How Does a Pulley Work? Fixed, Movable and the Rope Trade-Off

Why pull down to send a flag up?

On a windy morning at school, someone pulls down on a rope beside the flagpole, and the flag climbs up to the top. Their hands move toward the ground, but the flag moves toward the sky. How can a pull in one direction move something the other way?

The answer is hiding at the top of the pole: a small wheel with the rope looped over it. Science North, a science centre that is an agency of the Government of Ontario, uses a model flagpole in one of its school activities. In the model, thread spools act as the pulleys, and pulling the string raises the paper flag.^[4]

What is a pulley?

Britannica describes a pulley as a wheel that carries a flexible rope, cord, cable, chain or belt on its rim. Many pulleys have a groove around the edge so the rope stays in place instead of slipping off.

The pulley is one of the simple machines. Britannica lists it with the lever, the wedge, the wheel and axle, and the screw. Simple machines do not use engines or electricity. They help people by changing the direction of a force, the size of a force, or both. The Daily Read lesson on levers showed how a lever does this with a rigid bar. A pulley does it with a wheel and a rope.^[3]

A fixed pulley changes the direction

A fixed pulley is attached to one spot and stays there. The pulley at the top of a flagpole is a fixed pulley. So is the wheel above an old-fashioned well, where a bucket hangs on one end of the rope and a person pulls on the other end.

NDSU Extension, part of North Dakota State University, explains that with one fixed pulley the force you need is equal to the weight of the object. The Idaho National Laboratory puts it simply: a fixed pulley changes the direction of the pull, but it doesn't change the amount of force you use.

So why bother? Pulling down is often easier than lifting up. You can use your body weight, stand on the ground and keep the heavy thing away from you. A fixed pulley does not make the load feel lighter, but it lets you pull in a more comfortable direction.^[1]

A movable pulley shares the load

A movable pulley is not fixed in place. It is attached to the load and moves up and down with it. One end of the rope is tied to something above, like a hook in a ceiling beam. The rope runs down, under the movable pulley, and back up to your hands.

Now the load is hanging from two sections of rope instead of one. The Idaho National Laboratory explains that because the pulley is supported by two ropes, the amount of force you need is cut in half. Each rope section holds part of the weight, so your hands only have to hold one share. Real pulleys are not perfect, so the pull is about half, not exactly half.^[2]

The trade-off: less force, more rope

A movable pulley sounds like a free gift, but there is a cost. NDSU Extension says the trade-off is that the distance the rope must be pulled is increased. You apply a smaller force, but over a longer distance.

Here is why, with invented numbers. Suppose you want to lift a box of books 1 metre with a movable pulley. The box hangs from two rope sections. For the box to rise 1 metre, both rope sections must get 1 metre shorter. That means 2 metres of rope have to pass through your hands. You pull about half as hard, but you pull about twice as far.

This is the same deal you met with a lever: win on force, pay with distance. No simple machine gives you something for nothing.^[1]

Many pulleys working together

People can put several pulleys together in one machine. Britannica calls a combination of pulleys, blocks and rope a block and tackle. The more rope sections that hold up the moving pulleys, the more the load is shared, so the pull you need gets smaller. The trade-off grows too: you must pull even more rope.

Pulleys have helped people for a very long time. Britannica says the Greek inventor Archimedes, who lived more than 2,000 years ago, is reported to have used compound pulleys to pull a ship onto dry land. The word reported matters: it is a story written down long ago, not something anyone measured.^[3]

Pulleys you might see this week

NDSU Extension names flagpoles, window blinds and cranes as places where pulleys are used. When you tug the cord on some window blinds, a cord running over small pulleys lifts the slats. A construction crane uses steel cables over pulleys to lift heavy loads high above a building site. NDSU also explains that elevators use counterweights, which offset some of the force needed to lift the elevator car.

Science North links pulleys to the Ontario Grade 4 science curriculum, which asks students to describe the purposes of pulley systems. Next time you see a rope running over a wheel, ask two questions: Which way does the pull go, and which way does the load move? Does the pulley stay in one place, or does it move with the load?^[1]