This third unit on the MTM is the first significant deviation from the traditional modeling framework. I expect it to take approximately two weeks. It will begin with two carts “exploding” apart and whiteboard meetings to analyze the results (ratio of masses of carts -> ratio of velocities of carts).
From there they will proceed through some of the modeling materials for the Momentum Transfer Model as provided by the Modeling Materials. The main focus of the unit will be that momentum is a quantity that is swapped between objects, depicting those swaps with “interaction diagrams” (formally called system schema) (labels of types of forces withheld during this unit), and momentum diagrams (IF charts). Also along the way, I will try to emphasize the similarity between displacement (being term for a change in position) and impulse (being the term for change in momentum).
The first worksheet is the same as the first worksheet from the Modeling Materials. It looks at mainly qualitative events and has the students determine relative momenta or impulses. We then look numerous collisions to see if momentum is conserved in collisions as well as the explosions seen in the lab. We skip the second worksheet provided by the Modeling Materials, as most of these problems focus on calculating impulses from Force & time. These types of problems will be address later in the UFPM unit. The new second and third worksheets use momentum diagrams to solve collision problems. We end with additional problems for review.
The students goals for this unit are:
- create an interaction diagram including the identification of the system.
- create a momentum diagram (IF diagram) for an event.
- interpret a momentum diagram by creating a mathematical model of an event.
- correctly solve problems involving an exchange of momentum.
Posted in AP1, Momentum
Tagged AP1, Modeling
This second unit on the CAPM will proceed along the traditional modeling framework. I expect it to take approximately two and a half weeks. It will begin with ball rolling (or cart sliding) down and incline plane and whiteboard meetings to analyze the results.
From there they will proceed through the modeling materials for the Constant Velocity Particle Model as provided by the Modeling Materials. The first worksheet allows them to analyze additional data sets similar to what the saw in the lab. The second worksheet has the student create motion maps, position-time, velocity-time, and acceleration-time graphs for more complicated ramp systems. Worksheet 3 focuses on analyzing position-time and velocity-time graphs. Worksheet 4 has the student solve quantitative problems. We end with additional problems for review.
The students goals for this unit are:
- create and interpret graphical and mathematical representations of objects moving with constant acceleration.
- can correctly differentiate between acceleration and velocity.
- correctly interpret the meaning of the sign of acceleration.
- solve kinematic problems involving constant acceleration.
This introductory unit on the CVPM will proceed along the traditional modeling framework with only a few additions. I expect it to take approximately three weeks. It will begin with the Buggy Lab and whiteboard meetings to analyze the results. The only change from the traditional progression will be to first complete the “Graphing Practice” worksheet from the Scientific Methods unit.
From there they will proceed through the modeling materials for the Constant Velocity Particle Model as provided by the Modeling Materials. Thus the new worksheet 2 will be a worksheet that focuses on the students converting between the position-time graphs, motion maps, and verbal descriptions. Worksheet 3 will then add velocity-time graphs to the mix. Worksheet 4 brings back data analysis and converting to the other representations. Worksheet 5 does the same, but for slightly more difficult situations. We end with additional problems for review.
For those using Standards Based Grading, the first draft of may standards is as follows:
Students will be able to (SWBAT):
- design an experiment that properly controls variables
- report measurements and calculations with proper precision
- develop a mental model that correctly explains and predicts an event
- algebraically solve an equation for a given variable.
- create a scatter plot of independent and dependent data points
- linearize data points
- create a mathematical model of a graph.
- create and interpret graphical and mathematical representations of objects moving with constant velocity.
- distinguish between position, distance and displacement.
- solve problems involving average speed or average velocity.
I’m fully aware that this is a long list of standards, and quite possibly too many standards. Any feedback on whether or not the list should be adjusted (and how) would be greatly appreciated.