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Coulomb Pendulum Model

Two charges hanging from wires, repel each other. The simulation shows the motion and reports angle (from the vertical) for each charge. You can change the charge (in μC), initial position and damp the motion (set velocity equal to zero) of the charges. Users can examine the model if Ejs is installed. 

Exercises:

  1. For the same initial charge on each, push the v=0 button until the charges balance. What is the angle?
  2. If you increase the value of one charge, what difference do you expect in the angles where they will balance? Will it still be symmetric? Explain and then try it. 
  3. The charge is given in μC and the support string for each is 1m in length. Determine the mass of each (they have the same mass). 

References:

  • Giancoli, Physics for Scientists and Engineers, 4th edition, Chapter 21 (2008).

Credits:

The Coulomb Pendulum Model was created by Anne Cox and converted to JavaScript by Fremont Teng and Loo Kan Wee using the Easy Java Simulations (EJS) authoring and modeling tool.

You can examine and modify a compiled EJS model if you run the program by double clicking on the model's jar file.  Right-click within the running program and select "Open EJS Model" from the pop-up menu to copy the model's XML description into EJS.  You must, of course, have EJS installed on your computer. 

Information about EJS is available at: <http://www.um.es/fem/Ejs/> and in the OSP ComPADRE collection <http://www.compadre.org/OSP/>.

 

Translations

Code Language Translator Run

Credits

Anne J Cox; Fremont Teng; Loo Kang Wee

Introduction:

This briefing document provides an overview of the "Coulomb Pendulum JavaScript Simulation Applet HTML5" resource available on the Open Educational Resources / Open Source Physics @ Singapore website. This resource offers an interactive simulation of a classic physics experiment demonstrating Coulomb's Law, the fundamental law describing the electrostatic force between electrically charged particles. The document will outline the main features, pedagogical applications, technical aspects, and context of this simulation within the broader OSP@SG platform.

2. Main Themes and Important Ideas/Facts:

  • Simulation of Coulomb's Law: The core function of the applet is to visually demonstrate the repulsive force between two like charges hanging from wires. The simulation allows users to observe the motion of the charges and the resulting angle of the wires from the vertical as they reach a state of equilibrium. The "About" section explicitly states: "Two charges hanging from wires, repel each other. The simulation shows the motion and reports angle (from the vertical) for each charge."
  • Interactive Parameter Control: A key feature is the user's ability to manipulate several parameters affecting the system. These include:
  • Charge: Users can change the charge on each particle in microcoulombs (μC) using field boxes and sliders. The "Instructions" section details the "Charge Field Box and Slider."
  • Initial Position: When the simulation is paused, "Draggable Boxes" appear, allowing users to set the initial horizontal position of the charges. The description clarifies: "These boxes are draggable and allows the user to move and set the particle's initial position. Note that you won't see this option if the simulation is playing."
  • Damping: The simulation allows for the motion to be damped by setting the velocity of the charges to zero using the "Zero Velocity Button." This is helpful for quickly reaching equilibrium and analyzing the balanced state.
  • Educational Exercises: The resource includes three explicit exercises designed to guide student learning and exploration of Coulomb's Law:
  1. Observing the equilibrium angle with equal initial charges.
  2. Investigating the effect of unequal charges on the equilibrium angles and symmetry. This encourages predictive reasoning and experimental verification: "If you increase the value of one charge, what difference do you expect in the angles where they will balance? Will it still be symmetric? Explain and then try it."
  3. Using the simulation's measurements (angle, string length) and Coulomb's Law to determine the mass of the charges. This links the simulation to quantitative problem-solving.
  • Underlying Technology and Development: The simulation is a "JavaScript Simulation Applet HTML5," making it accessible through modern web browsers without the need for specific plugins (beyond potentially requiring "Ejs" for examining the model). It was created using the "Easy Java Simulations (EJS) authoring and modeling tool" by Anne Cox and converted to JavaScript by Fremont Teng and Loo Kan Wee. The resource highlights the open nature of the tool and the model: "You can examine and modify a compiled EJS model if you run the program by double clicking on the model's jar file. Right-click within the running program and select 'Open EJS Model' from the pop-up menu to copy the model's XML description into EJS. You must, of course, have EJS installed on your computer." Information about EJS and the OSP ComPADRE collection is provided via hyperlinks.
  • Integration and Embeddability: The resource offers an "Embed" option with an <iframe> tag, allowing educators to easily integrate the simulation into their own webpages or learning management systems. This promotes wider accessibility and use of the tool.
  • References and Credits: The resource provides a reference to a relevant textbook ("Giancoli, Physics for Scientists and Engineers, 4th edition, Chapter 21 (2008)") for further reading on the topic. It also explicitly credits the individuals involved in the creation and conversion of the model.
  • Learning Goals and Teacher Support: While the "Sample Learning Goals" section is empty ("[text]"), the "For Teachers" section and the included exercises clearly indicate the intended pedagogical use of the simulation in teaching electromagnetism. The detailed "Instructions" section further supports teachers and students in effectively using the applet.
  • Additional Features: The instructions mention other interactive elements such as "Play/Pause, Step and Reset Buttons" and "Toggling Full Screen," enhancing the user experience and control over the simulation.
  • Context within OSP@SG: The simulation is part of a larger collection of "Open Educational Resources / Open Source Physics @ Singapore," which aims to provide freely accessible and modifiable physics simulations for educational purposes. The extensive list of "Other Resources" demonstrates the breadth of topics covered by the OSP@SG project, ranging from mechanics and waves to electromagnetism, thermal physics, and even mathematical concepts. The "Popular Tags" section highlights "Electromagnetism" as a key area within the collection.

3. Analysis and Implications:

The Coulomb Pendulum simulation is a valuable tool for physics education. Its interactive nature allows students to actively explore the principles of Coulomb's Law by manipulating variables and observing the resulting effects. The included exercises provide a structured approach to learning and encourage quantitative reasoning. The open-source nature of the underlying EJS platform allows for potential modification and customization by educators with the necessary skills.

The availability of the embed code makes it easy to integrate the simulation into online learning environments, increasing its potential reach and impact. The reference to a standard physics textbook provides a link to more in-depth theoretical explanations.

The sheer number of other simulations listed on the page indicates a rich ecosystem of interactive learning resources available through OSP@SG, covering a wide range of physics and mathematics topics. This positions the Coulomb Pendulum simulation within a broader context of freely available, high-quality educational materials.

4. Recommendations:

  • Populate the "Sample Learning Goals" section with specific learning objectives that the simulation can help students achieve.
  • Consider providing more detailed theoretical background or links to relevant concepts within the simulation's description.
  • For teachers unfamiliar with EJS, providing more user-friendly ways to access and potentially modify the underlying model could further enhance the resource's value.
  • Highlight the connection to Coulomb's Law explicitly in the "About" section to immediately convey the core physics principle being demonstrated.

5. Conclusion:

The Coulomb Pendulum JavaScript Simulation Applet HTML5 is a well-designed and valuable open educational resource for teaching and learning about electrostatic forces. Its interactive features, guided exercises, and embeddability make it a useful tool for both students and educators. Its place within the extensive OSP@SG collection further underscores its contribution to freely accessible physics education materials.

 

 

Coulomb Pendulum Simulation Study Guide

Key Concepts

  • Coulomb's Law: The force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between their centers.
  • Electrostatic Repulsion: The force exerted by charges of the same sign, causing them to move away from each other.
  • Equilibrium: A state where the net force acting on an object is zero, resulting in no acceleration. In the context of the Coulomb pendulum, this is the balanced position of the charged spheres.
  • Angle of Displacement: The angle between the vertical and the string supporting a charged sphere in the Coulomb pendulum. This angle indicates the extent of the electrostatic repulsion.
  • Damping: A process that reduces the amplitude of oscillations in a system over time, often due to energy loss. The simulation allows for setting the velocity to zero to observe the equilibrium position without oscillations.
  • Microcoulomb (μC): A unit of electric charge equal to one millionth of a coulomb (\(1 \times 10^{-6}\) C).
  • Free Body Diagram: A diagram showing all the forces acting on an object, crucial for analyzing its equilibrium. In the Coulomb pendulum, these forces include electrostatic force, tension in the string, and gravitational force.
  • Trigonometry: The branch of mathematics dealing with the relationships between the sides and angles of triangles, essential for resolving forces in the Coulomb pendulum problem.
  • Easy Java Simulations (EJS): A free authoring and modeling tool used to create interactive simulations like the Coulomb Pendulum model. Users with EJS installed can examine and modify the underlying model.

Short Answer Quiz

  1. Describe the fundamental interaction being modeled in the Coulomb Pendulum simulation.
  2. What factors can a user directly manipulate in the Coulomb Pendulum simulation applet?
  3. Explain what happens when the "v=0" button is pressed in the simulation and why this is useful.
  4. According to the exercises provided, what is expected to happen to the angles of the charged spheres when the magnitude of one charge is increased?
  5. What are the primary forces acting on each charged sphere when the Coulomb pendulum is in equilibrium?
  6. What units are used for the charge and the length of the support string in the default simulation setup?
  7. Who created the original Coulomb Pendulum Model and who converted it to JavaScript?
  8. What is required for a user to be able to examine and modify the compiled EJS model of the simulation?
  9. State one way the simulation allows users to set the charge of the particles.
  10. What does the simulation report about the motion of the charged spheres?

Short Answer Quiz - Answer Key

  1. The Coulomb Pendulum simulation models the electrostatic repulsion between two like charges suspended from wires, causing them to move away from each other until they reach a state of equilibrium where the repulsive force is balanced by gravity and tension.
  2. Users can change the charge (in μC) of each sphere, their initial position (when paused using draggable boxes), and damp the motion by setting their velocity to zero.
  3. Pressing the "v=0" button sets the velocities of both charged particles to zero, effectively stopping any oscillations and allowing the user to observe the equilibrium position of the charges directly. This helps in determining the balanced angle without waiting for natural damping to occur.
  4. Increasing the value of one charge will cause the angles to be unequal at the new equilibrium position; the sphere with the increased charge will likely have a larger angle of displacement from the vertical, and the symmetry of the angles will be broken.
  5. The primary forces acting on each charged sphere at equilibrium are the electrostatic repulsive force from the other charge, the gravitational force pulling it downwards, and the tension in the supporting string acting upwards and inwards.
  6. The charge is given in microcoulombs (μC), and the support string for each pendulum is 1 meter in length.
  7. The Coulomb Pendulum Model was created by Anne Cox and converted to JavaScript by Fremont Teng and Loo Kan Wee.
  8. To examine and modify the compiled EJS model, a user needs to have the Easy Java Simulations (EJS) authoring and modeling tool installed on their computer and must run the program by double-clicking on the model's jar file, then select "Open EJS Model".
  9. Users can set the charge of the particles by inputting a value directly into the respective charge field boxes or by manipulating their respective sliders.
  10. The simulation shows the motion of the two charged spheres and reports the angle (from the vertical) for each charge as they move and settle into an equilibrium position.

Essay Format Questions

  1. Discuss the relationship between the magnitude of the charges on the pendulums and the equilibrium angle they achieve. How does the simulation allow you to explore this relationship experimentally?
  2. Explain the forces acting on one of the charged spheres in the Coulomb pendulum and how these forces balance when the system reaches equilibrium. Consider how changing the charge affects this equilibrium.
  3. Describe how the Coulomb Pendulum simulation could be used as an educational tool to help students understand Coulomb's Law and the concept of electrostatic force. What advantages does this interactive model offer compared to static diagrams or theoretical descriptions?
  4. Consider the scenario where the masses of the two charged spheres in the simulation were different. How would you expect this to affect their equilibrium positions and angles of displacement, even if their charges remained the same? Explain your reasoning.
  5. The simulation allows for damping the motion by setting the velocity to zero. Discuss the importance of damping (or the lack thereof in an ideal system) in reaching and observing the equilibrium state of the Coulomb pendulum.

Glossary of Key Terms

  • Coulomb (C): The standard unit of electric charge in the International System of Units (SI).
  • Electrostatics: The branch of physics that deals with phenomena arising from stationary or slow-moving electric charges.
  • Force: An interaction that, when unopposed, will change the motion of an object. It can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate.
  • Gravity: The force of attraction by which terrestrial bodies tend to move toward the center of the earth. More generally, the attraction that any two objects with mass exert on each other.
  • Tension: The pulling force transmitted axially by the means of a string, cable, chain, or similar one-dimensional continuous object, or by each end of a rod, truss member, or similar three-dimensional object.
  • Simulation: A model or representation of a real-world system or process, often used for educational or analytical purposes. In this context, it's a computer program that mimics the behavior of a Coulomb pendulum.
  • Applet: A small application, typically one designed to run within another application, such as a web browser. The Coulomb Pendulum model is presented as a JavaScript simulation applet.
  • Open Educational Resources (OER): Teaching, learning, and research materials that are freely available and openly licensed, permitting their re-use, re-purposing, adaptation, and redistribution by others.
  • HTML5: The latest evolution of the standard that defines HTML. It supports new multimedia elements and features, allowing for richer web applications like the Coulomb Pendulum simulation.
  • JavaScript: A high-level, often just-in-time compiled language that conforms to the ECMAScript specification. It is a programming language that makes web pages interactive and is used to run the Coulomb Pendulum simulation in a browser.

