Dynamic Model—Friction on Ice Now that you know how forces affect the motions of objects, you can use the Tracker video analysis tool to create dynamic models for a wide range of physical situations.

Tracker enables you to create two different types of mathematical models: analytical and dynamic. An analytical model enables you to enter mathematical expressions for x and y positions as a function of time. That’s sometimes useful, but from a physics perspective, a dynamic model is much more flexible and powerful.

A dynamic model enables you to set the initial conditions for a particular system (initial positions and velocities); then you can mathematically define any forces acting on that system. Once those are set up, the model acts like an object in space, responding to the forces you’ve imposed on it. It can continue moving forever, if that’s what the forces would do to an object in real life. By visually matching a marker for your model to the real motion on the video, you can define and refine a mathematical model for a wide range of real-world situations.

In the first two tasks of this Unit Activity, you’ll create dynamic models for motions in both one and two dimensions.

Activity Research – Creating a Dynamic Particle Model
Before you begin, do a little research and find out where you can get help in creating your models. In Tracker, you can always access illustrated help to do anything. In Tracker, you can always access the illustrated Help dialog (? In the Toolbar).

For this project, you’re going to need to check out the Tracker Help instructions for Dynamic Models. You can print this Help document, but it is available from Tracker anytime you need to refer to it.
For this project, you’re going to need to check out the Tracker Help instructions for creating a dynamic model.

Instructions – Building your Dynamic Model
Start your activity by opening this Tracker experiment: Ice Slide 2 model man.

Click play to watch the video. The other video controls allow you to rewind the video or step forward or backward one frame at a time.

In this activity, you’ll define a dynamic model for the motion of an adult sliding on ice. In the Ice_Slide2_model, a blank model setup is already in place for you. The file also has the man’s motion tracked with point mass Ice Slide 2.

For this one-dimensional motion, the vertical force of gravity and the normal force balance out. Although there is some air drag, the only significant force on the sliding man is kinetic friction. Review, if necessary, the force relationship for kinetic friction.

A dynamic model is already started for you in this file. Follow the two steps in the screen captures below to open the model setup and begin your modeling work.

1. From the top menu bar, select the point mass model man.
(from the blue pull-down control)

2. Open the Model Builder.
(from the “model man” pull-down menu)

3. Since you only have complete data table information starting at time t = 0.2 seconds, use that as your initial time. Enter data in each of the three sections:

parameters – Enter the man’s mass (displayed on the first frame of the video)
initial values – Enter those that apply to this x-direction motion: t, x, and vx.
force functions – Enter a function formula for kinetic frictional force in the x direction. (Hint: Use 9.81 for the acceleration of gravity in your formula.)
4. Finally, add a parameter in the Parameters section for the coefficient of kinetic friction. Use mk since you can’t enter in the parameter field.

Surfaces Coefficients of Kinetic Friction
wood on wood 0.200
steel on steel 0.600
plastic on snow 0.100
glass on glass 0.400
5. Here’s a table of some common coefficients of kinetic friction. You can use them for guidance as you begin to zero in on the coefficient of kinetic friction for this plastic disk sliding on ice. Take a first guess at the value of mk and run the video. See how closely the yellow modeled position matches the man’s observed position (green marker.) Modify the value of mk, trying to get as close as you can to matching the man’s observed position for the entire slide.

Part A
Once you’re satisfied with your model, record your model values in the table below.
Surfaces expresstion
parameter: m
parameter: mk
initial value: t
initial value: x
initial value: vx
force function: fx