A uniform beam AB AB\,AB has length 8 m and mass 20 kg. It rests horizontally on two supports at C C\,C and DDD, where AC=2AC=2AC=2 m and AD=6AD=6AD=6 m. A crate of mass 30 kg is placed on the beam with its centre of mass x x\,x m from AAA.
Find the set of possible values of x x\,x for which the beam remains in equilibrium on both supports.
53 exam-style questions on OCR A Level Maths 3.4 Moments (A-level only), covering 3.4.1 Moment of a force (A-level only), 3.4.2 Equilibrium of a rigid body (A-level only), and 3.4.3 Moments in static contexts (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.