动量守恒相图（A、B在碗内碰撞）
2020-09-06 04:04
本范例展示了动量守恒定律在二维平面内的几何相图表示。通过模拟物体A和B在碗状势场内的碰撞，利用点、圆、线段和向量等元素，直观描绘碰撞前后的动量变化与轨迹。该模型结合经典力学与解析几何，帮助学习者理解动量守恒及其在相空间中的几何意义。
所属专题
动量守恒相图分析
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.600.0" app="classic" platform="w" id="A2E42D36-40C3-4A79-BF1E-5B0EB0D537DD" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/apps/xsd/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1366" height="705" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.24377745241581258" orientation="1" />
</panes>
<views>
<view id="4097" visible="false" inframe="false" stylebar="true" location="1,1,1,1" size="400" window="100,100,700,550" />
<view id="512" toolbar="0 | 1 501 5 19 , 67 | 2 15 45 18 , 7 37 | 514 3 9 , 13 44 , 47 | 16 51 | 551 550 11 , 20 22 21 23 , 55 56 57 , 12 | 69 | 510 511 , 512 513 | 533 531 , 534 532 , 522 523 , 537 536 , 535 , 538 | 521 520 | 36 , 38 49 560 | 571 30 29 570 31 33 | 17 | 540 40 41 42 , 27 28 35 , 6 , 502" visible="false" inframe="false" stylebar="false" location="1,1,1" size="500" window="100,100,600,400" />
<view id="4" toolbar="0 || 2020 , 2021 , 2022 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="false" location="1,1" size="300" window="100,100,600,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 | 1009 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="1" visible="true" inframe="false" stylebar="false" location="1" size="1025" window="100,100,600,400" />
<view id="2" visible="true" inframe="false" stylebar="false" location="3" size="333" window="100,100,250,400" />
<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="300" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="300" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="false" stylebar="false" location="1" size="480" window="50,50,500,500" />
<view id="128" visible="false" inframe="false" stylebar="false" location="1" size="480" window="50,50,500,500" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="false" stylebar="true" location="1" size="900" window="50,50,500,500" />
</views>
<toolbar show="false" items="0 77 73 62 | 1 501 67 , 5 19 , 72 75 76 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 14 68 | 30 29 54 32 31 33 | 25 17 26 60 52 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="false" cmd="true" top="algebra" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="24"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="1025" height="705"/>
<coordSystem xZero="518.3100148065482" yZero="359.9624594793797" scale="38.44239384071702" yscale="38.44239384071702"/>
<evSettings axes="true" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="-1" lockedAxesRatio="1"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="0"/>
<axis id="0" show="true" label="v_A" unitLabel="" tickStyle="2" showNumbers="false"/>
<axis id="1" show="true" label="√k v_B" unitLabel="" tickStyle="2" showNumbers="false"/>
</euclidianView>
<algebraView>
<mode val="3"/>
</algebraView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="1"/>
<angleUnit val="degree"/>
<algebraStyle val="1" spreadsheet="1"/>
<coordStyle val="0"/>
</kernel>
<tableview min="-2" max="2" step="1"/>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<expression label="O" exp="(0, 0)" type="point"/>
<element type="point" label="O">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="15" y="32"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="0" y="0" z="1"/>
<pointSize val="3"/>
<pointStyle val="10"/>
</element>
<command name="Point">
<input a0="xAxis"/>
<output a0="B"/>
</command>
<element type="point" label="B">
<show object="false" label="true" ev="4"/>
<objColor r="21" g="101" b="192" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="7.619703834348241" y="0" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Circle">
<input a0="O" a1="B"/>
<output a0="c"/>
</command>
<element type="conic" label="c">
<show object="true" label="false" ev="4"/>
<objColor r="97" g="97" b="97" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="76"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-58.059886523181284" A3="0" A4="0" A5="0"/>
<eqnStyle style="specific"/>
</element>
<command name="Point">
<input a0="c"/>
<output a0="I"/>
</command>
<element type="point" label="I">
<show object="true" label="true" ev="4"/>
<objColor r="21" g="101" b="192" alpha="0"/>
<layer val="0"/>
<labelOffset x="-37" y="56"/>
