Pedagogical Physics Simulations

Brent Perreault

Concordia College Moorhead Minnesota

Abstract: 
The Wolfram Demonstration Project has opened up new possibilities for demonstrating mathematical concepts. There are a number of demonstrations that demonstrate physical concepts as part of the Demonstration Project. While each of these demonstrations are helpful in their context, when considering them for the classroom on a larger scale I found that there was room for some work to reorganize them and edit them so that they create a coherent picture of the phsyical concepts that they hold. I have taken up the task of creating similar simulations by both editing existing demonstrations, and creating new ones.

This research was supported by the Concordia College Physics Dept.

The Idea

Bringing two ideas together in a practical way

The Wolfram Demonstration Project

Embedded CDF Webpages

Outline

How is this different from the Demonstration Project?
	- These demonstratins focus on the specific concepts that are being taught.
	- Simulations allow for a chance to test our models and see what they predict.

A Website with Embedded CDFs

Conclusion

Wolfram Demonstrations as Teaching Aids

A Roller Coster: Conservation of Energy

Author: Brent Perreault

Adapted from:

“Roller Coasters” from the Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/RollerCoasters/

Contributed by: Ernest Lee

Simulates the motion

Demonstrates the Conservation of Energy

Illustrates the Force Diagram

Simulating Reality

Projectile Motion

Author: Brent Perreault

Adapted from:

"Animated Projectile Motion" from the Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/AnimatedProjectileMotion/

Contributed by: Rob Morris and Oleksandr Pavlyk

Demonstrates simple projectile motion

Allows us to estimate drag

How are they written?

Pendulum

Author: Brent Perreault

Adapted from:

"Nonlinearized Motion of a Simple Pendulum" from the Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/NonlinearizedMotionOfASimplePendulum/

Contributed by: Sarah Lichtblau

Inspired by: Rob Morris

Mathematica Code:

Manipulate[
If[run==T,run=0];
Module[
{sol,θ,t},T=4(Sqrt[(l/(g ))])EllipticF[(π/2),((Sin[θ0 Degree/2])^2)];
sol=NDSolve[{θ''[t]+(g/l)*Sin[θ[t]]==0,θ[0]==θ0 Degree,θ'[0]==0},θ,{t,0,T+.001},Method->"StiffnessSwitching"];
With[{θ0=(180/π)θ[run]/.First[sol]}
,
Labeled[Graphics[{
{Line[{{0,0},{l*Sin[θ0 Degree],-l*Cos[θ0 Degree]}}]},
{Lighter[Brown,.3],Rectangle[{-4,0},{4,.5}]},
{Darker[Red],Disk[{0,0},.07]},
{Blue,Disk[{l*Sin[θ0 Degree],-l*Cos[θ0 Degree]},.2]}
},
PlotRange->{{-4,4},{.5,-4}},ImageSize->{600,300}
]
,Style[Row[{"Period: ",Pane[T,53]," s",Spacer[30],"Frequency: ",Pane[1/T,53]," Hz",Spacer[30],"Time: ",Pane[run,31]," s"}],"Label"]
]]]
,
{{l,3,"Length"},.5,3.5,.1,Appearance->"Labeled"},
{{θ0,45,"Initial Angle"},0,90,Appearance->"Labeled"},{{m,1,"Mass"},.5,2,Appearance->"Labeled"},{{g,9.8,"Acceleration of Gravity"},.001,20,.001,Appearance->"Labeled"},
{{run,0,"Time"},0,Dynamic[T],.001,Appearance->"Labeled"},
{{run,0,"Release System"},0,Dynamic[T],.001,ControlType->Trigger,AnimationRate->1},
SynchronousUpdating->True,AutorunSequencing->{7,2}
]

Conclusion

The resulting website - for students and faculty

http://www.cord.edu/dept/physics/simulations/Home.html

The best way to allow students to use these simulations is to make them available online. I created a focused and organized group of cdf documents. This type of computable website can be used to demonstrate many other types of ideas.

Future CDF Work

Other CDF-based websites that bring together a coherent groups of demonstration and/or simulations.

Interactive textbooks, homework, and academic journal articles

Non-academic reports, data, and blogs.