Mechanical Movement 14 — Blocks and Tackle
How can six strands of rope lift six times the pull?
A block and tackle threads one rope back and forth between a fixed upper block and a moving lower block. Here each block has three sheaves and the rope’s dead end is tied to the upper block, so six strands hold up the moving block and its load. Each strand carries about one sixth of the weight, so the pull on the free end is about one sixth too, but you must haul six metres of rope to lift the load one metre. Friction in the six sheaves makes lifting a little harder than the ideal and lowering a little easier.
How it works, step by step
1. Six strands
The rope runs from a dead end on the fixed block, round three lower and three upper sheaves: six strands hold the moving block.
2. Lifting
Each strand carries about one sixth of 1962 N. Your pull: 376 N, a mechanical advantage of 5.21.
3. 6 m for 1 m
The load has risen 1.20 m while 7.20 m of rope passed through your hands: six times as far.
4. Lowering is easier
Friction now helps you hold back: only 283 N, a mechanical advantage of 6.94.
The key idea
F ≈ W / 6 — Six strands share the weight; you pay with six times the rope. Sheave friction makes lifting a little harder and lowering easier.
Six strands share the weight, so the pull is about a sixth. The price: six times as much rope through your hands.
Model and assumptions
Model: two blocks with 3 sheaves each on a common axle, dead end on the upper block, 6 supporting strands. Each sheave passes on a fraction e of the tension (e = 0.96 by default), so when lifting the tension grows by 1/e at every sheave toward the hauling end; when lowering it shrinks. g = 9.81 m/s². Lift 1.2 m, hold, then lower.
Frequently asked questions
How do you find a tackle’s mechanical advantage?
Count the rope strands that hold up the moving block: here six, so ideally 6 : 1.
Why is lifting harder than the ideal?
Each sheave loses a little to friction, so the tension grows along the rope toward your hand.
How much rope do you pull?
Six metres for every metre of lift.
Part of the 507 Mechanical Movements series
This is Movement No. 14 from Henry T. Brown’s 507 Mechanical Movements (1868), redrawn and simulated by BCRUZ.
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