Final answer:
The overpaid approximately $0.0155 for your 5 pounds of apples due to the slight variation in the gravitational acceleration at the mountain location, as the actual weight was less than what you were charged for.
Step-by-step explanation:
To determine how much you overpaid for the apples due to the slight difference in the value of acceleration due to gravity at the mountain location, we must understand that the weight of an object on Earth, which is its mass times the acceleration due to gravity (w = mg), is what determines its price in pounds at $1.99/lb.
Using the standard gravitational force value of 9.80 m/s², a 1.00-kg mass would have a weight of 9.80 N on Earth. However, you are at a location where the acceleration due to gravity is slightly less, at 9.79 m/s², which means that the weight of the apples would actually be slightly less too.
To find the difference in price, we convert the mass of the apples to kilograms because 1 pound = 0.454 kg. Then we calculate the weight using both values for acceleration due to gravity (standard Earth's and mountain's) and then find the corresponding price difference.
Calculation:
- Mass of 5 pounds of apples in kilograms = 5 × 0.454 kg = 2.27 kg.
- Weight using standard Earth's gravity = 2.27 kg × 9.80 m/s² = 22.246 N.
- Weight using mountain's gravity = 2.27 kg × 9.79 m/s² = 22.2113 N.
- Weight difference = 22.246 N - 22.2113 N = 0.0347 N.
- The price difference due to weight difference when converted to pounds and multiplied by the cost per pound (using 1 N = 0.225 lb) is: 0.0347 N × 0.225 lb/N × $1.99/lb ≈ $0.0155.
Therefore, you overpaid approximately $0.0155 for your 5 pounds of apples owing to the slight variation in gravitational acceleration at the mountain location.