This mobile-friendly simulation allows students to stretch and compress springs to explore relationships among force, spring constant, displacement, and potential energy in a spring. It was designed to promote understanding of the predictable mathematical relationships that underlie Hooke's Law. Note: The simulation is freely accessible; the Teacher Tips and teacher-created lesson plans are available to registered users only. Registration is cost-free.

This resource is part of PhET, the Physics Education Technology Project, a collection of simulation-based learning objects developed for learners of physics, chemistry, math, earth science, and biology.

Editor's Note:This simulation is an especially effective way to promote understanding of "restoring force", a topic of documented misconception among students in introductory physics courses.

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)

Conservation of Energy and Energy Transfer (PS3.B)

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)

Crosscutting Concepts (K-12)

Patterns (K-12)

Empirical evidence is needed to identify patterns. (9-12)

Cause and Effect (K-12)

Cause and effect relationships may be used to predict phenomena in natural or designed systems. (6-8)

Cause and effect relationships can be suggested and predicted for complex natural and human designed systems by examining what is known about smaller scale mechanisms within the system. (9-12)

Systems and System Models (K-12)

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)

NGSS Science and Engineering Practices (K-12)

Analyzing and Interpreting Data (K-12)

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 and use a model to 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)

Develop and use a model based on evidence to illustrate the relationships between systems or between components of a system. (9-12)

Using Mathematics and Computational Thinking (5-12)

Mathematical and computational thinking at the 9–12 level builds on K–8 and progresses to using algebraic thinking and analysis, a range of linear and nonlinear functions including trigonometric functions, exponentials and logarithms, and computational tools for statistical analysis to analyze, represent, and model data. Simple computational simulations are created and used based on mathematical models of basic assumptions. (9-12)

Create or revise a simulation of a phenomenon, designed device, process, or system. (9-12)

NGSS Nature of Science Standards (K-12)

Analyzing and Interpreting Data (K-12)

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)

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)

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)

Using Mathematics and Computational Thinking (5-12)

Mathematical and computational thinking at the 9–12 level builds on K–8 and progresses to using algebraic thinking and analysis, a range of linear and nonlinear functions including trigonometric functions, exponentials and logarithms, and computational tools for statistical analysis to analyze, represent, and model data. Simple computational simulations are created and used based on mathematical models of basic assumptions. (9-12)

AAAS Benchmark Alignments (2008 Version)

2. The Nature of Mathematics

2A. Patterns and Relationships

9-12: 2A/H1. Mathematics is the study of quantities and shapes, the patterns and relationships between quantities or shapes, and operations on either quantities or shapes. Some of these relationships involve natural phenomena, while others deal with abstractions not tied to the physical world.

4. The Physical Setting

4E. Energy Transformations

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.

4F. Motion

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.

9-12: 4F/H7. In most familiar situations, frictional forces complicate the description of motion, although the basic principles still apply.

9. The Mathematical World

9B. Symbolic Relationships

9-12: 9B/H5. When a relationship is represented in symbols, numbers can be substituted for all but one of the symbols and the possible value of the remaining symbol computed. Sometimes the relationship may be satisfied by one value, sometimes by more than one, and sometimes not at all.

11. Common Themes

11B. Models

6-8: 11B/M4. Simulations are often useful in modeling events and processes.

9-12: 11B/H1a. A mathematical model uses rules and relationships to describe and predict objects and events in the real world.

%0 Electronic Source %D November 5, 2015 %T PhET Simulation: Hooke's Law %I PhET %V 2023 %N 25 September 2023 %8 November 5, 2015 %9 text/html %U https://phet.colorado.edu/en/simulation/hookes-law

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