Final answer:
The absolute value of the work done by gravity on the hanging ball in a decelerating elevator is greater than the absolute value of the work done by the normal force because the normal force does not act on the ball, resulting in zero work done by the normal force.
Step-by-step explanation:
When considering the scenario where a ball hangs from a string in an elevator that is moving down and decelerating, the question asks if the absolute value of the work done by gravity is greater than, less than, or equal to the absolute value of the work done by the normal force.
The concept of work in physics is defined as the product of force and displacement in the direction of the force. Here, gravity is exerting a force downward, which is the weight of the ball, and this force is constant. Since the elevator is decelerating, the upward acceleration due to the tension in the string is less than the force of gravity. Therefore, the net force on the ball is in the downward direction, which means the ball moves slightly downward relative to the elevator as it slows down.
Recall that the normal force is the force exerted by a surface to support the weight of an object, and in this case, the elevator's floor would exert the normal force if the ball were in contact with it. However, since the ball is hanging by a string, the tension in the string provides the upward force and not the normal force.
Because work is force times displacement, and the displacement of the ball is downward when the elevator is decelerating, the work done by gravity would be positive since the force of gravity and the displacement are in the same direction. In the case of the normal force, since it's not in contact with the ball, the work done by the normal force is zero as there is no displacement in the direction of the normal force.
To sum up, the absolute value of the work done by gravity is greater than the absolute value of the work done by the normal force because there is no displacement related to the normal force, making the work done by it zero.