<?xml version='1.0' encoding='UTF-8'?><?xml-stylesheet href="http://www.blogger.com/styles/atom.css" type="text/css"?><feed xmlns='http://www.w3.org/2005/Atom' xmlns:openSearch='http://a9.com/-/spec/opensearchrss/1.0/' xmlns:georss='http://www.georss.org/georss' xmlns:gd='http://schemas.google.com/g/2005' xmlns:thr='http://purl.org/syndication/thread/1.0'><id>tag:blogger.com,1999:blog-603242458691764012</id><updated>2011-04-21T15:54:57.334-07:00</updated><category term='General'/><category term='Physics'/><title type='text'>The Peter Vlasveld Science Journal</title><subtitle type='html'></subtitle><link rel='http://schemas.google.com/g/2005#feed' type='application/atom+xml' href='http://pvsj.blogspot.com/feeds/posts/default'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/603242458691764012/posts/default?max-results=100'/><link rel='alternate' type='text/html' href='http://pvsj.blogspot.com/'/><link rel='hub' href='http://pubsubhubbub.appspot.com/'/><author><name>Fizzizist</name><uri>http://www.blogger.com/profile/16838707366517235413</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='32' height='30' src='http://1.bp.blogspot.com/_xBn5pA0uuHg/SQ5KOLaAMuI/AAAAAAAAAAc/F2apPU4ARd8/s1600-R/madscientist.jpg'/></author><generator version='7.00' uri='http://www.blogger.com'>Blogger</generator><openSearch:totalResults>3</openSearch:totalResults><openSearch:startIndex>1</openSearch:startIndex><openSearch:itemsPerPage>100</openSearch:itemsPerPage><entry><id>tag:blogger.com,1999:blog-603242458691764012.post-7714516114444294304</id><published>2008-12-24T03:19:00.000-08:00</published><updated>2008-12-24T03:20:09.186-08:00</updated><category scheme='http://www.blogger.com/atom/ns#' term='Physics'/><title type='text'>Coefficients of static friction in shows</title><content type='html'>&lt;p class="MsoNormal" align="center" style="text-align:center"&gt;&lt;b&gt;&lt;i&gt;&lt;u&gt;Lab: Measuring Coefficients of Friction&lt;o:p&gt;&lt;/o:p&gt;&lt;/u&gt;&lt;/i&gt;&lt;/b&gt;&lt;/p&gt;  &lt;p class="MsoNormal" align="center" style="text-align:center"&gt;&lt;b&gt;&lt;i&gt;&lt;u&gt; &lt;o:p&gt;&lt;/o:p&gt;&lt;/u&gt;&lt;/i&gt;&lt;/b&gt;&lt;/p&gt;  &lt;p class="MsoNormal"&gt;&lt;b&gt;Purpose:&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt;  &lt;ul style="margin-top:0in" type="disc"&gt;  &lt;li class="MsoNormal" style="mso-list:l0 level1 lfo1;tab-stops:list .5in"&gt;To      determine whether tread design affects the coefficient of static friction      for running shoes&lt;b&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/li&gt; &lt;/ul&gt;  &lt;p class="MsoNormal"&gt; &lt;o:p&gt;&lt;/o:p&gt;&lt;/p&gt;  &lt;p class="MsoNormal"&gt;&lt;b&gt;Materials:&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt;  &lt;ul style="margin-top:0in" type="disc"&gt;  &lt;li class="MsoNormal" style="mso-list:l0 level1 lfo1;tab-stops:list .5in"&gt;Meter      stick&lt;b&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/li&gt;  &lt;li class="MsoNormal" style="mso-list:l0 level1 lfo1;tab-stops:list .5in"&gt;Wooden      board&lt;b&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/li&gt;  &lt;li class="MsoNormal" style="mso-list:l0 level1 lfo1;tab-stops:list .5in"&gt;7      examples of shoes&lt;b&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/li&gt; &lt;/ul&gt;  &lt;p class="MsoNormal"&gt; &lt;o:p&gt;&lt;/o:p&gt;&lt;/p&gt;  &lt;p class="MsoNormal"&gt;&lt;b&gt;Hypothesis:&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt;  &lt;ul style="margin-top:0in" type="disc"&gt;  &lt;li class="MsoNormal" style="mso-list:l1 level1 lfo2;tab-stops:list .5in"&gt;I hypothesize      that the tread design will affect the coefficient of static friction of      the shoes.&lt;b&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/li&gt; &lt;/ul&gt;  &lt;p class="MsoNormal"&gt; &lt;o:p&gt;&lt;/o:p&gt;&lt;/p&gt;  &lt;p class="MsoNormal"&gt;&lt;b&gt;Procedure:&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt;  &lt;ul style="margin-top:0in" type="disc"&gt;  &lt;li class="MsoNormal" style="mso-list:l1 level1 lfo2;tab-stops:list .5in"&gt;Collect      observations of each shoe: size, heaviness, width, and a brief description      of what the tread looks like.&lt;b&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/li&gt;  &lt;li class="MsoNormal" style="mso-list:l1 level1 lfo2;tab-stops:list .5in"&gt;One by      one, place each shoe on the wooden board, and raise one side until the      shoe begins to slide downward. Take measurement of angle of inclination.      