The Pulley Puzzle

Why it matters

A 400 N crate. Your arms are good for 150 N. The warehouse has a box of pulleys. This is not a physics problem — it's a rigging problem.

The idea in plain words

The rigger's rule. Tap the terms.

ideal MA = number of rope segments supporting the load

Block & tackle with 4 segments lifts 400 N. Ideal effort? Real effort at η = 80%?

125 N — friction charges its fee

• the well pulley: single fixed — 1 segment: MA 1, VR 1 — direction changer only
• the effort halver: single movable — 2 segments share the load: MA 2, VR 2 — you pull twice the distance
• the multiplier: block & tackle — n segments: MA n, VR n — cranes, sail rigging, gym machines
• ideal = 400 ÷ 4 = 100 N
• real = 100 ÷ 0.8

Predict first

A single FIXED pulley has MA ≈ 1. Why does anyone use it?

The well, the flagpole, the gym cable: pulling down is easier and safer than hauling up. Direction is worth changing even at MA = 1.

• It changes the direction — you pull DOWN (with your weight) to lift UP — correct
• It secretly halves the effort
• Nobody should use it

What you do

Try each rig on the 400 N crate. Count the rope segments holding the load — that number IS the ideal MA.

Check yourself

In a movable-pulley rig you pull 4 m of rope. The load rises…

Half the effort, twice the pulling distance — energy stays honest: 2× less force × 2× more distance.

Real pulley systems have MA slightly LESS than the rope count because…

Each sheave rubs, and the moving block's own weight is extra load — MA_real = η × n.

To lift 600 N with at most 120 N of pull (ideal), you need at least…

n ≥ 600/120 = 5. (Real riggers then add margin for friction.)

• 2 m — VR = 2 means half the distance — correct
• 4 m
• 8 m
• friction in the sheaves and the weight of the lower block eat some effort — correct
• ropes stretch
• the formula overcounts
• 5 rope segments — correct
• 3 segments
• 10 segments