<labelMode val="3"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="7.619703834348241" y="0" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<caption val="I(v_0,0)"/>
</element>
<command name="Point">
<input a0="c"/>
<output a0="K"/>
</command>
<element type="point" label="K">
<show object="true" label="true" ev="4"/>
<objColor r="21" g="101" b="192" alpha="0"/>
<layer val="0"/>
<labelOffset x="15" y="8"/>
<labelMode val="0"/>
<animation step="0.1" speed="0.1" type="1" playing="false"/>
<ggbscript onUpdate="If(Angle(K,O,B)>90°,SetValue(K,B'))
If(y(K)<0,SetValue(K,B'_1))
"/>
<coords x="3.8058414216510403" y="6.601170926163514" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Line">
<input a0="K" a1="O"/>
<output a0="f"/>
</command>
<element type="line" label="f">
<show object="true" label="true" ev="4"/>
<objColor r="97" g="97" b="97" alpha="0"/>
<layer val="0"/>
<labelOffset x="12" y="33"/>
<labelMode val="3"/>
<coords x="6.601170926163514" y="-3.8058414216510403" z="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="102"/>
<eqnStyle style="explicit"/>
<caption val="v_A = v_B"/>
</element>
<command name="OrthogonalLine">
<input a0="I" a1="f"/>
<output a0="g"/>
</command>
<element type="line" label="g">
<show object="true" label="false"/>
<objColor r="97" g="97" b="97" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="3.8058414216510403" y="6.601170926163514" z="-28.999384473475793"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="76"/>
<eqnStyle style="explicit"/>
</element>
<command name="Intersect">
<input a0="f" a1="g"/>
<output a0="C"/>
</command>
<element type="point" label="C">
<show object="true" label="false"/>
<objColor r="97" g="97" b="97" alpha="0"/>
<layer val="0"/>
<labelOffset x="-13" y="33"/>
<labelMode val="0"/>
<coords x="110.36705863153821" y="191.42989366294603" z="58.05988652318127"/>
<pointSize val="3"/>
<pointStyle val="10"/>
</element>
<command name="Vector">
<input a0="I" a1="C"/>
<output a0="u"/>
</command>
<element type="vector" label="u">
<show object="false" label="false"/>
<objColor r="97" g="97" b="97" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-5.7187862604313064" y="3.297111054230442" z="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="204"/>
<coordStyle style="cartesian"/>
<startPoint exp="I"/>
</element>
<command name="Distance">
<input a0="C" a1="I"/>
<output a0="distanceIC"/>
</command>
<element type="numeric" label="distanceIC">
<value val="6.601170926163514"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="Point">
<input a0="g"/>
<output a0="S"/>
</command>
<element type="point" label="S">
<show object="false" label="false" ev="4"/>
<objColor r="21" g="101" b="192" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<animation step="0.1" speed="0.2" type="2" playing="false"/>
<ggbscript onUpdate="If(o>1,SetValue(S,F))
If(o<0,SetValue(S,I))"/>
<coords x="-2.9856194764848594" y="6.114396854411973" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Vector">
<input a0="C" a1="S"/>
<output a0="v"/>
</command>
<element type="vector" label="v">
<show object="false" label="false"/>
<objColor r="97" g="97" b="97" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-4.8865370504017935" y="2.8172858001815313" z="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="204"/>
<coordStyle style="cartesian"/>
<startPoint exp="C"/>
</element>
<expression label="w" exp="(u * v)" />
<element type="numeric" label="w">
<value val="37.233965099631284"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="Distance">
<input a0="C" a1="S"/>
<output a0="distanceCS"/>
</command>
<element type="numeric" label="distanceCS">
<value val="5.640509163617585"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="Slope">
<input a0="f"/>
<output a0="m"/>
</command>
<element type="numeric" label="m">
<value val="1.7344839668332295"/>
<show object="false" label="true"/>
<objColor r="21" g="101" b="192" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
</element>
<command name="Segment">
<input a0="O" a1="S"/>
<output a0="h"/>
</command>
<element type="segment" label="h">
<show object="false" label="false"/>
<objColor r="97" g="97" b="97" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-6.114396854411973" y="-2.9856194764848594" z="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="204"/>
<eqnStyle style="explicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="O" a1="I"/>
<output a0="i"/>
</command>
<element type="segment" label="i">
<show object="true" label="false"/>
<objColor r="97" g="97" b="97" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0" y="7.619703834348241" z="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="204"/>
<eqnStyle style="explicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Distance">
<input a0="O" a1="I"/>
<output a0="distanceOI"/>
</command>
<element type="numeric" label="distanceOI">
<value val="7.619703834348241"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="文字OI" exp="Name[O] + (Name[I]) + " = " + distanceOI" />
<element type="text" label="文字OI">
<show object="false" label="false" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<startPoint exp="Midpoint[O, I]"/>
</element>
<command name="Distance">
<input a0="O" a1="C"/>
<output a0="distanceOC"/>
</command>
<element type="numeric" label="distanceOC">
<value val="3.8058414216510412"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="文字OC" exp="Name[O] + (Name[C]) + " = " + distanceOC" />
<element type="text" label="文字OC">
<show object="false" label="false" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<startPoint exp="Midpoint[O, C]"/>
</element>
<expression label="文字IC" exp="Name[C] + (Name[I]) + " = " + distanceIC" />
<element type="text" label="文字IC">
<show object="false" label="false" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<startPoint exp="Midpoint[C, I]"/>
</element>
<expression label="文字CS" exp="Name[C] + (Name[S]) + " = " + distanceCS" />
<element type="text" label="文字CS">
<show object="false" label="false" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<startPoint exp="Midpoint[C, S]"/>
</element>
<command name="Distance">
<input a0="O" a1="S"/>
<output a0="distanceOS"/>
</command>
<element type="numeric" label="distanceOS">
<value val="6.804393621154552"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="文字OS" exp="Name[O] + (Name[S]) + " = " + distanceOS" />
<element type="text" label="文字OS">
<show object="false" label="false" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<startPoint exp="Midpoint[O, S]"/>
</element>
<expression label="k" exp="m^(2)" />
<element type="numeric" label="k">
<value val="3.0084346312015353"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="text1" exp=""k=" + k + """ />
<element type="text" label="text1">
<show object="false" label="false" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="1.4" size="10" style="0"/>
<startPoint x="9.8010992803149" y="8.861231425574205" z="1"/>
</element>
<command name="Distance">
<input a0="S" a1="K"/>
<output a0="EC"/>
</command>
<element type="numeric" label="EC">
<value val="6.808883177720004"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<auxiliary val="true"/>
</element>
<expression label="a" exp="distanceOC^(2) / distanceOI^(2)" />
<element type="numeric" label="a">
<value val="0.2494739448202623"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="b" exp="distanceIC^(2) / distanceOI^(2)" />
<element type="numeric" label="b">
<value val="0.7505260551797376"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="Intersect">
<input a0="c" a1="g" a2="2"/>
<output a0="F"/>
</command>
<element type="point" label="F">
<show object="true" label="true"/>
<objColor r="97" g="97" b="97" alpha="0"/>
<layer val="0"/>
<labelOffset x="-37" y="-8"/>
<labelMode val="3"/>
<coords x="-3.8178686865143736" y="6.594222108460883" z="1"/>
<pointSize val="3"/>
<pointStyle val="10"/>
<caption val="F(-0.5v_0,0.5√kv_0)"/>
</element>
<expression label="d" exp="((distanceCS * w)) / distanceIC^(3)" />
<element type="numeric" label="d">
<value val="0.7301207004986924"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="Distance">
<input a0="F" a1="S"/>
<output a0="distanceSF"/>
</command>
<element type="numeric" label="distanceSF">
<value val="0.9606617625459293"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="文字SF" exp=""" + F + Name[S] + " = " + distanceSF + """ />
<element type="text" label="文字SF">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<startPoint exp="Midpoint[F, S]"/>
</element>
<expression label="e" exp="distanceOS^(2) / distanceOI^(2)" />
<element type="numeric" label="e">
<value val="0.7974485539706123"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="Distance">
<input a0="S" a1="I"/>
<output a0="distanceIS"/>
</command>
<element type="numeric" label="distanceIS">
<value val="12.2416800897811"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="文字IS" exp="Name[S] + (Name[I]) + " = " + distanceIS" />
<element type="text" label="文字IS">
