question_answer 22)

As shown in Fig. 7.105, the two sides of a step ladder BA and CA are 1.6 m long and hinged at A. A rope DE, 0.5 m is tied half way up. A weight 40 kg is suspended from a point F, 1.2 m from B along the ladder BA. Assuming the floor to be frictionless and neglecting the weight of the ladder, find the tension in the rope and forces exerted by the floor on the ladder (Take ). Fig. 7.105  

Answer:

As shown in Fig. 7.106, let  and  be normal reactions of the floor at B and C respectively and be the tension in the rope DE. Then   or                                         ?(i) Consider the portion AC of the ladder. Balancing torques about A, we get   Fig. 7.106 From the geometry of the figure, we get   or                         Hence,  or   ?(2) Now consider the portion AB of the ladder. Balancing the torques about A, we get   But                       [using (2)] or            or                                ?(3) On solving (1) and (3), we get   and        .