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# Pulleys

by Chris Woodford. Last updated: May 18, 2017.

You've probably seen those amazing TV strongmen who can pull cars with their hair and drag trains with their teeth. But did you know science can make you strong too? If you need to lift huge weights, don't strain your back: use the power of science—and an amazing device called a pulley. Let's take a closer look at how they work!

Photo: A pulley mounted on a huge lifting frame to make it safer to use. Thanks to the power of pulleys, one person can lift far more than their own weight without straining any muscles. Photo by R. B. Hotard courtesy of US Marine Corps.

## What are pulleys?

Photo: Pulleys can help you lift heavier things because several ropes or chains support the extra weight. Photo by Sheldon Rowley courtesy of US Navy.

A pulley is simply a collection of one or more wheels over which you loop a rope to make it easier to lift things.

Pulleys are examples of what scientists call simple machines. That doesn't mean they're packed with engines and gears; it just means they help us multiply forces. If you want to lift a really heavy weight, there's only so much force your muscles can supply, even if you are the world's strongest man. But use a simple machine such as a pulley and you can effectively multiply the force your body produces.

## Let's be clear about mass and weight!

Before we go any further, let's be very clear about the difference between weight and mass. This will help in a moment when we talk about using pulleys to lift weights (which are really masses) with a certain amount of force. In a nutshell:

• Mass is the amount of stuff something is made from or contains, measured in kilograms (or pounds).
• Weight is the amount of force with which Earth's gravity pulls on a particular mass: the more massive something is, the more gravitational force, and the more we say it weighs.

Photo: How much force is a newton? This orange has a mass of about 100g (0.1kg) so I need to supply 1N (one newton) of force to hold it in mid-air. Loosely speaking, we say the orange "weighs" 100g; strictly speaking, it weighs 1N.

## How pulleys work

The more wheels you have, and the more times you loop the rope around them, the more you can lift.

### One wheel

If you have a single wheel and a rope, a pulley helps you reverse the direction of your lifting force. So, as in the picture below, you pull the rope down to lift the weight up. If you want to lift something that weighs 100kg, you have to pull down with a force equivalent to 100kg, which is 1000N (newtons). If you want to raise the weight 1m into the air, you have to pull the loose end of the rope a total distance of 1m at the other end.

Artwork: How pulleys work#1: With one wheel, a pulley simply reverses the direction of the force you apply. It doesn't alter the force in any other way.

### Two wheels

Now if you add more wheels, and loop the rope around them, you can reduce the effort you need to lift the weight. Suppose you have two wheels and a rope looped around them, as in the figure below. The 100kg mass (1000 newton weight) is now effectively supported by two sections of the same rope (the two strands on the left) instead of just one (ignoring the loose end of the rope you're pulling with), and this means you can lift it by pulling with a force of just 500 newtons—half as much! That's why we say a pulley with two wheels, and the rope wrapped around it this way, gives a mechanical advantage (ME) of two.

Mechanical advantage is a measurement of how much a simple machine multiples a force. The bigger the mechanical advantage, the less force you need, but the greater the distance you have to use that force. The weight rises 1m, but now we have to pull the loose end of the rope twice as far (2m). How come? To make the weight rise 1m, you have to make the two sections of rope supporting it rise by 1m each. To do that, you have to pull the loose end of the rope 2m. Notice that we can also figure out the mechanical advantage by dividing the distance we have to pull the rope by the distance the weight moves.

Artwork: How pulleys work#2: With two wheels, it's as though the weight is hanging from two ropes (the two strands of the same rope on the left), and a pulley halves the lifting force you need. It's like lifting the weight with two ropes instead of one. But you now have to pull the end of the rope twice as far to lift the weight the same distance.

### Four wheels

Okay, what if you use four wheels held together by a long rope that loops over them, as in the picture below? You can see that the 100kg mass (1000 newton weight) is now hanging from four sections of rope (the ones on the left, ignoring the loose end of the rope you're pulling with). That means each section of rope is supporting a quarter of the total 1000 newton weight, or 250 newtons, and to raise the weight into the air, you have to pull with only a quarter of the force—also 250 newtons. To make the weight rise 1m, you have to shorten each section of the rope by 1m, so you have to pull the loose end of the rope by 4m. We say a pulley with four wheels and the rope wrapped around like this gives a mechanical advantage of four, which is twice as good as a pulley with two ropes and wheels.

Artwork: How pulleys work#3: With four wheels and the rope working in four sections, a pulley cuts the lifting force you need to one quarter. But you have to pull the end of the rope four times as far.

### How a pulley is like a lever

You can probably see that a pulley magnifies force in a similar way to a seesaw, which is a kind of lever. If you want to lift someone four times heavier than you on a seesaw, you need to sit four times further away from the balancing point (fulcrum) than they are. If you move your end of the lever down by 4cm, their end of the seesaw moves up only 1cm. As they rise up, they gain a certain amount of potential energy equal to their weight multiplied by the distance they move. You lose exactly the same amount of energy—equal to your weight (four times smaller) times the distance you move (four times larger). You can shift their much bigger weight because you move your end of the seesaw over a much bigger distance: the leverage of the seesaw makes it possible to produce more force by working over a bigger distance.

The same thing is happening with a pulley, except that you're pulling on a rope instead of moving the end of a seesaw. To lift something four times heavier, you can use exactly the same force but only if you pull the rope four times further. If you look at what's happening on both sides of a pulley, and multiply the force by the distance moved, you'll find it's the same. On your side, you use a small force over a large distance. On the other side, there's a much bigger weight but it's moving a smaller distance.

Artwork: How a pulley works like a lever: Just like with a lever, a pulley can "magically" create more force—but only if you use that force over a longer distance. Why is that? Read on below!

## What's the catch?

Pulleys sound brilliant—and they are. But surely there must be a catch? If you can lift 100kg (1000 newtons) by pulling with the force-equivalent of only 25kg (250 newtons), surely you're doing only a quarter as much work and using only a quarter as much energy? And if that's true, you could build some kind of a pulley that would actually produce energy for you: put in only one unit of energy and get four units out! Sounds brilliant!

?

Unfortunately, such amazing things are strictly prohibited by a law of physics called the conservation of energy, which says you must always put in as much energy as you get out. So let's think about pulleys in terms of energy. If you raise a weight of 100kg (1000 newtons) a distance of 1 meter off the ground, you have to do the same amount of work whether you use a pulley or not: you have to move the same force over the same distance. If you use a pulley and reduce the force you're using by a quarter, you still have to do the same amount of work. It's just that you have to pull the end of the rope four times further to make each of the four supporting sections of rope rise by the same amount. That's the catch with a pulley. You pull with less force, but you have to pull further (and, generally speaking, use the force for longer). Far from using less energy with a pulley, you actually have to use a little bit more because of the friction where the rope rubs against the pulley wheels. But it seems and feels easier to use a pulley, and that's the important thing!

Photos: Pulley equipment. Left: These small pulley wheels have hooks on them so they're easy to hang from the ceiling. Note how the wheels have grooves in them so the rope doesn't slide off them. Photo by Paula Aragon. Right: Giant pulley wheels on the arm of a large railroad maintenance crane. This one uses huge strong wire rope.

## Find out more

### On other websites

• Pulleys and blocks and other tackle: A great collection of pulley photos compiled by Flickr user "Elsie" (Les Chatfield), who has a great eye for detail and revealing the hidden beauty in the mechanical world.

### Books

For some reason, there are loads of books about pulleys for young readers (6–10 age group). Here are just a few to start you off:

• Exploring Science: Machines: by Chris Oxlade, Anness, 2016. A hands-on introduction to gears, levers, pulleys, and engines through 20 simple experiments. This book helps to put pulleys in the broader context of simple machines. Ages 8–10.
• How pulleys work: by Jim Mezzanotte. Gareth Stevens, 2007. A 24-page guide that introduces pulleys and shows how we use them in all kinds of ways in everyday life. The emphasis here is on pulleys as a means of using forces to our advantage.
• What are pulleys?: by Helen Frost, Capstone Press, 2001. A very simple illustrated introduction for younger readers (ages 7–10, I'd guess).

These two are more general books that put the science of forces into a wider context:

• Can You Feel the Force by Richard Hammond. Dorling Kindersley, 2006/2015. A breezy book about forces and physics for younger readers. (I was one of the consultants and contributors to this book.)
• Force and Motion by Peter Lafferty. Dorling Kindersley, 2000. A classic DK Eyewitness books that covers the history of science as well as modern technology. Dated, but still useful.

• Mechanical Engineering Principles by John Bird and Carl Ross, 2014. A comprehensive (288 page) introduction to the general science and principles of mechanical engineering.
• A treatise on belts and pulleys by John Howard Cromwell, 1903. A classic book from an earlier age! Explains the theory of pulleys (with mathematics) and lots of illustrations. Available in various electronic book formats.

### Videos

• How pulleys work: A simple introduction by Charlie Marz. Unfortunately, he uses Imperial (American) units of feet and pounds, but you get the idea. If you're European, you can substitute meters and kilograms in your mind.
• How pulleys work: A longer and more involved introduction from Khan Academy. This one is explained clearly and very well, but suffers from scribbled mouse drawing and mixing up the units (Newtons, feet, meters).

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