A heavy promotional banner of mass MMM kg is suspended from two fixed points, PPP and QQQ, on a horizontal stadium roof beam by two light, inextensible cables. The shorter cable, attached at PPP, has a length of 5.05.05.0 m. The longer cable, attached at QQQ, has a length of 8.08.08.0 m. The banner is in equilibrium at a point OOO, which is exactly 3.03.03.0 m vertically below the level of the roof beam.
Show that the tension in the shorter cable is approximately 16%16\%16% greater than the tension in the longer cable.
Given that the tension in the longer cable is 120120120 N, calculate the value of MMM, giving your answer to two significant figures. (Use g=9.8 ms−2g = 9.8 \text{ ms}^{-2}g=9.8 ms−2).
139 exam-style questions on AQA A Level Maths 3.3 R: Forces and Newton's laws, covering 3.3.1 Concept of a force and Newton's first law, 3.3.2 Newton's second law, 3.3.3 Weight and motion under gravity, 3.3.4 Newton's third law and equilibrium, 3.3.5 Addition of forces and resultants (A-level only), and 3.3.6 Friction (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.