Question on Equilibrium using Trignometric Expressions

Topic : Equilibrium of Suspended Strings

Question : A particle A, of weight W, is suspended by two strings AB and AC. AB is inclined at 30degrees to the vertical and AC at angle P to the vertical. The tension in AB and AC are 40N and 60N respectively. Calculate the value of W and P.

Solution :

Since the system is in equilibrium,
60 Sin P = 40 Sin 30º ------- (1)
and 60 Cos P + 40 Cos 30º = W-----(2)

From (1) we get,
60 Sin P = 40 *(1/2)

60 Sin P/60 = 20/60
Sin P = 1/3

P = Sinˉ¹(1/3)

P= 19.469º


From (2) we get,
W = 60 Cos P + 40 Cos 30º

= 60 Cos (19.469º) + 40 Cos 30º

= 60 . 0.943 + 40 . 0.866

= 56.58 + 34.64

= 91.22N

So P = 19.469º

W = 91.22N