Question

Block A weight 4N and block weight 8N. The coefficient of kinetic friction is 0.25 for all surfaces. Find the force F to slide B at a constant speed when (a0 A rests on B and moves with it, (b) A is held at rest, and (c) A and B are connected by a light cord passing over a smooth pulley as shown in Fig. , respectively.

Answer 1

a. If blocks A and B move together, the friction between A and B is static and friction between B and ground will be of kinetic nature.

FBD of A + B

For A and B, both move with constant velocity; the net force acting on the system of A + B should be zero.

$F=f_r=\mu N=\mu (m_A+m_B)g$

b. If A is held at rest. The friction force on top and bottom surface of block B will be kinetic.

Friction at the top surface of block B,

$f_1=\mu N_1=\mu m_{A}g$

Friction at the bottom surface of block B,

$f_2=\mu N_2=\mu (m_A+m_B)g$

If block B moves with constant speed,

$F=f_1+f_2=\mu m_{A}g+\mu m_{A}g+\mu (m_A+m_B)g$

$F=\mu (2m_A+m_B)g$

c. Now A and B are connected by light string. If force is applied on block B, block B will move towards left. As blocks A and B are connected by string, block A will move towards right. The direction of friction force will be opposite to relative motion and its shown in Fig.

From FBD of A: $T=f_1=\mu N_1=\mu m_{A}g$

From FBD, of B: $F=f_1+f_2+T$

$=2f_1+f_2$

$=2\mu m_{A}g+\mu (m_A+m_B)g$

$\Rightarrow F=\mu (3m_A+m_B)g$