<show object="false" label="false" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<startPoint exp="Midpoint[S, I]"/>
</element>
<expression label="j" exp="(distanceSF * distanceIS / distanceOI^(2))" />
<element type="numeric" label="j">
<value val="0.2025514460293876"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="text4" exp=""恢復系數e=" + (LaTeX[d]) + """ />
<element type="text" label="text4">
<show object="false" label="false" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1" size="0" style="2"/>
<startPoint x="9.694788406802168" y="-0.7713213524218652" z="1"/>
</element>
<command name="Slope">
<input a0="i"/>
<output a0="m_1"/>
</command>
<element type="numeric" label="m_1">
<value val="0"/>
<show object="false" label="true"/>
<objColor r="21" g="101" b="192" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
</element>
<expression label="l" exp="m_1 / m" />
<element type="numeric" label="l">
<value val="0"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="Intersect">
<input a0="c" a1="yAxis" a2="2"/>
<output a0="A"/>
</command>
<element type="point" label="A">
<show object="false" label="true"/>
<objColor r="97" g="97" b="97" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0" y="7.6197038343482415" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<expression label="q" exp="x(K)" />
<element type="numeric" label="q">
<value val="3.8058414216510403"/>
<objColor r="99" g="219" b="219" alpha="0.5"/>
</element>
<command name="Rotate">
<input a0="B" a1="89.9°" a2="O"/>
<output a0="B'"/>
</command>
<element type="point" label="B'">
<show object="false" label="true"/>
<objColor r="21" g="101" b="192" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="0.013298885241831733" y="7.619692228878579" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Angle">
<input a0="B" a1="O" a2="B'"/>
<output a0="α"/>
</command>
<element type="angle" label="α">
<angleStyle val="0"/>
<value val="1.5690509975429023"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="1"/>
<labelMode val="2"/>
<lineStyle thickness="4" type="0" typeHidden="2" opacity="153"/>
<arcSize val="30"/>
</element>
<command name="Rotate">
<input a0="B" a1="0.1°" a2="O"/>
<output a0="B'_1"/>
</command>
<element type="point" label="B'_1">
<show object="false" label="true"/>
<objColor r="21" g="101" b="192" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="7.619692228878579" y="0.013298885241832092" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Angle">
<input a0="B" a1="O" a2="B'_1"/>
<output a0="β"/>
</command>
<element type="angle" label="β">
<angleStyle val="0"/>
<value val="0.0017453292519943294"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="1"/>
<labelMode val="2"/>
<lineStyle thickness="4" type="0" typeHidden="2" opacity="153"/>
<arcSize val="30"/>
</element>
<command name="Vector">
<input a0="I" a1="S"/>
<output a0="n"/>
</command>
<element type="vector" label="n">
<show object="false" label="false"/>
<objColor r="97" g="97" b="97" alpha="0"/>
<layer val="1"/>
<labelOffset x="-75" y="-28"/>
<labelMode val="0"/>
<coords x="-10.6053233108331" y="6.114396854411973" z="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="204"/>
<coordStyle style="cartesian"/>
<startPoint exp="I"/>
</element>
<expression label="o" exp="(u * n / ((2 * u^(2))))" />
<element type="numeric" label="o">
<value val="0.9272355031182137"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="text7" exp=""\frac{v_B_0}{v_A_0}=" + (LaTeX[l]) + """ />
<element type="text" label="text7">
<show object="false" label="false" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<startPoint x="16.404665704058367" y="10.208314623127297" z="1"/>
</element>
<expression label="text2" exp=""\frac{E_c}{E_0}=" + (LaTeX[a]) + """ />
<element type="text" label="text2">
<show object="false" label="false" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1" size="0" style="2"/>
<decimals val="3"/>
<startPoint x="9.599263227111466" y="6.7751678431435085" z="1"/>
</element>
<expression label="text3" exp=""\frac{ΔE_m_a_x}{E_0}=" + (LaTeX[b]) + """ />
<element type="text" label="text3">
<show object="false" label="false" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1" size="0" style="2"/>
<decimals val="3"/>
<startPoint x="15.903925086697706" y="6.775167843143509" z="1"/>
</element>
<expression label="text5" exp=""\frac{E'}{E_0}=" + (LaTeX[e]) + """ />
<element type="text" label="text5">
