Question

A 165-N sign is supported by two ropes. One rope pulls up and to the right 35.5° above the horizontal with a tension T1, and the other rope pulls up and to the left 50.5° above the horizontal with a tension T2, as shown in the figure. Find the tensions T1 and T2.

Answer 1

Weight of the sign, W = 165 N (Vertically downward direction)

T1 = ?

1 = 35.5 deg

T2 = ?

2 = 50.5 deg

Total vertical component of the tensions shall be balanced by the weight of the sign.

So, we have -

T1*sin35.5 + T2*sin50.5 = W = 165 N

=> T1*0.58 + T2*0.77 = 165---------------------------------(i)

Horizzontal components of the two tensions shall balance each other.

So -

T1*cos35.5 = T2*cos50.5

=> T1*0.81 = T2*0.64

=> T2 = 1.26*T1-----------------------------------------------(ii)

put the value of T2 from (i) into (ii) -

0.58*T1 + 0.77*1.26*T1 = 165

=> 1.55*T1 = 165

=> T1 = 165 / 1.55 = 106.4 N

So, T2 = 1.26*106.4 = 134.1 N