The coefficient of static friction, $\mu_{s}$, between block $A$ of mass 5 kg and the table is 0.4.

Question

The coefficient of static friction, $\mu_{s}$, between block $A$ of mass 5 kg and the table is 0.4. What would be the maximum mass value of hanging block $B$ so that the two blocks do not move? The string and the pulley are assumed to be smooth and massless.

Professor PC Thomas Classes · Answer

For no motion, the tension $T$ must be less than or equal to the maximum static friction on $A$. $T = m_B g$ and $f_{max} = \mu_s m_A g$. Therefore, $m_B g \le \mu_s m_A g \implies m_{B(max)} = \mu_s m_A = 0.4 	imes 5 = 2.0 \mathrm{~kg}$.