# Pulleys: Basic Mechanics

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• 0:01 Machines Multiply Force
• 2:15 What Is a Pulley?
• 4:56 Pulleys in the Real World
• 6:12 Lesson Summary

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Lesson Transcript
Instructor: Sarah Friedl

Sarah has two Master's, one in Zoology and one in GIS, a Bachelor's in Biology, and has taught college level Physical Science and Biology.

Like other simple machines, pulleys can help us lift and move heavy loads with less effort. In this video lesson, you'll learn how pulleys do this as well as how this is possible while still obeying the law of conservation of energy.

## Machines Multiply Force

A long time ago, there lived a smart guy named Archimedes. One day, Archimedes wrote a letter to the king. In this letter, Archimedes boasted to the king that if he had enough pulleys, he could move the entire world! The king knew Archimedes was smart, but he still understood the enormity of this claim and decided to make a bet with Archimedes.

He challenged Archimedes to move one of the ships in his arsenal. This ship was so large that it would take a great number of very strong men to move it, but Archimedes was not worried because he knew he had physics on his side! So the king loaded up the ship with cargo and passengers, while Archimedes sat far away and pulled his rope through the pulley system, moving the ship along with just his own two hands.

Though he lived a long time ago, you could say Archimedes was way ahead of his time! He understood machines and how they can be used to help do work that would otherwise be quite difficult. In fact, not only was he a great physicist and engineer, but he was also an inventor, designing machines like the lever, pump, and pulley.

A machine is something that multiplies or changes the direction of a force. In other words, you can essentially do more with less, so it's easier to move larger, heavier objects.

But this 'more with less' isn't exactly true. Machines still follow the law of conservation of energy, which states that the total amount of energy never changes. Energy can change from one form to another or transfer from one object to another, but it can't be created or destroyed.

So how then are you able to lift a heavier object without exerting more effort? We do this by increasing the distance of the work. You may remember from a previous lesson that work is simply force x distance. Because work is proportional to both force and distance, if you increase the force, more work is done. But if you increase the distance, more work is also done.

And because we follow the law of conservation of energy, for any machine, work input = work output. Using what we know about work, we can look at this in another way: (force x distance) input = (force x distance) output.

## What Is a Pulley?

Looking at it this way helps us understand how a pulley makes it easier to move heavier objects, like when Archimedes moved the king's ship. A pulley is a wheel that supports movement through a rope or cable. It's called a pulley because its main job is to, well, pull things!

For this lesson, we will assume that there is no friction between the pulley and the rope moving through it. We will also assume that the pulley's weight is negligible compared to the weight of the object, so we won't worry about that either.

There are two types of pulleys, and the assistance they offer with lifting heavy objects is a bit different. With a fixed pulley, the pulley is attached to the ceiling, so it's fixed in place. A rope runs through the pulley with an object attached to one end and you holding the other end. As you pull down on the rope, the object is lifted into the air so the direction of the force changes. Unfortunately, only the direction of the force is changed, not the magnitude. So we can lift this object higher in the air, but we don't get any assistance with the heaviness of the load.

In contrast, a movable pulley moves with the rope as it is pulled, so it both magnifies and changes the direction of the force. With a movable pulley, we can lift an object with less force because, as you pull up on one end, the weight of the object is distributed over the two sides of the rope. It's like lifting the object with two ropes instead of one! With this type of pulley, each side of the rope supports half of the object's weight so the load can be lifted with half the input force.

You may think this violates the law of conservation we discussed before, but there's something else going on here. Remember how work input = work output? Since work is force x distance, this means that as one changes, the other does as well in order to keep the equation equal. So if the force of the work input decreases, this means that the distance of the work input must increase to compensate. Likewise, if the force of the work output increases, the distance of the work output decreases.

Say you need to lift a pail of water from a deep well. Using a movable pulley, you can lift this pail with half the force, but you will have to use twice as much rope to do so. The pail only moves half the distance that your end of the rope did because the force it is lifted with is twice as much. For example, you would need to pull 2 meters of rope for every 1 meter that you raise the pail of water.

Who says you need just one pulley, though? Archimedes knew that he couldn't move the king's ship unless he used multiple pulleys. In fact, each time the rope is looped through a pulley, you increase the input distance and therefore the output force.

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