Repeat 3 times for each shoe so as to maintain accurate data.&lt;b&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/li&gt;  &lt;li class="MsoNormal" style="mso-list:l1 level1 lfo2;tab-stops:list .5in"&gt;Repeat      step 2 measuring data for rough side of wood as well as smooth side.&lt;b&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/li&gt;  &lt;li class="MsoNormal" style="mso-list:l1 level1 lfo2;tab-stops:list .5in"&gt;Use      angle of inclination to solve for each shoe’s coefficient of static      friction between its tread, and the wooden board.&lt;b&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/li&gt;  &lt;li class="MsoNormal" style="mso-list:l1 level1 lfo2;tab-stops:list .5in"&gt;Use      all data gathered to disprove or confirm hypothesis.&lt;b&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/li&gt; &lt;/ul&gt;  &lt;p class="MsoNormal"&gt; &lt;o:p&gt;&lt;/o:p&gt;&lt;/p&gt;  &lt;p class="MsoNormal"&gt;&lt;b&gt;Observations:&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt;  &lt;p class="MsoNormal"&gt;Shoe descriptions:&lt;/p&gt;  &lt;ol style="margin-top:0in" start="1" type="1"&gt;  &lt;li class="MsoNormal" style="mso-list:l2 level1 lfo3;tab-stops:list .5in"&gt;Skater      shoe: mildly heavy shoe, tread is flat and worn down with wavy pattern      through it&lt;/li&gt;  &lt;li class="MsoNormal" style="mso-list:l2 level1 lfo3;tab-stops:list .5in"&gt;Running      shoe #1: very lightweight shoe, tread is thick and in 2 separate blobs,      and also worn down to make it more flat.&lt;/li&gt;  &lt;li class="MsoNormal" style="mso-list:l2 level1 lfo3;tab-stops:list .5in"&gt;Running      shoe #2: also very lightweight shoe, tread is thick and has texture, also      in 2 blobs, not much tread is touching the surface of the wood.&lt;/li&gt;  &lt;li class="MsoNormal" style="mso-list:l2 level1 lfo3;tab-stops:list .5in"&gt;High      heal shoe: medium weight shoe, tread is very flat, thin and in 2 sections.&lt;/li&gt;  &lt;li class="MsoNormal" style="mso-list:l2 level1 lfo3;tab-stops:list .5in"&gt;Male      dress shoe #1: Heaviest shoe, tread has slight texture, but otherwise very      flat and very widespread.&lt;/li&gt;  &lt;li class="MsoNormal" style="mso-list:l2 level1 lfo3;tab-stops:list .5in"&gt;Male      dress shoe #2: Semi-lightweight shoe, tread has texture and is curvy.&lt;/li&gt;  &lt;li class="MsoNormal" style="mso-list:l2 level1 lfo3;tab-stops:list .5in"&gt;Sandal:      Heavier shoe, tread is wavy and blocky. &lt;/li&gt; &lt;/ol&gt;  &lt;p class="MsoNormal"&gt;Wood description: 58cm long, 30cm wide, one side is rough and other side is smooth.&lt;/p&gt;  &lt;p class="MsoNormal"&gt; &lt;o:p&gt;&lt;/o:p&gt;&lt;/p&gt;  &lt;p class="MsoNormal"&gt; &lt;o:p&gt;&lt;/o:p&gt;&lt;/p&gt;  &lt;p class="MsoNormal"&gt; &lt;o:p&gt;&lt;/o:p&gt;&lt;/p&gt;  &lt;p class="MsoNormal"&gt; &lt;o:p&gt;&lt;/o:p&gt;&lt;/p&gt;  &lt;p class="MsoNormal"&gt; &lt;o:p&gt;&lt;/o:p&gt;&lt;/p&gt;  &lt;p class="MsoNormal"&gt;Observations chart:&lt;/p&gt;  &lt;table border="1" cellspacing="0" cellpadding="0" style="border-collapse:collapse;  border:none;mso-border-alt:solid windowtext .5pt;mso-padding-alt:0in 5.4pt 0in 5.4pt"&gt;  &lt;tbody&gt;&lt;tr&gt;   &lt;td valign="top" style="border:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;Shoe&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border:solid windowtext .5pt;border-left:none;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;Surface&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border:solid windowtext .5pt;border-left:none;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;Test1&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border:solid windowtext .5pt;border-left:none;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;Test2&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border:solid windowtext .5pt;border-left:none;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;Test3&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border:solid windowtext .5pt;border-left:none;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;Test Average&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border:solid windowtext .5pt;border-left:none;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;Coefficient of Static Friction&lt;/p&gt;   &lt;/td&gt;  &lt;/tr&gt;  &lt;tr&gt;   &lt;td valign="top" style="border:solid