Question

A mass of 2kg is supported by two cords which makes angles of 30 and 50 with the vertical,find the force on the two cords

Answer 1

So,this is the diagram of the described situation,the strings are attached to a rigid support at their one end and the other end is connected to the particle.

Let, the string making an angle of 45 with the horizontal has a tension of T 1 and

the one making an angle of 30 has a tension of T2.

Now,

what we have done is that we have taken the vertical and

horizontal components of the tension in the two strings.

Now,considering the system to be in equilibrium,

see the diagram,the vertical component of the strings i.e

(T 1 sin 45 & T 2 sin 30) together will act to balance the weight of

the particle(mg)

So,we can say, T 1 sin 45 + T 2 sin 30 = mg. ...(1)

From horizontal equilibrium,we can say, T 1 cos 45 must balance T 2 cos 30 ,

as no other force is present in horizontal direction.

So,T 1 cos 45 = T 2 cos 30. ...(2)

Given,

mg = 10 ⋅ 10 = 100N

So,solving equation 1 & 2 we get,

T 1 = 89.65N and, T 2 = 73.20N