Question

A man of mass M is standing on a platform of mass $m_1$ and holding a string passing over a system of ideal pulleys. Another mass $m_2$ is hanging as shown.
$(m_2=20kg,m_1=10kg,g=10m{s}^{-2})$

Answer 1

(a) If $T=$ tension on string connecting $m_1$ and $m_2$, then, $2T=$ tension in other string.
Equilibrium of $m_2$ gives,
$T=m_{2}g=200N$
Equilibrium of $(M+m_1)$ gives,
$3T=W_{man}+m_{1}g$
or $600=W_{man}+100\Rightarrow W_{man}=500N$
(b) Total upward force on system is 4T and total downward force is weight of all. To accelerate COM upwards,
$T>200+100+500$
or $T>200N$
(c) To accelerate downwards,
$T<200N$
(d) In equilibrium, force on man
$N+400=500$
$\therefore N=100N$