Final answer:
The reading on the spring balance scale will be 97.44 N when a 14.0-kg block hangs from it inside an elevator that is moving downward and decelerating with an acceleration of 2.84 m/s^2.
Step-by-step explanation:
To determine the reading on the scale when a 14.0-kg block is attached to a spring balance in an elevator that is moving down and slowing with an acceleration of 2.84 m/s2, we need to calculate the apparent weight of the block.
First, let's consider the forces acting on the block.
The true weight of the block (due to gravity) is W = mg, where m is the mass of the block and g is the acceleration due to gravity (9.80 m/s2).
In this case, W = 14.0 kg × 9.80 m/s2 = 137.2 N.
However, since the elevator is accelerating downward, the reading on the scale will be less than the true weight.
The apparent weight can be calculated using Wapparent = mg - ma, where a is the acceleration of the elevator.
Plugging in the given values, Wapparent = 14.0 kg × (9.80 m/s2 - 2.84 m/s2) = 14.0 kg × 6.96 m/s2 = 97.44 N.
Therefore, the reading on the scale will be 97.44 N.