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.
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.