(a) A body P of mass q kg is suspended by two light inextensible strings AB and DB attached to a horizontal table. The strings are inclined at 30° and 60° respectively to the horizontal and the tension in AB is 48N. If the system is in equilibrium :
(i) sketch a diagram to represent the information ; (ii) calculate the tension in DB ;
Explanation
(i)
(ii) Using Lami’s theorem,
(frac{48}{sin 150} = frac{T}{sin 120})
(T = frac{48 sin 120}{sin 150})
(T = 83.14N)
The tension in DB is 83.14N.
(iii) Using Lami’s theorem,
(frac{10q}{sin 90} = frac{48}{sin 150})
(10q = frac{48 sin 90}{sin 150})
(10q = 96 implies q = 9.6kg)