Mechanical Advantage, Efficiency, & Simple Machines
After this lesson, students should be able to:
- Understand Mechanical Advantage and Efficiency
- Understand what a simple machine is and how it would help an engineer to build something.
- Identify six types of simple machines.
- Understand how the same physical principles used by engineers today to build skyscrapers were employed in ancient times by engineers to build pyramids.
Course Digital Resources:
Design: (verb) To plan out in systematic, often graphic form. To create for a particular purpose or effect. Design a building. (noun) A well thought-out plan.
Engineering: Applying scientific and mathematical principles to practical ends such as the design, manufacture and operation of efficient and economical structures, machines, processes and systems.
Force: A push or pull on an object.
Inclined plane: A simple machine that raises an object to greater height. Usually a straight slanted surface and no moving parts, such as a ramp, sloping road or stairs.
Lever: A simple machine that increases or decreases the force to lift something. Usually a bar pivoted on a fixed point (fulcrum) to which force is applied to do work.
Mechanical advantage : An advantage gained by using simple machines to accomplish work with less effort. Making the task easier (which means it requires less force), but may require more time or room to work (more distance, rope, etc.). For example, applying a smaller force over a longer distance to achieve the same effect as applying a large force over a small distance. The ratio of the output force exerted by a machine to the input force applied to it.
Pulley: A simple machine that changes the direction of a force, often to lift a load. Usually consists of a grooved wheel in which a pulled rope or chain runs.
Pyramid: A massive structure of ancient Egypt and Mesoamerica used for a crypt or tomb. The typical shape is a square or rectangular base at the ground with sides (faces) in the form of four triangles that meet in a point at the top. Mesoamerican temples have stepped sides and a flat top surmounted by chambers.
Screw: A simple machine that lifts or holds materials together. Often a cylindrical rod incised with a spiral thread.
Simple machine: A machine with few or no moving parts that is used to make work easier (provides a mechanical advantage). For example, a wedge, wheel and axle, lever, inclined plane, screw, or pulley.
Spiral: A curve that winds around a fixed center point (or axis) at a continuously increasing or decreasing distance from that point.
Tool: A device used to do work.
Wedge: A simple machine that forces materials apart. Used for splitting, tightening, securing or levering. It is thick at one end and tapered to a thin edge at the other.
Wheel and axle: A simple machine that reduces the friction of moving by rolling. A wheel is a disk designed to turn around an axle passed through the center of the wheel. An axle is a supporting cylinder on which a wheel or a set of wheels revolves.
Work: Force on an object multiplied by the distance it moves. W = F x d (force multiplied by distance).
Why do engineers care about simple machines? How do such devices help engineers improve society? Simple machines are important and common in our world today in the form of everyday devices (crowbars, wheelbarrows, highway ramps, etc.) that individuals, and especially engineers, use on a daily basis. The same physical principles and mechanical advantages of simple machines used by ancient engineers to build pyramids are employed by today’s engineers to construct modern structures such as houses, bridges and skyscrapers. Simple machines give engineers added tools for solving everyday challenges.
Task #1 ( Engineering Challenge)
How did the Egyptians build the Great Pyramids thousands of years ago (~2,500 BCE)? Could you build a pyramid using 9,000-kilogram (~10-ton or 20,000-lb) blocks of stone with your bare hands? That’s like trying to move a large elephant with your bare hands! How many people might it take to move a block that big? It would still be a challenge to build a pyramid today even with modern tools, such as jackhammers, cranes, trucks and bulldozers. But without these modern tools, how did Egyptian workers cut, shape, transport and place enormous stones? Well, one key to accomplishing this amazing and difficult task was the use of simple machines.
Simple machines are devices with no, or very few, moving parts that make work easier. Many of today’s complex tools are really just more complicated forms of the six simple machines. By using simple machines, ordinary people can split huge rocks, hoist large stones, and move blocks over great distances.
