Unit 3: Vertical Motion

The paradigm system for this unit was almost identical to that of the pendulum. Two different masses (or a heavy weight and a helium balloon) each tied to an elastic cord tied to different height stands the base of each was resting on its own Vernier force plate. On each force plate was a thick piece of pink foam insulation. The set up was extremely similar to the pendulum, except that in this case instead of pulling the weights up to an angle and releasing them we could cut the elastic, things that could be compared or varied included:

• the height of the fall or rise (in case of balloon with second string)
• the mass of the ball
  
• the change in the voltage of the force plate while interaction pathways was severed.
• the fall time by observing the time between the initial decrease of force in the force plate when the string was cut and its initial increase at the moment the mass contacted the foam.
  
• the radius and total depth of the left in the foam as well as the radius of each subsequent bounce.
• the size (in height and area) of the spike in the force plate voltage recorded for each bounce.
• the dependence of the spike on the whether the ball hit the foam, other packing material, the end of an elastic.

The idea was to repeat the same basic conceptual steps as in the pendulum modeling cycle but more quickly because now this would be the "second visit" to some of these concepts and so it would be a chance to see if any the student conception would transfer to this new but related system, and also to therefore start the process of freeing those concepts from the original context.

We started with the system creating system diagrams for the ball and the balloon before and after their strings were cut. Trying to identify the repulsive pathway of interaction between the earth and the balloon led to the discussion of air pressure about which my students had hardly any understanding.

This set up allowed some rich qualitative investigations as we tried as a class to make sense of the trace on the screen. Because of the setup the concept of the ball and earth both moving together and leaving a dent when they hit. These discussion really were fun.

I wanted it to be an authentic assessment to see if the students could grasp that the same conceptual steps and logical arguements that we went through with the pendulum would also work here.

• increased inertia would compensate for increased weight
• and since both average speed and fall time are increasing with the height of the fall then once again the simplest pair of relations would be if they were proportional to each other giving a square root and a square root.

However, I don't know how this would have worked out because I diverted at the last minute when I realized that many of my students lost all flow of the arguments as soon as we bogged down getting experimental data and moved from qualitative arguments and quick sketches of graphs to quantitative fits. To give them a little more exposure to LoggerPro before I gave them them analyzing the falling body data as an assessment I turned to the first exercise in "Den of Inquiry" i.e. measuring paragraphs and investigating the inverse relation between paragraph height and column width. I never came back to do the assessment because we got on a tangent, and now I am saving it for the midterm (I let you now how it comes out).

This is a dropped stitch which will need to be worked back in if I or anyone else plans to repeat this conceptual sequence.