A 57.6-kg person rides in elevator while standing on a scale.The elevator is traveling downward but slowing down at a rate of 1.9 m/s2.What is the reading on the scale?Express your answer in N, to at least one digit after the decimal point.

To solve this problem, we need to understand that the reading on the scale is the normal force exerted by the scale on the person. When the elevator is moving downward and slowing down, the person feels heavier. This is because the normal force is not only counteracting gravity, but also the deceleration of the elevator.

Step 1: Calculate the force of gravity on the person. The force of gravity (weight) can be calculated using the formula F = m * g, where m is the mass and g is the acceleration due to gravity. In this case, m = 57.6 kg and g = 9.8 m/s² (approximate value on Earth's surface).

F_gravity = 57.6 kg * 9.8 m/s² = 564.48 N

Step 2: Calculate the force due to the elevator's deceleration. The force due to the elevator's deceleration can be calculated using the formula F = m * a, where m is the mass and a is the acceleration. In this case, m = 57.6 kg and a = 1.9 m/s² (the deceleration of the elevator).

F_elevator = 57.6 kg * 1.9 m/s² = 109.44 N

Step 3: Add the two forces together. The total force (the reading on the scale) is the sum of the force of gravity and the force due to the elevator's deceleration.

F_total = F_gravity + F_elevator = 564.48 N + 109.44 N = 673.92 N

So, the reading on the scale is 673.92 N.