Friday, February 27, 2015

Tracker Comparing Car and Bicycle Modeling Activity

Tracker Comparing Car and Bicycle Modeling Activity
note from RGS
no video, model lookang

Goal: inspire the students to learn with modeling, a meaningfully and fun way to be like scientists, so as to promote the love for physics. 



http://weelookang.blogspot.sg/2015/02/tracker-comparing-car-and-bicycle.html
example from szu chuang, model by lookang
https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/lookangejss/02_newtonianmechanics_2kinematics/trz/carandbicycleaccelerationcomparison.trz


Steps to use Tracker as a modeling tool suitable for most physics examples

  1. Open Tracker using the Start|Programs|Tracker and click it to launch the program already installed from https://www.cabrillo.edu/~dbrown/tracker/ 
  2. From this modeling activity, we use the example in RGS notes Kinematics 2015 part 1 student.pdf
  3. First, calibrate the screen length to actual measurement in the video ( in this case, nothing as we are doing a brand new model with no video), Select the calibration stick 
  4. the calibration stick appears on the main panel view of tracker, we can move the 2 + ends to indicate the length of 1.00 m, tracker default seems to be 100 arbitrary units
  5. click the next icon which it the axes and move it to the left of the main view panel if desired, default is the centre of the main view panel.
  6. Create the Car Model, select Create|Dynamic Particle Model|Cartesian since the Car only moves in the x direction for example.
  7. the view for the Model A appears by default, things you may wish to do are change the name and color of the model, else for the tutorial, we just assume the default colors and names. In any model building process, we need to define the 1) initial states(values), and the 2) forces that act on the model of default mass m =1 kg.
  8. we can assume the units of m/s works for us, so the first thing is to define the model according to the questions in the example. 
  9. I hope we agree that initial speed of car is 60 km/hr = 60*1000/3600 m/s, Key in the initial values(state) of Model A is 60*1000/3600
    vx = 60*1000/3600 now
  10. click play to observe the effects of this new Model A that you have created! 
  11. Isn't it amazing!, Your first initial model moves according to your ideas. So you can see that an initial velocity vx = 60*1000/3600 moves the model A to the right as the axes x is pointing to the right.
  12. since the problem say $ \delta t = 3 s $ , $ \delta v = v_{final} - v{initial} = (68 -60)*1000/3600 $, therefore using acceleration $ a = \frac{\delta v}{\delta t} =   \frac{(68-60)(*1000/3600)}{3} $. Key in any mathematically valid expression to represent the force function in the x direction fx. remember $ F =ma $ and since mass m = 1, $ F = a $ for the rest of the modeling activity.
    fx = (68-60)*1000/3600/3 now
  13. At this point, your model A car is completed! you may wish to drag the calibration stick to maximize the view of the main view panel to observe the effects of fx = (68-60)*1000/3600/3.
  14. To examine the evidences of the acceleration, click on the right panel x axes to change to desired variable to display on the vertical axes, say ax the horizontal acceleration of model A car.
  15.  to get precise readings, click on any of the data points and tracker shows in on the bottom left yellow display the values of ax =2.667*1000/3600 
  16. Now, check that you understand your Model A car is of acceleration a = 2.667*1000/3600 before moving on to model B bicycle.
  17. to Model B, repeat the same step as Model A, select create|Dynamic Particle Model|Cartesian
  18. Model B is automatically created with default values and force all equal to zero.
  19. remember the question?
  20. think how you can model the bicycle as Model B. 

  21. with some thinking effort on your part, can you figure out the following screenshot as hints?
  22. the reason is since the bicycle problem say $ \delta t = 2 s $ , $ \delta v = v_{final} - v{initial} = (6 -0)*1000/3600 $ , therefore using acceleration $ a = \frac{\delta v}{\delta t} =   \frac{(6-0)(1000/3600)}{2} $. Key in any mathematically valid expression to represent the force function in the x direction fx. remember $ F =ma $ and since mass m = 1, $ F = a $ for the rest of the modeling activity.
  23. click play and observe the effects of the motion graph (main panel) and the x vs t graph which is a parabolic curve.
  24. to compare the 2 models right panel view, move mouse to the right panel and right click to select compare with for Model B views.
  25. despite the appearances of the 2 graphs ( x vs t), they are actually parabolic, it is just the acceleration are pretty small thus they appear to be pretty linear.
  26. now, click on the vertical axes label and choose ax 

  27. observe the evidences that Model A car ax = 2.67*1000/3600 and Model B bicycle ax = 3*1000/3600.
  28. to get a view that include the (0,0), right click on the right panel and select Show ax =0
  29. you can even drag the axes range to display so that it looks like your typical pen-paper presentations.
  30. the resource can be download here https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/lookangejss/02_newtonianmechanics_2kinematics/trz/carandbicycleaccelerationcomparison.trz
  31. let me know what you think about this way of  learning (modeling) and the examples you have tried below on my google+ comments and network learn together.