(* Content-type: application/vnd.wolfram.cdf.text *) (*** Wolfram CDF File ***) (* http://www.wolfram.com/cdf *) (* CreatedBy='Mathematica 9.0' *) (*************************************************************************) (* *) (* The Mathematica License under which this file was created prohibits *) (* restricting third parties in receipt of this file from republishing *) (* or redistributing it by any means, including but not limited to *) (* rights management or terms of use, without the express consent of *) (* Wolfram Research, Inc. For additional information concerning CDF *) (* licensing and redistribution see: *) (* *) (* www.wolfram.com/cdf/adopting-cdf/licensing-options.html *) (* *) (*************************************************************************) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 1063, 20] NotebookDataLength[ 152416, 2968] NotebookOptionsPosition[ 136030, 2665] NotebookOutlinePosition[ 152579, 2962] CellTagsIndexPosition[ 152536, 2959] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell["", "Text"], Cell[TextData[{ StyleBox["Elastic collision", "Title"], "\n" }], "Input", CellChangeTimes->{{3.4813240951254473`*^9, 3.4813241225346956`*^9}, { 3.48132545145723*^9, 3.4813254642024527`*^9}, 3.4860465658176575`*^9, { 3.603294405454404*^9, 3.603294414902944*^9}}], Cell[TextData[StyleBox["In the animation below, you control the parameters of \ an elastic collsion between a blue ball and a red ball. 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8/($CellContext`vb$$ - $CellContext`vr$$)) ( 2 (($CellContext`mb$$ $CellContext`vb$$ + $CellContext`mr$$ \ $CellContext`vr$$)/($CellContext`mb$$ + $CellContext`mr$$)) - \ $CellContext`vr$$)) HeavisideTheta[$CellContext`t$$ - 8/($CellContext`vb$$ - $CellContext`vr$$)], 0.2 + 2 (1 - $CellContext`sr$$)}], PointSize[0.05], Blue, Point[{-4.24 + $CellContext`vb$$ $CellContext`t$$ HeavisideTheta[ 8/($CellContext`vb$$ - $CellContext`vr$$) - $CellContext`t$$] + \ ($CellContext`vb$$ ( 8/($CellContext`vb$$ - $CellContext`vr$$)) + \ ($CellContext`t$$ - 8/($CellContext`vb$$ - $CellContext`vr$$)) ( 2 (($CellContext`mb$$ $CellContext`vb$$ + $CellContext`mr$$ \ $CellContext`vr$$)/($CellContext`mb$$ + $CellContext`mr$$)) - \ $CellContext`vb$$)) HeavisideTheta[$CellContext`t$$ - 8/($CellContext`vb$$ - $CellContext`vr$$)], 0.2}], PointSize[0.05], Gray, Point[{$CellContext`cm$$ ( 4 ($CellContext`mr$$ - $CellContext`mb$$)/($CellContext`mb$$ + \ $CellContext`mr$$) + $CellContext`t$$ ($CellContext`mb$$ 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FormatType -> Large], Text[ "=", {-2 + 5.6, -0.4}, Background -> White, FormatType -> Large], Text[$CellContext`vr$$, {-1.1 + 5.6, -0.4}, Background -> White, FormatType -> Large], Red, Text[ Subscript["V", "now, red"], {-3.8 + 5.6, -0.6}, Background -> White, FormatType -> Large], Text[ "=", {-2.2 + 5.6, -0.6}, Background -> White, FormatType -> Large], Text[ 0.01 Floor[ 0.5 + 100 $CellContext`vr$$ + 100 (2 ($CellContext`mb$$ $CellContext`vb$$ + $CellContext`mr$$ \ $CellContext`vr$$)/($CellContext`mb$$ + $CellContext`mr$$) - 2 $CellContext`vr$$) HeavisideTheta[$CellContext`t$$ - 8/($CellContext`vb$$ - $CellContext`vr$$)]], {-1.3 + 5.6, -0.6}, Background -> White, FormatType -> Large]}, Axes -> {True, False}], "Specifications" :> {{$CellContext`t$$, 0, 20}, {{$CellContext`mb$$, 1, "Mass blue"}, 0.4, 5, 0.2}, {{$CellContext`mr$$, 1, "Mass red"}, 0.4, 5, 0.2}, {{$CellContext`vr$$, -1, "V initial red"}, -2, -0.2, 0.2}, {{$CellContext`vb$$, 1, "V initial blue"}, 0.4, 2, 0.2}, {{$CellContext`cm$$, 0, "Show Center of Mass"}, {0, 1}}, {{$CellContext`sr$$, 1, "Show Red Ball"}, {0, 1}}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{531., {315., 322.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", GeneratedCell->False, CellAutoOverwrite->False, CellChangeTimes->{ 3.6032941501788025`*^9, 3.603294186867901*^9, {3.6032942295883446`*^9, 3.6032942451672354`*^9}, 3.603294784052058*^9, {3.6032948665597773`*^9, 3.6032948870879517`*^9}, 3.6032949370978117`*^9, 3.6032949980332975`*^9, 3.6032951356461678`*^9, 3.603295710455045*^9, 3.603295861927709*^9, 3.60329589533862*^9, 3.6032959393191357`*^9, 3.6034099862415557`*^9, 3.6034100243247337`*^9}], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`cm$$ = 0, 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($CellContext`vb$$ ( 8/($CellContext`vb$$ - $CellContext`vr$$)) + \ ($CellContext`t$$ - 8/($CellContext`vb$$ - $CellContext`vr$$)) ( 2 (($CellContext`mb$$ $CellContext`vb$$ + $CellContext`mr$$ \ $CellContext`vr$$)/($CellContext`mb$$ + $CellContext`mr$$)) - \ $CellContext`vb$$)) HeavisideTheta[$CellContext`t$$ - 8/($CellContext`vb$$ - $CellContext`vr$$)], 0.2}], PointSize[0.05], Gray, Point[{$CellContext`cm$$ ( 4 (($CellContext`mr$$ - $CellContext`mb$$)/($CellContext`mb$$ + \ $CellContext`mr$$)) + $CellContext`t$$ (($CellContext`mb$$ $CellContext`vb$$ + \ $CellContext`mr$$ $CellContext`vr$$)/($CellContext`mb$$ + \ $CellContext`mr$$))), 2 (1 - $CellContext`cm$$)}], Thickness[0.01], Gray, Line[{{4 (($CellContext`mr$$ - \ $CellContext`mb$$)/($CellContext`mb$$ + $CellContext`mr$$)) + \ $CellContext`t$$ (($CellContext`mb$$ $CellContext`vb$$ + $CellContext`mr$$ \ $CellContext`vr$$)/($CellContext`mb$$ + $CellContext`mr$$)), 2 - 2 $CellContext`cm$$}, { 4 (($CellContext`mr$$ - $CellContext`mb$$)/($CellContext`mb$$ + \ $CellContext`mr$$)) + $CellContext`t$$ (($CellContext`mb$$ $CellContext`vb$$ + \ $CellContext`mr$$ $CellContext`vr$$)/($CellContext`mb$$ + $CellContext`mr$$)), 0.5 + 2 (1 - $CellContext`cm$$)}}], Blue, Text[ Subscript["M", "blue"], {-4, -0.2}, Background -> White, FormatType -> Large], Text["=", {-2.9, -0.2}, Background -> White, FormatType -> Large], Text[$CellContext`mb$$, {-2.1, -0.2}, Background -> White, FormatType -> Large], Blue, Text[ Subscript["V", "initial, blue"], {-3.8, -0.4}, Background -> White, FormatType -> Large], Text["=", {-2, -0.4}, Background -> White, FormatType -> Large], Text[$CellContext`vb$$, {-1.1, -0.4}, Background -> White, FormatType -> Large], Blue, Text[ Subscript["V", "now, blue"], {-3.8, -0.6}, Background -> White, FormatType -> Large], Text["=", {-2.2, -0.6}, Background -> White, FormatType -> Large], Text[ 0.01 Floor[ 0.5 + 100 $CellContext`vb$$ + ( 100 (2 (($CellContext`mb$$ $CellContext`vb$$ + \ 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