Apparent weight in a lift refers to the perceived weight of an object or person inside a lift, which can change depending on the lift’s motion. This is an interesting situation. Numerical problems on this concept is usually asked in different exams. This topic is explained here so that you can answer these questions quickly.
The Concept
Understand this first: When a person of mass ‘m’ stands on a weighing machine, the weighing machine exerts a reaction ‘R’ on the person. This reaction ‘R’ determines the reading of the weighing machine.
Now let’s consider that a person of mass ‘m’ is standing on a weighing machine placed on the floor of a lift.
The forces acting on the person are:
– weight ‘mg’ acting downwards
– Reaction ‘R’ acting upwards
Case 1: The lift is stationary or moving up/down with uniform speed:
In this case, Net force on the person = 0
=> R – mg = 0
=> R = mg
So, the machine will show the actual weight of the person, since it shows the value of ‘R’.
Case 2: The lift is accelerating upwards with acceleration ‘a’.
In this case, the Net force on the person = ma
=> R – mg = ma
=> R = mg + ma
=> R = m ( g + a)
Remember, this ‘R’ determines the reading of the machine. So, the reading will be more than the actual weight of the person. Hence, apparent weight of a person becomes more in a lift accelerating upwards.
Case 3: The lift is accelerating downwards with acceleration ‘a’.
In this case, the Net force on the person = ma
=> mg – R = ma
=> R = mg – ma
=> R = m ( g – a)
Remember, this ‘R’ determines the reading of the machine. So, the reading will be less than the actual weight of the person. Hence, apparent weight of a person becomes less in a lift accelerating downwards.
Case 4: If the lift is in free fall:
In this case, acceleration of the person is also ‘g’. Means, in the above equation ‘a’ is equal to ‘g’. Hence, (g-a) is zero, meaning R is zero.
Hence, the apparent weight of the person will become zero.
Case 5: If downward acceleration is greater than ‘g’:
Then the person will rise from the floor of the lift and stick to the ceiling of the lift.