Problem 16 - College Physics

Question

Calculate the mass (in SI units) of (a) a 160 -lb human being; (b) a \(1.9-\) -lb cockatoo. Calculate the weight (in English units) of \((c)\) a 2300 -kg rhinoceros; (d) a 22 -g sparrow.

Step-by-Step Solution

Answer

(a) 72.57 kg, (b) 0.86 kg, (c) 5070.63 lb, (d) 0.0485 lb.

Step 1: Convert lbs to kg for the human being

To convert from pounds (lbs) to kilograms (kg), multiply the weight in pounds by 0.453592. For a 160 lb human: \[ 160 \text{ lb} \times 0.453592 \frac{\text{kg}}{\text{lb}} = 72.57472 \text{ kg} \] Thus, the mass of the human is approximately 72.57 kg.

Step 2: Convert lbs to kg for the cockatoo

Using the same conversion factor, convert 1.9 lb to kg: \[ 1.9 \text{ lb} \times 0.453592 \frac{\text{kg}}{\text{lb}} = 0.8618248 \text{ kg} \] The mass of the cockatoo is approximately 0.86 kg.

Step 3: Convert kg to lbs for the rhinoceros

To convert from kilograms to pounds, multiply the weight in kilograms by 2.20462. For a 2300 kg rhinoceros: \[ 2300 \text{ kg} \times 2.20462 \frac{\text{lb}}{\text{kg}} = 5070.626 \text{ lb} \] The weight of the rhinoceros is approximately 5070.63 lb.

Step 4: Convert grams to pounds for the sparrow

First, convert grams to kilograms by dividing by 1000, since 1 kg = 1000 g. Then convert kilograms to pounds using the conversion factor:Convert 22 g to kg:\[ 22 \text{ g} = 0.022 \text{ kg} \]Then convert 0.022 kg to lbs:\[0.022 \text{ kg} \times 2.20462 \frac{\text{lb}}{\text{kg}} = 0.04851064 \text{ lb}\]The weight of the sparrow is approximately 0.0485 lb.

Key Concepts

Mass Calculation

Mass calculation involves determining the amount of matter in an object, typically expressed in units like kilograms, grams, or pounds. Mass is a fundamental property of objects and does not change unless the object itself changes.

When working with problems involving mass, it's essential to understand that mass is distinct from weight. Mass is an intrinsic property of matter wherever it is, whereas weight is the force exerted on that mass due to gravity. In this context of unit conversion exercises, you deal with translating measurements from one system of units to another, such as converting a mass given in pounds to kilograms or in grams to kilograms.

To perform accurate mass calculations, it's crucial to use correct conversion factors. For example, converting between the customary units used in the United States and the metric system requires precise multiplication factors, which we'll delve into next.

Pounds to Kilograms

Converting pounds (lbs) to kilograms (kg) is a common task, especially when dealing with scientific data where the metric system is often favored. The conversion factor you need is: 1 pound ≈ 0.453592 kilograms.

To convert a given mass from pounds to kilograms, simply multiply the number of pounds by 0.453592.

• Example: For a person weighing 160 pounds, the calculation would be:
• \[160 \text{ lb} \times 0.453592 \frac{\text{kg}}{\text{lb}} = 72.57472 \text{ kg} \]

The resulting mass in kilograms, approximately 72.57 kg, can be used in a variety of scientific and medical applications, highlighting the importance of accurate unit conversions in these fields.

Kilograms to Pounds

Conversely, converting kilograms to pounds is often required when you need to present scientific data in a more familiar unit to audiences that are more comfortable with the Imperial system. Here, the conversion factor is: 1 kilogram ≈ 2.20462 pounds.

The conversion process involves multiplying the number of kilograms by 2.20462:

• Example: For a 2300 kg rhinoceros, the conversion would be:
• \[2300 \text{ kg} \times 2.20462 \frac{\text{lb}}{\text{kg}} = 5070.626 \text{ lb} \]

The weight of the rhinoceros would be approximately 5070.63 pounds. Understanding these conversions is crucial for fields such as zoology and transport where weights may need to be understood and applied in both metric and Imperial units.

Grams to Kilograms

Grams and kilograms are both part of the metric system, making their conversion straightforward yet vital. Since 1 kilogram equals 1000 grams, converting grams to kilograms involves dividing the number of grams by 1000.

• Step: Convert 22 grams to kilograms by dividing:
• \[22 \text{ g} = 0.022 \text{ kg} \]

This simple conversion is particularly important in science and cooking, where precision in measuring mass matters greatly. Once converted to kilograms, if you further need to convert this to pounds (as seen in the sparrow's case), you simply multiply by the kilogram-to-pound conversion factor, just as previously discussed. These basic conversions are essential for anyone working within different measurement systems or needing to communicate masses universally.