A pulley is a grooved wheel that carries a rope. On their own, pulleys change the direction of a force. Joined into a block and tackle, they divide the force, and the one skill you need is counting rope sections correctly.
Fixed and Movable Pulleys
A fixed pulley is attached to a support, such as a ceiling beam. The rope runs over the wheel, with the load on one side and your hand on the other. The tension in the rope is the same everywhere along it, so you must pull with a force equal to the load. All you gain is direction: you pull down to lift up.
A movable pulley is attached to the load and travels with it. The load hangs from the wheel, and the rope passes under it, so two rope sections share the weight. Each carries half, so you pull with half the load, but you must pull twice as much rope.
Counting Sections in a Block and Tackle
A block and tackle combines a fixed block and a moving block. The number that matters is how many sections of rope support the moving block, the one the load is attached to. In an ideal system, that number is the mechanical advantage.
Worked example: a block and tackle has six rope sections supporting the moving block, which carries a 1,200 N load that must rise 0.75 m.
- Effort: 1,200 / 6 = 200 N.
- Rope to pull: 6 x 0.75 = 4.5 m.
- Check with work: 200 N x 4.5 m = 900 N m, and the load's gain is 1,200 N x 0.75 m = 900 N m. Work in equals work out.
That last line is a good habit. If the work you put in does not match the work the load gains, a factor has been lost.
The Counting Trap
Do not count pulley wheels. Count the rope sections that pull on the moving block, and be careful with the free end, the part you hold.
If the free end comes off the fixed block and you pull it downward, that last section is held by the support, not by the load, so it does not count. If the free end comes off the moving block and you pull upward, it does count, and it adds one to the total. The wording or the picture will show which case you have.
Where You Meet Them
Pulley systems are in cranes and hoists, in sailing rigging, in lift shafts, in window blinds and in climbing and rescue kit. In every case the logic is the same: more supporting rope sections mean less effort and more rope to pull.
In a drawing, a pulley system often looks tangled. The reliable approach is to ignore the wheels and follow the rope: start at the free end, follow it round each wheel, and mark every point at which it goes up to or down from the moving block.
Try These Three
- A block and tackle has four sections supporting the moving block, which carries a 520 N load. What effort lifts it, and how much rope must you pull to raise it 2 m? Answer: 520 / 4 = 130 N, and 4 x 2 = 8 m of rope.
- A single fixed pulley is used to raise an 80 N bucket. What effort is needed, ignoring friction? Answer: 80 N. A fixed pulley only changes the direction of the pull.
- A rope is tied to a beam, passes under a pulley fixed to a 300 N load, and you pull the free end upward. What effort holds the load, and how far does the load rise when you pull 1 m of rope? Answer: two sections support the load, so 150 N, and the load rises 0.5 m.
What Friction Changes
Questions usually tell you to ignore friction and the weight of the pulleys and the rope. In practice, every wheel adds some friction, and a heavy moving block adds to the load. So the effort in a real block and tackle is always a little above the ideal figure, and the more wheels it has, the bigger that gap tends to be.
You can test the counting rule on real questions with the JobCannon mechanical reasoning test, or on the mechanical reasoning practice page. The same trade of force for distance also drives levers and hydraulic presses.