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Answer :
To solve this problem, we need to understand the forces acting on the person in the elevator. The person is subject to gravity and the acceleration of the elevator.
Gravitational Force: This is the weight of the person, which can be calculated using the formula:
[tex]F_{gravity} = m \cdot g[/tex]
where:
[tex]m = 60.0 \text{ kg}[/tex] (mass of the person), and
[tex]g = 9.80 \text{ m/s}^2[/tex] (acceleration due to gravity).Thus, the gravitational force is:
[tex]F_{gravity} = 60.0 \times 9.80 = 588 \text{ N}[/tex]Net Force in the Elevator: When the elevator is accelerating downwards with an acceleration of [tex]4.90 \text{ m/s}^2[/tex], this affects the apparent weight of the person. The apparent weight is the normal force, which is what the scale will read.
We use the equation for net force:
[tex]F_{net} = m \cdot (g - a)[/tex]
where:
[tex]a = 4.90 \text{ m/s}^2[/tex] (downward acceleration of the elevator).Calculate the Scale Reading: Substitute the values into the net force equation:
[tex]F_{net} = 60.0 \times (9.80 - 4.90)[/tex]
[tex]F_{net} = 60.0 \times 4.90 = 294 \text{ N}[/tex]
Therefore, the reading on the scale would be 294 N. The correct answer is (B) 294 N.
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