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Roller Coaster Model
Michael R. Gallis
Anne Cox, and
The EJS Roller Coaster model explores the relationship between kinetic, potential, and total energy as a cart travels along a roller coaster. Students can choose from five track configurations or create their own roller coaster curve and observe the resulting motion. As the simulation plays, energy bar graphs show the changing levels of kinetic and potential energy. Switch to "stepped motion" to see points at which both forms of energy reach maximum and minimum levels. Users can also control the initial speed of the cart and add friction, enabling the resource to be adaptable to a range of levels from middle school through high school.
This item was created with Easy Java Simulations (EJS), a modeling tool that allows users without formal programming experience to generate computer models and simulations. To run the simulation, simply click the Java Archive file below.
Please note that this resource requires
at least version 1.5 of
Editor's Note:Don't miss the lesson plan with accompanying guide sheets for both teachers and students. Click "Supplemental Documents" below. See Annotations for additional background information on the physics of roller coasters, recommended by The Physics Front editors.
Roller Coaster Energy Model: Teacher Version
The EJS Roller Coaster Energy Model: Teacher Version shows the motion and energy of a car on a roller coaster track. You can change the track shape and add… more... download 1290kb .jar
Published: June 17, 2009
Roller Coaster Energy Model: Student Version
The EJS Roller Coaster Energy Model: Student Version is a simulation for physical science (middle and high) school students. It shows the motion and energy… more... download 996kb .jar
Published: June 17, 2009
Roller Coaster Energy Model: Lesson Plan
A pdf file with a teacher lesson plan for use with the Roller Coaster Energy Model. This lesson plan is also packaged within the teacher version of the… more... download 145kb .pdf
Published: June 17, 2009
Roller Coaster Energy Model: Student Worksheet
A pdf file with a student worksheet for use with the Roller Coaster Energy Model. This worksheet is also packaged within the student version of the… more... download 88kb .pdf
Last Modified: March 21, 2010
Roller Coaster Model source code
The source code zip archive contains an XML representation of the Roller Coaster Model. Unzip this archive in your Ejs workspace to compile and run this… more... download 361kb .zip
Published: October 27, 2008
6-8: 4E/M1. Whenever energy appears in one place, it must have disappeared from another. Whenever energy is lost from somewhere, it must have gone somewhere else. Sometimes when energy appears to be lost, it actually has been transferred to a system that is so large that the effect of the transferred energy is imperceptible.
6-8: 4E/M4. Energy appears in different forms and can be transformed within a system. Motion energy is associated with the speed of an object. Thermal energy is associated with the temperature of an object. Gravitational energy is associated with the height of an object above a reference point. Elastic energy is associated with the stretching or compressing of an elastic object. Chemical energy is associated with the composition of a substance. Electrical energy is associated with an electric current in a circuit. Light energy is associated with the frequency of electromagnetic waves.
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.
6-8: 4F/M3a. An unbalanced force acting on an object changes its speed or direction of motion, or both.
9-12: 4F/H7. In most familiar situations, frictional forces complicate the description of motion, although the basic principles still apply.
11. Common Themes
6-8: 11B/M1. Models are often used to think about processes that happen too slowly, too quickly, or on too small a scale to observe directly. They are also used for processes that are too vast, too complex, or too dangerous to study.
6-8: 11B/M2. Mathematical models can be displayed on a computer and then modified to see what happens.
6-8: 11B/M4. Simulations are often useful in modeling events and processes.
12. Habits of Mind
12C. Manipulation and Observation
6-8: 12C/M3. Make accurate measurements of length, volume, weight, elapsed time, rates, and temperature by using appropriate devices.
