Wize University Physics Textbook (Master) > Force Vectors (Advanced Info)

Forces in Cartesian Vector Notation (Form) (2D)

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Any force vector can be written in the following form or notation, known as Cartesian Vector Form (CVF). We're using vector A in this example, but it could easily be F, or Q, or YYZ, or anything.

A⃗ =Axi +Ayj +Azk\vec{A}^{\,}=A_xi\ +A_yj\ +A_zkA=Ax​i +Ay​j +Az​k

 Given the forces shown.
      a) Express each as a cartesian vector                      (<9.6,11.5>kN, <-24,10>kN, <31.2,-18>kN)
      b) Find resultant Fx and Fy                                        (Fx=16.8 kN, Fy=3.5 kN)
      c) Find the resultant magnitude & direction             (17.2 kN @ 11.8°)

a) F1 = 15sin(40°)i + 15cos(40°)j 
          = [9.6i + 11.5j]kN

    F2 = -26(12/13)i + 26(5/13)j 
          = [-24i + 10j]kN

    F3 = 36cos(30°)i - 36sin(30°)j 
          = [31.2i - 18j]kN

b) Fxr = sum Fx's = 9.6 - 24 + 31.2 = 16.8 kN
    Fyr = sum Fy's = 11.5 + 10 - 18 = 3.5 kN

c) resultant magnitude:  Fr = sqrt (16.82 + 3.52) = 17.2 kN

    direction:    angle = tan-1(3.5/16.8) = 11.8°

                        angle is measured from the +x axis, the components put the resultant in the 1st quadrant

 Find horizontal and vertical components of a vector R shown in the Figure.  

Rx=15   Ry=25.9R_x=15\ \ \ R_y=25.9Rx​=15   Ry​=25.9

Rx=25.9   Ry=15R_x=25.9\ \ \ R_y=15Rx​=25.9   Ry​=15

Rx=15   Ry=−25.9R_x=15\ \ \ R_y=-25.9Rx​=15   Ry​=−25.9

Rx=25.9   Ry=−15R_x=25.9\ \ \ R_y=-15Rx​=25.9   Ry​=−15

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Given the forces shown.
a) Express each as a cartesian vector 
b) Find resultant Fx and Fy
c) Find the resultant magnitude & direction

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