Question

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

Answer 1

∑H = Sum of horizontal component

∑V = Sum of vertical component

First

∑H = 20 cos α + 20 cos(360° – β)

∑H = 20 cos α – 20 cos β ...(i)

 Now

∑V = 20 sinα + 20 sin(3600 – β)

–50 = –50 + 20 sin α + 20 sin β ...(ii)

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

Let additional single force be ‘R’ and its magnitude is equal to

R’ = R = [(20 cosα – 20 cosβ)² + (–50 + 20 sinα + 20 sinβ)²]^1/2

This force should act in direction opposite to the direction of force ‘R’