To solve these problems, we'll first need to calculate the mass of the man using the force exerted on the scale when the elevator is stationary. We'll then use Newton's second law to find the net force on the man in each case and thus the new scale readings.
1. Calculate the mass of the man:
Force (F) = mass (m) × acceleration due to gravity (g)
600 N = m × 9.81 m/s²
m ≈ 61.16 kg
Now let's analyze the different situations:
a) Ascending with an acceleration of 2 m/s²:
In this situation, the net force on the man is the sum of the gravitational force and the force due to the elevator's acceleration:
F_net = m × (g + a)
F_net = 61.16 kg × (9.81 m/s² + 2 m/s²)
F_net ≈ 720.96 N
b) Descending with an acceleration of 2 m/s²:
In this situation, the net force on the man is the difference between the gravitational force and the force due to the elevator's acceleration:
F_net = m × (g - a)
F_net = 61.16 kg × (9.81 m/s² - 2 m/s²)
F_net ≈ 479.04 N
c) Moving at a constant speed:
When the elevator is moving at a constant speed, the net force on the man is just the gravitational force, so the scale reading remains the same:
F_net = m × g
F_net = 61.16 kg × 9.81 m/s²
F_net ≈ 600 N
d) Descending with an acceleration a = g:
In this situation, the net force on the man is the difference between the gravitational force and the force due to the elevator's acceleration, which is equal to g:
F_net = m × (g - a)
F_net = 61.16 kg × (9.81 m/s² - 9.81 m/s²)
F_net = 0 N
So, the scale readings in each situation are:
a) ≈ 720.96 N
b) ≈ 479.04 N
c) ≈ 600 N
d) 0 N