### Pendulum Energy Model Package

Contributor: Barbara Christian, Mario Belloni, Wolfgang Christian, Anne Cox, Laura Fauver

Type Category: Assessment Materials, Instructional Materials

Types: Assessment Item, Answer Key, Problem Set, Simulation

Note: This resource, vetted by NSTA curators, is provided to teachers along with suggested modifications to make it more in line with the vision of the NGSS. While not considered to be “fully aligned,” the resources and expert recommendations provide teachers with concrete examples and expert guidance using the EQuIP rubric to adapted existing resources. Read more here.

#### Description

This simulation-based learning module for Grades 6-8 was developed to help students visualize changing kinetic and potential energy in a simple pendulum. It models a child on a swing suspended from a stationary point. Drag the swing to different heights, then activate the motion. As the swing moves in periodic motion, energy bar graphs are simultaneously displayed that show changing kinetic and potential energy. A third graph of TME (total mechanical energy) clearly shows that the total energy of the system is conserved, even though kinetic and potential energies are continuously changing. The “Supplemental Document” contains two problem sets designed specifically to accompany the simulation: 1) Conceptual activity with only energy data to explore transformation and conservation of energy, and 2) Quantitative activity that incorporates height and speed data for calculating the mass of the figure on the swing. Tables are provided for recording data. Complete answer key makes this a classroom-ready resource.

Intended Audience
Educator and learner

Educational Level
Middle School

Language
English

Access Restrictions
Free access - The right to view and/or download material without financial, registration, or excessive advertising barriers.

##### Performance Expectation

MS-PS3-1  Construct and interpret graphical displays of data to describe the relationships of kinetic energy to the mass of an object and to the speed of an object.

Clarification Statement:

Emphasis is on descriptive relationships between kinetic energy and mass separately from kinetic energy and speed. Examples could include riding a bicycle at different speeds, rolling different sizes of rocks downhill, and getting hit by a wiffle ball versus a tennis ball.

Assessment Boundary:

none

This resource is explicitly designed to build towards this performance expectation.

This PE pertains primarily to Activity 2, “Mechanical Energy in a Pendulum”, which commences on Page 10 of the supplemental worksheet. This activity introduces the formulas for calculating KE (kinetic energy) and PE (potential energy). Students will stop the simulation at preset points along the pendulum’s swing to record data for height and speed, kinetic energy, and potential energy (which are automatically generated). Using a data table provided in the worksheet, students will perform calculations using data they collected (plus the given formulas and the Earth’s gravitational constant)  to determine the mass of the figure on the swing. A detailed answer key is provided. To differentiate the instruction, teachers could easily fill in correct responses in portions of the data table to provide scaffolding for students who need help or struggle with the content.

##### Science and Engineering Practice

This resource is explicitly designed to build towards this science and engineering practice.

This Practice pertains primarily to Activity 1: “Pendulum Potential and Kinetic Energy”, which commences on Page 3 of the Supplemental Worksheet. In this exercise, students view automatically-generated bar graphs of Kinetic Energy, Potential Energy, and Total Energy, which are displayed in real time alongside the moving simulation of the child on a swing. They can very clearly see the changes in kinetic and potential energy, which are dependent on the position of the swing in its path of periodic motion. At the top of the swing motion, potential energy is greatest. At the bottom (mid-point on the simulation) kinetic energy is greatest. At any point in the motion, the kinetic energy plus potential energy will equal the total energy of the system. This is important because it’s a way to visualize conservation of energy in a system (a way to “see” what we cannot see). KEY TAKEAWAY: In the moving pendulum system, energy is constantly being converted between kinetic and potential, but the total energy of the system is unchanged. You can see this because the graph of total energy always stays at the same amount. Energy is conserved.

##### Science and Engineering Practice

This resource is explicitly designed to build towards this science and engineering practice.

This Practice pertains to Activity 2: “Mechanical Energy in a Pendulum”, which commences on Page 10 of the Supplemental Worksheet. In this exercise, students specifically use simple algebra to calculate the mass of an object on a swing from data on height and speed (given in the simulation). Algebraic expressions pertaining to the Earth’s gravitational constant, the Kinetic Energy formula, and the Potential Energy formula will be used to perform the calculations. The Kinetic Energy formula (½ mass times velocity squared) correlates explicitly with Disciplinary Core Idea MS-PS3.B.1 (see below). By including the Supplementary Worksheet Activity 2, teachers are able to quickly and easily introduce a lesson that integrates quantitative reasoning.

##### Disciplinary Core Idea

This resource is explicitly designed to build towards this disciplinary core idea.

This DCI pertains to Activity 1, “Mechanical Energy in a Pendulum”, which commences on Page 3 of the Supplemental Worksheet and accompanies the conceptual model, “Pendulum Energy Simulation”.  The bar graphs of KE (kinetic energy) and PE (potential energy) are displayed in real time as the simulation runs. Students will be able to quickly see that potential energy in the pendulum system is greatest when the swing is at the top of its periodic cycle. Kinetic energy is at its greatest at the bottom of the swing cycle.  They are further required to demonstrate this understanding in answering Activity 1 Study Questions. Teaching Tip: For students to comprehend how potential energy depends on relative position, they may need help understanding that the model is a “system” of objects.  This will also allow teachers to seamlessly integrate the Crosscutting Concept (see below).

##### Disciplinary Core Idea

This resource is explicitly designed to build towards this disciplinary core idea.

