### Notes:

The Equilibrium Concept Builder is an adjustable-size file that displays nicely on smart phones, on tablets such as the iPad, on Chromebooks, and on laptops and desktops. The size of the Interactive can be scaled to fit the device that it is displayed on. The compatibility with smart phones, iPads, other tablets, and Chromebooks make it a perfect tool for use in a 1:1 classroom.

### Teaching Ideas and Suggestions:

One of the most powerful tools of a Physics student is to think in terms of components. Understanding (and believing) that angled vectors can be replaced by two components - one along the x-axis and the other along the y-axis - can simplify most vector problems. After all, when all forces are up, down, right, and left, students generally find the problem to be easy. So the substituting of components for angled vectors is the first step of any two-dimensional analysis. By providing angle vectors on top of a background grid of squares, this Concept Builder quickly trains students to visualize components without needing to use a calculator. Students will quickly measure out squares along the x-axis and the y-axis from the origin out to the arrowhead of the vector. This, we hope, cultivates the habit of thinking in terms of components.

This Concept Builder consists of three difficulty levels. Each level includes four Question Groups. Students will get a question from each Question Group. All questions within the same Question Group are very similar in that the given vectors for those questions always lie in the same quadrant(s). All questions wiithin the same Difficulty Level will always provide the same number of given vectors. Students must analyze the given vectors and add two additional vectors in order to bring the object to equilibrium.

It is not necessary to start with the Apprentice Level or to finish with the Wizard Level. However, even for the stronger students, we recommend starting with the Apprentice Level in order to gain some confidence and familiarity with the interface and the use of the Force Pad for entering answers. That being said, the activity was designed such that classrooms can start and finish at the levels that are most appropriate for them. We recommend that teachers view the Questions or do the Concept Builder in order to make judgements about what works best for their specific classes.

The three difficulty levels are differentiated as follows:

• Apprentice Difficulty Level Questions 1-4: A single vector is given. The vector makes an angle to the traditional coordinate axes. Students must add an E/W vector and a N/S vector to balance the force.
• Master DifficultyLevel Questions 5-8: Two vectors are given. The vectors make an angle to the traditional coordinate axes. Students must add an E/W vector and a N/S vector to balance the forces.
• Wizard Difficulty Level Questions 9-12: Three vectors are given. The vectors make an angle to the traditional coordinate axes. Students must add an E/W vector and a N/S vector to balance the forces.

In order to complete a difficulty level, a student must successfully analyze all Question Groups of that level. A successful analysis involves adding two vectors to the given vector(s) in order to establish equilibrium. The Check Answers button can be used to check the answers. Feedback will be immediate and the Progress Report will be updated. Correctly analyzed Question Groups will display a star in the Progress Report. Incorrectly analyzed Question Groups will display a red background. When a red background is displayed, a student will have to answer two questions correctly from that Question Group in order to earn the star. When stars have been earned for all Question Groups of that difficulty level, the student is returned to the Main Menu and (if logged in as a Task Tracker user) the Trophy for that difficulty level is displayed.

The most valuable (and most overlooked) aspect of this concept-building activity is the Help Me! feature. Each situation is accompanied by a Help page that discusses in detail the specifics of the situation. Formulas, tips, suggestions, etc. are provided. This Help feature transforms the activity from a question-answering activity into a concept-building activity. The student who takes the time to use the Help pages can be transformed from a guesser to a learner and from an unsure student to a confident student. The "meat and potatoes" of the Help pages are in the sections titled "How to Think About This Situation:" Students need to be encouraged by teachers to use the Help Me! button and to read this section of the page. A student that takes time to reflect upon how they are answering the question and how an expert would think about the situation can transform their naivete into expertise.

### Related Resources

There are numerous resources at The Physics Classroom website that serve as very complementary supports for the Equilibrium Concept Builder. These include:
• Minds On Physics Internet Modules:
The Minds On Physics Internet Modules include a collection of interactive questioning modules that help learners assess their understanding of physics concepts and solidify those understandings by answering questions that require higher-order thinking. Assignments from the Forces in Two Dimensions module make for a great complement to this Concept Builder. They are best used in the middle to later stages of the learning cycle. We recommend missions F2D3 and F2D4 as accompanimenst to this activity. Visit the Minds On Physics Internet Modules.

Users may find that the App version of Minds On Physics works best on their devices. The App Version can be found at the Minds On Physics the App section of our website. The Forces in Two Dimensions module can be found on Part 2 of the six-part App series. Visit Minds On Physics the App.

Additional resources and ideas for incorporating Equilibrium into an instructional unit on Newton's Laws  can be found at the Teacher Toolkits section of The Physics Classroom website.  Visit Teacher Toolkits.