document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1195308>Question 1195308</A>: <I><SPAN STYLE=\"word-break: break-all;\">  A 100-ft steel tape weighing 2.2 lbs is of standard length under a tension of 12 lbs, supported for full length. This tape was used in laying out a line (found to be 1000.00 ft) on smooth level ground under a steady pull of 15 lbs. Assuming E = 29X 10° psi and that 3.53 cubic inches of steel weighs 1,0 lbs, determine the ff:\r<BR>\n" );
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document.write( "a) cross-sectional area of the tape\r<BR>\n" );
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document.write( "b) correction for increase in tension per tape length\r<BR>\n" );
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document.write( "c) correction for increase in tension whole length measured\r<BR>\n" );
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document.write( "d) Corrected length for the effect of increased tension. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848435 by </B><A HREF=/tutors/aboutme.mpl?userid=ElectricPavlov><B>ElectricPavlov(122)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ElectricPavlov><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848435\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **a) Cross-sectional Area of the Tape**\r<BR>\n" );
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document.write( "* **Find the volume of the tape:**<BR>\n" );
document.write( "    * Volume = Weight of tape / Density of steel<BR>\n" );
document.write( "    * Volume = 2.2 lbs / (1 lb / 3.53 in³) = 7.766 in³\r<BR>\n" );
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document.write( "* **Find the cross-sectional area:**<BR>\n" );
document.write( "    * Area = Volume / Length <BR>\n" );
document.write( "    * Area = 7.766 in³ / 100 ft * (12 in/ft) = 0.0647 in²\r<BR>\n" );
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document.write( "**b) Correction for Increase in Tension per Tape Length**\r<BR>\n" );
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document.write( "* **Formula:** <BR>\n" );
document.write( "    * Correction per unit length = (P - P₀) / (A * E) <BR>\n" );
document.write( "        * where:<BR>\n" );
document.write( "            * P = Applied tension during measurement (15 lbs)<BR>\n" );
document.write( "            * P₀ = Standard tension (12 lbs)<BR>\n" );
document.write( "            * A = Cross-sectional area of the tape (0.0647 in²)<BR>\n" );
document.write( "            * E = Modulus of elasticity of steel (29 x 10⁶ psi)\r<BR>\n" );
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document.write( "* **Calculate:**<BR>\n" );
document.write( "    * Correction per unit length = (15 lbs - 12 lbs) / (0.0647 in² * 29 x 10⁶ psi)<BR>\n" );
document.write( "    * Correction per unit length = 3 lbs / 1871300 psi <BR>\n" );
document.write( "    * Correction per unit length = 1.604 x 10⁻⁶ in/in\r<BR>\n" );
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document.write( "**c) Correction for Increase in Tension - Whole Length**\r<BR>\n" );
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document.write( "* **Total Correction:** Correction per unit length * Measured length<BR>\n" );
document.write( "    * Total Correction = 1.604 x 10⁻⁶ in/in * 1000 ft * (12 in/ft) <BR>\n" );
document.write( "    * Total Correction = 0.0192 in\r<BR>\n" );
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document.write( "**d) Corrected Length for the Effect of Increased Tension**\r<BR>\n" );
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document.write( "* **Corrected Length:** Measured length - Correction for tension<BR>\n" );
document.write( "    * Corrected Length = 1000.00 ft - (0.0192 in / 12 in/ft) <BR>\n" );
document.write( "    * Corrected Length = 1000.00 ft - 0.0016 ft <BR>\n" );
document.write( "    * Corrected Length = 999.9984 ft\r<BR>\n" );
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document.write( "**Therefore:**\r<BR>\n" );
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document.write( "* a) Cross-sectional area of the tape: 0.0647 in²<BR>\n" );
document.write( "* b) Correction for increase in tension per tape length: 1.604 x 10⁻⁶ in/in<BR>\n" );
document.write( "* c) Correction for increase in tension - whole length: 0.0192 in<BR>\n" );
document.write( "* d) Corrected length for the effect of increased tension: 999.9984 ft\r<BR>\n" );
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document.write( "**Note:**\r<BR>\n" );
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document.write( "* This calculation assumes that the tape is perfectly elastic within the range of applied tensions.<BR>\n" );
document.write( "* Other factors, such as temperature and sag, can also affect the accuracy of the measurement and may need to be considered for more precise results.<BR>\n" );
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