On a model ship, the mast OC has length 50 cm and weight 20 newtons. The mast is hinged to the deck at O, so that it can rotate in the vertical plane of the ship. Small smooth rings are fixed at points A and B on the deck in this plane such that AO=OB=50 cm. Threads from C are passed through these rings, and held at their ends by two children who exert forces of P newtons and Q newtons respectively. If Q = 10, calculate the value of P needed to hold the mast in equilibrium at 40° to the horizontal deck.
2. The attempt at a solution
I tried finding a simultaneous equation by resolving the forces horizontally and vertically, but I was unable to do so as there are 6 different forces (P,Q,tension in AC,tension in BC, tension in OC, weight of OC) and the angles between P and the deck and Q and the deck are unknown (I found the angles between AC and the deck and CB and the deck as 20° and 70° respectively (or it could be the other way round?).).