About

Topics

Scalars and vectors
Measurement of length and time

Description

Play with the vector sum Model. The simulation randomly generates different vector A and B every time the reset is clicked.
You can
drag the vector midpoint to re-position
drag the vector head to re-size
There are also 3 examples of how this simulation can be used by Teacher Mr. Ezzy Chan.
There are also 3 components representation to connect with the related simulation on components of a vector.

Challenge:

Take an example from your usual word problem and take a picture of it and try to use the simulation to represent the word problem. After you are done, the simulation should be able to calculate as well as draw the resultant vector. send your completed picture to This email address is being protected from spambots. You need JavaScript enabled to view it. to be included as an example in this simulation-model!
 

Translations

Code	Language		Translator	Run

Credits

wee loo kang; tina

Learning Objectives: https://sites.google.com/moe.edu.sg/a-level-physics-tlg/foundations-of-physics/quantities-measurement

Learning Outcomes: H2 - 1(h)(i)(j)

Curriculum Emphasis: Ways of Thinking and Doing [WOTD https://vle.learning.moe.edu.sg/mrv/moe-library/lesson/view/c788167e-5865-4166-b147-89330b50b6b2/cover  SLS lesson includes questions that can be repeated indefinitely with random values inserted. 

Vector Addition Study Guide

Key Terms Glossary

1. Scalar: A quantity that has only magnitude, such as speed, mass, or temperature.
2. Vector: A quantity that has both magnitude and direction, such as velocity, force, or displacement.
3. Magnitude: The size or amount of a quantity, represented by the length of a vector.
4. Direction: The orientation of a vector, often represented by an angle relative to a reference axis.
5. Resultant Vector: The single vector that represents the sum of two or more vectors.
6. Graphical Method (Tip-to-Tail): A visual method of vector addition where the tail of one vector is placed at the head of the previous vector, and the resultant vector is drawn from the tail of the first vector to the head of the last vector.
7. Parallelogram Method: A graphical method of vector addition for two vectors where the vectors are drawn as adjacent sides of a parallelogram, and the resultant vector is the diagonal of the parallelogram.
8. Components of a Vector: The projections of a vector onto two perpendicular axes (usually x and y), representing the vector's contribution in each direction.

Short-Answer Quiz

1. What is the key difference between a scalar and a vector quantity? Provide an example of each.
2. Describe the "tip-to-tail" method of vector addition.
3. How is the magnitude of a vector represented graphically?
4. Explain how to find the resultant vector when adding two vectors using the parallelogram method.
5. Can the magnitude of the resultant vector be smaller than the magnitudes of the individual vectors being added? Explain.
6. What are the components of a vector, and how are they useful in vector addition?
7. If two vectors are acting in opposite directions, how do you determine the direction of the resultant vector?
8. How can you use a vector diagram to solve a word problem involving forces or displacements?
9. What is the significance of the angle between two vectors when determining their resultant?
10. How does the simulation model from Open Educational Resources / Open Source Physics @ Singapore help in understanding vector addition?

Short-Answer Quiz Answer Key

1. A scalar quantity has only magnitude, while a vector quantity has both magnitude and direction. Speed is a scalar, while velocity is a vector.
2. In the tip-to-tail method, the tail of the second vector is placed at the head of the first vector. The resultant vector is then drawn from the tail of the first vector to the head of the second vector.
3. The magnitude of a vector is represented graphically by the length of the arrow representing the vector.
4. To add vectors using the parallelogram method, the vectors are drawn as adjacent sides of a parallelogram. The diagonal of the parallelogram starting from the common tail of the two vectors represents the resultant vector.
5. Yes, if the vectors being added are in opposite directions, the magnitude of the resultant vector can be smaller than the magnitudes of the individual vectors.
6. Components of a vector are the projections of the vector onto perpendicular axes (x and y). They are useful because vectors can be added by adding their corresponding components.
7. If two vectors act in opposite directions, the direction of the resultant vector will be the same as the direction of the vector with the larger magnitude.
8. A vector diagram can be used to represent the forces or displacements in a word problem as vectors. By applying the appropriate vector addition method, the resultant vector can be found, representing the net force or total displacement.
9. The angle between two vectors affects both the magnitude and direction of the resultant vector. The larger the angle, the smaller the magnitude of the resultant, and the direction changes as the angle changes.
10. The simulation model allows users to visually manipulate vectors, change their magnitudes and directions, and observe the resulting resultant vector, providing a dynamic understanding of vector addition.

Essay Questions

1. Explain the concept of vector addition and discuss the differences between the graphical method (tip-to-tail) and the parallelogram method of vector addition. Provide examples to illustrate your points.
2. Discuss the importance of understanding vector components in physics. How do vector components simplify the process of vector addition? Illustrate your answer with relevant examples.
3. Choose a real-world scenario involving vectors, such as the motion of a boat in a river with a current or the forces acting on an object on an inclined plane. Describe how you would use vector addition to analyze the situation and solve for the resultant vector.
4. Explain how you would determine the magnitude and direction of the resultant vector when adding more than two vectors. Can you use both the graphical and component methods in such cases?
5. Discuss the limitations of using graphical methods for vector addition. In what situations might analytical methods involving trigonometry or component calculations be more accurate or efficient?

