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Tension is horizontal rope tied to hooks at each end

  1. Sep 21, 2007 #1
    Want to make sure I'm doing this right... it seems too easy

    1. The problem statement, all variables and given/known data
    A horizontal rope is tightly tied to hooks between two walls separated by a distance of 5m. A 100N weight is suspended from the middle of the rope and it sags so that the middle of the rope is displaced a distance of 0.25m.

    a. What is the tension in the rope?
    b. What are the horizontal and vertical forces exerted on the hooks.


    2. Relevant equations



    3. The attempt at a solution
    I found the angle using arcTan(.25/2.5) = 5.7106 degrees. Then did 100N/tan(5.7106)=1000Ni and used sqrt(100N^2 + 1000N^2)= 1004.988N to find the rope's tension...
     
  2. jcsd
  3. Sep 21, 2007 #2

    learningphysics

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    The tension is half that... the vertical component of tension on either side of the weight has to be 50N.
     
  4. Sep 21, 2007 #3
    okay, thanks, i was thinking that might be the case
     
  5. Sep 21, 2007 #4
    So that would also make the horizontal forces on each hook 500N right?
     
  6. Sep 21, 2007 #5

    learningphysics

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    yes.
     
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