Question

Two identical ladders, each of mass M and length l are resting on a rough horizontal surface as shown in Fig. A block of mass m hangs from P. If the system is in equilibrium, find the magnitude and the direction of frictional force at A and B

Answer 1

For equilibrium (i) $\sum F_x=0\therefore F_{f1}=-F_{f2}$ or $N_1=N_2$
(ii) $\sum F_y=0$ $2N=2Mg+mg$ or $N=Mg+\frac{mg}{2}$
(iii)$\sum \tau =0$ about P for either ladder $+Mg\frac{1}{2}\cos \theta -N1\cos \theta +F_{j}l\sin \theta =0$
Or, $F_f=\frac{(M+m)g}{2}\cot \theta$