Question

A woman stands on a bathroom scale in an elevator that is accelerating upward at -1.5 m/s². The bathroom scale reads 600 N. What is the woman's mass?

Answer 1

The woman's mass is 75 kg.

Step-by-step explanation:

The bathroom scale in this scenario measures the normal force exerted by the woman's body on the scale. The normal force is equal to the woman's weight, which is the force of gravity acting on her mass.

Using Newton's second law, we can calculate the woman's weight and then determine her mass. We know that the net force is equal to the product of mass and acceleration: F_net = ma.

Since the elevator is accelerating upward at -1.5 m/s², the net force is equal to the sum of the woman's weight and the scale reading: F_net = weight + scale reading.

Using the given scale reading of 600 N, we can calculate the woman's weight:

600 N = weight - (75 kg)(9.8 m/s²)

Solving for weight, we get: weight = 735 N. This is equal to the woman's mass times the acceleration due to gravity: 735 N = mass * (9.8 m/s²). Therefore, the woman's mass is 75 kg.