Find the force P required to pull block B shown in figure. Coefficient of friction between A and B is 0.3 and between B and floor is 0.25. Mass of A = 20 kg and B = 30 kg.[Figure: block B rests on a horizontal floor and block A rests on top of B. A s…

Given: \(W_A = 20 \times 9.81 = 196.2\) N, \(W_B = 30 \times 9.81 = 294.3\) N, \(\mu_1 = 0.3\) (A–B), \(\mu_2 = 0.25\) (B–floor). A is held by the string; B is about to move right.

Block A: forces T (up-left at 30°), \(W_A\), \(N_1\) (up), friction \(F_1 = 0.3N_1\) to the right (B tends to drag A to the right).

\(\sum F_y = 0:\ N_1 + T\sin30^\circ = 196.2\); \(\sum F_x = 0:\ T\cos30^\circ = 0.3N_1\)

\(0.866T = 0.3(196.2 - 0.5T) \Rightarrow 1.016T = 58.86 \Rightarrow T = 57.93\) N

\(N_1 = 196.2 - 28.97 = 167.23\) N, \(F_1 = 50.17\) N

Block B: \(N_2 = N_1 + W_B = 167.23 + 294.3 = 461.53\) N, \(F_2 = 0.25 \times 461.53 = 115.38\) N; both \(F_1\) (from A) and \(F_2\) (from floor) act to the left on B.

\(P = F_1 + F_2 = 50.17 + 115.38\)

Answer: P = 165.55 N (tension in the string T = 57.93 N).