Physics Models and Physical Modeling:

This fall we have been working on the FOSS unit Mass Force and Models.  We began with the Pendulum module and the investigation covers the basic ideas of variables and what variables affect the frequency of a pendulum.  We made pendulums with string, paperclips, and pennies to test which of three variable might affect the frequency:  mass, release position (amplitude), or pendulum length.  In some sense, these pendulums could be considered as models, as they were not designed as part of a machine, to regulate a clock for example. 

When we tested length, we recorded our data and then hung the pendulums on the wall according to how many cycles they achieved in 15 seconds.  The lengths has been calibrated so that as the hooks, labeled from 5 to 21, increased in ordinal value, the length of the pendulum hanging there decreased, describing a half parabola.  It is really cool to look at and the kids are always amazed by it.  FOSS termed this physical model as a physical graph.  We talked a bit about what the graph shows, about the relationship between the length and the frequency, and then a bit about the underlying math, the parabolic relationship.

As an idea I’d like to see if we can plug the data points into Wolfram’s Alpha and get the equation of the parabola we found experimentally.

Then the students turn this physical model into a 2-D paper model be making what FOSS terms a pictograph, a graph that abstracts a little, but pretty closely resembles the physical wall graph.  From this they see the first step of abstraction.

Then they turn the same data into a 2-coordinate graph.  For many of them, this is one of the first 2-coordinate graphs they have done and just learning the mechanics is a good lesson.  I always insist on them labeling the axes with not only the number lines, but also with the units and the X and Y coordinates, as well as a title.  From here we work with this pretty abstracted model to get more a sense of the underlying physics.

If I can get them a calculator to give the equation, then we’ll have also tied in the Math, moving from the actual pendulum or pendulum model to a physical graph to a pictograph to a 2-coordinate graph to an equation, which is a mathematical model of the pendulum.  This will be pretty neat!

We may also need to build a really big pendulum using weight plates for some to let go of the misconception/alternative conception that while mass makes no difference at lower values of mass, it will certainly alter the frequency of a pendulum at higher values, with really big weights.