Answer :
Final answer:
The time it would take for 1.0 mg of dust to accumulate on an 8cm diameter scale from polluted air with a deposit rate of 10 tons per square mile per month is approximately 41 hours.
Explanation:
The problem essentially challenges us to convert a pollution deposit rate from tonnage per square mile per month into milligrams on a small circular scale in hours. To begin, we should understand the deposit rate is given as 10 tons per square mile per month. A ton is 2000 pounds, and given that 1 pound is approximately 453592.37 milligrams (mg), therefore, a ton is approximately 907184740 mg.
In a month (assume 30 days), the deposit over one square mile is thus 9071847400 mg. If we convert a square mile to square centimeters (1 square mile = 2.59 * 10^10 cm^2), we derived that the dust accumulation rate is approximately 0.35 mg per cm^2 per month.
Considering that the area of the analytic balance’s pan, which is circular and 8.00 cm in diameter, gives an approximate area of 50.27 cm^2. Thus, the monthly accumulation of dust on the balance is approximately 17.67 mg. From here, if we want to calculate the time for 1.0 mg of dust to accumulate, it will take approximately 0.057 of a month or approximately 41 hours.
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