Briefing Doc: Tip to Tail Vector Addition by Graphical Method

Source: Open Educational Resources / Open Source Physics @ Singapore: "Tip to Tail Vector Addition by Graphical Method JavaScript HTML5 Applet Simulation Model"

Main Themes:

• Vector Addition: The primary focus is on teaching the graphical method of vector addition, specifically the "tip to tail" method.
• Interactive Learning: The source emphasizes the use of a JavaScript HTML5 applet simulation model to facilitate hands-on learning and exploration of vector addition.
• Problem Solving: The simulation encourages students to apply their understanding of vector addition to real-world word problems and scenarios.

Most Important Ideas/Facts:

• Graphical Representation: Vectors are visually represented as arrows, where length corresponds to magnitude and direction indicates the vector's orientation.
• Tip to Tail Method: Vectors are added by placing the tail of one vector at the tip of the other. The resultant vector is drawn from the tail of the first vector to the tip of the last vector.
• Simulation Features: The applet allows users to reposition and resize vectors, providing an interactive platform for understanding vector addition.
• Educational Goals: The simulation aims to help students achieve learning outcomes related to adding vectors graphically and solving problems involving static point masses under the action of multiple forces.
• Challenge and Engagement: Students are challenged to translate traditional word problems into vector representations within the simulation, fostering deeper understanding and engagement.

Key Quotes:

• "(f) add two vectors to determine a resultant by a graphical method" - This highlights a key learning goal of the simulation.
• "Take an example from your usual word problem and take a picture of it and try to use the simulation to represent the word problem." - This encourages active application and problem-solving using the simulation.

Overall, this resource provides an interactive and engaging way for students to learn and practice the graphical method of vector addition, promoting conceptual understanding and problem-solving skills.

Apps

https://play.google.com/store/apps/details?id=com.ionicframework.vectorsumgraphical

https://itunes.apple.com/us/app/vector-sum-graphical/id1449949773?ls=1&mt=8 

http://iwant2study.org/lookangejss/01_measurement/ejss_model_vectorsum04/vectorsum04_Simulation.xhtml

For Teacher

 Video

https://notebooklm.google.com/notebook/dbab6363-3bd3-4a25-8bcc-21a3747cbc5a/audio

Versions:

1.  http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=216.0 summation of vectors by Fu-Kwun Hwang
2. https://weelookang.blogspot.com/2019/01/vector-addition-by-graphical-method.html

Other Resources

1. http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=1247.0 vector addition of 2 vectors by Fu-Kwun Hwang
2. http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=2018.0 summation of three vectors by Fu-Kwun Hwang
3. http://ophysics.com/k1.html by This email address is being protected from spambots. You need JavaScript enabled to view it..
4. http://ophysics.com/k2.html by This email address is being protected from spambots. You need JavaScript enabled to view it.
5. http://ophysics.com/k3.html by This email address is being protected from spambots. You need JavaScript enabled to view it.
6. https://www.geogebra.org/m/FCknj7c3 Vector Addition by ukukuku
7. https://ggbm.at/u2cgrc5q by tan Seng kwang

Tip to Tail Vector Addition by Graphical Method FAQ

What is the Tip to Tail Vector Addition by Graphical Method JavaScript HTML5 Applet Simulation Model?

This interactive simulation model is designed to help students understand the concept of vector addition using the graphical tip-to-tail method. Users can manipulate vectors on screen, observe their resultant, and connect this visual representation to mathematical calculations.

What topics does the simulation cover?

The simulation primarily focuses on scalars and vectors as well as measurement of length and time. It provides a visual and interactive way to understand how vectors are added graphically.

How does the simulation work?

The simulation presents two vectors, A and B, which are randomly generated each time the "reset" button is clicked. Users can interact with these vectors in the following ways:

• Re-position: Drag the midpoint of a vector to move it around the screen.
• Re-size: Drag the arrowhead of a vector to change its magnitude (length). The simulation automatically calculates and displays the resultant vector (A+B) based on the user's manipulations.

What are the learning goals of this simulation?

This simulation aims to help students:

• (f) add two vectors to determine a resultant by a graphical method
• (b) solve problems for a static point mass under the action of 3 forces for 2-dimensional cases (a graphical method would suffice)

What are some challenges to try with the simulation?

Try using the simulation to represent a word problem you might encounter in your studies. Adjust the vectors to match the problem's conditions, and see if the simulation accurately calculates and draws the resultant vector. You can even take a picture of your completed simulation and send it to This email address is being protected from spambots. You need JavaScript enabled to view it. to be featured as an example!

Where can I access the simulation?

You can access the simulation directly through this link: http://iwant2study.org/lookangejss/01_measurement/ejss_model_vectorsum04/vectorsum04_Simulation.xhtml

Are there mobile apps available for this simulation?

Yes! You can find the apps on the following platforms:

• Android: https://play.google.com/store/apps/details?id=com.ionicframework.vectorsumgraphical
• iOS: https://itunes.apple.com/us/app/vector-sum-graphical/id1449949773?ls=1&mt=8

Are there other resources related to vector addition?

Absolutely! You can find a curated list of additional resources, including other simulations, Java applets, and Geogebra examples, on the Open Educational Resources / Open Source Physics @ Singapore website. The specific page for the Tip to Tail Vector Addition simulation has direct links to these related resources.