Final answer:
To calculate the mass of the airplane, convert its weight from pounds to newtons and account for the gravitational acceleration in SI units. After the conversion, the mass of the airplane is approximately 7,300 kilograms.
Step-by-step explanation:
To calculate the mass of an airplane given its weight and local gravitational acceleration, you can use the formula weight = mass × gravity. In this case, the weight of the airplane is 16,000 lb (pounds) and the local gravitational acceleration is 32 fps² (feet per second squared). However, the mass should be in standard SI units, which means we must convert the weight from pounds to newtons and then find the mass in kilograms.
First, convert the airplane's weight to newtons. There are 4.44822 newtons in a pound, so:
16,000 lb × 4.44822 N/lb = 71,171.52 N
Now, to find the mass in kilograms, you rearrange the formula to mass = weight / gravity. Since the g provided is in fps², we should also convert to m/s² for consistency (1 fps² = 0.3048 m/s²):
32 fps² × 0.3048 m/s²/fps² = 9.7536 m/s²
Then calculate the mass:
71,171.52 N / 9.7536 m/s² ≈ 7,300 kg
So, the mass of the airplane is approximately 7,300 kilograms.