A uniform beam, ABABAB, of length 6 m and mass M M\,M kg, is at rest with A A\,A against a rough vertical wall. The beam is held in a horizontal position by a rope attached to B B\,B and to the vertical wall at the point CCC. A person of mass 3M 3M\,3M stands on the beam at P P\,P where AP=4AP = 4AP=4 m. The angle between the rope and the beam is α\alphaα, where tanα=512\displaystyle \tan \alpha = \frac{5}{12}tanα=125. The beam is modelled as a uniform rod, the person is modelled as a particle and the rope is modelled as a light inextensible string.
Find, in terms of MMM, the tension in the rope BCBCBC.
Find the direction of the force exerted on the beam 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.