Register here for our virtual June or August engineering design Professional Development workshops!

Lesson: Conservation of Energy: Pushing It Off a Cliff

Quick Look

Grade Level: 11 (9-12)

Time Required: 3 hours 15 minutes

(4 classes of 50 minutes each)

Lesson Dependency:

Subject Areas: Science and Technology

Photo shows a waterfall.
Waterfalls display both potential and kinetic energy
Copyright ©


This lesson focuses on the conservation of energy solely between gravitational potential energy and kinetic energy, moving students into the Research and Revise step. Students start out with a virtual laboratory, and then move into the notes and working of problems as a group. A few questions are given as homework. A set of associated activities focus on roller coasters to study the kinetic and potential energies found on the ride. The lesson is concluded in the Test Your Mettle phase of the Legacy Cycle.
This engineering curriculum aligns to Next Generation Science Standards (NGSS).

Engineering Connection

Engineers design solutions for our world. Engineers must first master the physical laws that rule our world before designing something that takes advantage of those laws. Different forms of energy are harnessed and used by many different types of engineers. The broader application of this lesson focuses on the transfer of energy within a vehicle and harnessing that energy so it is not lost.

Learning Objectives

After this lesson, students should be able to:

  • Describe the types of mechanical energy.
  • List the various forms of potential energy.
  • Apply the conservation of energy to problems strictly between gravitational potential energy and kinetic energy.
  • Explain why mechanical energy is not always conserved.

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 Standards Network (ASN), a project of D2L (

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.

NGSS Performance Expectation

HS-PS3-1. Create a computational model to calculate the change in the energy of one component in a system when the change in energy of the other component(s) and energy flows in and out of the system are known. (Grades 9 - 12)

Do you agree with this alignment?

Click to view other curriculum aligned to this Performance Expectation
This lesson focuses on the following Three Dimensional Learning aspects of NGSS:
Science & Engineering Practices Disciplinary Core Ideas Crosscutting Concepts
Create a computational model or simulation of a phenomenon, designed device, process, or system.

Alignment agreement:

Energy is a quantitative property of a system that depends on the motion and interactions of matter and radiation within that system. That there is a single quantity called energy is due to the fact that a system's total energy is conserved, even as, within the system, energy is continually transferred from one object to another and between its various possible forms.

Alignment agreement:

Conservation of energy means that the total change of energy in any system is always equal to the total energy transferred into or out of the system.

Alignment agreement:

Energy cannot be created or destroyed, but it can be transported from one place to another and transferred between systems.

Alignment agreement:

Mathematical expressions, which quantify how the stored energy in a system depends on its configuration (e.g. relative positions of charged particles, compression of a spring) and how kinetic energy depends on mass and speed, allow the concept of conservation of energy to be used to predict and describe system behavior.

Alignment agreement:

The availability of energy limits what can occur in any system.

Alignment agreement:

Models can be used to predict the behavior of a system, but these predictions have limited precision and reliability due to the assumptions and approximations inherent in models.

Alignment agreement:

Science assumes the universe is a vast single system in which basic laws are consistent.

Alignment agreement:

  • Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. (Grades 9 - 12) More Details

    View aligned curriculum

    Do you agree with this alignment?

  • Solve quadratic equations by inspection (e.g., for x² = 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) More Details

    View aligned curriculum

    Do you agree with this alignment?

  • Energy cannot be created nor destroyed; however, it can be converted from one form to another. (Grades 9 - 12) More Details

    View aligned curriculum

    Do you agree with this alignment?

  • Energy can be grouped into major forms: thermal, radiant, electrical, mechanical, chemical, nuclear, and others. (Grades 9 - 12) More Details

    View aligned curriculum

    Do you agree with this alignment?

Suggest an alignment not listed above

Worksheets and Attachments

Visit [] to print or download.

More Curriculum Like This

Elastic Potential Energy of Springs—It’s Tiggerific!

Students investigate potential energy held within springs (elastic potential energy) as part of the Research and Revise step. The lesson includes a dry lab that involves pogo sticks to solidify the concepts of spring potential energy, kinetic energy and gravitational energy, as well as conservation ...

A Tale of Friction

High school students learn how engineers mathematically design roller coaster paths using the approach that a curved path can be approximated by a sequence of many short inclines. They apply basic calculus and the work-energy theorem for non-conservative forces to quantify the friction along a curve...

preview of 'A Tale of Friction ' Lesson
High School Lesson
Kinetic and Potential Energy of Motion

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.

Pre-Req Knowledge

A working understanding of Newton's laws and flow charting. A firm understanding of how to use Microsoft Excel® or another spreadsheet program before attempting the dry lab (however, this can also be incorporated into the explanation of the lab).


Now that we have come up with a few ideas about the hybrid cars, we know that we need to know more about energy. So today we will learn about the two most basic types of energy and how they can be equated to each other. So, let's talk about energy (continue with lecture information provided in the Teacher Background section).

Lesson Background and Concepts for Teachers

Content Information

Pedagogically, make the first logical step in the conservation of energy between just two forms of mechanical energy. Typically, do this between kinetic energy, which is the energy of motion (KE = ½ mv2), and gravitational potential energy, which is the energy of position (GPE = mgh). However, consider using other forms of energy (that is, thermal, chemical, nuclear, electric, electromagnetic, elastic potential energy and energy carried by longitudinal waves [typically in the form of sound waves or seismic waves]).

