A woman weighs 120 lb. Determine (b) her mass in kilograms.
The Correct Answer and Explanation is :
To convert a weight measured in pounds (lb) to mass in kilograms (kg), we can use the following conversion factor: 1 pound is approximately equal to 0.453592 kilograms.
Calculation
Given:
- Weight in pounds = 120 lb
- Conversion factor = 1 lb ≈ 0.453592 kg
The formula to convert pounds to kilograms is:
[
\text{mass in kg} = \text{weight in lb} \times \text{conversion factor}
]
Substituting the values:
[
\text{mass in kg} = 120 \, \text{lb} \times 0.453592 \, \text{kg/lb}
]
Calculating the above expression:
[
\text{mass in kg} = 120 \times 0.453592 \approx 54.43104 \, \text{kg}
]
Thus, the mass of a woman weighing 120 lb is approximately 54.43 kg.
Explanation
The distinction between weight and mass is crucial in physics. Weight is the force exerted by gravity on an object, typically measured in pounds (lb) or newtons (N), while mass is a measure of the amount of matter in an object, measured in kilograms (kg) or grams (g). The conversion between these two units is dependent on the acceleration due to gravity, which varies slightly depending on where you are on Earth. However, for most practical purposes, the conversion factor remains consistent.
The formula used for this conversion is straightforward, utilizing the known relationship between pounds and kilograms. This process exemplifies how different measurement systems can be interconnected through conversion factors, allowing for calculations in various contexts—be it scientific, medical, or everyday scenarios.
Understanding these conversions is particularly important in fields like healthcare, engineering, and nutrition, where precise measurements are crucial for safety and effectiveness. For example, in medical settings, dosages may need to be calculated based on a patient’s weight in kilograms, making it essential to perform accurate conversions when initial data is given in pounds.