A uniform shelf, ABABAB, of length 4 m and mass 2M 2M\,2M kg, is at rest with A A\,A against a rough vertical wall. The shelf is held in a horizontal position by a steel cable attached to B B\,B and to the vertical wall at the point CCC. A heavy vase of mass 4M 4M\,4M is placed on the shelf at P P\,P where AP=3AP = 3AP=3 m. The angle between the cable and the shelf is α\alphaα, where tanα=43\displaystyle \tan \alpha = \frac{4}{3}tanα=34. The shelf is modelled as a uniform rod, the vase is modelled as a particle and the cable is modelled as a light inextensible string.
Find, in terms of MMM, the tension in the cable BCBCBC.
Find the direction of the force exerted on the shelf at AAA.
130 exam-style questions on Edexcel A Level Maths Applications of Forces, covering 7.1 Static Particles, 7.2 Modelling with Statics, 7.3 Friction and Static Particles, 7.4 Static Rigid Bodies, 7.5 Dynamics and Inclined Planes, and 7.6 Connected Particles 2. Each one has a worked solution and a mark scheme showing where the marks go.