The atmospheric pressure above a swimming pool changes from 771 to 772 mm of mercury. The bottom of the pool is a rectangle (11 m cross 21 m). By how much does the force on the bottom of the pool increase?
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To find the increase in force on the bottom of the pool, we need to consider the change in pressure and the area of the pool.
The change in pressure is given as the difference between the initial and final atmospheric pressures, which is 772 mmHg - 771 mmHg = 1 mmHg.
However, mmHg (millimeters of mercury) is not the standard unit for pressure. We need to convert it to a more commonly used unit such as pascals (Pa).
To convert mmHg to Pa, we use the conversion factor: 1 mmHg = 133.322 Pa.
So, we have 1 mmHg = 133.322 Pa.
Therefore, the change in pressure is 1 mmHg * 133.322 Pa/mmHg = 133.322 Pa.
Now, to calculate the increase in force on the bottom of the pool, we use the formula:
Force = Pressure * Area
The area of the pool is given as the product of its length and width, which is 11 m * 21 m = 231 m^2.
So, the increase in force on the bottom of the pool is:
Force = 133.322 Pa * 231 m^2 = 30,793.382 Pa·m^2.
Therefore, the force on the bottom of the pool increases by approximately 30,793.382 Pa·m^2.