# Lesson: Slide Right on By Using an Inclined Plane

### Summary

Students explore building a pyramid, learning about the simple machine called an inclined plane. They also learn about another simple machine, the screw, and how it is used as a lifting or fastening device. During the associated hands-on activity, students see how the angle of inclination and pull force can make it easier (or harder) to pull an object up an inclined plane.

### Engineering Connection

Engineers use simple machines to build taller, stronger and more durable buildings. They use inclined planes in the design of many devices. For example, ramps are inclined planes that make it easier for people in wheelchairs move to a higher location instead of using the stairs. Parking garages are designed on the use of inclined planes to get cars to the next level of parking. Screws are used to raise something or fasten two or more things together. Engineers design machines around large screws, such as drilling rigs to raise oil or dirt, and use smaller screws to fasten together a wide range of items, from the space shuttle to an electric toothbrush.

### Pre-Req Knowledge

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

### Learning Objectives

After this lesson, students should be able to:
• Describe inclined planes and how engineers use them in their everyday applications.
• Define a screw as is an inclined plane wrapped around a rod.
• Explain how a screw can be used to move materials, like rock, upwards.
• Describe how engineers take simple machines into consideration when designing contemporary projects.

### Introduction/Motivation

Simple machines help us complete a task more easily. What are some of the simple machines we have been studying? (Possible answers: Wedge, wheel and axle, lever, inclined plane, screw and pulley.) Today we are going to look at two of the six simple machines— the inclined plane and the screw.
The inclined plane is often the simplest of all the simple machines because it does not move when you use it; it just sits still. The purpose of an inclined plane is to move something from a lower height to a higher height. An inclined plane can be something as simple as a driveway or a staircase. Have you ever used one of these?
An inclined plane works by helping you lift things up to a higher level. Have you ever tried to carry something heavy up a ladder? It's pretty hard! How about carrying that object up a staircase instead? Is that easier? It sure is! Carrying a heavy object up a staircase is easier than a ladder, and carrying it up a smooth ramp is even easier. Why is that so? (Answer: You do not have to lift as much with your legs.)
There is always a trade-off, though, to moving something in a way that takes less effort. In an inclined plane the trade-off is distance. If you compare the length of a ladder to that of a ramp going up to the second floor of a building, you find that the length of the ladder is much shorter. The distance up the ramp is longer but it takes less effort to walk up. Have you experienced this mechanical advantage? People from ancient cultures figured this out a long time ago when they built the pyramids using long ramps to help them move the heavy stones to the top! Mechanical engineers today use inclined planes in many engineering designs for moving things up such as parking garages, tow trucks, conveyer belts and escalators.
A screw is another form of an inclined plane; it is simply an inclined plane wrapped around a rod, like a spiral. (If available, pass around a few screws for the students to examine.) A screw is also the second simple machine we are going to study today. Can you think of some everyday examples of inclined planes or screws? (Answers: Ladder, ramp, slide, stairs, bolt, screw, drill.)
While a screw is considered a simple machine, it depends upon another simple machine, the lever, to do work Have you ever seen or used a screw to hold some wood together? How do you get the screw into the wood? Well, you use a screwdriver or a drill. The screwdriver is a type of lever that helps turn the screw into the wood. A screw is really just a cylinder with an inclined plane wrapped around it. The pointed end of a screw works like a wedge (another simple machine!), but the screw is different from a wedge because it gets its power from being turned by a lever, not from applying a direct force to push it into an object.
A screw can function in two ways: it can raise up a weight, and it can fasten two or more objects together. An example of using a screw to raise a weight is when it is used to get oil. Oil coming from a deep well can easily be pumped out with the aid of the pumping screw. Archimedes was a famous mathematician and inventor who more than two thousand years ago designed the Archimedes screw — a machine that was turned by horses or people to raise water.
When we use a screw to fasten objects, the screw converts rotating motion of turning the screw into straight-line motion of the screw into wood or other material. That is what gives the screw its mechanical advantage. It takes less force to turn a screw into a hard material than to pound a wedge into the same material. Engineers today use screws in many engineering applications and designs such as drilling rigs that bring up oil, dirt or water. Have you ever seen a car jack raise a car to help change a flat tire? Well, that is an example of a screw as well. Engineers also use screw as fasteners for large objects such as sports stadiums or airplanes, and for smaller objects such as desks or MP3 players. Today we are going to take a closer look at two simple machines — the inclined plane and the screw. How do you think they may have helped build the ancient pyramids?

### Lesson Background and Concepts for Teachers

The mechanical advantage of a machine is the ratio of the load to the applied force. In other words, mechanical advantage determines how much force we need to perform a task. For example, the greater the mechanical advantage of a machine, the less force we need to have to perform a task such as moving an object. The opposite is true as well. Mathematically, mechanical advantage (MA) = load ÷ applied force. A good mechanical advantage is one that is greater than 1.

