TWO DIMENSIONAL FORCE SYSTEMS
Force F is resolved into two rectangular forces F x and F y as shown in Fig. 3.1.
F =F x +F y
F x and F y may further be written as a scalar times the appropriate unit vectors i, j in two dimensions (x and y directions respectively).
where F x and F y are scalar components of the vector F in x and y directions respectively.
F x= F cos θ
F y = F sin θ
F2 (cos2 θ + sin2 θ) = F1 + F2
F = √Fx2+Fy2
And θ tan -1 F y / F x
The unit vectors in – x and – y directions are – and – j. So, – F x i = F x (- i) ; it means that Fx in the- x direction. So in i, J and k system, the directions of F x, F y and F z can be found easily.
Refer Fig. 3.2.
The resultant of the two forces F 1and F2 is
where R x and R y are related to and the x and y components of R.