1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Trouble with algebra at the end of an elasticity problem

  1. Oct 14, 2012 #1

    K29

    User Avatar

    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

    User Avatar
    Homework Helper
    Gold Member

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

    K29

    User Avatar

    Thank you
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Trouble with algebra at the end of an elasticity problem
Loading...