what is the mass of a suitcase, in pounds if it weighs 19.5 kilograms ? using dimensional analysis
The Correct Answer and Explanation is:
To convert the mass of the suitcase from kilograms to pounds using dimensional analysis, we need to use the appropriate conversion factor between kilograms and pounds.
Step 1: Identify the Conversion Factor
The standard conversion factor between kilograms (kg) and pounds (lb) is:1 kg=2.20462 lb1 \, \text{kg} = 2.20462 \, \text{lb}1kg=2.20462lb
This means that for every 1 kilogram, there are 2.20462 pounds.
Step 2: Set Up the Dimensional Analysis
We start with the mass in kilograms, and use the conversion factor to cancel out kilograms and convert to pounds.Mass in pounds=19.5 kg×(2.20462 lb1 kg)\text{Mass in pounds} = 19.5 \, \text{kg} \times \left( \frac{2.20462 \, \text{lb}}{1 \, \text{kg}} \right)Mass in pounds=19.5kg×(1kg2.20462lb)
Step 3: Perform the Calculation
Now, we multiply the mass in kilograms by the conversion factor:19.5×2.20462=42.978 lb19.5 \times 2.20462 = 42.978 \, \text{lb}19.5×2.20462=42.978lb
So, the mass of the suitcase is approximately 42.98 pounds.
Explanation:
Dimensional analysis is a powerful technique that involves using conversion factors to switch between units. In this case, we wanted to convert mass from kilograms to pounds. By multiplying the mass in kilograms by the conversion factor, we were able to find the mass in pounds. This approach ensures that the units “cancel out” correctly, leaving us with the desired unit of pounds in the final result.
Thus, a suitcase weighing 19.5 kilograms is equivalent to approximately 42.98 pounds.
