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      <text>15.2.2.5 y coord of COM of lamina by horizontal strips</text>
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      <text><![CDATA[<p class="HELM_exercise">Exercise</p>
<p></p>
<p>In this exercise we divide the lamina into a number of horizontal slices; a typical slice is shown below.</p>
<figure class="HELM_figure"><img src="@@PLUGINFILE@@/15-2-2-3-fig2.svg" alt="" width="300" height="266" class="img-responsive atto_image_button_text-bottom"><br></figure>

<ol class="HELM_parts">

    <li>
        <p><span style="font-size: 0.9375rem;">In this case we will take a rectangle of width \(2 - x\) and height \(\delta y\). Find the mass \(m\) of this rectangle in term of \(\rho\) and \(y\).</span><br></p>
        <p><span style="font-size: 0.9375rem;">\(m=\) [[input:ans2]] [[validation:ans2]] [[feedback:prt2]]<br></span>Enter&nbsp;<code>rho</code>&nbsp;for \(\rho\).<br></p>
        <p>The moment about the \(x\)-axis is then \(m\bar{y}\).</p>
        <p>
        </p>
    </li>
    <li>
        <p>We take the sum of all such moments and letting \(\delta \to 0\) we obtain the integral:</p>
        <p><span style="font-size: 0.9375rem;">\(\displaystyle{\int_{y=0}^{y=2}}\)&nbsp;[[input:ans5]]\(\textrm{d}y\)[[validation:ans5]] [[feedback:prt5]]</span><br></p>
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    <li>
        <p><span style="font-size: 0.9375rem;">Evaluate the integral above.</span></p>
        <p>[[input:ans3]] [[validation:ans3]] [[feedback:prt3]]</p>
    </li>
    <li>
        <p><span style="font-size: 0.9375rem;">&nbsp;Hence find \(\bar{y}=\)[[input:ans6]] [[validation:ans6]] [[feedback:prt6]]</span><br></p>
    </li>
    <p></p>
</ol>]]></text>
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      <text><![CDATA[<ol class="HELM_parts">

    <li>\(\displaystyle (2 - x) \delta y, \rho (2 - x) \delta y, \rho (2 - x)y \delta y\)</li>

    <li>\(\displaystyle \int_{y=0}^{y=2} \rho (2 - y)y \textrm{d}y\)</li>

    <li>\(\displaystyle \frac{4 \rho}{3}\)</li>
    <li>As before the total mass is \(2 \rho\), and its moment about the \(x\)-axis is \(2 \rho \bar{y}\). Hence \( 2 \rho \bar{y} = \frac{4 \rho}{3}\) from which \(\bar{y} =\frac{2}{3}\) which was the result obtained in the previous exercise.</li>
</ol>]]></text>
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      <text><![CDATA[texput(deltay,"\\delta y");
ta2:rho*(2 - y)*deltay;
ta3:4*rho/3;
ta5:rho*(2 - y)*y;
ta6:2/3;]]></text>
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