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Difficulty: Very hardPulleys and Pulley Systems

Match each complex pulley system scenario to the correct required effort force to lift the load.

  • A block and tackle system with 5 supporting strands and 80% mechanical efficiency, lifting a 1000 N1000 \text{ N} load.250 N250 \text{ N}
  • A compound pulley system consisting of three separate movable pulleys arranged in series, lifting a 1600 N1600 \text{ N} load under ideal conditions.200 N200 \text{ N}
  • A single movable pulley pulling a 500 N500 \text{ N} load up a frictionless inclined plane that rises 3 m3 \text{ m} vertically for every 5 m5 \text{ m} of slope length.150 N150 \text{ N}
  • A differential pulley hoist with an outer radius of 15 cm15 \text{ cm} and an inner radius of 14 cm14 \text{ cm}, lifting a 1500 N1500 \text{ N} load under ideal conditions.50 N50 \text{ N}

Answer

System 1 requires 250 N, System 2 requires 200 N, System 3 requires 150 N, and System 4 requires 50 N.
Each system's effort force is determined by dividing the given load by the correct overall mechanical advantage, properly factoring in mechanical efficiency, geometric constraints, and compound combinations.

Step-by-Step Solution

1
Calculate the required effort for the block and tackle system.
Ideal MA = 5. Actual MA = 4. Effort = 250 N.
Actual MA is the product of ideal MA and mechanical efficiency. Effort is found by dividing the load by the actual MA.
2
Calculate the required effort for the compound series pulley system.
Total MA = 8. Effort = 200 N.
For multiple independent movable pulleys connected in series, their individual mechanical advantages (2) are multiplied together (2×2×22 \times 2 \times 2).
3
Calculate the required effort for the combined incline and movable pulley system.
Incline MA = 5/3, Pulley MA = 2. Total MA = 10/3. Effort = 150 N.
The total mechanical advantage of a compound simple machine system is the product of the component machines' MAs.
4
Calculate the required effort for the differential pulley hoist.
MA = 30. Effort = 50 N.
The MA formula for a differential pulley relies on the difference between the outer and inner radii: 2R/(R−r)2R / (R - r).

Key Concept

Calculating advanced mechanical advantage across varied complex pulley configurations
Estimated Time:4m 0s
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Topics

Pulleys and Pulley Systems

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