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 force exerted by the man on the plank.

Answer 1

The fixed pulley is taken as frame of reference. the forces on man and box with plank are shown in the figure. The forces are as follows:
$i$. Weight of the man $=mg$
$ii$. The tension in the string $=T$.
$iii$. The normal contact force between the man and the plank $=N$.
$iv$. The weight of the plank and box $=mg$
Referring to figure. The equation of motion of the man is given as
$T+N-Mg=Ma$
since $M>m$ and the box remains at rest, the man will have to be at rest
$T+N-Mg=0$ ...$\left(1\right)$
similarly referring to figure,
$T-N-mg=ma=0$ ...$\left(2\right)$
Solving $\left(1\right)$ and $\left(2\right)$ we obtain,
$T=\frac{(m+m)g}{2}$ and $N=\frac{(M-m)g}{2}$