What if a crane used more pulleys?

Olly wants to lift a big, heavy crate with a rope.

It is very hard on one rope. What if he used more pulleys?

Imagine lifting a 100-kilogram crate by pulling on one rope. You would have to pull as hard as the crate is heavy.

A pulley is a wheel with a grooved rim that guides a rope. Put several together, with some fixed at the top and some moving with the load, and you get a block and tackle. What happens if Olly's lifting machine uses more and more pulleys?

Britannica defines a block and tackle as a combination of rope and pulleys used to augment pulling force, with a fixed upper block and a lower block that rises with the load.

This lab uses a pulley model with a 100 kg load and asks how the pull, the length of rope hauled and the work done change as the number of supporting rope segments goes from one to four, and what friction does to the result.

With one rope, the pulley only changes direction. Olly pulls down, and the crate goes up.

But he must pull as hard as the crate is heavy.

Start with one piece of rope holding the crate. A single fixed pulley lets you pull down to lift the load up, which is handy, but it doesn't make the job easier.

In the model, you need a pull of about 981 newtons, which feels like lifting the whole 100 kilograms. And for every meter the crate rises, you pull one meter of rope. The mechanical advantage is 1.0.

OpenStax notes that an ordinary single pulley has a mechanical advantage of 1: it changes the direction of the force, not its size. With one supporting segment, the model needs 981 N (100 kg × 9.81 m/s²) and one meter of rope per meter of lift.

The work done on the load in the model's one-meter lift is 981 J, and with no friction the work put in is the same.

Now Olly uses more pulleys. Four pieces of rope hold up the crate.

Each piece holds a quarter. Olly's pull is much smaller! But he must pull lots more rope.

Now change to four rope segments holding the moving pulley and the crate. Each segment carries a quarter of the load.

The pull drops to about 245 newtons, which feels like lifting just 25 kilograms. But for every meter the crate rises, each of the four segments must get a meter shorter, so you pull 4 meters of rope. With six segments, the most the lab allows, the pull feels like 16.7 kilograms, and you haul 6 meters of rope per meter.

With four supporting segments the ideal mechanical advantage is 4: each segment carries 981 ÷ 4 = 245 N, and that is the pull required. Britannica's block and tackle explanation gives the reason for the distance: if the load rises one foot, each of the four links shortens one foot, so four feet of rope must be pulled.

Work in therefore stays at 981 J for a one-meter lift. With six segments the pull is 164 N and the rope hauled is 6 m per meter.

Each rope holding the crate shares the job.

More ropes, smaller share for each. But all the ropes must get shorter, so Olly pulls more rope.

One long rope runs around all the pulleys, so the pull is the same all along it. Every piece of rope holding up the moving pulley pulls up with that same force. Four pieces pulling up together hold four times your pull.

But a machine can't do more work than you put in. You make the force four times smaller, so you must pull four times as far. Friction makes it worse: in the model, at 80% efficiency, the pull with four ropes rises from 245 to about 307 newtons.

With a frictionless pulley and a massless rope the tension T is the same throughout, so n supporting segments exert n·T on the moving block: MA = n (OpenStax). Energy conservation fixes the rope travel: T × d_pull = W × h, so d_pull = n·h.

The model's limits: weightless pulleys and rope, no stretch, vertical segments, and friction as one fixed efficiency. Britannica notes that adding pulleys raises the force ratio but the gain may be offset by increased friction, which a single efficiency setting cannot show; the moving block's own weight also adds to the load.

People have used pulleys for a very long time.

Long ago, a scientist named Archimedes is said to have used pulleys to pull a ship onto land.

Pulleys are one of the five simple machines, along with the lever, wedge, wheel and axle, and screw. Combined with a rope into a block and tackle, they can lift heavy weights or pull hard in any direction.

They have a long history. Britannica reports that Archimedes, who lived more than 2,000 years ago, is said to have used compound pulleys to pull a ship onto dry land.

Britannica lists the pulley with the lever, wedge, wheel and axle, and screw as the five simple machines, and notes that grooved pulleys are called sheaves. A block and tackle can lift heavy weights or exert large forces in any direction.

Archimedes (3rd century BCE) is reported to have used compound pulleys to pull a ship onto dry land. The trade-off he relied on is the one this lab shows: pull with less force by hauling more rope.