Problem 51 - College Physics

Question

Baseball mass. Baseball rules specify that a regulation ball shall weigh no less than 5.00 ounces nor more than 5\(\frac{1}{4}\) ounces. What are the acceptable limits, in grams, for a regulation ball? (See Appendix D and use the fact that 16 oz \(=1\) lb.)

Step-by-Step Solution

Answer

Acceptable weight limits in grams are between 141.75g and 148.83g.

Step 1: Understand the Conversion Factor

To convert ounces to grams, we need to use the conversion factor that 1 ounce is approximately equal to 28.3495 grams.

Step 2: Convert the Lower Limit

Convert the lower limit of 5.00 ounces to grams using the conversion factor. Calculate: \[ 5.00 \text{ ounces} \times 28.3495 \text{ grams/ounce} = 141.7475 \text{ grams} \]

Step 3: Convert the Upper Limit

Now, convert the upper limit of 5\(\frac{1}{4}\) ounces to grams. This can be represented as 5.25 ounces. Calculate: \[ 5.25 \text{ ounces} \times 28.3495 \text{ grams/ounce} = 148.834875 \text{ grams} \]

Step 4: Present the Acceptable Limits

The acceptable limits for the weight of a regulation baseball in grams are thus between 141.7475 grams and 148.834875 grams.

Key Concepts

Conversion Factor

When converting between units, understanding the conversion factor is crucial. A conversion factor is a number used to change one set of units to another, by multiplying the given quantity. It's like a bridge that helps us translate measurements from one system to another. In this context, we are converting ounces to grams. Using an accurate conversion factor ensures your calculations are precise. For example, the conversion factor from ounces to grams is 1 ounce = 28.3495 grams. By multiplying the number of ounces by this factor, you can discover how many grams the measurement equals.

Ounces to Grams

Converting from ounces to grams is a useful skill, especially when working with different measurement systems. The ounce is primarily used in the United States, while grams are part of the metric system and widely used worldwide. To convert ounces to grams, identify how many ounces you have and use the conversion factor: 1 ounce = 28.3495 grams. Multiply the amount in ounces by 28.3495 to get the equivalent weight in grams. For instance, converting 5 ounces involves the calculation:

• 5 ounces × 28.3495 grams/ounce = 141.7475 grams

Understanding this process allows us to convert a range of measurements efficiently.

Baseball Weight Conversion

In baseball, the weight of a regulation ball is specified in ounces, but there may be times when you need this measurement in grams. The standard weight range for a regulation baseball is between 5 ounces and 5 1/4 ounces. To convert these limits into grams:

• Convert 5 ounces to grams: 5 × 28.3495 = 141.7475 grams
• Convert 5 1/4 ounces (or 5.25 ounces) to grams: 5.25 × 28.3495 = 148.834875 grams

Thus, the acceptable weight range for a regulation baseball is 141.7475 grams to 148.834875 grams. Knowing how to do this conversion allows players and equipment managers to accurately measure and ensure compliance with official baseball standards.