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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. 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3.526479318677928*^9}], Cell[CellGroupData[{ Cell["A Roller Coster: Conservation of Energy", "Subsubsection", CellChangeTimes->{ 3.483202458956718*^9, {3.514308604990972*^9, 3.514308608117634*^9}, 3.5210267664304323`*^9, {3.521028708835531*^9, 3.5210287232633567`*^9}, { 3.526480448129529*^9, 3.526480454234878*^9}, {3.5264848346526437`*^9, 3.5264848558668566`*^9}}], Cell["Author: Brent Perreault", "Text", CellChangeTimes->{{3.5137054472578125`*^9, 3.513705501024414*^9}}], Cell[CellGroupData[{ Cell[BoxData[ GraphicsBox[RasterBox[CompressedData[" 1:eJztnVuSozgWQDNiPqa3MJ+zpVlCbaB3WlGVNV9dvYH6TQRUph/ZGIHQmwvG xoZzQu3Aku7VfUj4Nk53//fLn//78q+Xl5f/NP/88e+Xl8v154Xj5+fp89y0 4+X63L7VnQu02XqOt9FzjRK5qtRMoYZFpk11/Ji+WDye92+r7+fFfbnGkuu9 eIQ4LBVJ+YRo5DPnRdITDp0TLRg6m/62nY/n08f5+H461G37fWqum57z4Xy2 jby0prMZOh4/jodLOx2bt6fzRSEA3B/KMKGSBy/DSKVcyYOn8krHqajvqed6 G6iol4qkfAIVNQAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADsizPA/lj72AEA AMCmWLu0AXh01j6jAAAAcdb+hNwUJ5e1zZnPDEeey/e1jx0AAABsirVLm03x 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False}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`bss$$ = 0.2, $CellContext`end$$ = 0.001, $CellContext`g$$ = 9.8, $CellContext`h$$ = 0, $CellContext`m$$ = 10, $CellContext`traj$$ = False, $CellContext`v$$ = 40, $CellContext`\[Theta]$$ = 45., $CellContext`\[Kappa]$$ = 0}, "ControllerVariables" :> { Hold[$CellContext`v$$, $CellContext`v$316294$$, 0], Hold[$CellContext`\[Theta]$$, $CellContext`\[Theta]$316295$$, 0], Hold[$CellContext`h$$, $CellContext`h$316296$$, 0], Hold[$CellContext`m$$, $CellContext`m$316297$$, 0], Hold[$CellContext`g$$, $CellContext`g$316298$$, 0], Hold[$CellContext`\[Kappa]$$, $CellContext`\[Kappa]$316299$$, 0], Hold[$CellContext`bss$$, $CellContext`bss$316300$$, 0], Hold[$CellContext`end$$, $CellContext`end$316301$$, 0], Hold[$CellContext`traj$$, $CellContext`traj$316302$$, False]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Module[{$CellContext`x$, $CellContext`y$, $CellContext`soln$, \ $CellContext`eqns$, $CellContext`t$, $CellContext`xmax$, $CellContext`ymax$}, \ $CellContext`eqns$ = { Derivative[ 2][$CellContext`x$][$CellContext`t$] == \ ((-($CellContext`\[Kappa]$$/( 2^Rational[1, 2] $CellContext`m$$))) $CellContext`bss$$^2) Derivative[1][$CellContext`x$][$CellContext`t$]^2, Derivative[1][$CellContext`x$][0] == $CellContext`v$$ Cos[$CellContext`\[Theta]$$ Degree], $CellContext`x$[0] == 0, Derivative[ 2][$CellContext`y$][$CellContext`t$] == -$CellContext`g$$ - \ (($CellContext`\[Kappa]$$/( 2^Rational[1, 2] $CellContext`m$$)) $CellContext`bss$$^2) Derivative[1][$CellContext`y$][$CellContext`t$]^2, Derivative[1][$CellContext`y$][0] == $CellContext`v$$ Sin[$CellContext`\[Theta]$$ Degree], $CellContext`y$[ 0] == $CellContext`h$$}; $CellContext`soln$ = Flatten[ Quiet[ NDSolve[$CellContext`eqns$, {$CellContext`x$, $CellContext`y$}, \ {$CellContext`t$, 0, Infinity}, Method -> { "EventLocator", "Event" -> $CellContext`y$[$CellContext`t$], "EventAction" :> Throw[$CellContext`tf = $CellContext`t$, "StopIntegration"], "Direction" -> -1}, MaxSteps -> Infinity]]]; $CellContext`bs = 10 $CellContext`bss$$; $CellContext`s = Evaluate[ ReplaceAll[{ $CellContext`x$[$CellContext`end$$], $CellContext`y$[$CellContext`end$$]}, $CellContext`soln$]]; \ $CellContext`ymax$ = First[ Quiet[ FindMaximum[{ ReplaceAll[ $CellContext`y$[$CellContext`t$], $CellContext`soln$], 0 <= $CellContext`t$ <= $CellContext`tf}, {$CellContext`t$, \ $CellContext`tf/2}]]]; $CellContext`xmax$ = ReplaceAll[ $CellContext`x$[$CellContext`tf], $CellContext`soln$]; Labeled[ Show[{ ParametricPlot[ ReplaceAll[{ $CellContext`x$[$CellContext`t$], $CellContext`y$[$CellContext`t$]}, $CellContext`soln$], \ {$CellContext`t$, 0, Min[$CellContext`tf, $CellContext`end$$]}, AxesOrigin -> {0, 0}, ImageSize -> {700, 500}, PlotRange -> {{(-3) Max[((0.007 $CellContext`xmax$) $CellContext`bs) 1.5, ((0.01 $CellContext`ymax$) $CellContext`bs) 1.5], Max[((0.007 $CellContext`xmax$) $CellContext`bs) 4, ((0.01 $CellContext`ymax$) $CellContext`bs) 4, 1.1 $CellContext`xmax$]}, {(-2) Max[((0.007 $CellContext`xmax$) $CellContext`bs) 1.5, ((0.01 $CellContext`ymax$) $CellContext`bs) 1.5], 1.5 $CellContext`ymax$}}, AxesLabel -> { Style["x(t)", Italic, Bold, "Label"], Style["y(t)", Italic, Bold, "Label"]}, ImagePadding -> 30], Graphics[{ Darker[Green, 0], Rectangle[{-$CellContext`xmax$, 0}, 2 {$CellContext`xmax$, -$CellContext`ymax$}]}], Graphics[{ Lighter[Blue, 0.9], Rectangle[{-$CellContext`xmax$, 0}, 2 {$CellContext`xmax$, $CellContext`ymax$}]}], ParametricPlot[ ReplaceAll[{ $CellContext`x$[$CellContext`t$], $CellContext`y$[$CellContext`t$]}, $CellContext`soln$], \ {$CellContext`t$, 0, Min[$CellContext`tf, $CellContext`end$$]}, AxesOrigin -> {0, 0}, ImageSize -> {650, 500}, PlotRange -> {{(-3) Max[((0.007 $CellContext`xmax$) $CellContext`bs) 1.5, ((0.01 $CellContext`ymax$) $CellContext`bs) 1.5], Max[((0.007 $CellContext`xmax$) $CellContext`bs) 4, ((0.01 $CellContext`ymax$) $CellContext`bs) 4, 1.1 $CellContext`xmax$]}, {(-2) Max[((0.007 $CellContext`xmax$) $CellContext`bs) 1.5, ((0.01 $CellContext`ymax$) $CellContext`bs) 1.5], 1.5 $CellContext`ymax$}}, AxesLabel -> { Style["x(t)", Italic, Bold, "Label"], Style["y(t)", Italic, Bold, "Label"]}, ImagePadding -> 30, PlotStyle -> If[$CellContext`traj$$, Blue, Lighter[Blue, 0.9]]], Graphics[{Black, Disk[ ReplaceAll[{ $CellContext`x$[ Min[$CellContext`tf, $CellContext`end$$]], $CellContext`y$[ Min[$CellContext`tf, $CellContext`end$$]]}, \ $CellContext`soln$], { Max[(0.007 $CellContext`xmax$) $CellContext`bs, ( 0.01 $CellContext`ymax$) $CellContext`bs], Max[(0.007 $CellContext`xmax$) $CellContext`bs, ( 0.01 $CellContext`ymax$) $CellContext`bs]}]}], Graphics[{Black, Disk[{0, $CellContext`h$$}, { Max[((0.007 $CellContext`xmax$) $CellContext`bs) 1.5, ((0.01 $CellContext`ymax$) $CellContext`bs) 1.5], Max[((0.007 $CellContext`xmax$) $CellContext`bs) 1.5, ((0.01 $CellContext`ymax$) $CellContext`bs) 1.5]}]}], Graphics[{Black, Rotate[ Rectangle[{ 0, $CellContext`h$$ - 1.5 Max[(0.007 $CellContext`xmax$) $CellContext`bs, ( 0.01 $CellContext`ymax$) $CellContext`bs]}, Max[(0.007 $CellContext`xmax$) $CellContext`bs, ( 0.01 $CellContext`ymax$) $CellContext`bs] {5, 1.5} + { 0, $CellContext`h$$}], $CellContext`\[Theta]$$ Degree, { 0, $CellContext`h$$}]}], Graphics[{ Darker[Brown], Rotate[ Rectangle[ Max[(0.007 $CellContext`xmax$) $CellContext`bs, ( 0.01 $CellContext`ymax$) $CellContext`bs] {-2, -1.5} + { 0, $CellContext`h$$}, Max[(0.007 $CellContext`xmax$) $CellContext`bs, ( 0.01 $CellContext`ymax$) $CellContext`bs] {2, 0.5} + { 0, $CellContext`h$$}], $CellContext`\[Theta]$$ Degree, { 0, $CellContext`h$$}]}], Graphics[ Table[{ Darker[Brown], Rotate[ Rectangle[ Max[(0.007 $CellContext`xmax$) $CellContext`bs, ( 0.01 $CellContext`ymax$) $CellContext`bs] 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