document.write( "Question 1090222: Given the Earth's radius of 4000 miles, and a mass of 200 pounds:
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document.write( "The weight on the surface is 200 pounds.
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document.write( "What is the weight in an elevator to the Earth's center at various depths?
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document.write( "Depth of 500 miles, 1000 miles, 2000 miles, etc.
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document.write( "-\Ignore any effects of pressure and temperature.
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Algebra.Com's Answer #704654 by ikleyn(52835)![]() ![]() You can put this solution on YOUR website! . \n" ); document.write( "When (and if) the body is placed inside the Earth at the radius \"r\" (the depth R-r), then the only the part of the Earth \n" ); document.write( "which is inside of the sphere of the radius \"r\" creates (produces) the gravity.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "The exterior spherical layers r < s < R produce ZERO gravity integral force.\r \n" ); document.write( "\n" ); document.write( "In other words, they do not make gravity force.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "This fact is known from the Newton times to all who know/knows Physics.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "And this effect MUST be accounted for in the solution of problems like this one.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "The situation (and the solution) is different comparing with the case when the body is lifted ABOVE the Earth surface.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Therefore, the solution by @Fombitz is incorrect and must be redone.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "----------- \n" ); document.write( " \r\n" ); document.write( "To get the feeling of this effect, imagine that the body is placed exactly at the center of the (spherical) Earth.\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "What is the gravity force and what is its direction in this case ?\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "The answer (quite unexpected ?) is: the gravitation force is ZERO in this case.\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( " Did I say \"unexpected\" ? - But if you think 5-10 seconds on it, you will get that is is correct \r\n" ); document.write( " and nothing else can happen (due to symmetry).\r\n" ); document.write( "\r \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |