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Extension of a rod

  1. May 19, 2009 #1
    Hi all,
    I have a rod which is part of a greater structure and I resolved the forces along the rod. This rod is under tension with a force FcosQ on the left end (force direction towards left) and FsinQ on the other end (force direction towards the right). I need to find the extension of the rod and I am using hooks law F=Ks*delta where Ks is the stretching force constant and delta is the extension of the rod. Now the problem is what is the force F that I should use in Hooks law.

    picture 1

    At first I thought I should use the resultant force F*(cosQ-sinQ) so that the extension of the rod is delta=F(cosQ-sinQ)/Ks. But this is wrong because if I pull a spring with 1000 N on one end and 1000 N on the other. The net force is zero, but I trust you would agree that it will stretch.

    Then I thought that the force acting on the rod that causes the extension is F*(cosQ+sinQ) because if you have a rubber band and pull it with a force FcosQ on one end and FsinQ on the other end, it will extend from both ends and hence the total extension is delta=F*(cosQ+sinQ)/Ks.
    But I guess this is also wrong because when we have a mass attached to a string and string attached to the ceiling, the tension in the string is F not 2F and we say that the extension of string is delta=F/k

    picture 2

    I feel bit confused!!!!! Your help would be greatly appreciated.
    Thanks a lot

    Attached Files:

  2. jcsd
  3. May 19, 2009 #2

    Doc Al

    User Avatar

    Staff: Mentor

    What other forces act on this rod? Assuming this is a static structure (is it?), there must be other forces balancing these two, else the rod will accelerate.
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