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 OCR A Level Maths 3.3 Forces and Newton's Laws, covering 3.3.1 Concept and vector nature of a force, 3.3.2 Newton's first law, 3.3.3 Newton's second law in a straight line, 3.3.4 Newton's second law with vectors (A-level only), 3.3.5 Newton's second law with resolved forces (A-level only), 3.3.6 Weight, 3.3.7 Gravitational acceleration, 3.3.8 Newton's third law, 3.3.9 Normal reaction force, 3.3.10 Smooth contact model, 3.3.11 Equilibrium with connected particles and pulleys, 3.3.12 Newton's third law with resolved forces (A-level only), 3.3.13 Equilibrium by resolving (A-level only), 3.3.14 Equilibrium of forces in two dimensions using vectors (A-level only), 3.3.15 Resolving forces for advanced problems (A-level only), 3.3.16 Resultant forces and components (A-level only), 3.3.17 Dynamics of a particle in a plane (A-level only), 3.3.18 Concept of a frictional force (A-level only), 3.3.19 Contact force components (A-level only), 3.3.20 Coefficient of friction (A-level only), 3.3.21 Static and limiting equilibrium on a rough surface (A-level only), 3.3.22 Motion of a body on a rough surface (A-level only), and 3.3 Forces and Newton's Laws. Each one has a worked solution and a mark scheme showing where the marks go.