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Homework Help: What's wrong with my answer?

  1. Feb 17, 2015 #1
    1. The problem statement, all variables and given/known dataThe question says
    A chain of mass per unit length k and length 1.5 m rest on a fixed smooth sphere of radius R= 2/π m
    . Tension in the thread is asked.The question figure is attached.

    2. Relevant equations

    3. The attempt at a solution
    IMG_20150217_145935.jpg IMG_20150217_145935.jpg
    I think that the tension has to balance two types of forces :
    1) rightward force of part AC(touching)
    2)downward force of part CB(hanging)
    Finding first type of force:
    Using Fbd(attached) of small part taken in touching part
    Then Ncos(theta)=(dm)g
    → N=(dm)g/cos(th.).......(1)
    Length of that part =R(d(th.))
    mass of that small part =Rk(d(th.))
    Using Fbd rightward force on the small part =Nsin(th.)=(dm)g(tan(th.))
    Now if I want to integrate it , i would have to use limits from 0 to π/2
    BUT tan (th.) is not integrable b/w 0 to π/2 . So whats wrong with my answer ?

    Attached Files:

  2. jcsd
  3. Feb 17, 2015 #2


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    I'm missing something in your force balance for the little chunk of chain. I see an N and an mg and they clearly don't balance. What force could possibly complete the picture ?
  4. Feb 20, 2015 #3
    It could have been friction BUT the sphere is smooth so , what can be the force (you are talking about ) left out that balances the tension of the thread ?
  5. Feb 21, 2015 #4


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    But you don't have the tension in the chain in the equation. Indeed, that's what's missing. Remember, it will not be constant along the the chain.
  6. Feb 21, 2015 #5
    You have to consider the tension on both sides of the element along the tangential direction!
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