document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1106811>Question 1106811</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The maximum load of a horizontal beam that is supported at both ends vari<bes jointly as the width and the square<BR>\n" );
document.write( "of the height and inversely as the length between the supports. A beam 6 m long, 0.1 m wide, and 0.06 m high<BR>\n" );
document.write( "supports a load of 360 kg. What is the maximum load supported by a beam 16 m long, 0.2 m wide, and 0.08 m high?  </SPAN>\n" );
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document.write( "The information tells us that the mass m that can be supported by a beam of length l, width w, and height (thickness) h is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+k%28%28w%29%28h%5E2%29%2Fl%29 ALIGN=MIDDLE  ALT=\"m+=+k%28%28w%29%28h%5E2%29%2Fl%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "where k is a constant.<br><BR>\n" );
document.write( "The value of the constant can be determined from the given information: When the length is 6m, the width is 0.1m, and the height is 0.06m, the maximum load is 360kg. So<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360+=+k%28%280.1%29%280.06%5E2%29%2F6%29 ALIGN=MIDDLE  ALT=\"360+=+k%28%280.1%29%280.06%5E2%29%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360+=+k%28.00036%2F6%29+=+k%28.00006%29 ALIGN=MIDDLE  ALT=\"360+=+k%28.00036%2F6%29+=+k%28.00006%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+6000000 ALIGN=MIDDLE  ALT=\"k+=+6000000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then using this constant with the new beam measurements,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+6000000%28%280.2%29%280.08%5E2%29%29%2F16 ALIGN=MIDDLE  ALT=\"m+=+6000000%28%280.2%29%280.08%5E2%29%29%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+6000000%28.00128%2F16%29+=+480 ALIGN=MIDDLE  ALT=\"m+=+6000000%28.00128%2F16%29+=+480\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "That is a general method for solving problems like this.  But if the numbers are fairly simple, as in this case, I find it easier just to modify the given mass according to each changed dimension of the beam.<br><BR>\n" );
document.write( "The length of the beam changes from 6m to 16m; since the mass varies inversely as the length, the maximum load decreases by a factor of 6/16 = 3/8.<BR>\n" );
document.write( "The width doubles from 0.1m to 0.2m; since the mass varies directly with the width, the maximum load increases by a factor of 2.<BR>\n" );
document.write( "The height changes from 0.06m to 0.08m; since the mass varies directly with the square of the height, the maximum load increases by a factor of (0.08/0.06)^2 = (4/3)^2 = 16/9.<br><BR>\n" );
document.write( "Then the new maximum load is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%2A%283%2F8%29%2A%282%29%2A%2816%2F9%29+=+360%2A%284%2F3%29+=+480 ALIGN=MIDDLE  ALT=\"360%2A%283%2F8%29%2A%282%29%2A%2816%2F9%29+=+360%2A%284%2F3%29+=+480\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );