Final answer:
To calculate the reading on the scale for the 14.0-kg block in an elevator with a downward acceleration of 1.84 m/s², we deduct the elevator's acceleration from the acceleration due to gravity and multiply by the mass. The apparent weight comes out to 111.44 N, which does not match any of the options provided, suggesting a possible error in the question.
Step-by-step explanation:
The student's question involves determining the reading on a scale in an elevator that is moving down with a certain acceleration. The concept being tested is the effect of acceleration on apparent weight in the context of Newton's second law of motion. When an elevator is accelerating downwards, the apparent weight of an object measured by a scale decreases because the scale accounts for the downward acceleration subtracted from the acceleration due to gravity. To find the apparent weight, we use the formula:
Fapparent = m(g - a)
where Fapparent is the apparent weight, m is the mass of the block, g is the acceleration due to gravity (9.8 m/s^2), and a is the acceleration of the elevator. For a 14.0-kg block and an elevator acceleration of 1.84 m/s^2:
Fapparent = 14.0 kg * (9.8 m/s^2 - 1.84 m/s^2)
Fapparent = 14.0 kg * 7.96 m/s^2
Fapparent = 111.44 N
Therefore, the reading on the scale would be 111.44 N, which corresponds to none of the options provided. It is possible there might be a typo or error in the provided options.