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# Dynamic Model—Friction on Ice Now that you know how forces affect...

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. (http://contentstore.ple.platoweb.com/content/sharedmedia/Tracker/applications/ice-slide-2-model/ice-slide-2-model.html)

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: tx, 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 μk in the parameter field.

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.

Part B

Describe how well you think your modeled position matches the observed position for the man.

Part C

Next, you'll compare your model for the man with your model for a boy sliding on the same sled along the same path. Keep the first Tracker experiment open, but also open this Tracker experiment: Ice Slide 1 model. (http://contentstore.ple.platoweb.com/content/sharedmedia/Tracker/applications/ice-slide-1-model/ice-slide-1-model.html)

From this file, select the point mass model boy and repeat the procedure you used to create the dynamic model for the man. Once again, use the initial values for time t = 0.20 seconds.

Try different values of the coefficient of friction and come up with a model that matches the motion of the child. Once again, modify the value of mk to get as close as you can to matching the boy's observed position for the entire slide.

Once you're satisfied with your model for the boy, record your model values in the table below.

Part D

Describe how well you think your modeled position matches the observed position for the boy.

Part E

Look at your recorded results and models for both the man and the boy. How close are the coefficients of friction for the sled on ice for the two runs? How confident would you feel about specifying a coefficient of kinetic friction for this sled on this ice surface, based on these results? Support your conclusion. What other variables might impact this coefficient result?

Part F

Finally, observe the values of horizontal acceleration for the point masses and the dynamic models for the man and the boy. What can you say about the acceleration?

Dynamic Model—Snowboard Jump

Assuming you've completed task 1, you know how to create a dynamic model for a one-dimensional motion. Your next challenge is to take that knowledge and create a dynamic model for a two-dimensional situation.

A blank Tracker experiment of a snowboarder jumping off a ramp is provided for creating the dynamic model. Before you start, answer the following question:

Part A

In the ice-slide situation, friction was the primary force acting on the disk sliders. For a snowboard jumper in the air, what force or forces will be most important for modeling the motion?

Part B

Now, open the Tracker experiment: Snowboard Jump Dynamic. (http://contentstore.ple.platoweb.com/content/sharedmedia/Tracker/applications/snowboard-jump-dynamic/snowboard-jump-dynamic.html)

In this Tracker experiment, the motion of the snowboarder has been tracked by mathematically creating a center of mass point. A dynamic model setup is also created in this file.

With the Tracker Help and your experience of creating the dynamic model for one-dimensional motion, create a dynamic model for the snowboarder once the snowboarder is airborne, at time t = 0. Repeat the procedure that you followed while creating the one-dimensional models for the ice sliders.

Use the center of mass point cm as your observed position and to provide initial input values for your dynamic model. For the value of acceleration due to gravity, g, use 9.81 meters/second2. The snowboarder's mass (along with his board) is displayed on the first video screen.

Note that each position measurement could easily be off by a centimeter or two in this video, so the initial velocity values derived from those positions could be off by several centimeters per second (±0.05 meters/second) here. If the theoretical force laws don't exactly work for you, adjust the initial velocity values slightly to see how close you can come to a perfect match.

Once you're satisfied with your model, record your model values in the table below.

Part C

How close did the theoretical "no drag" model come to the actual motion?

Part D

Describe any changes you made to the velocities recorded for time t = 0. Justify those changes as reasonable or not, based on reasonable measurement variations.

Part E

Based on the velocity and acceleration results from the snowboarder and his mathematical model, what can you say about the forces acting on the snowboarder?

Applying Newton's Laws to Sports

Imagine you and your friends are enjoying a lovely summer day skateboarding along a straight road. Skateboarding is a good pastime sport, but it also involves a lot of physics, especially Newton's laws of motion. Listed below are some activities involved while skateboarding along a straight road. Identify which of Newton's laws of motion is most relevant to each activity, and give reasons for the match.

Part A

The skateboarder pushes the skateboard into motion by applying a backward force on the road.

Part B

The moment the skateboard starts moving.

Part C

The skateboard continues to move once in motion.

Part D

The skateboarder stops after covering some distance.

Identify the Action and Reaction Forces

Newton studied the forces in an interaction between two objects and formulated the third law of motion, which states that to every action there is an equal and opposite reaction. Using this law, identify the action and reaction force involved in the scenarios specified in the table below. Also, add two more scenarios and identify the action and reaction force in them.

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