Wolfgang Christian, Mario Belloni, and Anne Cox
Barbara Christian and Laura Fauver
The EJS Pendulum Energy Model shows a pendulum and associated energy bar charts. Users can change the initial starting point of the pendulum. There are two versions of the model: one with only energy data given and one with additional height and speed data provided. This model is distributed with a middle-school physical science lesson plan (see the additional documents).
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)
Types of Interactions (PS2.B)
The gravitational force of Earth acting on an object near Earth's surface pulls that object toward the planet's center. (5)
Forces that act at a distance (electric, magnetic, and gravitational) can be explained by fields that extend through space and can be mapped by their effect on a test object (a charged object, or a ball, respectively). (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)
Conservation of Energy and Energy Transfer (PS3.B)
When the motion energy of an object changes, there is inevitably some other change in energy at the same time. (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)
Energy and Matter (2-12)
The transfer of energy can be tracked as energy flows through a designed or natural system. (6-8)
Energy may take different forms (e.g. energy in fields, thermal energy, energy of motion). (6-8)
Within a natural or designed system, the transfer of energy drives the motion and/or cycling of matter. (6-8)
Scientific Knowledge Assumes an Order and Consistency in Natural Systems (1-12)
Science assumes that objects and events in natural systems occur in consistent patterns that are understandable through measurement and observation. (6-8)
NGSS Science and Engineering Practices (K-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 and use a model to describe phenomena. (6-8)
AAAS Benchmark Alignments (2008 Version)
4. The Physical Setting
4E. Energy Transformations
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.
11. Common Themes
3-5: 11B/E3. A model of something is similar to, but not exactly like, the thing being modeled. Some models are physically similar to what they are representing, but others are not.
3-5: 11B/E4. Models are very useful for communicating ideas about objects, events, and processes. When using a model to communicate about something, it is important to keep in mind how it is different from the thing being modeled.
6-8: 11B/M4. Simulations are often useful in modeling events and processes.
6-8: 11B/M5. The usefulness of a model depends on how closely its behavior matches key aspects of what is being modeled. The only way to determine the usefulness of a model is to compare its behavior to the behavior of the real-world object, event, or process being modeled.
Common Core State Standards for Mathematics Alignments
Standards for Mathematical Practice (K-12)
MP.2 Reason abstractly and quantitatively.
Ratios and Proportional Relationships (6-7)
Analyze proportional relationships and use them to solve real-world
and mathematical problems. (7)
7.RP.2.b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
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.
W. Christian, M. Belloni, and A. Cox, Computer Program PENDULUM ENERGY JS MODEL PACKAGE, Version 1.0 (2015), WWW Document, (https://www.compadre.org/Repository/document/ServeFile.cfm?ID=13423&DocID=4016).
Christian, W., Belloni, M., & Cox, A. (2015). Pendulum Energy JS Model Package (Version 1.0) [Computer software]. Retrieved September 26, 2022, from https://www.compadre.org/Repository/document/ServeFile.cfm?ID=13423&DocID=4016
Christian, Wolfgang, Mario Belloni, and Anne Cox. Pendulum Energy JS Model Package. Vers. 1.0. Computer software. 2015. 26 Sep. 2022 <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=13423&DocID=4016>.
%0 Computer Program %A Christian, Wolfgang %A Belloni, Mario %A Cox, Anne %D March 19, 2015 %T Pendulum Energy JS Model Package %7 1.0 %8 March 19, 2015 %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=13423&DocID=4016
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