Evaluate resultant of the system:

Q: Figure given below shows two vertical forces and couple of moment 2000 Nm acts on horizontal rod, which is fixed at end A. Determine resultant of the system

Resultant of the system

  V = -4000 + 2500 = -1500N

R = ( ∑V²)^1/2

= 1500N (acting downwards)

for finding the position of the resultant, apply varignon's theorem here

i.e Moment of resultant = sum of moment of all the forces about any point. Let from point A, and distance of resultant is 'd' m from A

R.d = 4000 × 1 + 2000 - 2500 × 2.5 -1500 × d = -250       d = 0.166 m from point A

(ii) Equivalent system through A

Equivalent system consists of:

1. A single force R passing through given point, and

2. A single moment ( ∑M) Where,

R  = the resultant of all force acting on the body

∑M = Sum of all moments of all the forces about point A. Therefore single force is = 1500 N; and couple = 250 Nm