Q5 of 21 Page 109

A man of mass 60 kg is standing on a light weighing 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 he manages to keep the box at rest

(a) What is the weight shown by the machine?


(b) What force should the man exert on the rope to get his correct weight on the machine?


(a) let T is the tension in the rope


M1 = Mass of man = 60 kg


M2 = Mass of the machine = 30 kg


Free body diagram



We consider man and machine together as a mass of (M1 + M2)


When the system is in static equilibrium





Now forces acting on man are also balanced



N = normal reaction = readings of weight on machine





(b) Now the man pulls down the rope with the force F


So, now the free body diagram is



At static equilibrium





Forces acting on the man are







Actual weight of man


So if N = 588N




Thus man must exert a force of 882 N on the rope to get the correct weight on the machine.


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