windowtext .5pt;border-top:none;   mso-border-top-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;1&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;Smooth&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;26&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;24&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;23&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;25&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;tan &lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;q&lt;/span&gt;&lt;/span&gt; =mu&lt;/p&gt;   &lt;p class="MsoNormal"&gt;&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;\&lt;/span&gt;&lt;/span&gt;tan 25=0.47&lt;/p&gt;   &lt;p class="MsoNormal"&gt;&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;\&lt;/span&gt;&lt;/span&gt;mu = 0.47&lt;/p&gt;   &lt;/td&gt;  &lt;/tr&gt;  &lt;tr&gt;   &lt;td valign="top" style="border:solid windowtext .5pt;border-top:none;   mso-border-top-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;1&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;Rough&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;53&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;54&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;53&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;53&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;tan 53 = 1.32&lt;/p&gt;   &lt;/td&gt;  &lt;/tr&gt;  &lt;tr&gt;   &lt;td valign="top" style="border:solid windowtext .5pt;border-top:none;   mso-border-top-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;2&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;Smooth&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;45&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;46&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;44&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;45&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;tan 45 = 1.0&lt;/p&gt;   &lt;/td&gt;  &lt;/tr&gt;  &lt;tr&gt;   &lt;td valign="top" style="border:solid windowtext .5pt;border-top:none;   mso-border-top-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;2&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;Rough&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;46&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;50&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;49&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;49&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;tan 49 = 1.15&lt;/p&gt;   &lt;/td&gt;  &lt;/tr&gt;  &lt;tr&gt;   &lt;td valign="top" style="border:solid windowtext .5pt;border-top:none;   mso-border-top-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;3&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;Smooth&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;45&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;48&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;49&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;48&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;tan 48 = 1.11&lt;/p&gt;   &lt;/td&gt;  &lt;/tr&gt;  &lt;tr&gt;   &lt;td valign="top" style="border:solid windowtext .5pt;border-top:none;   mso-border-top-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;3&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;Rough&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;49&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;50&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;47&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;49&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;tan 49 = 1.15&lt;/p&gt;   &lt;/td&gt;  &lt;/tr&gt;  &lt;tr&gt;   &lt;td valign="top" style="border:solid windowtext .5pt;border-top:none;   mso-border-top-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;4&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;Smooth&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;25&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;31&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;27&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;27&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;tan 27 = 0.5&lt;/p&gt;   &lt;/td&gt;  &lt;/tr&gt;  &lt;tr&gt;   &lt;td valign="top" style="border:solid windowtext .5pt;border-top:none;   