Mechanical Movement 13 — Movable Pulley
Why does a movable pulley halve the pull?
Mechanism No. 13 from 507 Mechanical Movements: “In this the lower pulley is movable. One end of the rope being fixed, the other must move twice as fast as the weight, and a corresponding gain of power is the result.” The load hangs from the movable pulley, which is held up by two strands of the same rope: one tied to the beam, one rising to a fixed guide pulley. Each strand carries half the weight, so the free end needs only about half the force, but it must travel twice as far. The upper pulley only turns the pull downward.
How it works, step by step
1. Holding still
Two strands hold the movable pulley, each with 245 N: half of the 491 N load. Your pull is also 245 N.
2. Start lifting
Friction in two pulleys adds a little: you pull 269 N instead of the ideal 245 N.
3. Twice as far
The load has risen 44 cm and 88 cm of rope has passed through your hand: two for one.
4. Lowering
Going down, friction helps: only 223 N lets the load down. Mechanical advantage 2.20.
The key idea
F ≈ W / 2 — Two strands share the weight, so the pull is about half; the free end moves twice as far as the load.
The weight hangs on two strands, so the pull is about half. The price: the rope moves twice as far as the load.
Model and assumptions
Ideal: F = W/2, free end moves 2 × the load. With pulley efficiency η, lifting needs F = W / (η(1 + η)) and lowering only F = W·η² / (1 + η). The beam anchor carries the fixed-end strand; the upper hook carries the rising strand plus your pull.
Frequently asked questions
Why does a movable pulley halve the force?
Two strands of the same rope hold it up, each carrying half the weight.
What is the trade-off?
The free end moves twice as far as the load.
Why is the real pull a bit more than half?
Friction in the pulleys; lowering, friction helps and the pull is a bit less.
Part of the 507 Mechanical Movements series
This is Movement No. 13 from Henry T. Brown’s 507 Mechanical Movements (1868), redrawn and simulated by BCRUZ.
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