document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1090222>Question 1090222</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the Earth's radius of 4000 miles, and a mass of 200 pounds:<BR>\n" );
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document.write( "The weight on the surface is 200 pounds.<BR>\n" );
document.write( "What is the weight in an elevator to the Earth's center at various depths?<BR>\n" );
document.write( "Depth of 500 miles, 1000 miles, 2000 miles, etc.<BR>\n" );
document.write( "-\Ignore any effects of pressure and temperature.<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 #704639 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=704639\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The assumption here is that the Earth is a point mass.<BR>\n" );
document.write( "All of the mass of the Earth is concentrated at the point where the radius is equal to zero (or a small <BR>\n" );
document.write( "value compared to the radius of the Earth and the values where the measurements are taken).<BR>\n" );
document.write( "Weight is inversely proportional to the distance from the center of the earth.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=k%2FD%5E2 ALIGN=MIDDLE  ALT=\"W=k%2FD%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=WD%5E2 ALIGN=MIDDLE  ALT=\"k=WD%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=200%2A%284000%29%5E2 ALIGN=MIDDLE  ALT=\"k=200%2A%284000%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=%28200%2A%284000%29%5E2%29%2FD%5E2 ALIGN=MIDDLE  ALT=\"W=%28200%2A%284000%29%5E2%29%2FD%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W%2F200=%284000%2FD%29%5E2 ALIGN=MIDDLE  ALT=\"W%2F200=%284000%2FD%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then for example, when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=500 ALIGN=MIDDLE  ALT=\"D=500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W%2F200=%284000%2F500%29%5E2 ALIGN=MIDDLE  ALT=\"W%2F200=%284000%2F500%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W%2F200=%288%29%5E2 ALIGN=MIDDLE  ALT=\"W%2F200=%288%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=64%2A200 ALIGN=MIDDLE  ALT=\"W=64%2A200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=12800 ALIGN=MIDDLE  ALT=\"W=12800\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lbs ALIGN=MIDDLE  ALT=\"lbs\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Uniform density solution:<BR>\n" );
document.write( "So the gravitational force is a function of the two masses involved and the distance between them.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F=GMm%2FR%5E2 ALIGN=MIDDLE  ALT=\"F=GMm%2FR%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If you allow the mass of the Earth to change as a function of its radius (R) (assuming uniform density)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M=rho%2A%284%2F3%29pi%2AR%5E3=kR%5E3 ALIGN=MIDDLE  ALT=\"M=rho%2A%284%2F3%29pi%2AR%5E3=kR%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=a%2AR%5E3%2Am%2FR%5E2 ALIGN=MIDDLE  ALT=\"W=a%2AR%5E3%2Am%2FR%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=a%2AmR ALIGN=MIDDLE  ALT=\"W=a%2AmR\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Where \"a\" is a constant (from all of the constants put together).<BR>\n" );
document.write( "So then your mass doesn't change so it's also a constant.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=bR ALIGN=MIDDLE  ALT=\"W=bR\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can then use the value at the earth to calculate the value of b.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200=b%284000%29 ALIGN=MIDDLE  ALT=\"200=b%284000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1%2F20 ALIGN=MIDDLE  ALT=\"b=1%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=R%2F20 ALIGN=MIDDLE  ALT=\"W=R%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" > valid for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3CR%3C4000 ALIGN=MIDDLE  ALT=\"0%3CR%3C4000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Again that's a simple solution using uniform density model. \r<BR>\n" );
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