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Use components to find Direction of the resultant of the three pulls?

  1. Sep 22, 2011 #1
    Workmen are trying to free an SUV stuck in the mud. To extricate the vehicle, they use three horizontal ropes, producing the force vectors shown in the figure. (985N @ 31 Degrees Quad 1, 788 N 32 degrees Quad 2, and 411N 53 degrees quad 3.



    How do I find the direction of the resultant of the three pulls? Enter your answer as the angle counted from +x axis counterclockwise direction.



    I have already found the three x components of the three pulls. I have already found the y components of each of the three pulls. And I have already found the magnitude of the resultant of the three pulls. All of my answers to those parts are correct. I just dont understand what I am supposed to do to find the direction of the resultant of the three pulls. Please help!
     
  2. jcsd
  3. Sep 22, 2011 #2
    Please explain what '32 degrees Quad 2' and '53 degrees Quad 3' mean?
     
  4. Sep 22, 2011 #3
    V1 points north east, V2 points north west, and V3 points Southwest. Angle theta (31, 32, 53) is between the vector and the x axis. carteesion plane
     
  5. Sep 22, 2011 #4
    y components:
    985N sin(31)= 507
    788N cos(32)= 668
    411N sin(53)=-328

    x components:
    985N cos(31)= 844
    788N sin(32)= -417
    411N cos(53)= -247

    tan^-1 (507/844)= 30.98
    tan^-1 (668/-417)= -58.02
    tan^-1 (-328/-247)= 53.01
     
  6. Sep 22, 2011 #5
    Sum Fx= 179.4
    Sum Fy= 847

    total Fsum: rad (179)^2 + (847)^2 = 865 magnitude of the resultant of the three pulls
     
  7. Sep 22, 2011 #6
    Suppose the resultant R is in the 4th quad i.e. NW. Then the angle A between the resultant R and the resultant of all x-components, X, is given by cosA = X/R.
     
  8. Sep 22, 2011 #7
    So are you saying I should use cos^-1 (x/865)? I'm not sure i'm following what x would be! :/
     
  9. Sep 22, 2011 #8
    If the angle 32 degrees is betweem 788N and the negative x-axis, then the y-comp is given by 788sin32 and not by 788cos32.
     
  10. Sep 22, 2011 #9
    wait! cos^-1 (179/865) = 77.77????????????? degreees!???
     
  11. Sep 22, 2011 #10
    yayy! the answer was 77 degrees. Thanks for the guidance. regarding the sin cos stuff with the components all those answers were correct so i might have explained the quads incorrectly. thanks for urrrrr help!
     
  12. Sep 22, 2011 #11
    I said X , the resultant of all x-components of the three given forces.
     
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