Question 3.5
A mass $m_1$ is joined to a massless, frictionless, movable pulley with a light,
inextensible string, through another pulley that hangs from a fixed support.
Two masses $m_2$ and $m_3$ are joined by a light, inextensible string that wraps
around the movable pulley. Take the vertically downward direction as posi-
tive. Denote the accelerations of the masses $m_1$, $m_2$ and $m_3$ by $a_1$, $a_2$ and $a_3$
respectively. Show that
$a_1 = \frac{(-4m_2m_3 + m_1m_3 + m_1m_2)}{(4m_2m_3 + m_1m_3 + m_1m_2)}g$,
$a_2 = \frac{(4m_2m_3 - 3m_1m_3 + m_1m_2)}{(4m_2m_3 + m_1m_3 + m_1m_2)}g$,
$a_3 = \frac{(4m_2m_3 + m_1m_3 - 3m_1m_2)}{(4m_2m_3 + m_1m_3 + m_1m_2)}g$.
where $g$ is the acceleration due to gravity.
