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What is wrong with my solutionÉ

  1. Apr 10, 2009 #1
    Can someone tell me how to correct my solution to get the right answerÉ

    A 1 kg pigeon sits on the middle of a clothesline whose supports are 10 m apart. The clothesline sags by 1 m. If the weight of the clothesline is negligible, find the tension in it.

    Here is my solution.

    let T1x, T2x, T1y and T2y be x and y components of tension of the left and right parts of the clothesline respectively when its middle sags by 1 m.

    T1x+T2x=0

    equivalently, we have -T1*cos u+T2*cosu=0

    so, let T1=T2=T

    next equation, T1y+T2y+w=0 where w is the weight of the pigeon

    rewriting the equation gives
    T1*sinu+T2*sinu+w=0

    with T1=T2=T, 2T*sinu-mg=0

    isolating T and solving gives T=mg/(2*sinu)

    = (1 kg)(9.8 m/s squared)/(2*1/sqrt(26))

    = 25 N

    The answer in the book is 26 N.

    How do you get 26 N.
     
  2. jcsd
  3. Apr 10, 2009 #2
    If you take g to be 10m/sec/sec then you can round up the answer to 26N
     
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