# 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.

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## 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 Expectations

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 Practices

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.

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 Ideas

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).

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 Concepts

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