This DCI pertains to  Activity 2: “Mechanical Energy in a Pendulum”, which commences on Page 10 of the Supplemental Worksheet. In this exercise, students specifically use algebraic formulas to calculate the mass of an object on a swing from height and speed data (given in the simulation). Algebraic expressions pertaining to the Earth’s gravitational constant, the Kinetic Energy formula, and the Potential Energy formula will be used to perform the calculations. The DCI alignment is very tight here, as Core Idea MS-PS3.A.2 explicitly references the Kinetic Energy formula (½ mass times velocity squared).  This activity could serve as a good precursor to a conceptual discussion of conservation of energy.

##### Crosscutting Concept

This resource appears to be designed to build towards this crosscutting concept, though the resource developer has not explicitly stated so.

The system in this model includes the following components: * The chain attached to the swing * The swing seat * The child figure sitting on the seat * A stationary object that holds the chain in place (not visible in this model) Energy doesn’t just disappear in our swing system; the mechanical energy is being converted between kinetic (energy of motion) and potential (stored energy). This model is a particularly effective resource for helping students visualize the flow of kinetic and potential energy in a simple system (child on a swing). It would be an ideal way to underscore the difference between energy transfer (occurring when energy changes location) and energy conversion (the transformation of energy from one form to another). Most common physical systems involve energy conversion. In this model, potential energy is converted to kinetic energy (and the reverse) when the swing moves.  Other types of systems also undergo energy conversion, (i.e., mechanical energy is converted to electrical energy in an electric generating plant; gravitational potential energy is converted to mechanical energy in a windmill). By helping students to think in terms of systems, teachers pave the way for future mastery of many engineering and physics concepts. This particular resource also embeds data tables that aid students in entering initial inputs and other inputs that occur at checkpoints along the path of motion.

#### Resource Quality

• Alignment to the Dimensions of the NGSS: The Pendulum Energy Model Package meets grade-appropriate elements of the Three Dimensions of the NGSS in the following ways: 1. Activity 1 involves using a simulation to build understanding of energy conversion in a pendulum system and Activity 2 involves the explicit task of using the simulation as the basis for data collection to explore how kinetic energy is related to mass of the moving object. To calculate the mass of the swinging object, students will use algebraic formulas. 2. The resource explicitly addresses two Disciplinary Core Ideas within Middle School Physical Science. In Activity 1, students explore how energy is transformed from kinetic-to-potential (and the reverse) in an object moving with periodic motion. Activity 2 applies the Kinetic Energy Formula and the Potential Energy Formula to values recorded by students while using the simulation. 3. The resource presents the pendulum as a system involving a child going back-and-forth on a swing. Most of the physical processes that occur on Earth do not happen in isolation -- they are part of a system of interacting objects. The Pendulum Energy Model provides a simple, yet robust way to invite discussion about systems and why it’s important to think about interactions. When presented only with a mathematical formula, students lose out on the big picture. The problem set is phrased to maintain a consistent focus on the system of the child on a swing.
• Instructional Supports: The computational accuracy of the model is exemplary, which means teachers will not need to spend valuable time double-checking the mathematical outputs. The model can also serve as  a springboard to discuss the role of computer models in the Engineering Design process (i.e., engineers often rely on simulations before building prototypes). The resource stops short of asking students to defend claims or clarify explanations, but provides opportunities to express and represent ideas in writing and through drawings/diagrams.  Discussion questions were crafted to tease out prior student knowledge, but do not follow through to identify prior learning required or to explain how prior learning will be built upon.     The scientific accuracy of this resource is impeccable. The three layers of editorial feedbacks ensure that Open Source Physics models are both computationally accurate and pedagogically appropriate.     The authors have not included ideas for supporting struggling learners or extending the lesson for students with high interest or learners who are Gifted/Talented.
• Monitoring Student Progress: Formative Assessment:  Embeds formative assessment processes throughout that evaluate student learning to inform instruction.  This component is one of the greatest strengths of the Pendulum Energy Model. At multiple points within the Student Worksheet, learners are prompted to express ideas, respond to conceptual questions with no explicit “right-or-wrong” answer, relate the model to their everyday experiences, and consider different ways of visualizing energy conversion and conservation of energy through multiple representations (i.e., bar graphs, pie charts, mathematical expressions, and written explanations). Scoring Guidance:  Rubrics and scoring guidelines are not included, but the Answer Key provides example correct responses and notes to guide teachers. Differentiated Assessment:  Students who struggle with mathematics will be able to take equal part in the conceptual activity and extend their own learning through written explanations and drawings of the physical process under study. Learners with high interest can access the source code for the model to create their own initial inputs. The activities embed ways for all students to be successful: through raw data analysis, written expression, algebraic reasoning, and/or spatial representation of the concepts under study.
• Quality of Technological Interactivity: The Pendulum Energy Model meets all of the following criteria for Technological Interactivity: Interactivity:  The object is responsive to student input in a way that creates an individualized learning experience.  The simulation was specifically developed to engage young adolescents in interactively exploring energy transformation in a pendulum system. The individual user must set the initial height position and manipulate the start, stop, pause, and stepped motion tools. The model automatically generates the bar graphs of changing kinetic and potential energies, and also generates values for height and speed of the pendulum. This does not detract from the interactivity; rather, it is a necessary scaffold for introducing the concepts. Purposeful integration with learning goals:  The resource is directly related to the Core Ideas noted above. The tools for manipulating the simulation are intuitive and were developed to enhance student understanding of energy transformation and conservation within a system. Usability and Design:  The Pendulum Energy resource package was authored by experienced middle school science teachers, who crafted it as an ideal system to facilitate ease of use among students with little or no prior experience with kinetic/potential energy conversion. Most learners could figure out how to use the simulation without much teacher guidance. The object appears to function flawlessly on the intended platform:  In 2015, the model was rewritten to HTML5. It runs very smoothly on all major browsers.

National Science Teaching Association
1840 Wilson Boulevard, Arlington VA 22201
(T) 703.243.7100 (F) 703.243.7177