Next Generation Science Standards
Students who demonstrate understanding can: (6-8)
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. (MS-PS3-5)
Disciplinary Core Ideas (K-12)
Forces and Motion (PS2.A)
The motion of an object is determined by the sum of the forces acting on it; if the total force on the object is not zero, its motion will change. The greater the mass of the object, the greater the force needed to achieve the same change in motion. For any given object, a larger force causes a larger change in motion. (6-8)
Definitions of Energy (PS3.A)
Motion energy is properly called kinetic energy; it is proportional to the mass of the moving object and grows with the square of its speed. (6-8)
A system of objects may also contain stored (potential) energy, depending on their relative positions. (6-8)
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)
Conservation of Energy and Energy Transfer (PS3.B)
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. (9-12)
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)
Relationship Between Energy and Forces (PS3.C)
When two objects interact, each one exerts a force on the other that can cause energy to be transferred to or from the object. (6-8)
Crosscutting Concepts (K-12)
Systems and System Models (K-12)
Models can be used to represent systems and their interactions—such as inputs, processes and outputs—and energy and matter flows within systems. (6-8)
When investigating or describing a system, the boundaries and initial conditions of the system need to be defined and their inputs and outputs analyzed and described using models. (9-12)
Models (e.g., physical, mathematical, computer models) can be used to simulate systems and interactions—including energy, matter, and information flows—within and between systems at different scales. (9-12)
Energy and Matter (2-12)
The transfer of energy can be tracked as energy flows through a designed or natural system. (6-8)
Energy cannot be created or destroyed—it only moves between one place and another place, between objects and/or fields, or between systems. (9-12)
Science is a Human Endeavor (3-12)
Science is a result of human endeavors, imagination, and creativity. (9-12)
NGSS Science and Engineering Practices (K-12)
Analyzing and Interpreting Data (K-12)
Analyzing data in 6–8 builds on K–5 and progresses to extending quantitative analysis to investigations, distinguishing between correlation and causation, and basic statistical techniques of data and error analysis. (6-8)
Analyze and interpret data to provide evidence for phenomena. (6-8)
Analyzing data in 9–12 builds on K–8 and progresses to introducing more detailed statistical analysis, the comparison of data sets for consistency, and the use of models to generate and analyze data. (9-12)
Analyze data using tools, technologies, and/or models (e.g., computational, mathematical) in order to make valid and reliable scientific claims or determine an optimal design solution. (9-12)
Developing and Using Models (K-12)
Modeling in 6–8 builds on K–5 and progresses to developing, using and revising models to describe, test, and predict more abstract phenomena and design systems. (6-8)
Develop a model to predict and/or describe phenomena. (6-8)
Modeling in 9–12 builds on K–8 and progresses to using, synthesizing, and developing models to predict and show relationships among variables between systems and their components in the natural and designed worlds. (9-12)
Use a model to provide mechanistic accounts of phenomena. (9-12)
Common Core State Standards for Mathematics Alignments
Standards for Mathematical Practice (K-12)
MP.4 Model with mathematics.
Ratios and Proportional Relationships (6-7)
Understand ratio concepts and use ratio reasoning to solve
6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
Expressions and Equations (6-8)
Reason about and solve one-variable equations and inequalities. (6)
6.EE.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
Work with radicals and integer exponents. (8)
8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that ?2 is irrational.
Use functions to model relationships between quantities. (8)
8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
This animated tutorial is part of The Physics Classroom collection, and provides additional background information on the transformation of energy on a roller coaster and a good explanation of why mechanical energy is conserved.
This resource is part of 2 Physics Front Topical Units.
Topic: Kinematics: The Physics of Motion Unit Title: The Case of Roller Coasters
Roller coasters offer an inherently interesting way to study energy transformation in a system. This simulation lets students choose from 5 track configurations or create their own design, then watch the resulting motion. Energy bar graphs are simultaneously displayed as the coaster runs its course. Students can adjust the initial speed and friction, or switch to stepped motion to see exact points where kinetic and potential energy reach maximum and minimum levels. Includes lesson plan and student guide.
Topic: Conservation of Energy Unit Title: Conservation of Energy
Roller coasters offer an inherently interesting way to study energy transformation. This scaffolded activity lets students choose from 5 track configurations or create their own design, then observe the resulting motion. Energy bar graphs are simultaneously displayed as the roller coaster runs its course. Students can adjust the initial speed of the car, add friction, or switch to stepped motion to see the exact points at which kinetic and potential energy reach maximum and minimum levels. Includes lesson plan and student guide.
%0 Computer Program %A Gallis, Michael %D October 27, 2008 %T Roller Coaster Model %E Christian, Wolfgang %8 October 27, 2008 %U http://www.compadre.org/Repository/document/ServeFile.cfm?ID=8228&DocID=873
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