MTH304 Assignment 3 Solution and Discussion

Q. 1
A nonuniform beam AB of length 8 m and mass 8 kg rests on a pivot at the midpoint C. When a mass of 2 kg rests on the beam 1.5 m from B, the system is in equilibrium. Find the distance between A and the centre of mass of the beam.Q. 2
A uniform rod AB of length 10 m and weight 5 N rests on two supports at B and C, where C is 1 m from A. A weight of 6 N is attached to the rod 2 m from A. Given that when a load is attached 0.5 m from A, the rod is on the point of tilting about C, Find the weight of this load in Newton. 
Q.1 Solution:
Anti clockwise moment = Clockwise moment
8gN * d = 2gN * 2.5m
8d = 5Nm
d = 5/8
d = 0.625m
= 4 – d
= 4 – ( 0.625)
= 3.375mQ. 2 Solution:
R = 0
Taking moment about ‘C’
w * 0.5 = 6 * 1N + 5 * 4m
0.5w = 26Nm
w = 26/0.5m
w = 52 N