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      <text>4.1.2.2 Engineering Example 3</text>
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      <text><![CDATA[<h5>Engineering Example 3<br></h5>
<p><br></p>
<h5>Vintage car brake pedal mechanism<br></h5>
<p><br></p>

<h6>Introduction<br></h6>
<p>The figure bellow shows the structure and some dimensions of a vintage car brake pedal arrangement as far as the brake cable. The <strong>moment</strong> of a force about a point is the product of the force and the perpendicular distance from the point
    to the line of action of the force. The pedal is pivoted about the point \(A.\) The moments about \(A\) must be equal as the pedal is stationary.</p>
<p><br></p>

<h6>Problem in words<br></h6>
<p>If the driver supplies a force of \(900\, \textrm{N}\), to act at point \(B\), calculate the force (\(F\)) in the cable.</p>
<p><br></p>

<h6>Mathematical statement of the problem<br></h6>
<p>The perpendicular distance from the line of action of the force provided by the driver to the pivot point \(A\) is denoted by \(x_1\) and the perpendicular distance from the line of action of force in the cable to the pivot point \(A\) is denoted by \(x_2.\) Use trigonometry to relate \(x_1\) and \(x_2\) to the given dimensions.Calculate clockwise and anticlockwise moments about the pivot and set them equal.</p>

<figure class="HELM_figure">
<img src="@@PLUGINFILE@@/Brake.svg" alt="Structure and dimensions of vintage car brake pedal arrangement" width="453" height="232" class="img-responsive atto_image_button_text-bottom">
</figure>
<p><br></p>

<h6>Mathematical analysis<br></h6>
<p>The distance \(x_1\) is found by considering the right-angled triangle shown bellow and using the definition of cosine.</p>
<figure class="HELM_figure">
  <img src="@@PLUGINFILE@@/fig2.svg" alt="A right angle triangle with an ngle 40 degrees, and hypotenuse 210mm" width="484" height="73" class="img-responsive atto_image_button_text-bottom">
</figure>

<p>The distance \(x_2\) is found by considering the right-angled triangle shown bellow.</p>
<figure class="HELM_figure">
  <img src="@@PLUGINFILE@@/fig3.svg" alt="A right angle triangle with one angle 15 degrees and hypotenuse 75mm" width="456" height="91" class="img-responsive atto_image_button_text-bottom">
</figure>

<p>Equating moments about \(A:\)</p>
<p>\(\qquad 900 x_1 = F x_2 \qquad\) so \(\qquad F = 2013\, \textrm{N}.\)</p>
<p><br></p>

<h6>Interpretation<br></h6>
<p>This means that the force exerted by the cable is \(2013\, \texrtm{N} in the direction of the cable. This force is more than twice that applied by the driver. In fact, whatever the force applied at the pedal the force in the cable will be more than twice that force. The pedal structure is an example of a lever system that offers a mechanical gain.</p>]]></text>
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<file name="fig2.svg" path="/" encoding="base64">[encoded data, 38452 characters]</file>
<file name="fig3.svg" path="/" encoding="base64">[encoded data, 43932 characters]</file>
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