A man of mass 60kg standing on a light weighing machine kept in a box of mass 30kg. The box is hanging from a pulley fixed to the ceiling through a light rope and the other end held by man. If the man manages to keep the box at rest, what is the weight shown by the weighing machine? What force should he exert on the rope to get his correct weight on machine?
Answers
Answer:
Let the tension force be T in the rope. The downward forces acting on the system of the man and the box are the weight of the man and the weight of the box. The upward forces are T and T on each side of the rope.
As the system is in a static equilibrium:
T+T=(60+30)g
=>T=45kgf or 45g Newtons=450N if g=10m/s
2
The forces acting on the man are: Tension T, reaction from the weighing machine, and weight 60 g. So,
Normal−reaction of the weighing machine =60−T=15kgf.
(i) The weighing machine shows its normal reaction force as the weight of the person standing on it. So weight displayed =15kg.
(ii) Suppose the man pulls down the rope with a force F and the tension becomes T.
The forces acting downwards on the rope at the two ends are: F, weights of man and the box. The upward forces are Tension T on each side of rope.
The system being in equilibrium:2T=F+60kgf+30kgf=F+90kgf
=>T=45kgf+F/2
=> Normal reaction force from the weighing machine on the man
N=60+F−T=15kgf+F/2
If N is to become 60kgf, then F has to be 90kgf or 900N