The atmospheric pressure above a swimming pool changes from 755 to 765 mm of mercury.The bottom of the pool is a rectangle (12 m x 24 m). By how much does the force on the bottomof the pool increase?
Question
The atmospheric pressure above a swimming pool changes from 755 to 765 mm of mercury.The bottom of the pool is a rectangle (12 m x 24 m). By how much does the force on the bottomof the pool increase?
Solution
To solve this problem, we need to understand that pressure is force per unit area. Therefore, we can calculate the change in force by multiplying the change in pressure by the area.
Step 1: Calculate the change in pressure The change in pressure is the final pressure minus the initial pressure. In this case, that's 765 mmHg - 755 mmHg = 10 mmHg.
Step 2: Convert the pressure to Pascals 1 mmHg is approximately equal to 133.322 Pascals (Pa). Therefore, the change in pressure is 10 mmHg * 133.322 Pa/mmHg = 1333.22 Pa.
Step 3: Calculate the area of the bottom of the pool The area is length times width. In this case, that's 12 m * 24 m = 288 m^2.
Step 4: Calculate the change in force The change in force is the change in pressure times the area. Therefore, the change in force is 1333.22 Pa * 288 m^2 = 383807.36 Newtons.
So, the force on the bottom of the pool increases by 383807.36 Newtons.
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