Final answer:
To lift a 500N box 2 meters high with a force of 100N, you would have to pull out 10 meters of rope, as the force applied is one fifth of the box's weight, requiring five times the distance in rope pulled.
Step-by-step explanation:
The question involves a basic understanding of simple machines and the principle of conservation of energy. In the scenario given, if it takes 100N of continual force to lift a 500N box 2 meters into the air with a pulley system, it involves understanding the relationship between the force applied, the distance over which the force is applied, and the mechanical advantage of the pulley system. In ideal conditions (assuming 100% efficiency), the work done on the rope (force times distance) is equal to the work done on the box. Because the force applied (100N) is one fifth of the weight of the box (500N), you would have to pull the rope through a distance that is five times greater than the distance the box is lifted.
Therefore, to lift the box 2 meters high, you would have to pull out 10 meters of rope. The correct answer is E) 10.
Reference information such as the mechanical advantage of pulleys, work done during lifting, and tension in ropes as mentioned in other examples and practice problems help us understand and derive the concept more effectively.