A uniform shelf, ABABAB, of length a a\,a m and mass m m\,m kg, is at rest with A A\,A against a rough vertical wall. The shelf is held in a horizontal position by a wire attached to B B\,B and to the vertical wall at CCC. The tension in the wire is 6mg. A decorative ornament of mass 4m is placed on the shelf at P P\,P where AP=xAP = xAP=x. The angle between the wire and the shelf is 30∘30^\circ30∘. The ornament is modelled as a particle and the wire is modelled as a light inextensible string.
Find x x\,x in terms of aaa.
The reaction force at A A\,A makes an angle θ \theta\,θ with the shelf. Find the value of tanθ\tan \thetatanθ.
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.