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Homework Help: Trouble with algebra at the end of an elasticity problem

  1. Oct 14, 2012 #1

    K29

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    I have a spherical shell with inner radius [itex]a_{1}[/itex] and outer radius [itex]a_{2}[/itex]

    I have worked out that the tension at [itex]r=a_{1}[/itex] is
    [itex]\tau=\frac{2a_{1}^3+a_{2}^3}{2(a_{2}^{3}-a_{1}^{3})}P_{1}[/itex]

    ([itex]P_{1}[/itex] is pressure from the inside of the shell, causing the tension.

    Now if the shell is not very thick. [itex]t=a_{2}-a_{1}[/itex] is small. [itex]\frac{t}{a_1}<<1[/itex]

    and I should be able to show

    [itex]\tau\approx\frac{a_{1}}{2t}P_{1}[/itex]

    But I am not sure about the first step to take in getting there. Any ideas? Please help.
     
  2. jcsd
  3. Oct 14, 2012 #2

    TSny

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    Homework Helper
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    You can factor a difference of cubes.
     
  4. Oct 15, 2012 #3

    K29

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    Thank you
     
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