Question

A man of mass M is standing on a plank kept in a box. The plank and box as a whole has mass m. A light string passing over a fixed smooth pulley connects the man and box. If the box remains stationary, find the tension in the string and force exerted by the man on the plank. (Given M>m)

Answer 1

The fixed pulley is taken as frame of reference. The forces on man and box with plank are shown in $Fig.6.52$.
The forces are as follows :
$a$. Weight of the man =Mg
$b$. Tension in the string=T
$c$. Normal contact force between the man and the plank=N
$d$. The weight of the plank and box=mg
The box remains at rest, the man will have to be at rest
Referring to free-body diagram of man, the equation of motion of the man is given as
$T+N-Mg=0$.......(i)
Referring to the free-body diagram of lift,
$T-N-mg=0$........(ii)
Solving (i) and (ii), we obtain
$T=\frac{(M+m)g}{2}$ and $N=\frac{(M-m)g}{2}$