Spring Scale
2020-06-01 12:58
This GeoGebra applet dynamically demonstrates the construction and working principle of a spring scale. Using geometric constructions and vector transformations, it accurately builds components such as the spring, dial, hook, and pointer. Users can interact via sliders or dragging to simulate the stretching process under force, visually illustrating the linear functional relationship (Hooke's Law)
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.583.0" app="classic" platform="d" id="517dc30b-3b58-4be6-b045-c6d8da600b73" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/apps/xsd/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1440" height="860" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.1423611111111111" 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="4097" visible="false" inframe="false" stylebar="true" location="1,1" size="310" window="100,100,700,550" />
<view id="1" visible="true" inframe="false" stylebar="true" location="1" size="1413" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="true" location="3" size="205" 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" toolbar="0" visible="false" inframe="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" 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="1413" height="738"/>
<coordSystem xZero="445.1509982597579" yZero="289.5315981597087" scale="18.331724802834373" yscale="18.331724802834493"/>
<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>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
<startAnimation val="true"/>
</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="false" label="false" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-68" y="42"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="3.1401324473763585" y="0.5803367709449085" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Circle">
<input a0="A" a1="15"/>
<output a0="弹簧秤"/>
</command>
<element type="conic" label="弹簧秤">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="255" alpha="0.0" fillType="4" hatchAngle="45" hatchDistance="50"/>
<layer val="1"/>
<labelMode val="0"/>
<lineStyle thickness="1" type="0" typeHidden="1" opacity="0"/>
<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="-214.8027774452234" A3="0.0" A4="-3.1401324473763585" A5="-0.5803367709449085"/>
<eqnStyle style="specific"/>
</element>
<command name="Point">
<input a0="弹簧秤"/>
<output a0="B"/>
</command>
<element type="point" label="B">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="2"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="14.72647138338306" y="-8.946296950363742" z="1.0"/>
<pointSize val="7"/>
<pointStyle val="3"/>
</element>
<command name="Rotate">
<input a0="B" a1="30°" a2="A"/>
<output a0="B'"/>
</command>
<element type="point" label="B'">
<show object="false" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="17.93751316346925" y="-1.8768005762545166" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Midpoint">
<input a0="B" a1="B'"/>
<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="2"/>
<labelMode val="0"/>
<coords x="16.331992273426156" y="-5.4115487633091295" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Line">
<input a0="A" a1="C"/>
<output a0="f"/>
</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="2"/>
<labelMode val="0"/>
<coords x="5.991885534254038" y="13.191859826049797" z="-26.47103552128373"/>
<lineStyle thickness="1" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
</element>
<command name="Point">
<input a0="f"/>
<output a0="G"/>
</command>
<element type="point" label="G">
<show object="false" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="2"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="-4.457486971394053" y="4.031257754823331" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="f"/>
<output a0="下限"/>
</command>
<element type="point" label="下限">
<show object="false" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="2"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="38.05204633343332" y="-15.277032435928117" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="f"/>
<output a0="上限"/>
</command>
<element type="point" label="上限">
<show object="false" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="2"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="19.290900499472684" y="-6.755516909621856" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="上限" a1="下限"/>
<output a0="g"/>
</command>
<element type="segment" label="g">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="2"/>
<labelMode val="0"/>
<coords x="8.52151552630626" y="18.761145833960633" z="-37.646470197482984"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Point">
<input a0="g"/>
<output a0="D"/>
</command>
<element type="point" label="D">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="153" b="0" alpha="0.0"/>
