A 83.0-kg person stands on a scale in an elevator. What is the apparent weight when the elevator is
(a) accelerating upward with an acceleration of 1.80 m/s2
Force=mg+ma
To determine the apparent weight of a person in an elevator, we need to consider the gravitational force acting on the person and the net force acting on the person due to the acceleration of the elevator.
The apparent weight of a person in an elevator can be calculated using the following equation:
Apparent Weight = Weight + Net Force
1. Determine the weight of the person:
The weight of a person can be calculated using the formula:
Weight = mass × gravitational acceleration
Given that the mass of the person is 83.0 kg and the gravitational acceleration is approximately 9.8 m/s², we can calculate the weight.
Weight = 83.0 kg × 9.8 m/s² = 813.4 N
2. Determine the net force on the person:
The net force acting on the person is the difference between the gravitational force and the force due to the acceleration of the elevator.
Net Force = gravitational force - force due to acceleration
The gravitational force acting on the person is the weight, which we calculated as 813.4 N.
The force due to acceleration is calculated using the formula:
Force due to acceleration = mass × acceleration
Given that the mass of the person is 83.0 kg and the acceleration of the elevator is 1.80 m/s², we can calculate the force due to acceleration.
Force due to acceleration = 83.0 kg × 1.80 m/s² = 149.4 N
Net Force = 813.4 N - 149.4 N = 664 N
3. Calculate the apparent weight:
Now that we have the weight and the net force, we can calculate the apparent weight using the formula:
Apparent Weight = Weight + Net Force
Apparent Weight = 813.4 N + 664 N = 1477.4 N
Therefore, the apparent weight of the person in the elevator, when it is accelerating upward with an acceleration of 1.80 m/s², is approximately 1477.4 N.