Wize University Statics Textbook (Master) > Force Vectors
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.
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
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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
