Problem 22 - College Physics

Question

(a) Compared with a 2-L soda bottle, a half-gallon soda bottle holds (1) more, (2) the same amount of, (3) less soda. (b) Verify your answer for part (a).

Step-by-Step Solution

Answer

A half-gallon soda bottle holds less soda than a 2-L soda bottle.

Step 1: Convert Gallons to Liters

First, we need to convert the volume of the half-gallon soda bottle to liters. We know that 1 gallon is approximately 3.785 liters. Therefore, a half-gallon is 0.5 times 3.785 liters, which is 1.8925 liters.

Step 2: Compare Volumes

Now that we have both volumes in liters, we can compare them directly. The half-gallon soda bottle holds 1.8925 liters, while the 2-L soda bottle holds exactly 2 liters. Thus, the half-gallon soda bottle holds less soda since 1.8925 liters is less than 2 liters.

Step 3: Verify by Recalculating

Verify the calculation to ensure accuracy. Convert 0.5 gallons to liters again: \(0.5 \times 3.785 = 1.8925\) liters. Since 1.8925 liters is indeed less than 2 liters, our previous comparison is verified.

Key Concepts

Liters to Gallons Conversion

Volume conversion between liters and gallons is a commonly encountered task when dealing with liquid measurements. Both of these units are used around the world, but in different regions. While liters are widely used in most countries, gallons are primarily used in the United States.

To convert liters to gallons, or vice versa, you can utilize their conversion factor. One gallon is approximately equal to 3.785 liters. Therefore, to convert gallons to liters, you multiply the number of gallons by 3.785.

• Example: To convert a half-gallon to liters, calculate: \(0.5 \times 3.785 = 1.8925\) liters.

This simple multiplication allows you to easily switch between these two volume units. Always verify your conversion to ensure your answer is correct, as accuracy is key in scientific computations.

Unit Comparison

Understanding how different units compare to each other is essential for making correct assessments in science and day-to-day problems. Units such as liters and gallons can be directly compared once converted to the same type. This comparison helps determine relative sizes and make proper judgments.

In the case of the soda bottle problem, we have two volumes: a 2-liter soda bottle and a half-gallon soda bottle. By converting the gallon measurement to liters (1.8925 liters for the half-gallon), we can compare them:

• 2-liter soda bottle: 2 liters
• Half-gallon soda bottle: 1.8925 liters

Since 1.8925 liters is less than 2 liters, we conclude that the half-gallon soda bottle holds less soda than the 2-liter bottle. This direct unit comparison technique applies to any physical measurement, making it a valuable skill.

Problem-Solving in Physics

Problem-solving is a fundamental aspect of physics that involves breaking down complex issues into manageable steps. In this scenario, the problem was to determine which of two soda bottles holds more liquid. Approach such problems by identifying given figures and required conversions.

The first step here involved converting units to maintain consistency, thus easing the comparison. After conversion, the actual comparison of numbers involved checking which was larger or smaller. This clear breakdown into steps makes the problem more systematic and less daunting.

• Identify the initial units and values
• Perform necessary conversions
• Compare the consistent units
• Verify your final result

By following these systematic steps, students not only solve the problem presented but also build a robust problem-solving framework that can be applied across various physics challenges.