mso-border-top-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;4&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;Rough&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;37&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;38&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;40&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;38&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;tan 38 = 0.78&lt;/p&gt;   &lt;/td&gt;  &lt;/tr&gt;  &lt;tr&gt;   &lt;td valign="top" style="border:solid windowtext .5pt;border-top:none;   mso-border-top-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;5&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;Smooth&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;42&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;41&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;43&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;42&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;tan 42 = 0.9&lt;/p&gt;   &lt;/td&gt;  &lt;/tr&gt;  &lt;tr&gt;   &lt;td valign="top" style="border:solid windowtext .5pt;border-top:none;   mso-border-top-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;5&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;Rough&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;53&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;54&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;52&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;52&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;tan 52 = 1.28&lt;/p&gt;   &lt;/td&gt;  &lt;/tr&gt;  &lt;tr&gt;   &lt;td valign="top" style="border:solid windowtext .5pt;border-top:none;   mso-border-top-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;6&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;Smooth&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;31&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;33&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;31&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;32&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;tan 32 = 0.62&lt;/p&gt;   &lt;/td&gt;  &lt;/tr&gt;  &lt;tr&gt;   &lt;td valign="top" style="border:solid windowtext .5pt;border-top:none;   mso-border-top-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;6&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;Rough&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;36&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;37&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;36&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;36&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;tan 36 = 0.73&lt;/p&gt;   &lt;/td&gt;  &lt;/tr&gt;  &lt;tr&gt;   &lt;td valign="top" style="border:solid windowtext .5pt;border-top:none;   mso-border-top-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;7&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;Smooth&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;40&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;41&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;39&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;40&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;tan 40 = 0.84&lt;/p&gt;   &lt;/td&gt;  &lt;/tr&gt;  &lt;tr&gt;   &lt;td valign="top" style="border:solid windowtext .5pt;border-top:none;   mso-border-top-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;7&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;Rough&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;47&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;48&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;49&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;48&lt;span style="font-family:Symbol;mso-ascii-font-family:   &amp;quot;Times New Roman&amp;quot;;mso-hansi-font-family:&amp;quot;Times New Roman&amp;quot;;mso-char-type:symbol;   mso-symbol-font-family:Symbol"&gt;&lt;span style="mso-char-type:symbol;mso-symbol-font-family:   Symbol"&gt;°&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext .5pt;   border-right:solid windowtext .5pt;mso-border-top-alt:solid windowtext .5pt;   mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"&gt;   &lt;p class="MsoNormal"&gt;tan 48 = 1.11&lt;/p&gt;   &lt;/td&gt;  &lt;/tr&gt; &lt;/tbody&gt;&lt;/table&gt;  &lt;p class="MsoNormal"&gt;*Test1, test2, and test3 are all the observed angles of inclination.