Final answer:
The apparent weight of a person with a mass of 45 kg in an elevator accelerating downward at 2.5 m/s² is 328.5 N.
Step-by-step explanation:
To calculate the apparent weight of a person in an elevator that is accelerating downward, we will use the concept of net force and Newton's Second Law of Motion. The apparent weight is the reading that would be displayed on a scale that the person is standing on inside the elevator.
The real weight (W) of the person is the product of their mass (m) and the acceleration due to gravity (g), which is W = mg. For a mass of 45 kg, this is 45 kg × 9.8 m/s² = 441 N (where g = 9.8 m/s² is the acceleration due to gravity).
When the elevator accelerates downward at 2.5 m/s², the downward force due to acceleration is F = ma, so F = 45 kg × 2.5 m/s² = 112.5 N. The apparent weight is the real weight minus this force: 441 N - 112.5 N = 328.5 N. Therefore, the apparent weight of the person would be 328.5 N.