Answer :
Final answer:
The girl experiences an acceleration of -3.24 m/s² as the elevator begins to move. The negative sign indicates a downward acceleration.
Explanation:
In physics, the force that the scale reads is essentially a measure of the girl's weight in the elevator. As the elevator begins to ascend, the scale reads her apparent weight which includes both her mass and the force of the elevator moving upward, giving us a reading of 339 N.
Therefore, to find the acceleration, we first identify the force of gravity on the girl which is her mass times gravitational acceleration (9.8 m/s²).
Thus,
51.7 kg * 9.8 m/s² = 506.66 N.
As the apparent weight (339 N) is less than the weight due to gravity (506.66 N), we know the elevator is accelerating downward. We can use Newton's second law, Fnet = ma, to find this acceleration.
The net force (Fnet) is the difference between the girl's weight and the scale reading:
506.66 N - 339 N = 167.66 N.
Dividing this by the girl's mass gives us the acceleration:
167.66 N / 51.7 kg = 3.24 m/s² downward (indicated as '-3.24 m/s²' to show the downward direction)
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