Calculate Additional force required to maintain equilibrium:

For the system shown in figure find the additional single force required to maintain equilibrium.

Sol.: Let and be the angles as shown in figure Resolved all the forces horizontal and in vertical direction. When we add single force the magnitude of which is equal to resultant of force system and direction is opposite the direction of resultant. Let;

ΣH = Sum of the horizontal component

ΣV = Sum of the vertical component

First

         H = 20cosα + 20cos(360° - β)

ΣH = 20cosα  - 20cosβ                                             ...(i)

Now

ΣV = 20sinα  + 20sin(3600 -  β ) -50 = -50 + 20sinα    + 20sinβ                ...(ii)

Hence resultant of the system = R = (  ∑H2  + ∑V2)1/2

Let the additional single force be 'R' and its magnitude is equal to

R' = R = [(20cosα  - 20cosβ )2 + (-50 + 20sinα  + 20sinβ  )2]1/2    .......ANS