However, it took more than just simple machines to build the pyramids. It also took tremendous planning and a great design. Planning, designing, working as a team and using tools to create something, or to get a job done, is what engineering is all about. Engineers use their knowledge, creativity and problem-solving skills to accomplish some amazing feats to solve real-world challenges. People call on engineers to use their understanding of how things work to do seemingly impossible jobs and make everyday activities easier. It is surprising how many times engineers turn to simple machines to solve these problems.
Imagine that you are living in 6,000 BCE and have been hired as chief engineers for a pyramid building project. The construction of the pyramids was an amazing feat, one of the Seven Wonders of the World. How did people move the massive 9,000 to 18,000 kilogram stones (equals 10-20-tons or one to two elephants!) into position? How were they arranged into such a precise and beautiful shape? It would be an incredibly complicated project to build the pyramids today, even with modern equipment and technology, but think about how difficult it must have been to do it 8,000 years ago. Instead of using today’s automated, high-powered tools, trucks and cranes, they used simple machines and the hard labor of many people. Can you imagine? During this unit, we are going to get a taste of how difficult that massive undertaking was as we design and build a pyramid, as if we were living in ancient times.
Building a pyramid is a huge project, so let’s take it step by step. The first step is to choose a location. Maybe you have heard this advice before: “The three most important factors of any real estate are location, location, location.” There are many considerations in choosing a location. The location at which we decide to build our pyramid influences its structural safety and stability (will it hold up), its accessibility (closeness) for transporting materials to the site, the difficulty to build the pyramid, its total cost, and how convenient it is for people to visit.
For your project today, a surveyor was commissioned to examine four possible sites at which the pyramid could be built. He will provide the engineering project teams with his evaluation of each site. As chief engineers for the project, it is up to you to select the location for the pyramid. Let’s make some decisions about what characteristics we want in our site. We should consider:
- How close do we want the site to be to the quarry (the source of the stones)?
- Must the site be flat or can we make an angled foundation work?
- Could our foundation be made of sand or must it be rock?
- Do we want the site to be near or far from the river, and why?
- Are there reasons why we would want the pyramid to be close to the palace? Or, would it be better to be far from the palace?
- Should the pyramid be located near or far from a city?
Like engineers, determining the answers to these questions helps us identify the features we want in a building site. Next, we can rank these preferences so it is clear which are the most important to our project team. We will use the surveyor’s descriptive information to compare the sites. We will base our site decision on the logic of our team’s values and priorities, which we will communicate clearly to the Egyptian leader when we explain our reasons for choosing that site.
Video – Pyramids (Flyover)
Video – Building the Pyramids of Egypt
Before you turn in your Assignment #1 make sure you have considered these questions:
- What is the advantage of this site?
- What are some possible disadvantages?
- How might these disadvantages be overcome?
- Examine closely the environmental and weather conditions in the Egyptian desert because these are additional factors to consider in a huge construction project
For the other sites consider these questions:
- What, if any, were some positive features of this site?
- What were the negative features of this site?
- Why did you decide against this site?
Task #2 (Unit 7 Exam)
Now it is time to take the test!
Go to Socrative.com
Enter room “A89559b4”
There are 40 questions total to take. You must get above a 70% to pass the exam.
Common Core State Standards (California):
L.7.3a. Choose language that expresses ideas precisely and concisely, recognizing and eliminating wordiness
Next Generation Science Standards:
HS-PS2-1. Analyze data to support the claim that Newton’s second law of motion describes the mathematical relationship
among the net force on a macroscopic object, its mass, and its acceleration. [Clarification Statement: Examples of data could
include tables or graphs of position or velocity as a function of time for objects subject to a net unbalanced force, such as a falling object, an object rolling down a ramp, or a moving object being pulled by a constant force.] [Assessment Boundary: Assessment is limited to one-dimensional motion and to macroscopic objects moving at non-relativistic speeds.]
HS-PS2-2. Use mathematical representations to support the claim that the total momentum of a system of objects is
conserved when there is no net force on the system. [Clarification Statement: Emphasis is on the quantitative conservation of momentum in interactions and the qualitative meaning of this principle.] [Assessment Boundary: Assessment is limited to systems of two macroscopic bodies moving in one dimension.]