Notes

This Concept Builder can be used at any time during a study of momentum conservation in collisions. There are five understandings that emerge (or are at least strengthened) from the exercise. They are:

• Students learn to calculate the momentum of an object from its mass and velocity.
• Students learn to calculate the momentum change of an objects as the post-collision value minus the pre-collision value.
• Students learn that the system momentum is the sum of the two individual object's momentum.
• Students learn that the total momentum of the system before the collision is equal to the total momentum of the system after the collision.
• Students learn that the momentum change of one of the objects is equal and opposite to the momentum change of the other object.

The Concept Builder is based on the theme that if you keep track of the momentum of objects involved in a collision you notice that the total amount is the same before and after the collision. The keeping track part of this statement infers that you can keep track of momentum in the same way that you might keep track of money. When keeping track of money, you might set up a ledger table that lists the amount of money in various accounts at the beginning of the month and at the end of the month. This accounting procedure lists the various locations that money might be located in the form of a table. And such a table usually has a bottom line - often titled Total. This is exactly what a Momentum Table does - it keeps track of the various locations or objects that contain momentum and keeps track of that momentum. A Momentum Table also lists the total amount of momentum before and after the collision.

There are three difficulty levels in this Concept Builder. Each difficulty level consists of six Question Groups. The Question Groups each have two questions. Students are delivered one of the two questions (randomly-chosen) in each group. Four of the Question Groups involve the completion of a Momentum Table. They must calculate momenta values and enter them in the table. They must also calculate system momenta values and change values. When they check their answers, any incorrect values are listed with a red dot. Students are told what the red dot means. They can continue checking answers until they get the entire table correct. While four of the Question Groups involve completion of a Momentum Table, two of the Question Groups involve the analysis of a completed Momentum Table. The analysis is in the form of a Multiple Choice question. They are given five statements and they must identify which statement describes a set of two highlighted cells in the Momentum Table. One of these Question Groups focuses on the Before- and After-Collision momentum of the system, The other Question Group focuses on the Momentum Change of the Red Cart compared to the Blue Cart. There are two different multiple choice questions in each of these Question Groups. The Momentum Table is different and the order of options is randomly scrambled. If students miss the question, then they will be delivered the other question in the Question Group at a later time in the exercise; they must answer it correctly and then they will receive (at some later time) the original question that they missed.

The three difficulty levels are differentiated from one another in the following manner:
 

• Apprentice: Question Groups 1-6. Collision between two carts. One cart is initially at rest. The two carts collide, bounce apart, and move with different speeds after the collision. The momentum value of one object before the collision is stated. A momentum change value or a post-collision momentum for one of the carts is stated. Students must use momentum conservation to complete a momentum table.
• Master: Question Groups 7-12. Collision between two carts. One cart is initially at rest. The two carts collide, bounce apart, and move with different speeds after the collision. Mass, speed, and direction information for before and after the collision are stated. Students must use momentum conservation and the momentum equation to complete a momentum table.
• Wizard: Question Groups13-18. Question Groups 7-12. Collision between two carts. Both objects are moving before the collision. For some of the Question Groups, one of the carts has a negative momentum. In all cases, the two carts collide, bounce apart, and move with different speeds after the collision. Mass, speed, and direction information for before and after the collision are stated. Students must use momentum conservation and the momentum equation to complete a momentum table.

It is likely that not every difficulty level is appropriate for every classroom. We recommend that teachers preview the Concept Builder before assigning it to students in order to insure that the assigned difficulty levels are appropriate for their students. The Questions can be viewed in a separate file if desired.

The most valuable (and most overlooked) aspect of this concept-building tool 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 Concept Builder 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.

There are numerous resources at The Physics Classroom website that serve as very complementary supports for the Keeping Track of Momentum (Hit and Bounce Collisions) Concept Builder. These include:

Additional resources and ideas for incorporating the Keeping Track of Momentum (Hit and Bounce Collisions) Concept Builder into an instructional unit on Momentum and Collisions can be found at the Teacher Toolkits section of The Physics Classroom website. Visit Teacher Toolkits.