Inclined Plane

The purpose of an inclined plane as a simple machine is to move something from a lower height to a higher height with less effort. An object simply placed on a tilted surface often slides down the surface (see Figure 1) because of the force in the downhill direction. In other words, the forces in this scenario are unbalanced (i.e. there is no upward force to counteract the downward force and therefore, the object would slide down).The rate at which the object slides down is dependent upon how tilted the surface is; the greater the tilt of the surface, the faster the rate at which the object will slide down it. This is measured by the angle of inclination. Students can find this using a protractor. Friction also affects the movement of an object on a slope. Friction is a force that offers resistance to movement when one object is in contact with another. Imagine now that you were on the downside of the object and applying force to keep the object in the same place (not moving). To keep the object stationary, the force you would have to apply would need to equal the downward force due to gravity. That would be an example of balanced forces. If you wanted to push the force upwards, you would need to exceed the force of gravity.
To understand an object's motion on an inclined plane, it is important to analyze the forces acting upon it. The force of gravity (also known as weight) acts in a downward direction. When the angle of inclination is greater, and the slope is steeper there is more weight component to overcome. With a shallower slope the weight component is easier to overcome and requires less effort.
The mechanical advantage of an inclined plane depends upon its slope and height. To find the mechanical advantage of an inclined plane, divide the length of the slope by its height.
Mechanical advantage of an inclined plane = length of slope ÷ height of plane
An inclined plane produces a mechanical advantage to decrease the amount of force needed to move an object to a certain height; it also increases the distance the object must move. The object moving up an inclined plane needs to move the entire length of the slope of the plane to move the distance of the height. For example, if you have a ramp with a slope length 20 meters that rises 5 meters high, then your trade-off is moving the 20 meters distance versus lifting straight up 5 meters, and your mechanical advantage is 4.

Screw

A screw is a simple machine that has two purposes. It can be used to fasten two or more objects together or it can be used to lift up a heavy object. In most applications, a lever is used to turn the screw. A good example of this is a screwdriver. It is the circumference of the lever or screwdriver and the pitch of the screw that determines the mechanical advantage of the screw.
The pitch of a screw is the distance between adjacent threads on that screw. The pitch can be calculated by dividing a certain distance by the number of threads on screw. For example, if you have a screw fastener with 5 threads over an inch of the screw, then the pitch of the screw is 1/5. One complete revolution of the screw into an object is equal to the distance of the pitch of a screw. Or, in this example, one turn of the screw would move the screw a distance of 1/5 inch.
The mechanical advantage of a screw is found approximately by dividing the circumference of the lever by the pitch of the screw. For example, if an 8 inch wrench is used to tighten a bolt with a pitch of 1/5 inch, then the mechanical advantage is π*8 inches / (1/5 inch)= 126.
Mechanical advantage of a screw = circumference ÷ pitch
If our same screw with 1/5 pitch is turned using a 1-inch circumference screwdriver, then the mechanical advantage becomes 1 ÷ 1/5, or 5.

### Vocabulary/Definitions

 The angle on the bottom of the ramp, formed by the ramp and a horizontal line (see Figure 1). A force that resists motion between two bodies in contact. Sloping, slanting or leaning. To deviate from the horizontal. 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. 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. A region extending south and east from central Mexico to include parts of Guatemala, Belize, Honduras and Nicaragua. In pre-Columbian times it was inhabited by diverse civilizations, such as the Mayan and the Olmec. A large block of stone, especially one used in architecture or sculpture. The vertical distance between two threads on a screw. The cause of motion or change. 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. ramp: An inclined surface or roadway connecting different levels. A simple machine that lifts or holds materials together. Often a cylindrical rod incised with a spiral thread. 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. An inclined line, surface, plane, position or direction. The amount or degree of deviation from the horizontal. A curve that winds around a fixed center point (or axis) at a continuously increasing or decreasing distance from that point.

### Associated Activities

• Watch It Slide! - Students recreate the difficult task of raising a monolith of rock to build a pyramid using inclined planes. They compare the push and pull of different-sized blocks or objects up an inclined plane. They determine the angle of inclination, and learn the changes that happen when the angle is increased or decreased.

### Lesson Closure

Today, we learned about two simple machines; the inclined plane and the screw. Who can give me an example of an inclined plane? (Possible answers: Ramp, staircase, escalator.) How does an inclined plane help us do work? (Possible answer: We push objects up an inclined plane.) What is the trade-off? (Answer: Distance) What are two ways screws are used? (Answer: To fasten objects or to lift something.) What other simple machine often helps us use a screw? (Answer: A lever.) What has an engineer designed that uses an inclined plane or a screw? (Possible answers: Parking garage, ramp, escalator, drilling rig, holding parts of something together, such as an airplane or MP3 player.)
Conduct summary assessment activities as described in 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.

### Assessment

Pre-Lesson Assessment

Know / Want to Know / Learn (KWL) Chart: Create a classroom KWL chart to help organize learning about a new topic. On a large sheet of paper or on the classroom board, draw a chart with the title "Simple Machines: Inclined Planes and Screws." Draw three columns titled, K, W and L, representing what students know about inclined planes and screws, what they want to know about inclined planes and screws and what they learned about inclined planes and screws and their mechanical advantages. Fill out the K and W sections during the lesson introduction as facts and questions emerge. Fill out the L section at the end of the lesson.

