In this lesson, students are introduced to both potential energy and kinetic energy as forms of mechanical energy. A hands-on activity demonstrates how potential energy can change into kinetic energy by swinging a pendulum, illustrating the concept of conservation of energy. Students calculate the potential energy of the pendulum and predict how fast it will travel knowing that the potential energy will convert into kinetic energy. They verify their predictions by measuring the speed of the pendulum.
Each TeachEngineering lesson or activity is correlated to one or more K-12 science, technology, engineering or math (STEM) educational standards.
All 100,000+ K-12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standard Network (ASN), a project of JES & Co. (www.jesandco.org).
In the ASN, standards are hierarchically structured: first by source; e.g., by state; within source by type; e.g., science or mathematics; within type by subtype, then by grade, etc.
Click on the standard groupings to explore this hierarchy as it applies to this document.
- Colorado: Math
- 2. describe patterns using variables, expressions, equations, and inequalities in problem-solving situations; (Grades 5 - 8)  ...show
- 4. distinguish between linear and nonlinear functions through informal investigations; and (Grades 5 - 8)  ...show
- 5. solve simple linear equations in problem-solving situations using a variety of methods (informal, formal, graphical) and a variety of tools (physical materials, calculators, computers). (Grades 5 - 8)  ...show
- 2. construct, use, and explain procedures to compute and estimate with whole numbers, fractions, decimals, and integers; (Grades 5 - 8)  ...show
- 4. select and use appropriate algorithms for computing with commonly used fractions and decimals, percents, and integers in problem-solving and determine whether the results are reasonable. (Grades 5 - 8)  ...show
- a. Add, subtract, multiply and divide rational numbers including integers, positive and negative fractions and decimals (Grade 8)  ...show
- b. Use representations of linear functions to analyze situations and solve problems (Grade 8)  ...show
- Colorado: Science
- Common Core State Standards for Mathematics: Math
- 3. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. (Grade 6)  ...show
- 4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R. (Grades 9 - 12)  ...show
- b. Solve quadratic equations by inspection (e.g., for x<sup>2</sup> = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. (Grades 9 - 12)  ...show
- International Technology and Engineering Educators Association: Technology
- E. Energy is the capacity to do work. (Grades 6 - 8)  ...show
- Next Generation Science Standards: Science
- Develop a model to describe that when the arrangement of objects interacting at a distance changes, different amounts of potential energy are stored in the system. (Grades 6 - 8)  ...show
- Construct, use, and present arguments to support the claim that when the motion energy of an object changes, energy is transferred to or from the object. (Grades 6 - 8)  ...show
- Recognize that engineers need to understand the many different forms of energy in order to design useful products
- Explain the concepts of kinetic and potential energy.
- Understand that energy can change from one form into another.
- Understand that energy can be described by equations.
Lesson Background and Concepts for Teachers
|Energy:||Energy is the capacity to do work.|
|Mechanical energy:||Energy that is composed of both potential energy and kinetic energy.|
|Potential energy:||The energy of position, or stored energy.|
|Kinetic energy:||The energy of motion.|
|Conservation of energy:||A principle stating that the total energy of an isolated system remains constant regardless of changes within the system. Energy can neither be created nor destroyed.|
- Swinging Pendulum - Students predict how fast a pendulum will swing by converting potential energy into kinetic energy. They verify their predictions by measuring its speed.
- Swinging Pendulum (for High School)
- What are examples of dangerous unsafe placement of objects? (Possible answers: Boulders on the edge of a cliff, dishes barely on shelves, etc.).
- What has more potential energy: a boulder on the ground or a feather 10 feet in the air? (Answer: The feather because the boulder is on the ground and has zero potential energy. However, if the boulder was 1 mm off the ground, it would probably have more potential energy.)
Lesson Summary Assessment
- How can you throw a ball and have its energy change from kinetic to potential and back to kinetic without touching the ball once it relases from your hand? (Answer: Throw it straight up in the air.)
- If a mass that weighs 8 kg is held at a height of 10 m, what is its potential energy? (Answer: PE = (8 kg)*(9.8 m/s2)*(10 m) = 784 kg*m2/s2 = 784 J)
- Now consider an object with a kinetic energy of 800 J and a mass of 12 kg. What is its velocity? (Answer: v = sqrt(2*KE/m) = sqrt((2 * 800 J)/12 kg) = 11.55 m/s)
Lesson Extension Activities
Argonne Transportation - Laser Glazing of Rails. September 29, 2003. Argonne National Laboratory, Transportation Technology R&D Center. October 15, 2003. http://www.anl.gov/index.html
Asimov, Isaac. The History of Physics. New York: Walker & Co., 1984.
Jones, Edwin R. and Richard L. Childers. Contemporary College Physics. Reading, MA: Addison-Wesley Publishing Co., 1993.
Kahan, Peter. Science Explorer: Motion, Forces, and Energy. Upper Saddle River, NJ: Prentice Hall, 2000.
Luehmann, April. Give Me Energy. June 12, 2003. Science and Mathematics Initiative for Learning Enhancement, Illinois Institute of Technology. October 15, 2003. http://www.iit.edu/~smile/ph9407.html
Nave, C.R. HyperPhysics. 2000. Department of Physics and Astronomy, Georgia State University. October 15, 2003. hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
The Atoms Family - The Mummy's Tomb – Raceways. Miami Museum of Science and Space Transit Planetarium. October 15, 2003. http://www.miamisci.org/af/sln/mummy/raceways.html
Bailey Jones, Matt Lundberg, Chris Yakacki, Malinda Schaefer Zarske, Denise Carlson
© 2004 by Regents of the University of Colorado.
Integrated Teaching and Learning Program, College of Engineering, University of Colorado Boulder
Last modified: May 21, 2015