You are in an elevator and you are standing on a scale that shows your weight in Newtons.

You are in an elevator and you are standing on a scale that shows your weight in Newtons. If the lift is accelerating downward at 1.90 m / s2, how much weight does the scale show? Your weight is 75 kg.

a = 1.9 m / s ^ 2.
m = 75 kg.
g = 9.8 m / s ^ 2.
P -?
Two forces act on a person in an elevator: the force of gravity m * g vertically downward and the reaction of the floor N directed vertically upward.
Let’s write 2 Newton’s law for a person in an elevator: m * a = m * g – N.
N = m * g – m * a = m * (g – a).
Weight P is the force with which a person presses on the floor.
According to Newton’s 3 law, the force with which a person presses on the floor, with such force the floor presses on a person: P = N.
P = m * (g – a).
P = 75 kg * (9.8 m / s ^ 2 – 1.9 m / s ^ 2) = 592.5 N.
Answer: the scales show weight P = 592.5 N.