Post-Introduction Assessment

Informal Discussion: Solicit, integrate and summarize student responses on the board.
• What are some everyday examples of inclined planes? (Possible answers: Wheelchair ramp, sidewalk curb that turns into a ramp for strollers and bicycles, playground slide, slide that sends gumballs out of the machine, ladder, escalator.)
• What are some everyday examples of screws? (Possible answers: Drilling rig, car jack, bolt, screw fasteners that hold parts of something together, such as an airplane or MP3 player.)
• How do engineers use inclined planes and screws in modern designs? (Possible answers: Inclined planes are incorporated into the design of conveyor belts or ramps used to move objects up. Parking garages are designed using large inclined planes. Screws are used in fastening objects together, such as airplanes and computers, and to bring up material, as in drilling for oil, water or dirt.)

Lesson Summary Assessment

KWL Chart (Conclusion): As a class, finish column L of the KWL Chart as described in the Pre-Lesson Assessment section. List all of the things students learned about inclined planes and screws and their mechanical advantages. Were all of the W questions answered? What new things did they learn?
Closing Discussion: Ask students to explain why it is easier to pull a cart or block up a long, shallow ramp than taking it up steps, a ladder or a steep ramp. Ask them to give examples of mechanical advantage using an inclined plane or a screw.
Bingo: Provide each student with a sheet of paper containing a list of the lesson vocabulary terms. Have each student walk around the room and find a student who can define one vocabulary term. Students must find a different student for each word. When a student has all terms completed s/he shouts "Bingo!" Continue until two or three (or most) students have bingo. Ask the students who shouted "Bingo!" to give definitions of the vocabulary terms.
Using the Equations: Provide additional sample problems (similar to the examples given in the Lesson Background) for students to calculate themselves the mechanical advantage of an inclined plane and of a screw. Have them use the equations provided in the Lesson Background for the mechanical advantage of an inclined plane and a screw.
• Examples: A handicap ramp has a length of 24 feet and rises 2 feet high. What is the mechanical advantage of the ramp? (Answer: 24/2 = 12)
• A standard ¼-20 screw has 20 threads/inch. What is the mechanical advantage if you use a screwdriver with a circumference of 2 inches? (Answer: 2/(1/20)=40)

### Lesson Extension Activities

Have students build upon their understanding of inclined planes by discussing different uses for ramps. In what situation might you make a ramp shorter/longer, shallower/steeper? When might you add friction to make the ramp work better? Draw pictures of different ramps for different uses. How do they differ?
Have students look at an assortment of different screws and calculate the mechanical advantage of each. Which one has the greatest mechanical advantage, the least? Have them screw different fasteners into wood. Can you feel and see the difference in mechanical advantage of a screw that has close threads vs. one that has threads farther apart?
Have students research Archimedes' screw and write a brief report describing how this device works, drawing sketches and providing their own examples of everyday ways it might be used to help people.
Have students investigate balanced versus unbalanced forces on their own at home. Instruct them to follow these steps and answer the given questions:
• Construct two inclined planes out of everyday materials in your home (e.g. cereal boxes, books, etc.). Make sure one has a steep slope and one has a shallower slope.
• Pick an object that rolls (i.e. marble, toy car, etc).
• Unbalanced forces: Put the object on the top of the inclined plane and observe what it does. Does it roll down? If so, why? (Answer: The object should roll down both planes because unbalanced forces cause motion of an object in the direction of net force.)
• Balanced forces: Now, apply your finger to the bottom of the object to hold it in place. Do this with both planes. On which plane did you have to apply more force to balance the forces? (Answer: The steeper plane.) When forces are balanced, does an object move? (Answer: No. Balanced forces cause an object to stay in the same place.)

### References

Henderson, Tom. Lesson 3: Forces in Two Dimensions: Inclined Planes. The Physics Classroom (a high school physics tutorial). Accessed January 25, 2006. http://www.compadre.org/precollege/items/detail.cfm?ID=2014

Wright, Richard. Ladies and gentleman... the inclined plane! PCS Education Systems, Inc. Accessed January 25, 2006. http://www.weirdrichard.com/inclined.htm

### Contributors

Travis Reilly, Malinda Schaefer Zarske, Lawrence E. Carlson, Jacquelyn F. Sullivan, Denise W. Carlson, with design input from the students in the spring 2005 K-12 Engineering Outreach Corps course.

© 2005 by Regents of the University of Colorado.

### Supporting Program

Integrated Teaching and Learning Program, College of Engineering, University of Colorado Boulder

### Acknowledgements

The contents of these digital library curricula were developed by the Integrated Teaching and Learning Program under National Science Foundation GK-12 grant no. 0338326. However, these contents do not necessarily represent the policies of the National Science Foundation, and you should not assume endorsement by the federal government.