How much rope must be pulled to haul 10 feet of rope with a 4:1 TMA system?

In a 4:1 TMA (Tensioned Mechanical Advantage) system, the mechanical advantage multiplies the input effort, meaning that for every unit of length of rope you pull, you can move the load four times that length. Essentially, pulling 1 foot of rope results in the load being lifted by ¼ of a foot.

To determine how much rope must be pulled to haul up 10 feet of rope with this system, you need to account for the mechanical advantage. Since it’s a 4:1 system, for every 4 feet of rope you want to lift, you must pull 1 foot of rope.

If the goal is to move 10 feet of rope upwards, you would multiply the required vertical distance (10 feet) by 4, because the system will require pulling 4 feet of rope for every 1 foot of rise. Thus, to move 10 feet of rope, you must pull 40 feet of rope.

This is articulated in the principles of mechanical advantage, where the amount of rope pulled increases proportionally based on the mechanical system's ratio.