Question

The 50-lb block A and the 25-lb block B are supported by an incline that is held in the position shown. Knowing that the coefficient of static friction is 0.15 between all surfaces of contact, determine the value of ? for which motion is impending. Fig. P8.12

Answer 1

Given that, mass of block 'A', m_A = 50 lb mass of block 'B', m_B = 25 lb static friction, mu_s = 0.15 therefore motion impends F = mu_s - N Free body: block 'A' Impending notion Sigma Fy = 0: N_1 - 50 cos theta = 0 N_1 = 50 cos theta Sigma F_x = 0: T - 50 sin theta + mu_1 N_1 = 0 T = 50 sin theta - mu_1 (50 cos theta) Free body: Block B Impending motion Sigma F_y = 0: N_2 - N_1 - 25 cos theta = 0 N_2 = 50 cos theta + 25 cos theta N_2 = 75 cos theta Sigma F_x = 0: T - mu_1 N_1 - mu_2 N_2 - 25 sin theta = 0 T = mu_1 (50 cos theta) + mu_2 (75 cos theta) + 25 sin theta because mu_1 = mu_2 = 0.15 T = 0.15 times 125 cos theta + 25 sin theta - (2) Eqn (1) - eqn(2) 0 = 50 sin