Final answer:
The work done by tension on the elevator is negative because the tension force and the displacement are in opposite directions. The work done by gravity on the elevator is also negative as gravity acts downward. The total work done on the elevator is negative due to the negative work done by tension and gravity.
Step-by-step explanation:
Part A: The work done by tension on the elevator is negative. When the elevator is ascending but slowing down, the tension force acts in the opposite direction of the displacement. Work is defined as the product of the force applied and the displacement in the direction of the force. Since the tension force and the displacement are in opposite directions, the work done by tension is negative.
Part B: The work done by gravity on the elevator is also negative. Gravity acts downward, which is the opposite direction of the elevator's displacement. Therefore, the work done by gravity is negative.
Part C: The total work done on the elevator is the sum of the work done by tension and the work done by gravity. Since both of these values are negative, the total work done on the elevator is negative as well.