If a system of three concurrent and coplanar forces is in equilibrium, then Lami’s theorem states that the magnitude of each force of the system is proportional to sine of the angle between the other two forces. The constant of proportionality is same for all three forces.
Let us consider three coplanar and concurrent forces which act at a common point O as shown in Figure 3.20. If the point is at equilibrium, then according to Lami’s theorem
Lami’s theorem is useful to analyse the forces acting on objects which are in static equilibrium.
A baby is playing in a swing which is hanging 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.
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.
From this, the tension on each string is T = mg / 2cosθ