## Lamina Suspended at Angle to Horizontal

In general for a system to be in equilibrium, the forces must balance in each direction, and the moments about any point must sum to zero.

When a lamina is suspended by two inelastic strings, we can find the tensions in the strings by resolving vertically and taking moments about a point where one of the strings is attached to the lamina.

The equilateral triangle of mass in the form of a lamina of massbelow is attached to two strings, one a quarter of a side from a vertex and the other at a vertex, so that the topmost side AB is at an angleto the horizontal.

The centre of gravity O is two thirds of the distance from A to the midpoint of the side BC, and and the line from A to the midpoint of BC bisects the angle A so makes an anglewith AB and an anglewith the horizontal.

Resolving vertically for the lamina gives

(1)

Taking moments about A gives

which simplifies to (2)

(2)-(1) givesthen