A scientific sensor unit, SSS, of mass M M\,M kg is suspended from a horizontal overhead crane beam by two light, inelastic steel cables. The cable attached to point P P\,P on the beam has a length of 2.5 m. The cable attached to point Q Q\,Q on the beam has a length of 1.7 m. The sensor unit hangs in equilibrium at a vertical depth of exactly 1.5 m below the level of the beam.
Show that the tension in the shorter cable is exactly 70% greater than the tension in the longer cable.
Given that the tension in the shorter cable is 3.4g Newtons, calculate the value of MMM.
87 exam-style questions on OCR (MEI) A Level Maths 3.4 Forces, covering 3.4.1 Language relating to forces, 3.4.2 Acceleration due to gravity, 3.4.3 Identify forces and draw force diagrams, 3.4.4 Resultant of concurrent forces, 3.4.5 Equilibrium of a particle, 3.4.6 Resolve a force into components (A-level only), 3.4.7 Equilibrium condition for resultant zero (A-level only), 3.4.8 Forces in equilibrium sum to zero (A-level only), 3.4.9 Equations for a particle in equilibrium (A-level only), 3.4.10 Frictional force and normal contact force (A-level only), 3.4.11 Model friction with F ≤ μR (A-level only), and 3.4.12 Apply Newton's Laws to friction problems (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.