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 #704664 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=704664\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given the Earth's radius of 4000 miles, and a mass of 200 pounds:<BR>\n" );
document.write( "------<BR>\n" );
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( "Inside a solid sphere of constant density, the gravitational force varies linearly with distance from the center, becoming zero by symmetry at the center of mass. This can be seen as follows: take a point within such a sphere, at a distance r from the center of the sphere. Then you can ignore all the shells of greater radius, according to the shell theorem. So, the remaining mass m is proportional to r^3, and the gravitational force exerted on it is proportional to m/r^2, so to r^3/r^2 = r, so it is linear in r.<BR>\n" );
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document.write( "Weight = 200*(4000 - d)/4000 where d = the depth in miles.<BR>\n" );
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