Apparent Weight of a man in a Lift and Law of Conservation of Momentum

Apparent weight of a man in a lift:
Let a man of mass m is standing on a weighing machine placed in a lift or elevator. The actual weight mg of man acts on weighing machine and it offer a reaction R given by treading of weighing machine.
The reaction R exerted by the surface of contact on the man is apparent weight of the person. The value of R (apparent weight) comes out different in different situation.
i) When the lift moves upwards with acceleration a as shown in figure, the net upward force on the man is R – mg
Therefore R-mg = ma  R = ma + mg
Apparent weight = R = m (g + a)
So, when lift accelerate upwards, apparent weight of the man inside it increases.
ii) When the lift accelerates downwards with acceleration a as shown in figure:
The net downward force on the man is mg -R = ma
The apparent weight, R = m(g-a)
So, when lift accelerate downwards, apparent weight of the man inside it decreases.
iii) When the lift is at rest or moving with constant velocity v (a= 0) downward or upward as shown in figure.
Since, acceleration is zero a = 0, so the net force on the man is
R – mg = mx0
 R = mg
Apparent weight = Actual weight.
So, when lift is at rest or moving with constant velocity, the apparent weight of a man is equal to his actual weight.
Law of conservation of linear Momentum: The total momentum of an isolated system (No external force) remains constant or conserved.

i.e. Total momentum before collision = total momentum after collision.
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