A 45.0-kg person steps on a scale in an elevator. The scale reads 460 n. What is the magnitude of the acceleration of the elevator?

The magnitude of the acceleration of the elevator is 0.422 m/s²

Explanation:

Lets explain how to solve the problem

Due to Newton's Law ∑ Forces in direction of motion is equal to mass

multiplied by the acceleration

We have here two forces 460 N in direction of motion and the weight

of the person in opposite direction of motion

The weight of the person is his mass multiplied by the acceleration of

gravity

→ W = mg, where m is the mass and g is the acceleration of gravity

→ m = 45 kg and g = 9.8 m/s²

Substitute these values in the rule above

→ W = 45 * 9.8 = 441 N

The scale reads 460 N

→ F = 460 N, W = 441 N, m = 45 kg

→ F - W = ma

→ 460 - 441 = 45 a

→ 19 = 45 a

Divide both sides by 45

→ a = 0.422 m/s²

The magnitude of the acceleration of the elevator is 0.422 m/s²