document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=426518>Question 426518</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Engineers use complex mathematical formulas when designing aircrafts. For example, stringers used in the wing of an air plane must be able to support a certain load. Engineers have to use a stringer with the right diameter for the job. Using a smaller size poses a safety hazard. Using a larger size is a waste of material and will result in increased cost to the plane's operator.\r<BR>\n" );
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document.write( "Let's assume that the stress S on a rod is given by the formula,\r<BR>\n" );
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document.write( "S = (load)/(cross sectional area).\r<BR>\n" );
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document.write( "Let's assume that the air plane uses an aluminium rod with diameter 20mm to support a load of 5 x 10^4 Newton.  Engineers know that maximum stress on Aluminium is 1 x 10^ 8 Newtons/m^2. How do we determine whether the rod can withstand the load?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #296694 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=296694\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The cross sectional area of a rod = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28pi%29r%5E2 ALIGN=MIDDLE  ALT=\"%28pi%29r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Therefore A = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28pi%29%2810%29%5E2+=+314.16 ALIGN=MIDDLE  ALT=\"%28pi%29%2810%29%5E2+=+314.16\"   DISABLED_style= \"max-width:90%; height:auto;\" > mm^2<BR>\n" );
document.write( "Convert the area to square meters: 314.16 mm^2*(1 m/1000 mm)^2 = 3.1416 x 10^-4<BR>\n" );
document.write( "We are given S = 1 x 10^8, and L = 5 x 10^4<BR>\n" );
document.write( "For the rod to withstand the load, we need the stress to be less than 1 x 10^8<BR>\n" );
document.write( "Since S = L/A, we have S = 5 x 10^4/3.1416 x 10^-4 = 1.59 x 10^8 N/m^2.<BR>\n" );
document.write( "This value is greater than the maximum stress of 1 x 10^8, so the rod will not withstand the load. </SPAN>\n" );
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