&lt;/p&gt;  &lt;p class="MsoNormal"&gt; &lt;o:p&gt;&lt;/o:p&gt;&lt;/p&gt;  &lt;p class="MsoNormal"&gt;&lt;b&gt;Analysis:&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt;  &lt;p class="MsoNormal" style="text-indent:.5in"&gt;Through analysis of the data that I have collected in this experiment, it is apparent that it is not the tread itself that makes a change in the coefficient of static friction, but the type and heaviness of the shoe itself. Though it does provoke a very miner change, it does not prove my hypothesis to be even remotely possible given the data shown in my observations. Ways to improve the quality of this data could be if we were to lengthen the board to get a more accurate angle of inclination, or possibly having an even wider range of shoes might make a difference in results. &lt;/p&gt;  &lt;p class="MsoNormal"&gt; &lt;o:p&gt;&lt;/o:p&gt;&lt;/p&gt;  &lt;p class="MsoNormal"&gt;&lt;b&gt;Conclusion:&lt;/b&gt;&lt;/p&gt;  &lt;span style="font-size:12.0pt;font-family:&amp;quot;Times New Roman&amp;quot;;mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;;mso-ansi-language:EN-US;mso-fareast-language:EN-US; mso-bidi-language:AR-SA"&gt;&lt;span style="mso-tab-count:1"&gt;            &lt;/span&gt;In conclusion, my hypothesis was proved incorrect due to the fact that the data did not show a change due to tread, but a change due to shoe type and weight. So therefore, if shoe designers care about the coefficient of static friction of there shoes they should look at these factors and not at the tread itself.&lt;/span&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/603242458691764012-7714516114444294304?l=pvsj.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://pvsj.blogspot.com/feeds/7714516114444294304/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=603242458691764012&amp;postID=7714516114444294304' title='2 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/603242458691764012/posts/default/7714516114444294304'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/603242458691764012/posts/default/7714516114444294304'/><link rel='alternate' type='text/html' href='http://pvsj.blogspot.com/2008/12/coefficients-of-static-friction-in.html' title='Coefficients of static friction in shows'/><author><name>Fizzizist</name><uri>http://www.blogger.com/profile/16838707366517235413</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='32' height='30' src='http://1.bp.blogspot.com/_xBn5pA0uuHg/SQ5KOLaAMuI/AAAAAAAAAAc/F2apPU4ARd8/s1600-R/madscientist.jpg'/></author><thr:total>2</thr:total></entry><entry><id>tag:blogger.com,1999:blog-603242458691764012.post-2132822442950886080</id><published>2008-11-27T05:38:00.001-08:00</published><updated>2008-11-27T15:51:41.584-08:00</updated><category scheme='http://www.blogger.com/atom/ns#' term='Physics'/><title type='text'>Physics of the Centrifuge</title><content type='html'>This is the paper that I wrote for a physics class on centrifuges I thought why not post it on my blog:&lt;div&gt;&lt;br /&gt;&lt;/div&gt;&lt;div&gt;&lt;blockquote&gt;&lt;/blockquote&gt;&lt;blockquote&gt;&lt;/blockquote&gt;&lt;p class="MsoTitle"&gt;&lt;/p&gt;&lt;blockquote&gt;&lt;p class="MsoTitle"&gt;Physics of the Centrifuge&lt;/p&gt;  &lt;p class="MsoNormal"&gt; &lt;o:p&gt;&lt;/o:p&gt;&lt;/p&gt;  &lt;p class="MsoNormal"&gt;&lt;span style="mso-tab-count:1"&gt;            &lt;/span&gt;The basic description of a centrifuge is any type of device that uses centrifugal force to push an object outward. This paper will discuss how they do this, and some applications of centrifuges being used around the world today. We will also discuss the cost of them and how common they are in society, as well as the impact they have had on individual users, and on society in general.&lt;/p&gt;  &lt;p class="MsoNormal"&gt; &lt;o:p&gt;&lt;/o:p&gt;&lt;/p&gt;  &lt;p class="MsoNormal"&gt;&lt;span style="mso-tab-count:1"&gt;            &lt;/span&gt;First let’s look at centrifugal force. This plays a key role in the design and use of a centrifuge and is essentially the objective of a centrifuge. What I mean by this is that the goal of a centrifuge is to achieve a high degree of centrifugal force acting on the object in question. A real life example of this type of force is if I have a bucket full of water, and I spin it in a circle quickly, the centrifugal force will push on the water, and at the same time the bottom of the bucket will keep the water from spilling out of the bottom. Centrifugal force is actually the opposing force to the centripetal force that keeps an object in circular motion. We can calculate this force using the following formula, &lt;/p&gt;  &lt;p class="MsoNormal"&gt;F=(m x v^2)/r, where “F” is centripetal force, “m” is mass of object in circular motion, “v” is the velocity of the object, and r is the radius or distance from center of the centrifuge to the object in motion. Since centrifugal force is the opposite of centripetal force, we use the same formula; only the resulting force must be negative.