Question

A beam is supported on its fulcrum at the point A, which is at mid-span, and forces act as shown in Figure.Calculate (a) force F for the beam to be in equilibrium, (b) the new position of the 23 N force when F is decreased to 21 N, if equilibrium is to be maintained.

Answer 1

(a) The clockwise moment, M1, is due to the 23 N force acting at a distance of 100 mm from the fulcrum, i.e.

M1 = 23 × 100 = 2300 N mm

There are two forces giving the anticlockwise moment M2. One is the force F acting at a distance of 20 mm from the fulcrum and the other a force of 12 N acting at a distance of 80 mm. Thus

M2 = (F × 20) + (12 × 80) N mm

clockwise moment = anticlockwise moments

i.e. 2300 = (F × 20) + (12 × 80)

Hence F × 20 = 2300 − 960

i.e. force, F = 1340/20 = 67 N

(b) The clockwise moment is now due to a force of 23 N acting at a distance of, say, d from the fulcrum. Since the value of F is decreased to 21 N, the anticlockwise moment is (21×20)+ (12 × 80) N mm

Applying the principle of moments

23 × d = (21 × 20) + (12 × 80)

i.e. distance, d = 420 +960/23 = 1380/23

= 60 mm