If a person has a weight of 145 lb at sea level, by how much is their weight reduced when flying on an airplane at an altitude of 10700 m?
To determine how much a person's weight is reduced when flying on an airplane at a certain altitude, we need to understand the concept of gravitational force and how it changes with respect to altitude.
The weight of an object is the force exerted on it due to gravity. At sea level, the acceleration due to gravity is approximately 9.8 m/s². As altitude increases, however, the value of gravity decreases gradually. This is because the Earth's gravitational pull weakens as you move further away from its center.
To calculate the weight at a specific altitude, we need to use the following formula:
Weight = mass × gravity
Given that the person's weight at sea level is 145 lb (pounds), we can convert that to kilograms (kg). Since 1 lb is approximately equal to 0.4536 kg, the person's weight in kg is:
Weight (kg) = 145 lb × 0.4536 kg/lb
Now, we can calculate the weight at the altitude of 10700 m using the acceleration due to gravity at that altitude:
Gravity = 9.8 m/s² × (6371 km / (6371 km + 10.7 km))²
Note: The radius of the Earth is approximately 6371 km, and we add the altitude (10700 m) to it.
Finally, we can calculate the reduced weight:
Reduced weight = Weight (kg) × Gravity
By following these steps and making the necessary calculations, we can determine the reduced weight.