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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.
Solution
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
- The weight on the weighing machine inside the lift is recorded as 50 kg - wt
∴ mg = 50 kg - wt
- 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 - 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) - 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 = 1 m/s2) - Therefore, the elevator must be accelerated downwards with an acceleration of 1 m/s2 at that time.
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