A rigging instructor is teaching trainees how to calculate mechanical advantage. Match each described frictionless pulley system to its Ideal Mechanical Advantage (IMA) and the effort force required to lift a load.
- System 1: A single fixed pulley where the effort rope is pulled downward.IMA = 1; Effort = 120 lbs
- System 2: A single movable pulley where the rope is anchored to a ceiling support and the free end is pulled upward.IMA = 2; Effort = 60 lbs
- System 3: A block and tackle with two fixed pulleys and one movable pulley; the rope anchors to the movable block.IMA = 3; Effort = 40 lbs
- System 4: A block and tackle with two fixed pulleys and two movable pulleys; the rope anchors to the fixed block.IMA = 4; Effort = 30 lbs
Answer
System 1 matches IMA = 1 (120 lbs), System 2 matches IMA = 2 (60 lbs), System 3 matches IMA = 3 (40 lbs), and System 4 matches IMA = 4 (30 lbs).
Each system's mechanical advantage corresponds directly to the number of supporting rope strands. Dividing the 120 lb load by the respective IMA yields the correct effort force.
Step-by-Step Solution
Key Concept
The Ideal Mechanical Advantage of a pulley system equals the number of rope strands that directly support the movable pulley block.