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Vectors Help

  1. Feb 22, 2014 #1
    1. The problem statement, all variables and given/known data
    A cord 7m long has its ends tied to a horizontal board 5m apart. A weight of 50 N is suspended from a ring so that the weight is free to slide along the cord in a vertical plane. A horizontal force pulls the ring to a position such that the cords on either side of the ring measure 4m and 3m. Find the tension in the cord and the horizontal force.


    2. Relevant equations

    The component method.

    3. The attempt at a solution
    So far, I still cant figure out how to draw the diagram. If the horizontal board is 5m apart, does that mean the cord would act as a hypotenuse? And would the cord be 4m above the x-axis and 3m below the x-axis? Someone please help me, I've been stuck on this question for a day now.
     
  2. jcsd
  3. Feb 22, 2014 #2
    It is a fairly confusing way of wording it, but from what I can tell, you basically have a board, with a 7 meter long rope being formed into a triangle. The 7 meters of cord form a point with the ring, so that 4 meters of the cord is on one side, and 3 meters of the cord on the other side. I am not sure if you picked up on it, but this gives you the three sides, making a 3-4-5 triangle.
     
  4. Feb 22, 2014 #3
    But how would you figure out the angles? Would you assume that it was making a 45 degree angle with the horizontal axis? Actually, it is a 90 degree angle right, since a^2+b^2=c^2?
     
  5. Feb 22, 2014 #4
    A 3-4-5 triangle is a well known triangle type, which very specific angles to it. The angle between the 3 and 4 leg is 90 degrees, for example.
     
  6. Feb 22, 2014 #5
    I tried solving it but I got the wrong answer, can you please see what I did wrong and tell me.

    fx=T1cos45-T2cos45=0
    Fy=T1sin45+T2sin45-Fg=0

    T1cos45=T2cos45
    T2=(T1cos45)/(cos45)

    Fy=T1sin45+(T1cos45/cos45)(sin45)=Fg
    T1(sin45+sin45)=490
    T1=350
     
    Last edited: Feb 22, 2014
  7. Feb 22, 2014 #6
    A 3-4-5 triangle does not have 45 degree angles. It has the following:

    Between 3 and 4: 90
    Between 4 and 5: 36.87
    Between 5 and 3: 53.13
     
  8. Feb 22, 2014 #7
    Was my method correct though?
     
  9. Feb 22, 2014 #8
    It is difficult to say. I cant tell if you are using one triangle or two, but it looks like you have split it in two, which I am not 100% sure that you need to do. Odds are that you will also need to compare the forces with a "base" with no force, although I am not sure that is needed. (The base being that the length of cord on each side is 3.5 meters) There is a height difference between the base, and what you have, and that height difference is an upward force. (when decomposed)
     
  10. Feb 22, 2014 #9
    If it were to be one triangle, how could you find the tension of the cord? I assume that my method isn't correct since the tension for T1 and T2 are different even though it is one cord.
     
  11. Feb 22, 2014 #10
    I dont have the time to really look into the problem, but the first thing that hit me was that the change in height between the base triangle and the 3-4-5 triangle would give you a change in potential energy, which could be calculated, and turned into the y component of the additional force. Although it is a horizontal force, after the new position is found, it will no longer be horizontal, because as the ring slides over, the distance from the board to the ring shrinks, and the horizontal force becomes diagonal. If it stayed horizontal the whole time, it would be moving upwards to compensate, and the ring would slide all the way to one side.
     
  12. Feb 22, 2014 #11
    Draw a vertical line through the ring that intersects the 5 m board. This divides the big triangle into two smaller triangles that are geometrically similar to the big triangle. You have enough information to solve for all the sides of these two smaller triangles. This will allow you resolve the tension T in the cord into components in the x and y directions. The components to the left of the ring will be different from the components to the right of the ring. But, this will give you enough information to do a force balance on the ring and mass in the horizontal and vertical directions, and solve for the tension and the horizontal force on the ring.

    chet
     
  13. Feb 22, 2014 #12
    Is the concept of Fg used when solving for this? I'm not sure whether gravitational force is required.
     
  14. Feb 22, 2014 #13
    Sure it is.

    Chet
     
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