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Two Dimensional Force Systems

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

[Note that ‘f2y; acts in negative y direction which is having unit vector-

where R x and R y are related to  and the x and y components of R.