Understanding the Forces

* Weight (Fg): This is the force of gravity acting on the passenger, calculated as mass (m) times acceleration due to gravity (g). We'll assume g = 9.8 m/s².

* Normal Force (Fn): This is the force the floor exerts on the passenger, acting perpendicular to the surface.

* Net Force (Fnet): The difference between the upward normal force and the downward weight force. This net force causes the acceleration of the passenger.

Setting Up the Equations

1. Weight: Fg = m * g

2. Net Force: Fnet = Fn - Fg

3. Newton's Second Law: Fnet = m * a (where 'a' is the acceleration)

Solving for Acceleration

1. Calculate the passenger's mass:

Since weight = mass * gravity, m = Fg / g = 650 N / 9.8 m/s² ≈ 66.3 kg

2. Calculate the net force:

Fnet = Fn - Fg = 620 N - 650 N = -30 N

(The negative sign indicates the net force is downward)

3. Calculate the acceleration:

a = Fnet / m = -30 N / 66.3 kg ≈ -0.45 m/s²

Answer:

The magnitude of the elevator's acceleration is 0.45 m/s² downward.