A horizontal beam, ABABAB, of length d d\,d m and mass M M\,M kg, is pivoted at A A\,A to a rough vertical wall. The beam is supported by a cable attached to B B\,B and to the wall at CCC. The tension in the cable is 4Mg4Mg4Mg. A weight of mass 2M 2M\,2M is placed on the beam at P P\,P where AP=xAP = xAP=x. The angle between the cable and the beam is 45∘45^\circ45∘. The beam is modelled as a uniform rod, the weight is modelled as a particle and the cable is modelled as a light inextensible string.
Find x x\,x in terms of ddd.
The reaction force at A A\,A acts at an angle θ \theta\,θ to the horizontal. Find the value of tanθ\tan \thetatanθ.
