Figure 1. Notice the pulleys used by this by this crane — an example of how a modern device uses simple machines to perform complex tasks. copyright

General knowledge of pyramids. Familiarity with the six simple machines introduced in Lesson 1 of this unit.

We are well underway in learning about simple machines and building the ancient Egyptian pyramids that we have been hired as engineers to design and construct. Now, we are going to go deeper into our understanding of pulleys to see if we can use this knowledge to help make our work easier.

No one knows for sure if pulleys were one of the simple machines that ancient cultures used to build pyramids. A few people believe that the beautiful and massive pyramids could not possibly have been built using something as simple as simple machines. Some people have wild theories about how the pyramids came to be — that perhaps aliens from another planet came to Earth and built them. Well, we do not know about that, but we do know that human beings are very creative and resourceful when they want to be. As long as we limit ourselves to materials and technologies that would have been available to the ancient Egyptians, it is acceptable for us to use our knowledge to construct pulley systems to build our pyramid.

Figure 2. A pulley on a fishing boat. copyright

A pulley is a simple machine consisting of a string (or rope) wrapped around a wheel (sometimes with a groove) with one end of the string attached to an object and the other end attached to a person or a motor. Pulleys may seem simple, but they can provide a powerful mechanical advantage so lifting tasks may be done easily.

Pulleys are used in many ways, everyday. What kind of pulleys can you think of? Some common examples are large construction cranes that use pulleys to lift heavy objects with what would normally be a very underpowered motor (see Figure 1), weight machines at a gym, some elevators, flagpoles, window blinds, bicycle rings/chains, clotheslines, water well bucket/rope, zip lines, motors, rock climbing devices, and sailing and fishing boats (see Figure 2).

An elevator is a modern engineering use of a pulley system that performs much like the raising of a large stone for pyramid building. Without the use of pulleys, an elevator would require a large motor to pull the cable straight up. Instead of using a large motor, some elevators use a large weight that takes advantage of gravity to help raise the elevator car (see Figure 3). In this situation, the powering motor can be much smaller and only be used to determine the direction the elevator should go.

Figure 3. Adding a counterweight and two pulleys with a motor in the middle makes an elevator easier to move. copyright

But how can a wheel with string over it help us move the huge stones required to build a pyramid? Well, pulleys help us by changing the direction of the force we use to lift an object. Is it easier for you to pull up on a rope or pull down on a rope? By using a pulley, we do not have to pull up on a rope to lift a heavy object attached to it, but instead we can pull down on it. Think of a flagpole as an example. When you pull down on the rope of a flagpole, the flag goes up the pole to wave in the air. That's because a flagpole has a pulley on it. By using pulleys to redirect force, a stone could be lifted off the ground, allowing more people to grab on to the rope, and adding weight so workers have to pull less. To simplify this effort even more, workers using a pulley could move a large stone up a ramp by pulling on a rope while walking down the ramp, using gravity to their advantage.

The real mechanical advantage of a pulley is in using many pulleys at once. Using multiple pulleys decreases the amount of force necessary to move an object by increasing the amount of rope used to raise the object. The mechanical advantage (MA) of a pulley system is equal to the number of ropes supporting the movable load. (That means, do not count ropes that are only used for redirecting, see Figures 6 and 7.) We know from other lessons on simple machines that to gain a greater mechanical advantage, there is a trade-off. With a pulley, the trade-off is distance. So, if two pulleys are used together, the amount of force required is cut in half, but twice the amount of rope is needed to be pulled to raise the object to the same desired height. (Illustrate this concept to students by conducting the following classroom demonstration; see Figure 4.)

Figure 4. (left) Using one wrap of the rope, it is difficult to pull the brooms together. (right) Using several wraps makes it easier to pull the brooms together. copyright

How can pulleys make our lives easier? Pulleys are powerful simple machines. They can change the direction of a force, which can make it much easier for us to move something. If we want to lift an object that weighs 10 kilograms one meter high, we can lift it straight up or we can use a pulley, so we can pull down on one end to lift the object up. It is much easier to use the pulley because, as long as we weigh more than 10 kilograms, we can just hang onto the end of the rope and take advantage of gravity so our weight provides all the necessary force to lift the object.

Pulleys can also provide us with a mechanical advantage when we use several together and more rope. This process lessens the amount of force required to lift something.

While we do not know if pulleys were used by ancient pyramid builders, we know pulleys are an ideal simple machine for many of the tasks required to build a pyramid. In today's highly-technical world, engineers still use pulleys to make difficult tasks easier. Without them, our lives would be much more difficult.

Conduct summary assessment activities as described in the Assessment section. Conclude by finishing the KWL Chart and assigning Word Problems in which students calculate the mechanical advantage of an inclined plane (see the Assessment section).

In other lessons of this unit, students study each simple machine in more detail and see how each could be used as a tool to build a pyramid or a modern building.