Question

Solve the following problem.

As I was standing on a weighing machine inside a lift it recorded 50 kg wt. Suddenly for a few seconds, it recorded 45 kg wt. What must have happened during that time? Explain with complete numerical analysis.

Answer 1

The weight recorded by the weighing machine is always apparent weight and a measure of reaction force acting on the person. As the apparent weight (45 kg-wt) in this case is less than actual weight (50 kg-wt) the lift must be accelerated downwards during that time.

Numerical Analysis

1. The weight on the weighing machine inside the lift is recorded as 50 kg - wt
   ∴ mg = 50 kg - wt
   
2. This weight acts on the weighing machine which offers a reaction R given by the reading of the weighing machine
   ∴ R = 45 kg-wt = `9/10` mg
3. The forces acting on the person inside the lift are as follows:
   a. Weight mg downward (exerted by the earth)
   b. Normal reaction (R) upward (exerted by the floor)
4. As, R < mg, the net force is in downward direction and given as,
   mg - R = ma
   But R = `9/10`mg
   ∴ mg - `9/10` mg = ma
   ∴ `"mg"/10 = "ma"`
   ∴ a = g/10
   ∴ a = 1 m/s²      (∵ g = 10 m/s²)
5. Therefore, the elevator must be accelerated downwards with an acceleration of 1 m/s² at that time.