A scaffolding plank, ABABAB, of length L L\,L m and mass 2M 2M\,2M kg, is at rest with A A\,A against a rough vertical wall. The plank is held in a horizontal position by a rope attached to B B\,B and to the vertical wall at the point CCC. The tension in the rope is 3Mg3Mg3Mg. A toolbox of mass M M\,M is placed on the plank at P P\,P where AP=xAP = xAP=x. The angle between the rope and the plank is 60∘60^\circ60∘. The plank is modelled as a uniform rod, the toolbox is modelled as a particle and the rope is modelled as a light inextensible string.
Find x x\,x in terms of LLL.
The force exerted on the plank at A A\,A by the wall acts in a direction which makes an angle θ \theta\,θ with the horizontal. Find the value of tanθ\tan \thetatanθ.
