Question

5. A string ABCD whose extremely A is fixed weights W1 and W2 attached to it at B and C possess
round a smooth peg at D carrying a weight of 1000N at the free end E. If in a state of equilibrium BC is
horizontal and AB and CD makes angle of 150° & 1200 respectively with. Make calculation for
a) the tension in position AB,BC,CD and DE of the string
b) the value of weight W1 and W2
c) the pressure on the peg D​

Answer 1

Answer:

First string ABCD is split in to two parts, and consider the joints B and C separately Let T1 = Tension in String AB T2 = Tension in String BC T3 = Tension in String CD T4 = Tension in String DE  T4 = T3 = 40 N Since at joint B and C three forces are acting on both points. But at B all three forces are unknown and at point C only two forces are unknown  SO Apply lamis theorem first at joint C, T2 /sin 150° = W2/sin 120° = 40/sin 90° = 20N T2 = {sin 150° × 40}/sin 90° W2 = {sin 120° × 40}/sin 90° = 34.64N Now for point B, We know the value of T2  So, Again Apply lamis theorem at joint  B, T1/sin 90° = W1/sin 150° = T2/sin 120° T1 = {sin 90° × 20}/sin 120°  = 23.1 N W1 = {sin 150° × 20}/sin 120° = 11.55N