15_C_3B - When t =-1 and t = 1 we have u = a b and u = |a...

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When t = - 1 and t = 1 we have u = a + b and u = | a - b | respectively. Therefore F = 2 π km σ a 2 Z | a - b | a + b u 2 + b 2 - a 2 2 bu 3 ± - u du ab ² = π km σ a b 2 Z a + b | a - b | ³ 1 + b 2 - a 2 u 2 ´ du = π km σ a b 2 ³ u - b 2 - a 2 u ´µ µ µ µ a + b | a - b | . There are now two cases to consider. If the mass m is outside the sphere, so that b > a and | a - b | = b - a , then F = π km σ a b 2 ± ( a + b ) - ( b - a ) - ( b - a ) + ( b + a ) ² = 4
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This note was uploaded on 03/08/2012 for the course MATH 120 taught by Professor Onurfen during the Spring '12 term at Middle East Technical University.

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