滑轮组力学几何模型演示
2020-07-23 12:06
本GeoGebra范例演示了滑轮组的几何构造与力学原理。通过平移、旋转、圆和切线等几何命令,构建了包含滑轮、绳索、挂钩和重物的动态模型。该模型直观展示了滑轮组中各部件的相对位置与运动关系,适用于物理力学与几何作图的交叉教学,帮助理解简单机械的几何特征。
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.580.0" app="classic" platform="d" id="03f87cf9-80a1-4989-b86f-d9f99530555d" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/apps/xsd/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1936" height="1056" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.934400826446281" orientation="1" />
</panes>
<views>
<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 | 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 , 66 || 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 || 66 68 || 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="true" location="3" size="1909" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="true" location="3" size="200" window="100,100,600,400" />
<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="64" visible="false" inframe="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="4097" visible="false" inframe="false" stylebar="true" location="1" size="380" window="100,100,700,550" />
<view id="70" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
</views>
<toolbar show="false" items="0 39 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="true" cmd="true" top="algebra" />
<dockBar show="true" east="true" />
</perspective>
</perspectives>
<labelingStyle val="0"/>
<font size="12"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="1909" height="936"/>
<coordSystem xZero="727.1871401974507" yZero="560.6820197287643" scale="25.492346740298217" yscale="25.49234674029801"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="3"/>
<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="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<spreadsheetView>
<prefCellSize height="24"/>
</spreadsheetView>
<algebraView>
<mode val="1"/>
<auxiliary show="true"/>
<collapsed val="0,1,3,4,5,6"/>
</algebraView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<tableview min="-2.0" max="2.0" step="1.0"/>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="point" label="A">
<show object="true" label="false" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0.0"/>
<layer val="3"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="4.4645893515419" y="15.443145495366903" z="1.0"/>
<pointSize val="9"/>
<pointStyle val="4"/>
</element>
<element type="point" label="挂钩点A">
<show object="false" label="false" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0.0"/>
<layer val="1"/>
<labelOffset x="67" y="44"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="0.511736540386799" y="20.683249538245967" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Translate">
<input a0="挂钩点A" a1="(-0.35, -5)"/>
<output a0="O"/>
</command>
<element type="point" label="O">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="3"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="0.16173654038679908" y="15.683249538245967" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Circle">
<input a0="O" a1="1.5"/>
<output a0="e"/>
</command>
<element type="conic" label="e">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="243.74047478738862" A3="0.0" A4="-0.16173654038679908" A5="-15.683249538245967"/>
<eqnStyle style="specific"/>
</element>
<command name="Tangent">
<input a0="A" a1="e"/>
<output a0="f" a1="g"/>
</command>
<element type="line" label="f">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.6150374201258622" y="-3.7032210840652557" z="64.39986087096571"/>
<lineStyle thickness="9" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<element type="line" label="g">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="1.1930059985702233" y="-3.8599130758668263" z="54.28291735253835"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="Intersect">
<input a0="e" a1="f"/>
<output a0="C"/>
</command>
<element type="point" label="C">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="3"/>
<labelMode val="0"/>
<coords x="0.7613682674766441" y="17.058182915492765" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<expression label="α" exp="30° - (180° * Distance[A, C] / ((1.5 * π)))" />
<element type="angle" label="α">
<angleStyle val="3"/>
<value val="-2.169783424112875"/>
</element>
<command name="Circle">
<input a0="O" a1="2.23"/>
<output a0="d"/>
</command>
<element type="conic" label="d">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="241.0175747873886" A3="0.0" A4="-0.16173654038679908" A5="-15.683249538245967"/>
<eqnStyle style="specific"/>
</element>
<command name="Point">
<input a0="d"/>
<output a0="R"/>
</command>
<element type="point" label="R">
<show object="false" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="-1.9838682480229415" y="16.290933742379323" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Translate">
<input a0="挂钩点A" a1="(-1.4, 2.8)"/>
<output a0="A1"/>
</command>
<element type="point" label="A1">
<show object="false" label="true" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.8882634596132009" y="23.483249538245968" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Translate">
<input a0="挂钩点A" a1="(-1.4, -1.38)"/>
<output a0="A2"/>
</command>
<element type="point" label="A2">
<show object="false" label="true" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.8882634596132009" y="19.303249538245968" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="image" label="挂钩">
<file name="ba431d132013afbc74aeb0dd6812ee6e/挂钩3.png"/>
<inBackground val="false"/>
<startPoint number="0" exp="A2"/>
<startPoint number="2" exp="A1"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="1.0"/>
<layer val="1"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<selectionAllowed val="false"/>
</element>
<element type="image" label="框">
<file name="80d83e64ad61935d8c4783e957d0bb60/滑轮框.png"/>
<inBackground val="false"/>
<startPoint number="0" exp="(x(挂钩点A) - 0.85, y(挂钩点A) - 7.15)"/>
<startPoint number="2" exp="(x(挂钩点A) - 0.85, y(挂钩点A) - 1.35)"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="1.0"/>
<layer val="2"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<selectionAllowed val="false"/>
</element>
<command name="Rotate">
<input a0="R" a1="α" a2="O"/>
<output a0="R1"/>
</command>
<element type="point" label="R1">
<show object="false" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="1.8733325316633276" y="17.11270368673976" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="k" exp="-20 + Distance[A, C] / 2" />
<element type="numeric" label="k">
<value val="-17.97996335021662"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="Rotate">
<input a0="R1" a1="90°" a2="O"/>
<output a0="R2"/>
</command>
<element type="point" label="R2">
<show object="false" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="-1.2677176081069939" y="17.394845529522495" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Translate">
<input a0="框" a1="(0, k)"/>
<output a0="框2"/>
</command>
<element type="image" label="框2">
<file name="80d83e64ad61935d8c4783e957d0bb60/滑轮框.png"/>
<inBackground val="false"/>
<startPoint number="0" x="-0.3382634596132009" y="-4.446713811970655" z="1"/>
<startPoint number="2" x="-0.3382634596132009" y="1.3532861880293439" z="1"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="1.0"/>
<layer val="2"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<command name="Translate">
<input a0="e" a1="(0, k)"/>
<output a0="e2"/>
</command>
<element type="conic" label="e2">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="3.051053042593054" A3="0.0" A4="-0.16173654038679908" A5="2.2967138119706547"/>
<eqnStyle style="specific"/>
</element>
<command name="Translate">
<input a0="O" a1="(0, k)"/>
<output a0="O2"/>
</command>
<element type="point" label="O2">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="3"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="0.16173654038679908" y="-2.2967138119706547" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Translate">
<input a0="O" a1="(0, -2)"/>
<output a0="O1"/>
</command>
<element type="point" label="O1">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="0.16173654038679908" y="13.683249538245967" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Tangent">
<input a0="O1" a1="e2"/>
<output a0="h" a1="i"/>
</command>
<element type="line" label="h">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="15.839162026040274" y="-1.4933770411755365" z="17.87247944037457"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<element type="line" label="i">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="15.839162026040274" y="1.493377041175536" z="-22.99602197781"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="Intersect">
<input a0="e2" a1="i"/>
<output a0="B"/>
</command>
<element type="point" label="B">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="1.6551135815623352" y="-2.1559124877943066" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="O1" a1="B"/>
<output a0="j"/>
</command>
<element type="segment" label="j">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="15.839162026040274" y="1.493377041175536" z="-22.99602197781"/>
<lineStyle thickness="9" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="C" a1="A"/>
<output a0="l"/>
</command>
<element type="segment" label="l">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="1.6150374201258622" y="3.7032210840652557" z="-64.39986087096571"/>
<lineStyle thickness="9" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Translate">
<input a0="O" a1="(-1.5, 0)"/>
<output a0="O'"/>
</command>
<element type="point" label="O'">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="3"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="-1.3382634596132008" y="15.683249538245967" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Translate">
<input a0="O2" a1="(-1.5, 0)"/>
<output a0="O2'"/>
</command>
<element type="point" label="O2'">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="3"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="-1.3382634596132008" y="-2.2967138119706547" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="O'" a1="O2'"/>
<output a0="m"/>
</command>
<element type="segment" label="m">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="17.97996335021662" y="0.0" z="24.061927956779453"/>
<lineStyle thickness="9" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="image" label="轮">
<file name="6d6bced4a1214b196782d338986423d1/轮.png"/>
<inBackground val="false"/>
<startPoint number="0" exp="R2"/>
<startPoint number="2" exp="R1"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="1.0"/>
<layer val="1"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<selectionAllowed val="false"/>
</element>
<command name="Translate">
<input a0="轮" a1="(0, k)"/>
<output a0="轮2"/>
</command>
<element type="image" label="轮2">
<file name="6d6bced4a1214b196782d338986423d1/轮.png"/>
<inBackground val="false"/>
<startPoint number="0" x="-1.2677176081069939" y="-0.5851178206941263" z="1"/>
<startPoint number="2" x="1.8733325316633276" y="-0.8672596634768617" z="1"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="1.0"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<command name="Segment">
<input a0="O2" a1="(x(O2), y(O2) - 4)"/>
<output a0="n"/>
</command>
<element type="segment" label="n">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="4.0" y="0.0" z="-0.6469461615471964"/>
<lineStyle thickness="9" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="image" label="pic1">
<file name="f9eaceb8c1a786df6c9a63cd31c8fd72/一篮.png"/>
<inBackground val="false"/>
<startPoint number="0" exp="(x(O2) - 3.43, y(O2) - 9.95)"/>
<startPoint number="2" exp="(x(O2) - 3.43, y(O2) - 3.44)"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="1.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
</construction>
</geogebra>