<layer val="2"/>
<labelMode val="0"/>
<animation step="2" speed="(-b)" type="3" playing="true"/>
<coords x="22.04186387769635" y="-8.005034255060242" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="1"/>
</element>
<expression label="a" exp="x(G) - Distance[G, D] + 25" />
<element type="numeric" label="a">
<value val="-8.562261850619208"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<element type="image" label="刻度板">
<file name="0dbef1cf32a170038de1560a5c9815b6/弹簧测力计90.png"/>
<inBackground val="false"/>
<startPoint number="0" exp="B"/>
<startPoint number="1" exp="B'"/>
<auxiliary val="false"/>
<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"/>
<auxiliary val="false"/>
</element>
<command name="OrthogonalLine">
<input a0="D" a1="g"/>
<output a0="h"/>
</command>
<element type="line" label="h">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="2"/>
<labelMode val="0"/>
<coords x="-18.761145833960633" y="8.52151552630626" z="481.74564635487957"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="Point">
<input a0="h"/>
<output a0="E"/>
</command>
<element type="point" label="E">
<show object="false" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="2"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="21.1450011924332" y="-9.97958579807116" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="h"/>
<output a0="F"/>
</command>
<element type="point" label="F">
<show object="false" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="2"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="22.85945298657461" y="-6.205013066743314" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="image" label="pic1">
<file name="5722e9c97691e3ebbb05e72211bdc1ee/弹簧测力计91.png"/>
<inBackground val="false"/>
<startPoint number="0" exp="E"/>
<startPoint number="1" exp="F"/>
<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="Circle">
<input a0="D" a1="1.5"/>
<output a0="称钩"/>
</command>
<element type="conic" label="称钩">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="255" alpha="0.0" fillType="4" hatchAngle="45" hatchDistance="50"/>
<layer val="5"/>
<labelMode val="0"/>
<ggbscript val="aa=If(|v|>0,true,false)
StartAnimation( D, aa)"/>
<ggbscript onUpdate="b=v*u/5"/>
<lineStyle thickness="1" type="0" typeHidden="1" opacity="0"/>
<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="547.6743366275831" A3="0.0" A4="-22.04186387769635" A5="8.005034255060242"/>
<eqnStyle style="specific"/>
</element>
<command name="Vector">
<input a0="G" a1="C"/>
<output a0="u"/>
</command>
<element type="vector" label="u">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="5"/>
<labelMode val="0"/>
<coords x="20.789479244820207" y="-9.44280651813246" z="0.0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<coordStyle style="cartesian"/>
<startPoint exp="G"/>
</element>
<command name="Angle">
<input a0="Vector[(0, -1)]" a1="u"/>
<output a0="α"/>
</command>
<element type="angle" label="α">
<angleStyle val="0"/>
<value val="1.1444461986300136"/>
<show object="false" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<layer val="5"/>
<labelMode val="1"/>
<lineStyle thickness="5" type="0" typeHidden="2" opacity="178"/>
<arcSize val="30"/>
</element>
<expression label="p" exp="p(x) = If[a - 0.3 < x < x(G), (0.6 * sin(((30 * π) * (x - x(G)) / (x(G) - a)))) + y(G)]" />
<element type="function" label="p">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.0"/>
<layer val="5"/>
<labelMode val="0"/>
<lineStyle thickness="3" type="0" typeHidden="1" opacity="178"/>
</element>
<command name="Rotate">
<input a0="p" a1="α + 90°" a2="G"/>
<output a0="p1"/>
</command>
<element type="curvecartesian" label="p1">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="5"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="3" type="0" typeHidden="1"/>
</element>
<command name="Point">
<input a0="g"/>
<output a0="零刻度线"/>
</command>
<element type="point" label="零刻度线">
<show object="false" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="5"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="22.04186387769635" y="-8.005034255060242" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Vector">
<input a0="零刻度线" a1="D"/>
<output a0="v"/>
</command>
<element type="vector" label="v">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="5"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="0.0" y="0.0" z="0.0"/>
<lineStyle thickness="1" type="0" typeHidden="1" opacity="178"/>
<coordStyle style="cartesian"/>
<startPoint exp="零刻度线"/>
</element>
<expression label="b" exp="(v * u / 5)" />
<element type="numeric" label="b">
<value val="0.0"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
</element>
<command name="If">
<input a0="abs(v) > 0" a1="true" a2="false"/>
<output a0="aa"/>
</command>
<element type="boolean" label="aa">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
</construction>
</geogebra>