### Notes:

The Universal Gravitation 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 Concept Builder 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:

Many Physics courses include a unit on Satellite Motion and Gravitation. Even those who don't often devote a small portion of the course discussing field forces such as the gravitational force. These forces are unique in terms of the dependency on distance between the two interacting objects. In the case of gravitation, the field force follows an inverse square relationship between force and separation distance. While difficult to demonstrate in a laboratory environment, we are fans of the Physics Interactive activity titeld Gravitation. We believe that it provides a great pre-cursor to this activity. This Concept Builder is intended for use near the middle stages of a learning cycle on Newton's law of Universal Gravitation.

Most physics courses spend considerable time using physics formulas to solve numerical word problems. Algebraic manipulation and substitution of known values into the formula is a typical activity. But we think that physics formulas are much more than recipes for solving problems for an unknown quantity. Physics formulas are tools to guide our thinking about how a variation in one quantity might affect another quantity in the formula. And that is what this activity is all about. Students think proportionally about the law of Universal Gravitation: Fgrav = G•m1•m2/d2. In the prrocess of completing this Concept Builder, students must ponder how an alteration in one or both masses would effect the force of gravitational acttraction between them. And they must ponder how an alteration in the separation distance between objects would effect the gravitational force. This task is much different than the algebraic manipulation of a formula and substitution of known values. This task will help students gain a better intuition for the relationship between force, the masses of objects, and their separation distance.

This Concept Builder was intended as an in-class activity. After some discussion of the gravitation law and the proportional relationships, allow students an opportunity to interact with the questions. The Concept Builder includes three activities. Teachers using the Concept Builder with their classes should preview the activity (or view the Questions in the separate file) in order to judge which levels would be most appropriate for their students. There is no redundancy from one activity to another activity. That is, all the questions in the third activity are unique to that activity.  Our summary of the three activities is as follows:

• Mass Attraction: 5 questions on the effect of object mass on gravitational force
• Diluted by Distance: 5 questions on the effect of separation distance on gravitational force
• Putting it All Together (most difficult): 6 questions on the dual effect of object mass and separation distance on gravitational force

We can imagine it being profitable to allow students to make judgements as to what level to begin with and to progress from easier to more difficult levels.

In order to complete an activity, a student must correctly analyze each question for that activity. If a student's analysis is incorrect, then the student will have to correctly analyze the same or very similar question twice in order to successfully complete the activity. This approach provides the student extra practice on questions for which they exhibited difficulty. As a student progresses through na activity, a system of stars and other indicators are used to indicate progress on the activity. A star is an indicator of correctly analyzing the question. Once a star is earned, that question is removed from the que of questions to be analyzed. Each situation is color-coded with either a yellow or a red box. A red box indicates that the student has incorrectly analyzed the question and will have to correctly analyze it twice before earning a star. A yellow box is an indicator that the question must be correctly analyzed one time in order to earn a star. Once every question in an activity has been analyzed, the student earns a medal which is displayed on the Main Menu. This system of stars and medals allows a teacher to easily check-off student progress or offer credit for completing assigned activities.

The most valuable (and most overlooked) aspect of this Concept Builder is the Help Me! feature. Each question group is accompanied by a Help page that discusses the specifics of the question. 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 Universal Gravitation 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 CG6 and CG7 of the Circular Motion and Gravitation module provide great complements to this Concept Builder. They are best used in the middle to later stages of the learning cycle. 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 Circular Motion and Gravitation module can be found on Part 2 of the six-part App series. Visit Minds On Physics the App.

• Physics Interactives: As mentioned above, our Physics Interactives section include an interactive simulation that makes for a perfect pre-cursor to this Concept Builder. It is called Gravitational Fields and is accompanied by a well-organized activity sheet that guides students to the key highlights of the activity.

Visit Gravitational Fields

• Calculator Pad: For those teachers committed to the use of equations as tools for algebraic problem-solving, the section of our website that provides the best support is the Calculator Pad. There you will find a set of problems of varying difficulty and complexity on most topics of interest. Each problem is accompanied by an answer and an audio-guided help file. It's a great tool for students attempting to improve their problem-solving ability.

Visit the Circular Motion and Gravitation Problem Set at the Calculator Pad

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