1. The problem statement, all variables and given/known data A plank of length 2L leans against a wall.It starts to slip downward without friction.At what fraction of the initial height does the top of the plank lose contact with the wall . 2. Relevant equations 3. The attempt at a solution Let the normal force from the vertical wall on top of the plank be N1. Let the normal force from the floor on bottom of the plank be N2. Let x and y represent the coordinate of the CM with origin at the bottommost point of the wall. Let θ be angle which plank makes with the floor at any instant. The top of the plank loses contact when N1 = 0. Now,we have N2-Mg = Md2y/dt2 (1) N1 = Md2x/dt2 (2) N1Lsinθ-N2LCosθ = [M(2L)2/12]d2θ/dt2 On simplifying , N1Lsinθ-N2LCosθ = (ML2/3)d2θ/dt2 (3) Another relation we can obtain is x=Lcosθ Differentiating,dx/dt = -Lsinθ(dθ/dt) Again differentiating , d2x/dt2 = -L[cosθ(dθ/dt)2+sinθd2θ/dt2] (4) How should I proceed further ? I would be grateful if some member could help me with the problem . Edit :Fixed errors .Erroneously typed d2x/dt2 in place of d2y/dt2 and vica versa .