### Summary

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.

### Engineering Connection

### Educational Standards

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.

### Learning Objectives

- 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.

### Introduction/Motivation

*potential energy*and

*kinetic energy*as two different kinds of

*mechanical energy*. Give definitions of each and present the equations, carefully explaining each variable, as discussed in the next section,

*PE = mass x g x height*

### Lesson Background and Concepts for Teachers

*Work*is done when a force moves an object over a given distance. The capacity for work, or energy, can come in many different forms. Examples of such forms are mechanical, electrical, chemical or nuclear energy.

*mechanical energy*, the form of energy that is easiest to observe on a daily basis. All moving objects have mechanical energy. There are two types of mechanical energy: potential energy and kinetic energy.

*Potential energy*is the energy that an object has because of its position and is measured in Joules (J). Potential energy can also be thought of as stored energy.

*Kinetic energy*is the energy an object has because of its motion and is also measured in Joules (J). Due to the principle of

*conservation of energy,*energy can change its form (potential, kinetic, heat/thermal, electrical, light, sound, etc.) but it is never created or destroyed.

*PE*). It can be expressed mathematically as follows:

*PE = mass x g x height*or

*PE = weight x height*

^{2}or 32.2 feet/sec

^{2}. In the metric system, we would commonly use mass in kilograms or grams with the first equation. With English units it is common to use weight in pounds with the second equation.

*KE*) is energy of motion. Any object that is moving has kinetic energy. An example is a baseball that has been thrown. The kinetic energy depends on both mass and velocity and can be expressed mathematically as follows:

*KE*stands for kinetic energy. Note that a change in the velocity will have a much greater effect on the amount of kinetic energy because that term is squared. The total amount of mechanical energy in a system is the sum of both potential and kinetic energy, also measured in Joules (J).

*Total Mechanical Energy = Potential Energy + Kinetic Energy*

*and*kinetic energy. A simple example would be the design of a roller coaster — a project that involves both mechanical and civil engineers. At the beginning of the roller coaster, the cars must have enough potential energy to power them for the rest of the ride. This can be done by raising the cars to a great height. Then, the increased potential energy of the cars is converted into enough kinetic energy to keep them in motion for the length of the track. This is why roller coaters usually start with a big hill. As the cars start down the first hill, potential energy is changed into kinetic energy and the cars pick up speed. Engineers design the roller coaster to have enough energy to complete the course

*and*to overcome the energy-draining effect of friction.

### Vocabulary/Definitions

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. |

### Associated Activities

- 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)

### Lesson Closure

### Assessment

Pre-Lesson Assessment

*Discussion Questions:*Solicit, integrate and summarize student responses.

- What are examples of dangerous unsafe placement of objects? (Possible answers: Boulders on the edge of a cliff, dishes barely on shelves, etc.).

Post-Introduction Assessment

*Question/Answer:*Ask the students and discuss as a class:

- 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

*Group Brainstorm:*Give groups of students each a ball (example, tennis ball). Remind them that energy can be converted from potential to kinetic and vice versa. Write a question on the board and have them brainstorm the answer in their groups. Have the students record their answers in their journals or on a sheet of paper and hand it in. Discuss the student groups' answers with the class.

- 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.)

*Calculating:*Have students practice problems solving for potential energy and kinetic energy:

- 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/s
^{2})*(10 m) = 784 kg*m^{2}/s^{2}= 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

*spring potential*or

*elastic potential energy*. In this case, energy is stored when you compress or elongate a spring. Have the students search the Internet or library for the equation of spring potential energy and explain what the variables in the equation represent. The answer is

*PE*

_{spring}= ½ k∙x^{2}*k*is the spring constant measured in N/m (Newton/meters) and x is how far the spring is compressed or stretched measured in m (meters).

### References

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

### Contributors

Bailey Jones, Matt Lundberg, Chris Yakacki, Malinda Schaefer Zarske, Denise Carlson

### Copyright

© 2004 by Regents of the University of Colorado.

### Supporting Program

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

### Acknowledgements

Last modified: March 27, 2015