Answer :
Final answer:
The person's apparent decrease in weight in the elevator indicates that the elevator is accelerating downward. By applying Newton's second law, and using the known weight of the person, we calculate the magnitude of the elevator's acceleration to be 1.3 m/s² downward.
Explanation:
The subject of this question is determining the acceleration of an elevator based on the apparent weight of a person inside. This is a classic Physics problem involving Newton's second law of motion.
When a person weighs themselves on solid ground, the force they feel is due to gravity pulling them downwards. This weight force in pounds can be converted to a force in Newtons, the SI unit for force, by multiplying by the conversion factor 4.448. So, on the ground, the actual force on the person is 153 lb * 4.448 N/lb = 680.384 N.
Inside the elevator, the person feels lighter. This means the elevator is accelerating downwards. The apparent weight in the elevator is therefore less than their actual weight. Converting the 133 lb apparent weight, we get 133 lb * 4.448 N/lb = 591.984 N.
Applying Newton's second law, which states F=ma, we can solve for acceleration (a). The net force on the person is the difference between their weight force and the apparent force given by the scale - F= w - Fs. We have F = ma, so rearranging, we get a = F/m. Here, m is mass, which is weight divided by gravitational acceleration (9.8 m/s²), and F is the net force.
When we calculate, (680.384 N - 591.984 N) / (680.384 N/9.8 m/s²) = 1.3 m/s² . Therefore, the magnitude of the elevator's acceleration is 1.3 m/s² downward.
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