Lesson: Slide Right on By Using an Inclined PlaneContributed by: Integrated Teaching and Learning Program, College of Engineering, University of Colorado Boulder
Educational Standards :
Pre-Req Knowledge (Return to Contents)
General knowledge of pyramids. Familiarity with the six simple machines introduced in Lesson 1 of this unit.
Learning Objectives (Return to Contents)
After this lesson, students should be able to:
Introduction/Motivation (Return to Contents)
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 & Concepts for Teachers (Return to Contents)
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.
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.
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 (Return to Contents)
Associated Activities (Return to Contents)
Lesson Closure (Return to Contents)
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 (Return to Contents)
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.
Informal Discussion: Solicit, integrate and summarize student responses on the board.
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.
Lesson Extension Activities (Return to Contents)
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:
References (Return to Contents)
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
ContributorsTravis 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.
Copyright© 2005 by Regents of the University of Colorado.
Supporting Program (Return to Contents)Integrated Teaching and Learning Program, College of Engineering, University of Colorado Boulder
Acknowledgements (Return to Contents)
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.