<show object="false" label="false" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1" size="0" style="2"/>
<decimals val="3"/>
<startPoint x="9.503738047420764" y="3.8138872727317805" z="1"/>
</element>
<expression label="text6" exp=""\frac{ΔE}{E_0}=" + (LaTeX[j]) + """ />
<element type="text" label="text6">
<show object="false" label="false" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1" size="0" style="2"/>
<decimals val="3"/>
<startPoint x="16.047212856233756" y="3.527311733659677" z="1"/>
</element>
<command name="Mirror">
<input a0="F" a1="O"/>
<output a0="F'"/>
</command>
<element type="point" label="F'">
<show object="true" label="true"/>
<objColor r="97" g="97" b="97" alpha="0"/>
<layer val="1"/>
<labelOffset x="11" y="29"/>
<labelMode val="3"/>
<coords x="3.8178686865143736" y="-6.594222108460883" z="1"/>
<pointSize val="3"/>
<pointStyle val="10"/>
<caption val="I_2(0.5v_0,-0.5√kv_0)"/>
</element>
<command name="Mirror">
<input a0="F'" a1="f"/>
<output a0="F''"/>
</command>
<element type="point" label="F''">
<show object="true" label="true"/>
<objColor r="97" g="97" b="97" alpha="0"/>
<layer val="1"/>
<labelOffset x="-43" y="-16"/>
<labelMode val="3"/>
<coords x="-7.6197038343482415" y="-2.6645352591003757e-15" z="1"/>
<pointSize val="3"/>
<pointStyle val="10"/>
<caption val="F_2(-v_0,0)"/>
</element>
<command name="Vector">
<input a0="I" a1="F"/>
<output a0="r"/>
</command>
<element type="vector" label="r">
<show object="true" label="true"/>
<objColor r="97" g="97" b="97" alpha="0"/>
<layer val="1"/>
<labelOffset x="40" y="21"/>
<labelMode val="3"/>
<coords x="-11.437572520862615" y="6.594222108460883" z="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="204"/>
<coordStyle style="cartesian"/>
<startPoint exp="I"/>
<caption val="2N-1次碰撞"/>
</element>
<command name="Vector">
<input a0="F'" a1="F''"/>
<output a0="p"/>
</command>
<element type="vector" label="p">
<show object="true" label="true"/>
<objColor r="97" g="97" b="97" alpha="0"/>
<layer val="1"/>
<labelOffset x="4" y="75"/>
<labelMode val="3"/>
<coords x="-11.437572520862615" y="6.5942221084608805" z="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="204"/>
<coordStyle style="cartesian"/>
<startPoint exp="F'"/>
<caption val="2N次碰撞"/>
</element>
<expression label="text8" exp=""α""/>
<element type="text" label="text8">
<show object="true" label="false" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<startPoint x="5.635956166985905" y="0.2143340704236042" z="1"/>
</element>
<expression label="text9" exp=""2α""/>
<element type="text" label="text9">
<show object="true" label="false" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<startPoint x="-1.4798430000031402" y="0.18817304407437963" z="1"/>
</element>
<command name="OrthogonalLine">
<input a0="F" a1="xAxis"/>
<output a0="t"/>
</command>
<element type="line" label="t">
<show object="true" label="false" ev="4"/>
<objColor r="97" g="97" b="97" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="-1" y="0" z="-3.8178686865143736"/>
<lineStyle thickness="5" type="10" typeHidden="1" opacity="51"/>
<eqnStyle style="explicit"/>
</element>
<command name="Intersect">
<input a0="t" a1="xAxis"/>
<output a0="D"/>
</command>
<element type="point" label="D">
<show object="true" label="false"/>
<objColor r="97" g="97" b="97" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="-3.8178686865143736" y="0" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="F" a1="D"/>
<output a0="f_1"/>
</command>
<element type="segment" label="f_1">
<show object="true" label="false"/>
<objColor r="97" g="97" b="97" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="6.594222108460883" y="0" z="25.175874099813594"/>
<lineStyle thickness="5" type="10" typeHidden="1" opacity="204"/>
<eqnStyle style="explicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="F" a1="F'"/>
<output a0="s"/>
</command>
<element type="segment" label="s">
<show object="true" label="false"/>
<objColor r="97" g="97" b="97" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="13.188444216921766" y="7.635737373028747" z="0"/>
<lineStyle thickness="5" type="10" typeHidden="1" opacity="204"/>
<eqnStyle style="explicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="text10" exp=""v_0=√(2gR)""/>
<element type="text" label="text10">
<show object="true" label="false" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<startPoint x="7.977910700988009" y="1.0135284405236924" z="1"/>
</element>
</construction>
</geogebra>