&lt;/p&gt;  &lt;p class="MsoNormal"&gt; &lt;o:p&gt;&lt;/o:p&gt;&lt;/p&gt;  &lt;p class="MsoNormal"&gt;&lt;span style="mso-tab-count:1"&gt;            &lt;/span&gt;Therefore, a centrifuge machine basically does the same thing as my arm with the bucket of water, spinning an object rapidly in a circle. A common application of this is in a lab, when scientists must separate a mixture due to the density of the substances, they will use a centrifuge to spin a test tube rapidly, and since this increases the gravitational force on the substance inside, the more dense substances will go to the bottom of the mixture leaving the less dense substances on top.&lt;/p&gt;  &lt;p class="MsoNormal"&gt; &lt;o:p&gt;&lt;/o:p&gt;&lt;/p&gt;  &lt;p class="MsoNormal"&gt;&lt;span style="mso-tab-count:1"&gt;            &lt;/span&gt;Another common application of this is when testing greater forces of gravity on a human being. Centrifuges simulate the affects of a pilot pulling up quickly when flying a plane, or when an astronaut is in a rocket being launched into space. Both of these scenarios increase the force of gravity due to the fact that as gravity is pushing down, they are rising up at a high velocity. So, to simulate this in a centrifuge, you use the person as the water in the bucket going back to the example from before. Using centrifugal force as gravitational force by spinning a capsule containing a person attached to an arm made of some kind of metal rapidly, you can simulate what it is like to have gravity increased to a level in which a person may black out due to the gravitational force pushing the blood from there brain down toward their feat.&lt;/p&gt;  &lt;p class="MsoNormal"&gt; &lt;o:p&gt;&lt;/o:p&gt;&lt;/p&gt;  &lt;p class="MsoNormal"&gt;&lt;span style="mso-tab-count:1"&gt;            &lt;/span&gt;Designing a centrifuge is not as complicated as some might think due to the fact that the purpose is not as complicated as some might think. Though, there are many factors that come into play when looking at how it is run on the inside. Using a series of gears, powered by some sort of generator we can create the circular motion needed, and increasing or decreasing the speed all depends on the size of the gears. One factor that plays a key role when looking at rotation at high velocity is friction. Some type of lubricant must be used to reduce friction on the parts so that the constant and intense motion of metal on metal does not create heat energy, which would destroy the inner workings of the machine.&lt;span style="mso-spacerun: yes"&gt;  &lt;/span&gt;&lt;/p&gt;  &lt;p class="MsoNormal"&gt; &lt;o:p&gt;&lt;/o:p&gt;&lt;/p&gt;  &lt;p class="MsoNormal"&gt;&lt;span style="mso-tab-count:1"&gt;            &lt;/span&gt;There are certain applications of centrifugal force where there are no actual centrifuge machines, such as our bucket and water example, but not just simple applications like that. I am talking about at amusement parks. Almost every ride you see at an amusement park usually deals with using centrifugal and centripetal force to give people the ride of their lives. Especially when looking at a ride that has multiple loops. These rides usually use the velocity at which you are traveling to create centrifugal force, which in turn, keeps you in your seat.&lt;/p&gt;  &lt;p class="MsoNormal"&gt; &lt;o:p&gt;&lt;/o:p&gt;&lt;/p&gt;  &lt;p class="MsoNormal"&gt;&lt;span style="mso-tab-count:1"&gt;            &lt;/span&gt;The cost of a centrifuge varies from centrifuge to centrifuge. One for testing people will cost several millions of dollars where as a centrifuge testing the density of a mixture will cost only a few hundred dollars. There applications are well worth any price though if it is crucial for scientific research. That is why they are quite common in science labs and test facilities. It really all depends on what is being tested.