A baby is playing in a swing which is hanging Rigid support with the help of two identical chains is at rest. Identify the forces acting on the baby. Apply Lami's theorem and find out the tension acting on the chain.

Explanation

The baby and the chains are modeled as a particle hung by two strings as shown in the figure. There are three forces acting on the baby. (i) Downward gravitational force along negative y direction (mg) (ii) Tension (T) along the two strings
These three forces are coplanar as well as concurrent as shown in the following figure.

By using Lami.s theorem
` (T)/(sin (180 - theta)) = (T)/(sin (180 - theta)) = (mg)/(sin(2theta) )`
since ` sin (180 - theta) = sin theta " and " sin (2 theta) = 2 sin theta cos theta `
we get ` (T)/(sin theta) = (mg)/(2 sin theta cos theta)`
from this, the tension on each string is ` T = (mg)/(2 cos theta)`