Grade 12th passMechanics
With what force should the man pull the string so that weighing machine shows his actual weight?
With what force should the man pull the string so that weighing machine shows his actual weight?
1 Answer
Arun
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 = 45 kg f or 45 g Newtons = 450 N if g = 10m/s^2
T + T = (60 + 30) g
=> T = 45 kg f or 45 g Newtons = 450 N 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 = 15 kg f.
Normal reaction of the weighing machine = 60 - T = 15 kg f.
(i) The weighing machine shows its normal reaction force as the weight of the person standing on it. So weight displayed = 15 kg.
(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 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: 2 T = F + 60 kg f + 30 kg f = F + 90 kg f
=> T = 45 kg f + F/2
=> Normal reaction force from the weighing machine on the man
N = 60 + F - T = 15 kg f + F/2
=> T = 45 kg f + F/2
=> Normal reaction force from the weighing machine on the man
N = 60 + F - T = 15 kg f + F/2
If N is to become 60 kg f, then F has to be 90 kg f or 900 Newtons
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