&lt;/p&gt;  &lt;p class="MsoNormal"&gt; &lt;o:p&gt;&lt;/o:p&gt;&lt;/p&gt;  &lt;p class="MsoNormal"&gt;&lt;span style="mso-tab-count:1"&gt;            &lt;/span&gt;In conclusion, the impact that centrifuge technologies have had on individuals and society in general has been a very good impact. They help scientists in ways that no other machines can, and they have helped to train pilots and astronauts so that when they are actually in the sky, they will know what to do when in a situation of extreme gravitational pull. They have had no negative impact at all really since their invention, and hopefully will help in new discoveries for science in the coming years.&lt;/p&gt;  &lt;p class="MsoNormal"&gt; &lt;o:p&gt;&lt;/o:p&gt;&lt;/p&gt;  &lt;p class="MsoNormal"&gt;&lt;span style="mso-tab-count:1"&gt;            &lt;/span&gt;&lt;/p&gt;&lt;/blockquote&gt;&lt;p class="MsoNormal"&gt;&lt;span style="mso-tab-count:1"&gt;&lt;/span&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/603242458691764012-2132822442950886080?l=pvsj.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://pvsj.blogspot.com/feeds/2132822442950886080/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=603242458691764012&amp;postID=2132822442950886080' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/603242458691764012/posts/default/2132822442950886080'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/603242458691764012/posts/default/2132822442950886080'/><link rel='alternate' type='text/html' href='http://pvsj.blogspot.com/2008/11/this-is-paper-that-i-wrote-for-physics.html' title='Physics of the Centrifuge'/><author><name>Fizzizist</name><uri>http://www.blogger.com/profile/16838707366517235413</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='32' height='30' src='http://1.bp.blogspot.com/_xBn5pA0uuHg/SQ5KOLaAMuI/AAAAAAAAAAc/F2apPU4ARd8/s1600-R/madscientist.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-603242458691764012.post-7764974527525208811</id><published>2008-11-06T17:32:00.001-08:00</published><updated>2008-11-06T17:42:02.472-08:00</updated><category scheme='http://www.blogger.com/atom/ns#' term='General'/><title type='text'>Introduction</title><content type='html'>&lt;span class="Apple-tab-span" style="white-space:pre"&gt; &lt;/span&gt;OK so hello my name is Peter &lt;span class="blsp-spelling-error" id="SPELLING_ERROR_0"&gt;Vlasveld&lt;/span&gt; and this blog is being created for me to have a more formal blog than the random blabber that I post on "Boring Blog of Peter &lt;span class="blsp-spelling-error" id="SPELLING_ERROR_1"&gt;Vlasveld&lt;/span&gt;". I will post papers in physics that I write. I am writing one this weekend about centrifuges which I will post.&lt;div&gt;&lt;br /&gt;&lt;/div&gt;&lt;div&gt;&lt;span class="Apple-tab-span" style="white-space:pre"&gt; &lt;/span&gt;This will be a science based blog and will contain all of my non-classified work in science. Meaning that I will post things that I am able to post without worrying about people taking it and... doing things with it. So yes this will be much more of a formal blog meaning actual thought out researched papers and whatnot. Possibly even interesting to read but I really don't know. I am an &lt;span class="blsp-spelling-error" id="SPELLING_ERROR_2"&gt;ammature&lt;/span&gt; writer and scientist so anyone who is more experienced and happens to come across it on the web can give there insight and even if you are not experience what so ever you can still tell me what you think so.. happy blogging everyone&lt;br /&gt;&lt;/div&gt;&lt;div&gt;&lt;br /&gt;&lt;/div&gt;&lt;div&gt;Edit: I forgot to mention on a sidenote that this is also a skeptical blog so you may see me write more formal entries about my skeptical view on things.&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/603242458691764012-7764974527525208811?l=pvsj.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://pvsj.blogspot.com/feeds/7764974527525208811/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=603242458691764012&amp;postID=7764974527525208811' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/603242458691764012/posts/default/7764974527525208811'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/603242458691764012/posts/default/7764974527525208811'/><link rel='alternate' type='text/html' href='http://pvsj.blogspot.com/2008/11/introduction.html' title='Introduction'/><author><name>Fizzizist</name><uri>http://www.blogger.com/profile/16838707366517235413</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='32' height='30' src='http://1.bp.blogspot.com/_xBn5pA0uuHg/SQ5KOLaAMuI/AAAAAAAAAAc/F2apPU4ARd8/s1600-R/madscientist.jpg'/></author><thr:total>0</thr:total></entry></feed>
