In a simple 3:1 mechanical advantage system, how much rope would be pulled if a load drops 50 feet down a 200-ft vertical shaft?

In a system with a mechanical advantage of 3:1, this means that for every 3 feet of rope pulled, the load moves only 1 foot. Therefore, to determine how much rope would need to be pulled when the load drops 50 feet, you can use the ratio defined by the mechanical advantage.

If the load drops 50 feet, applying the 3:1 mechanical advantage means you would pull three times that distance of rope. So, you multiply the distance the load moves by the mechanical advantage ratio:

50 feet (load drop) x 3 (mechanical advantage) = 150 feet of rope pulled.

This calculation confirms that when using a 3:1 mechanical advantage, the amount of rope needed to be pulled to achieve a specific movement of the load is directly related to that mechanical advantage. Hence, pulling 150 feet of rope results in a 50-foot drop of the load.