A system consists of three masses $m_1, m_2$ and $m_3$ connected by a string passing over a pulley.

Question

A system consists of three masses $m_1, m_2$ and $m_3$ connected by a string passing over a pulley. Mass $m_1$ hangs freely and $m_2$ and $m_3$ are on a rough horizontal table (coefficient of friction $\mu$). The downward acceleration of mass $m_1$ is (Assume $m_1=2m, m_2=m, m_3=m$)

Professor PC Thomas Classes · Answer

Driving force = $m_1 g = 2mg$. Opposing friction = $\mu(m_2 + m_3)g = \mu(2m)g = 2\mu mg$. Net force = $2mg - 2\mu mg$. Total mass = $m_1 + m_2 + m_3 = 4m$. Acceleration $a = \frac{2mg(1-\mu)}{4m} = \frac{g(1-\mu)}{2}$.