Sample Learning Goals

[text]

For Teachers

 

Instructions

Charge Field Box and Slider

 
The charge of the particles can be set by inputting inside their respective field boxes
or by toggling their respective sliders.
 

Zero Velocity Button

 
Pressing this button will set the velocities of the two particles to zero.
 

Draggable Boxes

 
When the simulation is paused, two draggable boxes and texts will appear over the lines.
 
These boxes are draggable and allows the user to move and set the particle's initial position.
 
Note that you won't see this option if the simulation is playing.
 

Toggling Full Screen

Double clicking anywhere in the panel will toggle full screen.
 
Note that this won't work if the simulation is playing.
 

Play/Pause, Step and Reset Buttons

Plays/Pauses, steps and resets the simulation respectively.

Research

[text]

Video

  1. https://www.youtube.com/watch?v=Lu_ejsOeD-U by ETDtogo 
  2. https://www.youtube.com/watch?v=N6rgTYMy9Cw by ETDtogo 
  3. https://www.youtube.com/watch?v=LlPRzY6EvVI  by ETDtogo 

 Version:

Other Resources

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Frequently Asked Questions: Coulomb Pendulum Simulation

What is a Coulomb pendulum and how does this simulation model it?

A Coulomb pendulum typically involves two charged objects suspended by strings that repel each other due to electrostatic forces described by Coulomb's Law. This JavaScript simulation models such a system by showing the motion and reporting the angle from the vertical for each charged object. It allows users to visualize the interaction between these charges and how they reach an equilibrium position.

What parameters can be changed in the Coulomb pendulum simulation?

Users of the simulation can modify several parameters to observe their effects on the system. These include the charge on each particle (in micro Coulombs, μC), the initial position of the charges, and the damping of the motion (by setting the velocity to zero). Sliders and input fields are provided for adjusting the charges, and draggable boxes appear when the simulation is paused to set initial positions.

What kind of experiments or investigations can be conducted using this simulation?

The provided exercises suggest a few investigations. Users can observe the equilibrium angle when both charges are equal and stationary. They can also explore how changing the magnitude of one charge affects the equilibrium angles and whether the system remains symmetric. Furthermore, given the charge and string length, users are challenged to determine the mass of the identical charged particles.

What is the role of the "v=0" button in the simulation?

The "v=0" button, also labeled as the "Zero Velocity Button," allows users to immediately halt the motion of the charged particles by setting their velocities to zero. This is particularly useful for observing the equilibrium position of the charges without the influence of kinetic energy or oscillations.

What is EJS and why is it mentioned in the context of this simulation?

EJS stands for Easy Java Simulations, which is a free authoring and modeling tool used to create interactive simulations like this Coulomb pendulum model. The model was originally created using EJS and then converted to JavaScript (HTML5) for broader accessibility via web browsers. Users who have EJS installed on their computers can examine and modify the underlying model by downloading and running its JAR file, then opening the EJS model from within the running program.

How can this Coulomb pendulum simulation be used for teaching or learning?

This simulation offers a visual and interactive way to understand Coulomb's Law and electrostatic repulsion. Students can explore the relationship between charge, distance (represented by the angle of the pendulum), and the resulting equilibrium. Teachers can use it to pose questions, conduct virtual experiments, and encourage students to make predictions and test their understanding of electrostatic forces. The included exercises provide specific learning objectives.

Are there any resources provided to help understand the physics behind the simulation?

Yes, the simulation page references Giancoli's "Physics for Scientists and Engineers," specifically Chapter 21 of the 4th edition (2008), which likely covers Coulomb's Law and electrostatic forces in detail. Additionally, the page provides links to YouTube videos that may offer explanations or demonstrations related to the Coulomb pendulum.

Where can I find more information about EJS and other similar simulations?

More information about the Easy Java Simulations (EJS) tool can be found at the provided link: http://www.um.es/fem/Ejs/. Additionally, the Open Source Physics (OSP) ComPADRE collection at http://www.compadre.org/OSP/ hosts a variety of physics simulations and resources, including those created with EJS.

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