A 60 kg man stands on a spring scale in the lift. At some instant he finds, scale reading has changed from 60 kg to 50 kg for a while and then comes back to the original mark. What should we conclude
Correct Answer :
The lift while in constant motion upwards, is stopped suddenly
Solution :
The correct option is: The lift while in constant motion upwards, is stopped suddenly.
Let us analyze the situation step-by-step using Newton's laws of motion:
1. Understanding the Scale Reading:
A spring scale measures the normal reaction force () exerted by the scale on the person standing on it. The scale is calibrated to display mass in kilograms by dividing the normal force by the acceleration due to gravity ():
When the lift is stationary or moving with a constant velocity (zero acceleration), the normal reaction force is equal to the actual gravitational force acting on the person:
Initially, the man's mass is 60 kg and the scale reads 60 kg, which means the acceleration of the lift is zero.
2. Analyzing the Decrease in Scale Reading:
The scale reading drops from 60 kg to 50 kg. This decrease in apparent weight indicates that the normal reaction force has decreased:
For the normal force to decrease, there must be a net downward acceleration () acting on the lift. According to Newton's second law:
Rearranging for gives:
This confirms that a lower scale reading corresponds to a downward acceleration ().
3. Determining the Motion of the Lift:
A downward acceleration can occur in two scenarios:
- The lift starts moving downwards from rest (speeding up in the downward direction).
- The lift is moving upwards and begins to slow down to a stop (decelerating while moving upwards).
After the temporary drop to 50 kg, the scale reading returns to the original 60 kg mark. This indicates that the acceleration returns to zero. This sequence corresponds to a lift that was initially moving upwards at a constant speed (60 kg reading), decelerated to a stop (50 kg reading during deceleration), and finally came to rest (60 kg reading at rest).
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