A body of mass m is suspended by two strings making angles α and β with the horizontal (as shown in the figure). Find the tensions in the strings?
Take the body of mass in as the system. The forces acting on the system are
(i) Mg downwards (by the earth),
(ii) T1 along the first string (by the first string) and
(iii) T2 along the second string (by the second string).
These forces are shown in figure. As the body is in equilibrium, these forces must add to zero. Taking horizontal components,
T1cosα−T2cosβ=0
T1cosα=T2cosβ ------------------(i)
or,
Taking vertical components,
T1sinα+T2sinβ−mg=0-------------(ii)
Eliminating T2 from (i) and (ii),
T1sinα+T1cosαcosβsinβ=mg
or,
T1=mgsinα+cosαcosβsinβ=mgcosβsin(α+β)
From(i),
T2=mgcosαsin(α+β)