Determine magnitude and direction of the resultant force:

A system of forces is acting at the corner of a rectangular block as shown in the figure. Determine magnitude and direction of the resultant force.

Sol.: Let R be resultant of given system. And  ∑ H and  ∑ V be the horizontal and vertical component of the resultant.

∑H = 25 - 20 = 5KN                                                                                     ...(i)

∑V = -50 - 35 = - 85KN                                                                          ...(ii)

R² = ∑H² + ∑V²

R² = (5)2  + (-85)²

R = 85.14N                                                                               .......ANS

Let Resultant makes an angle of θ with the horizontal tanθ = ∑V/ ∑H = -85/5

θ= - 86.63º                                                                          .......ANS

Let resultant 'R' is at perpendicular distance'd' from the point A,

For finding position of resultant that is 'd', taking moment about point 'A'., or apply the varignon's theorem

R.d = 25 X 3 + 35 X 4

d = (75 + 140)/85.14

d =  2.53 m from the point A       .......ANS