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Determine largest force when three ropes are joined at a point

  1. May 8, 2012 #1
    1. The problem statement, all variables and given/known data

    Three ropes, numbered 1-3, are joined at one point. Three persons pull in each separate rope, so that the rope is at rest. The angles between the ropes are shown in the figure (note that it is the lengths as illustrated, and not the size of the forces). Arrange the drag forces in the ropes, called F1, F2 and F3 respectively, according to their size (eg, "F1 <F2 <F3" or "F1 = F3 <F2").

    http://bayimg.com/EaoNIaaDh [Broken]

    2. Relevant equations

    No equations needed. Maybe some basic trigonometry.

    3. The attempt at a solution

    My thoughts:

    First I conclude that the force depends on the length of the rope. If one rope is much shorter than the two other, then the force needed for the system to be at rest will be much larger for that rope. The same works in the opposite direction(large rope-->small force).

    Since F_3 is significantly longer than F_1 and F_2, I conclude that both F_1 and F_2 are larger than F_3. Notice now that the length of rope 1 and 2 are equal. If forces F_1 and F_2 were equal, then the angle of F_3 with the horizontal axis would be 45 degrees which is not the case. The angle is actually less than 45 degrees and therefore is F_2 larger than F_1.

    Hence: F_2>F_1>F_3. Correct answer: F_3>F_1>F_2
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. May 8, 2012 #2

    tiny-tim

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    hi zeralda21! :smile:

    (try using the X2 button just above the Reply box :wink:)

    the length of the ropes has nothing to do with it

    hint: draw a vector triangle :wink:
     
  4. May 9, 2012 #3
    Hi Tiny-tim :)

    When drawing a vector triangle, I believe that I will need the magnitude and direction of a force. The direction is shown in the figure(along the rope of course) but how do I know the magnitude?
     
  5. May 9, 2012 #4

    tiny-tim

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    d'oh! :rolleyes:

    that's the whole point of vector triangles …

    you can still draw them without all the information

    in this case, you know the directions, so isn't there only one way the sides can join up? :wink:
     
  6. May 9, 2012 #5
    Sorry about my incompetence of the subject tiny-tim :shy:

    Yes, the forces can join in one way. And since F_3 is the hypotenuse of that triangle it means that F_3 is the largest force. But this right angled triangle can look different dependent on the magnitude of the forces. See picture for two examples:

    http://bayimg.com/CAOpEaadh [Broken]

    How can I tell which one is larger?
     
    Last edited by a moderator: May 6, 2017
  7. May 9, 2012 #6

    tiny-tim

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    not following you :confused:

    in your original picture http://bayimg.com/EaoNIaaDh [Broken] the directions are fixed …

    just slide the lines along until they join up! :wink:
     
    Last edited by a moderator: May 6, 2017
  8. May 9, 2012 #7

    I don´t really get it,sorry....The lines have lenghts (5, 5 ,7.5). I can´t see how it is possible to construct a triangle of these lenghts....
     
    Last edited by a moderator: May 6, 2017
  9. May 9, 2012 #8

    tiny-tim

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    ah, no, the lengths are the lengths of the ropes

    the tensions could be anything

    but the directions of the tensions are, obviously, the same as the (given) directions of the ropes!

    does it make sense now? :smile:
     
  10. May 9, 2012 #9
    I´m not sure I am following good enough.. Correct me if I´m wrong:

    *"just slide the lines along until they join up! ---> I need to construct a triangle where the lengths are the lengths of the rope(5,5,7.5) since the lines represents the lengths of the rope. I am stuck at this.

    "tensions could be anything" OK.

    "but the directions of the tensions are, obviously, the same as the (given) directions of the ropes! - Yes, I get this.
     
  11. May 9, 2012 #10

    tiny-tim

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    no

    forget the lengths

    you need to construct a triangle where the directions are the directions of the rope

    since the lines represents the lengths of the rope and their directions,

    and the triangle represents the forces of tension in the ropes :wink:
     
  12. May 9, 2012 #11
    Alright, like this then : http://bayimg.com/haOPFaAdH [Broken].

    If I follow "and the triangle represents the forces of tension in the ropes this:

    In case ,my triangle is right, then the largest force is clearly, F_3, since it is a hypotenuse. But what about the other two vectors?
     
    Last edited by a moderator: May 6, 2017
  13. May 9, 2012 #12
    If I return to original picture I can form a smaller triangle that is equilateral to the "triangle of directions". For simplicity I chose lengths 3 (F_1), 4 (F_2) and hypotenuse 5 (F_3), therefore F_1 is larger than F_2. Is this OK?
     
  14. May 9, 2012 #13

    tiny-tim

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    mmm … i'd be more convinced if you did it by altering the original diagram :wink: (http://bayimg.com/EaoNIaaDh [Broken]), so we can see how you did it
    measure them! :smile:

    (count squares)

    EDIT: oh you did

    yes, it's 6 squares along the bottom and 4.5 along the side :smile:
     
    Last edited by a moderator: May 6, 2017
  15. May 9, 2012 #14
    Well, there you go :biggrin: Thanks a lot tiny-tim!
     
    Last edited by a moderator: May 6, 2017
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