In the system shown in Fig. P5.34, block A has mass m ,

Chapter 8, Problem 83P

(choose chapter or problem)

In the system shown in Fig. P5.34, block A has mass \(m_A\), block B has mass \(m_B\), and the rope connecting them has a nonzero mass \(m_{\text {rope }}\). The rope has a total length L, and the pulley has a very small radius. You can ignore any sag in the horizontal part of the rope.

(a) If there is no friction between block A and the tabletop, find the acceleration of the blocks at an instant when a length d of rope hangs vertically between the pulley and block B. As block B falls, will the magnitude of the acceleration of the system increase, decrease, or remain constant? Explain.

(b) Let \(m_A=2.00 \mathrm{~kg}\), \(m_B=0.400 \mathrm{~kg}, m_{\text {rope }}=0.160 \mathrm{~kg}\), and \(L=1.00 \mathrm{~m}\). If there is friction between block A and the tabletop, with \(\mu_{\mathrm{k}}=0.200\) and \(\mu_{\mathrm{s}}=0.250\), find the minimum value of the distance d such that the blocks will start to move if they are initially at rest.

(c) Repeat part (b) for the case \(m_{\text {rope }}=0.040 \mathrm{~kg}\). Will the blocks move in this case?