Determine resultant of four forces:

Determine resultant of four forces tangent to the circle of radius 3m shown in the figure given below. What will be the location of it with respect to the center of the circle?             

Let resultant be 'R' that makes an angle of θ with the horizontal X axis. And at a distance of x from point 'O'. Let ∑H and ∑V be the horizontal and vertical component.

H = 150 - 100 cos 45º = 79.29N                                                               ...(i)

V = 50 - 100 sin 45º - 80 = -100.7N         ...(ii)

R = {  H²  + V²}^1/2

R = {(79.29)2  + (100.7)2}1/2

R = 128.17N                                                                            .......ANS

Calculation For angle θ

tanθ   =     ∑V/ ∑ H

= -100.71/79.28

θ= -51.78º                                                                              .......ANS

Calculate distance'd'

In accordance to Varignon's theorem, R.d = ∑M

(By taking moment about point 'O')

That is, 128.17 X d = 150 X 3 -50 X 3 + 100 X 3 - 80 X 3

d = 2.808 m                                                                            .......ANS