### Notes:

The Vertical Spring: Velocity and Force 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:

For many teachers, the topic of vibrational motion is a stand-alone topic, often placed in the Mechanics section of the coure. For others, vibrational motion is a segue into the study of mechanical waves. Wherever it is placed, this Concept Builder provides an in-depth look at the relationship between the velocity, the forces, and the location of the vibrating mass on a vertical spring along its back-and-forth path. Students must be able to identify where the speed is greatest and where it is least (zero) and how it is changing between two positions. They must be able to identify where the net force is the greatest and where it is the least (zero) and how it is changing between two positions. Finally, students must be able to identify the free-body diagram for the three locations in the given path and describe how the magnitude and direction of the gravity and tension force changes (or not) as the mass moves from one location to another location. The three locations in this activity are the equilibrium position, a position below the equilibirum position, and a position above the equilibrium position (but below the relaxed spring position). In all instances, the spring is stretched and never compressed.

This Concept Builder can be used as an in-class activity or (for those with Task Tracker subscriptions) as assigned homework/practice. After some discussion, demonstrations, lab work, and practice with the concepts of velocity and force and its connection to the location of the mass along its back-and-forth path, allow students to attempt the Concept Builder. The Concept Builder includes three unique and independent 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 activities would be most appropriate for their students. Our summary of the three activities is as follows:
• Speed Analysis: Question Groups 1 - 4 ... Identify the locations the path of the vibrating mass where the speed is smallest, greatest, and zero.
• Force Analysis: Question Groups 5 - 8 ... Identify the locations the path of the vibrating mass where the net force is smallest, greatest, and zero.
• Graphical Analysis: Question Groups 9 - 14 ... Identify the free-body diagram and answer questions about the magnitude and direction of the individual forces.
In order to complete an activity, a student must correctly analyze each question in 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 an activity, a system of stars and other indicators are used to indicate progress on the level. 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 trophy which is displayed on the Main Menu (for those students with Task Tracker accounts). This system of stars and trophies 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 a few resources at The Physics Classroom website that serve as very complementary supports for the Vertical Spring: Velocity and Force Concept Builderr. These include:
• Science Reasoning Center
Our Science Reasoning Center provides teachers with a set of reading passages that can be used in class to cultivate and practice skills associated with analyzing data, evaluating models, and and interpreting graphs (among other skills). Our Mass on a Spring passage describes the up and down motion of a mass on a spring using a diagram, a position-time graph, and a velocity-time graph. The 12 questions target a student's ability to select values from a graph, to combine information from two different graphs to draw appropriate conclusions, to identify the amplitude and the period, and to interpret the graphs in light of information on a diagram.

Visit the Waves Chapter of the Science Reasoning Center.

• Physics Interactives Simulations
One of our simulations at the Physics Interactives section makes an incredible complement to this activity. The Mass on a Spring simulation animates the up and down motion of a mass on a spring. The accompanying ready-to-use activity to this simulation provides loads of student practice and investigation into the concepts of period and frequency and the effect that spring constant and mass have upon them.

Visit the Mass on a Spring.

• Curriculum/Practice: If your study of a vibrating mass on a spring (and vibrational motion) is a lead-in to a unit on waves, we would like to call your attention to our Curriculum Corner section with a complete set of think sheets on the topic of wave motion.

Visit the Curriculum Corner - Wave Basics

Additional resources and ideas for incorporating this Vertical Spring: Velocity and Force Concept Builder into an instructional unit on Vibrations and Waves can be found at the Teacher Toolkits section of The Physics Classroom website.  Visit Teacher Toolkits.