#870 Why does a pulley make weights easier to lift?

Why does a pulley make weights easier to lift? They increase mechanical advantage.

The pulley is an invaluable invention that has helped humankind immeasurably. Without it, many of the things we take for granted, such as elevators, wouldn’t work. The pulley was possibly invented in Ancient Egypt in roughly 2600 BC. A pulley has been found from 1990 BC, but it is thought that the Egyptians used pulleys to lift the enormous stone blocks that were used to make the Great Pyramid. It is thought that the pulley could have been invented even earlier in Mesopotamia. The first civilization sprang up in the Fertile Crescent and the first cities were built here. Archaeologists think that the new agriculture, irrigation, and building would have necessitated the invention of a pulley because people wouldn’t have been able to lift the weights without it.

A pulley can make it much easier to lift any weight, assuming the pulley and the ropes or chains are strong enough. However, a pulley doesn’t reduce the weight of the object, it just reduces the force required to lift it.

To talk about force, we need to look at mass, weight, and force first. Mass is the amount of matter that an object has. It is dictated by the amount of atoms in it and what type of atoms they are. The mass of an object never changes, whether you are in a vacuum or standing on the surface of the sun. The weight of an object is how much gravity is acting on it. If I have a 1 kg bag of coffee on my table, it has a mass of 1 kg and a weight, here on Earth, of 1 kg. If I take that bag of coffee to the surface of the sun, it still has a mass of 1 kg, but its weight is now about 28 kg. A force is something external that can change a body’s state of rest or motion. Forces are measured in Newtons. If I pick that 1 kg bag of coffee up off the table, I have to overcome the weight of 1 kg, which means I need a force that is equal to 1 kg, which is 9.81 Newtons (Let’s call it 10). My body makes this force by burning sugar to make energy.

So, how does a pulley reduce the force it takes to lift an object? Let’s imagine you have a box that weighs 200 kg and you want to put it on top of a 2 m high table. If you put your hands on either side of the box and lift, your body will have to generate a force to overcome the 200 kg, which is about 2,000 N. There are people that can do that, but it is not easy. Many of us find it easier to pull than to lift, which is why we can push a car, but not lift a car. If you use a pulley with one wheel you can change the direction of the force. Let’s tie a rope to the top of our box and fasten a pulley to the roof. A pulley is a box that holds a free spinning wheel that has a groove in it to hold a rope or a chain. We feed the rope through the pulley and now if we pull the rope horizontally, we can lift the box vertically. This has not reduced the force, but it has changed the direction. We have to pull the rope 2 m to raise the box 2 m and we have to apply 2,000 N of force.

The magic of a pulley comes in when we increase the number of wheels. If we add a second wheel to our pulley, we now only have to apply 1,000 N of force to lift the same weight, but we have to pull the rope for 4 m instead of 2 m. That is because the second wheel puts a loop in the rope so when you are pulling the box, two pieces of rope are pulling at the same time. You only need to put 1,000 N of force on each half of the rope to pull the weight. However, you sacrifice distance. You now have to pull the two pieces of rope 2 m each, which is a total of 4 m. Every time you add a wheel, it reduces the amount of force you need to use. If you have 4 wheels, you only need to supply 500 N, which is one quarter of the 2,000 N we need, but you need to pull the rope 8 m. If you have ten wheels in the pulley, you only need to use 200 N of force, but you need to pull the rope for 20 m. The more wheels you add to the pulley, the less force you need to lift the weight, but the longer rope you need.

It seems confusing, but each wheel adds an extra piece of rope that is lifting its share of the weight. Thinking about them as people can help. If one person lifts 200 kg, they need 2,000 N and they only have to pull one rope the required distance. If 10 people lift 200 kg with one rope each, they only need to provide 200 N apiece, but they need to pull ten pieces of rope the required distance, which makes it ten times longer.

We use pulleys everyday in so many ways. An elevator is a very good example. To lift an elevator full of people would require a huge force, but that force can be lowered by using pulleys. Cranes use them as well. They are everywhere. And this is what I learned today.

Photo by Skitterphoto: https://www.pexels.com/photo/brown-rope-on-a-pulley-69756/

Sources

https://info.designatronics.com/blog/pulleys-did-you-know

https://byjus.com/physics/force/