Question

Fig. shows two vertical forces and a couple of moment 2000 Nm acting on a horizontal rod, which is fixed at end A. 

1. Determine the resultant of the system 

2. Determine an equivalent system through A.

Answer 1

(i) Resultant of the system 

∑V = –4000 + 2500 = –1500 N R = (∑V²)^1/2 

= 1500 N (acting downwards) 

for finding the position of the resultant, apply varignon’s theorem i.e Moment of resultant = sum of moment of all the forces about any point. Let from point be 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 consist of: 

1. A single force R passing through the 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. 

Hence single force is = 1500 N; And couple = 250 Nm.