• 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. (HS-PS3-1)

• 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. (9-12)
• At the macroscopic scale, energy manifests itself in multiple ways, such as in motion, sound, light, and thermal energy. (9-12)

• When the motion energy of an object changes, there is inevitably some other change in energy at the same time. (6-8)
• Energy cannot be created or destroyed, but it can be transported from one place to another and transferred between systems. (9-12)
• 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. (9-12)

• 9-12: 4E/H1. Although the various forms of energy appear very different, each can be measured in a way that makes it possible to keep track of how much of one form is converted into another. Whenever the amount of energy in one place diminishes, the amount in other places or forms increases by the same amount.
• 9-12: 4E/H9. Many forms of energy can be considered to be either kinetic energy, which is the energy of motion, or potential energy, which depends on the separation between mutually attracting or repelling objects.

• 9-12: 4F/H1. The change in motion (direction or speed) of an object is proportional to the applied force and inversely proportional to the mass.

• A-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

• F-IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.^?
• F-IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

• RST.11-12.9 Synthesize information from a range of sources (e.g., texts, experiments, simulations) into a coherent understanding of a process, phenomenon, or concept, resolving conflicting information when possible.

• RST.9-10.10 By the end of grade 10, read and comprehend science/technical texts in the grades 9—10 text complexity band independently and proficiently.

Short tutorial that uses an animation to illustrate the work/energy relationship in a roller coaster. The author breaks down the associated equation to show how total mechanical energy is conserved in the system.

• Physical Sciences K-8 The Case of Roller Coasters Unit
• Physics First The Case of Roller Coasters Unit

For teachers wanting some background information on energy transformation: this tutorial features an animated roller coaster with moving bar graphs that depict kinetic and potential energy as the car descends and climbs.   It is a great example of a system in which TME (Total Mechanical Energy) remains the same during the course of the motion.

• Physical Sciences K-8 Energy Transformation Unit

This tutorial features an animated roller coaster with moving bar graphs that depict kinetic and potential energy as the car descends and climbs. It is an example of a system in which TME (Total Mechanical Energy) remains the same during the course of the motion.

• Physics First Energy Transformation Unit
• Conceptual Physics Energy Transformation Unit
• Algebra-Based Physics Energy Transformation Unit
• AP/Calculus-Based Physics Energy Transformation Unit