Pulleys and Mechanical Advantage

How pulleys change the direction or size of a force, making lifting heavy loads easier.

What Is a Pulley?

A pulley is a wheel with a grooved rim through which a rope or cable runs. It is one of the six simple machines.

Fixed Pulley

The pulley is attached to a fixed point (e.g., a ceiling). The wheel rotates but does not move up or down.

Changes the direction of force (pull down → load goes up)
Does not reduce the size of the force needed

Use: Flag poles, window blinds, cranes

Movable Pulley

The pulley is attached to the load and moves with it.

Does not change direction
Halves the force needed to lift the load
But you must pull the rope twice as far

Note

Energy is still conserved: using less force over a greater distance still equals the same work done. $W = F \times d$

Block and Tackle (Combined Pulleys)

Multiple pulleys working together:

Number of rope sections supporting the load	Mechanical advantage
1	1 (single fixed pulley)
2	2 (movable pulley)
4	4

Mechanical advantage: $MA = \frac{\text{load force}}{\text{effort force}}$

A movable pulley is used to lift a 200 N box. How much effort force is needed?

A movable pulley gives MA = 2. $\text{Effort} = \frac{200}{2} = 100 \text{ N}$ You pull with 100 N but must pull twice the distance the box moves.

Real-World Uses

Construction cranes (multiple movable pulleys)
Elevator counterweights
Theatre stage rigging
Rock climbing rope systems

Real world: construction crane with block and tackle

A construction crane uses a six-rope block-and-tackle system (MA = 6) to lift a 12 000 N steel beam. The cable tension needed: $F = \frac{12\,000}{6} = 2000\text{ N}$ . The crane motor only needs to exert 2000 N, but must reel in 6 m of cable for every 1 m the beam rises. Pulleys make lifting massive loads possible with relatively small motors.

Real world: theatre stage rigging

A theatre flies system uses multiple pulleys to lift a 300 N scenic flat with a single operator. A 3-rope system (MA = 3) means the operator pulls with $\frac{300}{3} = 100\text{ N}$ — easy enough to do quickly during a live performance. Stage rigging relies on pulley mechanical advantage for safe, rapid scene changes.

Tip The mechanical advantage of a pulley system equals the number of rope sections directly supporting the load. Count only the segments attached to the moving pulley block, not the effort side.

Practice Problems

A block-and-tackle system has 4 supporting rope sections. What effort is needed to lift a 400 N load?

Show answer

MA = 4. Effort = 400 ÷ 4 = 100 N

Why doesn't a pulley system create 'free' energy even though it reduces effort?

Show answer

The effort must act over a greater distance. Work = force × distance remains the same. Energy is conserved — pulleys only change how force is applied.