Pulleys: Fixed, Movable, and Block-and-Tackle
A pulley is a grooved wheel with a rope that changes the direction of a force or, in a system with several rope sections, multiplies it; the ideal mechanical advantage of a pulley system equals the number of rope sections supporting the load. In brief: a fixed pulley only changes the direction of the effort (MA = 1). A movable pulley halves the effort (MA = 2) but needs twice the rope length to be pulled. A block and tackle combines fixed and movable pulleys to reach a larger MA, such as 4 for four supporting sections.
Cranes, sailboats, window blinds and gym machines use pulleys. This guide describes the three types, explains how to count supporting ropes, compares the arrangements in a table, works through a block-and-tackle example with friction and corrects common mistakes.
What is a fixed pulley?
The axle of a fixed pulley is attached to a support, such as a beam. The rope passes over the wheel; pulling down on one end lifts the load on the other. The tension is the same along the rope (ignoring friction), so the effort equals the load: MA = 1. It is useful because it is easier to pull down, using body weight, than to lift up. The effort moves the same distance as the load. Examples: a flagpole, a well, a curtain rail.
What is a movable pulley?
The load hangs from the pulley wheel, which moves with the load. The rope goes around the wheel, with one end fixed to the support and the other pulled by the effort. Two rope sections support the load, each with the tension T, so 2T = W and the effort is half of the load (ideal MA = 2). To lift the load by 1 m, the effort end must move 2 m. The weight of the movable pulley itself adds to the load.
What is a block and tackle?
A block and tackle uses one or more fixed pulleys and one or more movable pulleys in two blocks, with a single rope that passes around them. The ideal MA equals the number of rope sections that attach to the movable block (supporting the load), not counting the rope section that the person pulls if it leaves from a fixed pulley. With n supporting sections, the ideal effort is W ÷ n, and the rope end moves n times the distance of the load. In real systems, friction in the pulleys and the weight of the movable block reduce the efficiency, so the actual effort is larger.
Pulley systems compared
| Arrangement | Supporting ropes | Ideal MA | Rope pulled per 1 m of lift |
|---|---|---|---|
| Single fixed pulley | 1 | 1 | 1 m |
| Single movable pulley | 2 | 2 | 2 m |
| Block and tackle (4 ropes) | 4 | 4 | 4 m |
| Block and tackle (6 ropes) | 6 | 6 | 6 m |
Worked example: lifting a load
A block and tackle has four rope sections supporting a load of 800 N. Use g = 9.8 m/s2.
- Ideal MA: 4.
- Ideal effort: 800 ÷ 4 = 200 N.
- Real system with 80 percent efficiency: efficiency = MA ÷ IMA, so MA = 0.80 × 4 = 3.2. The effort = 800 ÷ 3.2 = 250 N.
- Rope length: to lift the load by 2.0 m, the rope end must be pulled 4 × 2.0 = 8.0 m.
- Work check: input = 250 × 8.0 = 2,000 J. Output = 800 × 2.0 = 1,600 J. Efficiency = 1,600 ÷ 2,000 = 80 percent. The energy dissipated is 400 J.
- Mass lifted: the load of 800 N corresponds to a mass of 800 ÷ 9.8 = 82 kg.
How did pulleys develop?
Pulleys were used in ancient Mesopotamia from about 1500 BCE to draw water. Archimedes is credited with designing compound pulleys to launch a ship single-handedly, according to the account of Plutarch. Block-and-tackle systems were used on sailing ships and in cranes in the Middle Ages and in building cathedrals. Today they are found in elevators, cranes and exercise machines.
Which mistakes are common?
Mistake 1: Counting the rope that the person pulls when the rope goes down from a fixed pulley
Only count the sections that support the movable block.
Mistake 2: Ignoring friction and the weight of the movable pulley
Real efforts are larger than the ideal value.
Mistake 3: Thinking that pulleys reduce the work needed
The force is smaller, but the distance is longer. The work is the same or greater.
Mistake 4: Assuming that a fixed pulley provides a force advantage
It changes only the direction of the force.