 4: Calculate the Weight Density

Perform the division:\[\text{Weight Density} = \frac{0.00301}{108} \approx 0.00002787 \text{ lb/in}^3\]

Step 5: Verify the Units

Make sure the units of the weight density are correct, which is lb/in³, as we are dividing weight (lb) by volume (in³).

Key Concepts

Volume Calculation

Calculating the volume is a fundamental step in understanding and solving physics problems involving density. Volume is the amount of space occupied by an object or substance and is often measured in cubic units, like cubic inches (in³) or cubic centimeters (cm³). For problems involving gases, liquids, or solids, you often need to know the volume to proceed with further calculations.
To determine volume effectively, always keep in mind:

• The shape of the object. Different shapes have different volume formulas. For a rectangular prism, use length × width × height. For a cylinder, use π × radius² × height.
• Make sure to measure all sides if you need to calculate the volume from scratch.
• If given directly, like in our ammonia gas problem where 108 in³ was given, you can skip the formula-step regarding the calculation of volume.

Finding volume accurately helps in obtaining precise measurements, which is essential for calculating the weight density as seen in physics and real-world applications.

Weight Calculation

Weight calculation involves determining how heavy a substance is, which is crucial for further calculations in physics. Unlike mass, which is a measure of the amount of matter, weight is a measure influenced by gravity and is usually measured in pounds (lb) or newtons (N).
In the given exercise, weight has already been provided as 0.00301 lb for the ammonia gas with a volume of 108 in³. If calculating weight from mass, use the formula:
\[\text{Weight} = \text{Mass} \times \text{Gravitational Acceleration}\]For Earth, gravitational acceleration is approximately 9.8 m/s². When weight is supplied, like in our problem, you can straightforwardly use this value for further calculations of density or other related physics properties.
Remember, understanding weight is vital as it serves as a key component in calculating density, which provides insights into the substance's properties and usage in various fields.

Physics Problem Solving

Physics problems often require a step-by-step approach to solve effectively. These steps may include understanding the problem, choosing the right formulas, and accurately substituting given values.
In our ammonia gas exercise, the key steps are:

• Identify what is given: 108 in³ volume and 0.00301 lb weight.
• Select the correct formula: Weight Density = Weight / Volume.
• Substitute the values into the formula: \[\text{Weight Density} = \frac{0.00301}{108}\].
• Perform the necessary calculations: This involves simple division in our case, leading to a weight density of approximately 0.00002787 lb/in³.

Always verify the units to ensure they fit the context of the problem. Understanding these steps makes problem solving in physics clear, methodical, and approachable, providing a systematic way to unravel complex real-world situations.