Dynamic Modeling

Double-click the green arrow to open the video in Tracker. Note that the video has already been calibrated and a viscous model (depends linearly on v) has been created as an example.

Study the viscous model inspector and note that it defines two user parameters: the acceleration of gravity "g" and an overall viscosity constant "b." Identify the gravitational force and viscous force terms in the "force y" function. When vy is negative in this function, what is the sign of the viscous force term?

The viscosity parameter and initial conditions have been set by trial and error to match the motion of the mass 5 cup reasonably well (step through the video to confirm this). Try changing their values to see how the behavior of the model changes. Note that the initial values of x and y start the model right over the cup in the video.

Temporarily hide the viscous model by unchecking "Visible" in its track menu. Then create a new Dynamic Particle Model to model the drag force (depends on v2).

1. Set the correct mass of the particle model on the toolbar.
2. In the model inspector, define the parameters "g" and an overall drag constant "d."
3. Enter a force y function with gravitational and drag force terms. When vy is negative in your function, does the drag force term have the right sign?
4. Using trial and error, set the drag constant and initial conditions to match the motion of the mass 5 cup as closely as possible.
5. Save your work in a Tracker data file.

Can you get the drag model to match the real cup's motion as well as the viscous model does? Can you tell which of the two force types is a better model for air resistance?

I n the next two exercises you will look at these models in more detail.