Figure shows a man of mass 60 kg standing on a light weighting machine kept in a box of mass 30 kg. The box is hanging from a pulley fixed to the ceiling through a light rope, the other end of which is held by the man himself. If the man manages to keep the box at rest, what is the weight shown by the machine? What force should he exert on the rope to get his correct weight on the machine?

Explanation

The fixed pulley is taken as frame of reference. The forces on man and box with plank are shown in fig.

The force are as follows:
(a) Weight of the mag=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
Refferring 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=((M+m)g)/(2) and N=((M-m)g)/(2)`.