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In a two-pulley system, how far will the movable pulley rise compared to the fixed pulley?

  1. Equal distance

  2. Half the distance

  3. Double the distance

  4. One quarter the distance

The correct answer is: Half the distance

In a two-pulley system, particularly when dealing with a movable pulley, the relationship between the distance the movable pulley rises and the distance the rope is pulled is crucial to understand. When you pull down on the rope that goes over the fixed pulley, you effectively create a scenario where the length of rope on both sides of the movable pulley must be taken into account. As you pull down on the rope, the movable pulley will rise, but because the force applied to the system is effectively shared by two segments of rope (one on each side of the movable pulley), the distance that the pulley rises will be half of the distance that you have pulled the rope. For example, if you pull the rope down by one meter, the movable pulley will only rise by half a meter since both sections of the rope are supporting the load together. This principle reflects the mechanical advantage offered by the movable pulley, making it easier to lift an object but also resulting in the travel distance of the load being shorter in comparison to the distance the rope is pulled. Thus, the movable pulley rises half the distance compared to the displacement of the fixed pulley.