<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="stack">
    <name>
      <text>4.4.2.5 Rotating mechanism</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p class="HELM_exercise">Exercise</p>
<p>The crank mechanism shown below has an arm \(OA\) of length \( {@len1@}\, \textrm{mm}\) rotating anticlockwise about \(O\) and a connecting rod \(AB\) of length \( {@len2@}\, \textrm{mm}.\) \(B\) moves along the horizontal line \(OB.\)
</p>
<p>What is the value of angle \(\hat{B}\) and length \(OB\) when \(OA\) has rotated by \(\displaystyle {@rot@}\) of a complete revolution from the horizontal?</p>

<figure class="HELM_figure">
  <img src="@@PLUGINFILE@@/Ex4Fig4.svg" alt="Rotation mechanism" width="357" height="95" class="img-responsive atto_image_button_text-bottom">
</figure>

<p>\( \hat{B} = \) [[input:ans1]] [[validation:ans1]] [[feedback:prt1]] Keep 3 decimal places.</p>
<p>\( OB = \) [[input:ans2]] [[validation:ans2]] [[feedback:prt2]] Keep 1 decimal place.</p>]]></text>
<file name="Ex4Fig4.svg" path="/" encoding="base64">[encoded data, 15968 characters]</file>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>First we find that the angle at \(O\) is \( \hat{O} = \displaystyle {@rot@} \times 360^{\circ} = {@angO@}^{\circ}.\)</p>
<p>By the Sine rule:</p>
<p>\( \dfrac{OA}{\sin B} = \dfrac{AB}{\sin B} \Rightarrow \dfrac{@len1@}{\sin B} = \dfrac{@len2@}{\sin {@angO@}} \Rightarrow \sin B = \dfrac{@len1@}{@len2@} \sin {@angO@} = {@decimalplaces(sinB,3)@}.\)</p>
<p>So, \( \quad \hat{B} = {@BB@}^{\circ}.\)</p>
<p>Hence, \(\quad \hat{A} = 180^{\circ} - ({@angO@}^{\circ} + {@BB@}^{\circ}) = {@AA@}^{\circ}.\)</p>
<p>Using the sine rule again:</p>
<p>\( \dfrac{OA}{\sin B} = \dfrac{OB}{\sin A} \Rightarrow \dfrac{@len1@}{\sin {@BB@}} = \dfrac{OB}{\sin {@AA@}}\) from which \( \, OB = {@OB@}\, \textrm{mm}.\)</p>]]></text>
    </generalfeedback>
    <defaultgrade>1</defaultgrade>
    <penalty>0.1</penalty>
    <hidden>0</hidden>
    <idnumber/>
    <stackversion>
      <text>2025073100</text>
    </stackversion>
    <questionvariables>
      <text>len1: rand([30,35,40]);
len2: rand([50,55,60,65,70]);
rot: rand([1/6, 1/8, 1/9, 1/12]);
angO: 360*rot;

sinB: len1*sin(angO*%pi/180)/len2;
BB: decimalplaces(asin(sinB)*180/%pi,3);
AA: 180-(angO+BB);
OB: decimalplaces(len1*sin(AA*%pi/180)/sin(BB*%pi/180),1);</text>
    </questionvariables>
    <specificfeedback format="html">
      <text/>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>\( OA = {@len1@}, AB = {@len2@}, \hat{O} = {@angO@}, \hat{B} = {@BB@}, OB= {@OB@} \)</text>
    </questionnote>
    <questiondescription format="moodle_auto_format">
      <text/>
    </questiondescription>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <prtcorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Correct answer, well done.]]></text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Your answer is partially correct.]]></text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Incorrect answer.]]></text>
    </prtincorrect>
    <decimals>.</decimals>
    <scientificnotation>*10</scientificnotation>
    <multiplicationsign>dot</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <logicsymbol>lang</logicsymbol>
    <matrixparens>[</matrixparens>
    <isbroken>0</isbroken>
    <variantsselectionseed/>
    <input>
      <name>ans1</name>
      <type>numerical</type>
      <tans>BB</tans>
      <boxsize>7</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
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      <syntaxattribute>0</syntaxattribute>
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      <showvalidation>3</showvalidation>
      <options>maxdp:3, mindp:3</options>
    </input>
    <input>
      <name>ans2</name>
      <type>numerical</type>
      <tans>OB</tans>
      <boxsize>8</boxsize>
      <strictsyntax>1</strictsyntax>
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      <options>maxdp:1, mindp:1</options>
    </input>
    <prt>
      <name>prt1</name>
      <value>1.0000000</value>
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        <name>0</name>
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        <answertest>NumAbsolute</answertest>
        <sans>ans1</sans>
        <tans>BB</tans>
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        <truescoremode>=</truescoremode>
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        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prt1-1-T</trueanswernote>
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          <text/>
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        <falsescore>0</falsescore>
        <falsepenalty/>
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        <falseanswernote>prt1-1-F</falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
    </prt>
    <prt>
      <name>prt2</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackstyle>1</feedbackstyle>
      <feedbackvariables>
        <text/>
      </feedbackvariables>
      <node>
        <name>0</name>
        <description/>
        <answertest>NumAbsolute</answertest>
        <sans>ans2</sans>
        <tans>OB</tans>
        <testoptions>0.2</testoptions>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1</truescore>
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        <trueanswernote>prt2-1-T</trueanswernote>
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          <text/>
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        <falseanswernote>prt2-1-F</falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
    </prt>
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    <qtest>
      <testcase>1</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>dispdp(BB,3)</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>dispdp(OB,1)</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt1-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt2</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt2-1-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>2</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>dispdp(ev(BB+1,simp),3)</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>dispdp(ev(OB+1,simp),1)</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt1-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt2</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt2-1-F</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>3</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>dispdp(ev(BB+0.001),3)</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>ev(OB+0.1)</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt1-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt2</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt2-1-T</expectedanswernote>
      </expected>
    </qtest>
  </question>
</quiz>
