Wong, D., Sng, P. P., Ng, E. H., & Wee, L. K. (2011). Learning with multiple representations: an example of a revision lesson in mechanics. Physics Education, 46(2), 178.

My first journal paper in http://iopscience.iop.org/0031-9120/46/2/005

simulation can be found here http://weelookang.blogspot.com/2010/09/ejs-open-source-bouncing-ball-with-drag.html

## Learning with multiple representations: an example of a revision lesson in mechanics

- Author
- Darren Wong
^{1}, Sng Peng Poo^{2}, Ng Eng Hock^{2}and Wee Loo Kang^{3} - Affiliations
^{1 }Natural Sciences and Science Education, National Institute of Education, Singapore^{2 }Anderson Junior College, Singapore^{3 }Educational Technology Division, Ministry of Education, Singapore- Journal
- Issue
- Citation
- Darren Wong
*et al*2011*Phys. Educ.***46**178

- Abstract
- We describe an example of learning with multiple representations in an A-level revision lesson on mechanics. The context of the problem involved the motion of a ball thrown vertically upwards in air and studying how the associated physical quantities changed during its flight. Different groups of students were assigned to look at the ball's motion using various representations: motion diagrams, vector diagrams, free-body diagrams, verbal description, equations and graphs, drawn against time as well as against displacement. Overall, feedback from students about the lesson was positive. We further discuss the benefits of using computer simulation to support and extend student learning.
- PACS
- Subjects
- Dates
- Issue 2 (March 2011)Received 10 December 2010 , in final form 20 December 2010 the draft PDF is also available legally here at http://www.compadre.org/osp/items/detail.cfm?ID=10817Bouncing Ball with Drag Model with the multi representations such as scientific graphs versus time and displacement sy, world view and energy bars.
# Bouncing Ball with Drag Model

A bouncing ball model here is simulated by both continuous dynamics, and discrete transitions where the system dynamics can change and the state values can jump. The continuous dynamics of a bouncing ball is simulated using the evolution page given (simplified version) by dy/dt = vy dvy/dt = ay = g - (k/mass)*vy - (k2/mass)*vy*vy; // to simulate gravity constant g, drag forces models are Fdrag = k*vy and Fdrag2=k2*vy*vy the discrete transition is simulated by the event handler in Ejs by selecting Type = zero crossing Zero Condirtion codes are if (vy<0) return yground-(y); // bounced at the yground return 0; // time continues Action code is vy=-e*vy; //# Possible Exercise for Multiple Representation Revision Lesson:

Instructions: A ball is thrown vertically upwards with vy = 30 m/s and assuming ay = -10 m/s^2 at time t = 0s. It is caught at the height of release on the way down at time t = 6s. Do the following exercises, paying attention particular attention to the following moments: 1. just after release from the hand (t = 0s); 2. on its way up (t = 1s & t = 2s); 3. at the highest point (t = 3s); 4. on its way down (t = 4s & t = 5s); 5. just before landing on hand (t = 6s). A Vector Diagrams Draw vector diagrams to show the position of the ball at equal time intervals with its corresponding velocity vector (blue) and acceleration vector (black). Think about how you would describe the velocity and acceleration of the ball on its way up, at the top and on its way down. Use the simulation to assess your initial vector diagram by selecting the upmenubar of checkboxes, for velocity vy, acceleration ay and so on.Figure showing how the simulation display the instantaneous vy and ay at a particular time say = 1.25 sB Force Diagrams Draw free body diagrams showing momentum and all forces (use different colour for different forces, use red for net force) acting on the ball for the upward and downward motion. Think about how you would describe the change in momentum of the ball on its way up, at the top and on its way down.Figure showing how the simulation display the force of gravity FG at a particular time say = 0.95 sC Graphs Draw graphs of displacement, velocity, acceleration with time/displacement to show the motion of the ball.Figure showing how the simulation can draw the graphs of displacement vs t, velocity vs t and acceleration vs t from t = 0 to 6+ sD Energy graphs Draw the KE (red) and PE (blue) graphs wrt time and displacement for the motion of the ball. Think about how you would describe the transformation of energy of the ball in its flight.Figure showing how the simulation can draw the graphs of energies vs t, and energies vs sy from t = 0 to 6+ sE Equations Write down the equations of motion that describe the motion of the ball.Figure showing how the simulation data tool allow students to analyze the data through a parabola curve fit arriving at the value of parameter a b and c to allow students to deduce the equation of motion as sy = a*t^2 + b*t + cWhat is the average velocity of the ball?Figure showing how the simulation data tool allow students to do a statistics mean of vy = -1.657E-1 = 0What is the average acceleration of the ball?Figure showing how the simulation data tool allow students to do a statistics mean of ay = -9.81With air resistance, does it take longer to go up or come down?Figure showing how the simulation different runs light blue( k=0) and blue( k = 0.3) can visually display the graphs of s vs t to reduce it takes longer to come down but also a comparison with the no air resistance case is possible too.Advanced Learner: Please submit your remix model that model features that are not available in the existing virtual lab and share your model with the world through NTNUJAVA Virtual Physics Laboratory http://www.phy.ntnu.edu.tw/ntnujava/index.php?board=28.0. Impacting the world with your model now.### Credits:

The Bouncing Ball with Drag Model was created by Loo Kang WEE with contributions of open source codes from Francisco Esquembre & Fu-Kwun Hwang, using the Easy Java Simulations (EJS) version 4.2 authoring and modeling tool. An applet version of this model is available on the NTNU website < http://www.phy.ntnu.edu.tw/ntnujava/ >. You can examine and modify this compiled EJS model if you run the model (double click on the model's jar file), right-click within a plot, and select "Open EJS Model" from the pop-up menu. You must, of course, have EJS installed on your computer. Information about EJS is available at: <**http://www.um.es/fem/Ejs/**> and in the OSP comPADRE collection <**http://www.compadre.org/OSP/**>.