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 the force exerted by the man on the plank.

Explanation

The fixed pulley is taken as frame of reference. The forces on man and box with plank are shown in 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 gt m` and the box remains at rest, the man will have to be at rest
`T+N-Mg=0 " " ...(1)`
Similarly referring to figure,
`T-N-mg=ma=0" " ...(2)`
Solving (1) and (2) we obtain,
`T=((M+m)g)/(2) and N=((M-m)g)/(2)`