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Pulley System Effort Force

F=WnF = \frac{W}{n}

Worked example: 800 N load on a 4-part tackle → 200 N — press Try an example to run it live, then adjust anything.

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Pulley System Effort Force explained

WFn

In a block and tackle the load hangs from several sections of the same rope, and since the tension is identical everywhere along an ideal rope, each section carries an equal share: F = W ⁄ n, where n counts only the sections actually pulling up on the moving block. An 800 N load on a four-part tackle needs just 200 N of pull. Plutarch tells of Archimedes using a compound pulley to draw a fully laden ship out of Syracuse harbour single-handed, to King Hiero's astonishment.

The price, again, is rope: to raise the load 1 m you must haul n metres through your hands, so the work is unchanged. Count carefully — the classic error is including the rope section you are pulling on when it runs off a fixed pulley (a fixed pulley only changes direction, adding nothing to n) and forgetting to include it when it leaves the moving block. Real tackle loses roughly 5–10% per sheave to friction, so a nominal 4:1 rigging typically pulls closer to 3.3:1.

Pulley System Effort Force formula

F=WnF = \frac{W}{n}
Where
  • FF= Effort force (N)
  • WW= Load (N)
  • nn= Supporting rope sections

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