Final answer:
The absolute value of the work done by both gravity and the normal force on a ball hanging from the ceiling of a decelerating elevator is zero because there is no displacement of the ball in the direction of either force.
Step-by-step explanation:
When considering the scenario where a ball hangs by a string from the ceiling of an elevator that is moving down and getting slower, it's important to analyze the forces at play to determine the work done by gravity compared to the work done by the normal force. In physics, work is defined as the product of force and displacement in the direction of the force. For the gravitational force, it is the weight of the ball times the vertical displacement.
If the elevator is getting slower while moving downward, it means it is decelerating. The ball itself will have no displacement because it is hanging; therefore, gravity does no work on the ball as work is only done when there's displacement in the direction of the force. The tension in the string provides the normal force, which acts upward and also does no work for the same reason as gravity; the string isn't stretching or contracting, and thus there is no displacement in the direction of the tension.
So, in this case, the absolute value of the work done by both gravity and the normal force is zero. It's important to note that even though the elevator is decelerating, this does not create any displacement for the ball or the string, and thus no work is done by either force on the ball.