Using a simple 3:1 mechanical advantage system, how many feet of rope are pulled through the system to raise a person 50 feet?

Using a simple 3:1 mechanical advantage system, how many feet of rope are pulled through the system to raise a person 50 feet?

• A. 50
• B. 100
• C. 150
• D. 200

Answer: (C)

In a 3:1 mechanical advantage system, three strands of rope share the load, so the rope must be pulled three times the distance the load rises (ignoring friction and stretch). That means for every 1 foot the person is raised, you pull 3 feet of rope. So raising someone 50 feet requires pulling 3 × 50 = 150 feet of rope. In real life, friction and pulley inefficiency can require a bit more rope, but the ideal ratio is 3:1, giving 150 feet here.

In a 3:1 mechanical advantage system, three strands of rope share the load, so the rope must be pulled three times the distance the load rises (ignoring friction and stretch). That means for every 1 foot the person is raised, you pull 3 feet of rope. So raising someone 50 feet requires pulling 3 × 50 = 150 feet of rope. In real life, friction and pulley inefficiency can require a bit more rope, but the ideal ratio is 3:1, giving 150 feet here.