The conservation of energy states that the total energy at any two points in time for a close system. For basic purposes, the assumption that we always deal with a closed system can be taken.

E1 = E2 (1)

Here, we assume that the only forms of energy that can be dealt with are kinetic and gravitational potential energies.

KE1 + GPE1 = KE2 + GPE2 (2)


½ mv1 2 + mgh1 = ½ mv 2 2 + mgh2


½ v1 2 + gh1 = ½ v2 2 + gh2 (3)

Therefore, we see that (3) is true regardless of the mass of the object. To start out, problems should be solely KE at one point and GPE at the other. This also requires careful placement of your ground level. So (3) can reduce to:

gh1 = ½ v2 2 (4)

Only after a few problems, should the case in which we have to include other terms to have (3) be true should be attempted. Just before the second associated activity Energy on a Roller Coaster should the concept of adding other forms of energy be discussed and the law of Conservation of Energy always be expressed as in (1).

Lecture Information

Write the word "energy" on the classroom board. List some of the reasons (from the last lesson) that relate to conservation of energy, and ask: What are some of the forms of energy? Expect students to give answers such as "solar' or "wind," but steer them into the actual names of the forms of energy. Flow chart these responses on the board (which also serves as a lead-in for a later lesson). Circle kinetic and gravitational potential energy, and tell them these two are our focus first.

Choose two student volunteers (pick two who are friends) and pick two lightweight objects from the classroom such as a sponge and a plastic water bottle. Ask the class: Which object will transfer more energy (hurt more) if thrown at a person at the same speed? Listen to the class answers and have the volunteers throw/receive the objects to confirm (this is why friends are chosen). Write on the board that KE a mass. Then, ask the class: Which transfers more kinetic energy (hurts more), an object thrown at low speed or the same object at a higher speed? The class answers and the volunteers test and confirm (again, it helps if they are friends in order to avoid any serious throwing). Then place velocity into the equation to have "KE a mv." Next, explain that KE is proportional to the square of velocity and that a constant is associated with KE. Then place the ½ and the square into the equation and replace "a" with "=" to have "KE = ½ mv2."

Next, determine the equation for gravitational potential energy. Pick two objects from around the room, but this time make sure they have a larger difference in mass (for example, a sponge and the CRC Handbook of Chemistry and Physics). Remind students about the storage of mechanical energy. Ask the class: Which object has more energy stored in it if held at the same height. Expect many to answer correctly, and some to not be sure. Explain that we can tell from dropping them and seeing which transfers the most energy to the floor. One way to determine which transfers the most energy is by the loudness of the impact. Expect them to immediately determine the answer, but demonstrate anyway. Then, write on the board, "GPE a m." Ask: Which one has more stored energy, a book at 1 m from the floor or 2 m from the floor? Demonstrate this. Then include height in the equation for "GPE a mh." Remind students that the attraction of the object to the ground is also determined by something else. Wait until students determine that it must be gravity. Then include g and substitute "=" for "a" for "GPE = mgh.

For further background on the physcis presented in this lesson, select the lecture 11 video at: Optionally, you could show students clips from this video, or if you feel appropriate, show students the entire lecture.

At this point, have students conduct the Energy Skate Park associated activity. Assign finishing the virtual lab as homework.

Then work on the classroom board several problems from the text on the conservation of energy between these two forms of energy. Inform students about the real-life presence of friction, as well as what friction does. Next, have students conduct the Energy on a Roller Coaster associated activity.

Associated Activities

  • Energy Skate Park - Using an online simulation set at a skate park, students make graph predictions before using the virtual laboratory to create graphs of energy vs. time under different conditions. Students' comprehension of potential and kinetic energy and conservation of energy is strengthened as they predict behavior based on their understanding of these energy concepts and experimentation with the simulation.
  • Energy on a Roller Coaster - Students use a roller coaster track to collect position data. They calculate velocity and energy data, and then relate the conversion of potential and kinetic energy to the conversion of energy used in a hybrid car, learning about energy lost to friction.


conservation of energy: The total amount of energy within a closed system is equal at any two points in time.

friction: Transfer of energy from mechanical energy into other forms.

gravitational potential energy: Energy stored due to position in the vertical dimension.

kinetic energy: Energy of motion.

potential energy: Energy that is stored.


Informal Assessment: While doing problems with the class, make sure to only do the first problem for them. Then solve another with help from the class. Have students individually solve all additional problems, with individual help from the teacher and other students who have had their work checked by the teacher.

Lab Reports: Evaluate student lab reports from the virtual lab and dry lab. Have the reports be in a format that the teacher is comfortable with, but that also allows for the checking of the understanding of the concepts by students.

Quiz: At lesson end and after both associated activities have been conducted, administer the Conservation of Energy Quiz. Review student answers to gauge their depth of comprehension.


© 2013 by Regents of the University of Colorado; original © 2006 Vanderbilt University


Joel Daniel (funded by the NSF-funded Center for Compact and Efficient Fluid Power at the University of Minnesota); Megan Johnston

Supporting Program

VU Bioengineering RET Program, School of Engineering, Vanderbilt University


The contents of this digital library curriculum were developed under National Science Foundation RET grant nos. 0338092 and 0742871. However, these contents do not necessarily represent the policies of the NSF, and you should not assume endorsement by the federal government.

Last modified: January 19, 2021

User Comments & Tips

Free K-12 standards-aligned STEM curriculum for educators everywhere.
Find more at