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Potential Energy of System (Uniform Rod and String)

  1. Mar 22, 2012 #1

    FeDeX_LaTeX

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    1. The problem statement, all variables and given/known data
    http://desmond.imageshack.us/Himg339/scaled.php?server=339&filename=53171696.jpg&res=medium [Broken]


    2. Relevant equations
    GPE = mgh, EPE = λx^2 / 2l


    3. The attempt at a solution

    I'm taking the horizontal line through A as the zero-level for potential energy. Clearly, the GPE of the rod is mgacosθ + constant. To find the elastic potential energy, I noted that:

    [tex]EPE = \frac{0.5mgx^2}{4a}[/tex]

    I said that the extension x is given by the length of BC minus the natural length. To get BC, I used the cosine rule;

    BC2 = 16a2 + 4a2 - 16a2cosθ

    So BC = 2a√(5 - 4cosθ).

    Then,

    [tex]EPE = \frac{mg(2a \sqrt{5 - 4 \cos \theta} - 2a)^2}{8a}[/tex]

    Which, to me, simplifies to:

    [tex]EPE = mga(3 - 2 \cos \theta - \sqrt{5 - 4 \cos \theta})[/tex]

    The total potential energy V can thus be expressed as:

    [tex]V = -mga(\cos \theta - 3 + \sqrt{5 - 4 \cos \theta}) + \mathbb{constant}[/tex].

    This is almost identical to what they've got, except without the 3. Where have I gone wrong?

    Thanks.
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Mar 22, 2012 #2

    FeDeX_LaTeX

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    Sigh... just realised in the mark scheme they've counted the +3 as 'a constant' so negligible. Ugh. Sorry to whoever was reading this thread.
     
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