The atmospheric pressure above a swimming pool changes from 755 to 765mm of mercury. The bottom of the pool is a 12m x 24m rectangle. By how much does the force on the bottom of the pool increase?
To calculate the force on the bottom of the pool, we need to first calculate the area of the bottom:
Area = length x width = 12m x 24m = 288m²
Next, we need to calculate the change in pressure:
ΔP = P2 - P1 = 765mmHg - 755mmHg = 10mmHg
We convert the pressure to SI units (Pascals) for the calculation:
1mmHg = 133.322 Pa
ΔP = 10mmHg x 133.322 Pa/mmHg = 1333.22 Pa
Finally, we can calculate the increase in force using the formula:
Force = pressure x area
ΔF = ΔP x Area = 1333.22 Pa x 288m² = 384057.6 N
Therefore, the force on the bottom of the pool increased by approximately 384058 N.
To find the increase in force on the bottom of the pool, we can use the equation:
Force = Pressure × Area
First, let's calculate the initial force on the bottom of the pool:
Pressure (initial) = 755 mmHg
Area = length × width = 12 m × 24 m = 288 m²
Force (initial) = Pressure (initial) × Area
= 755 mmHg × 288 m²
Next, let's calculate the final force on the bottom of the pool:
Pressure (final) = 765 mmHg
Force (final) = Pressure (final) × Area
= 765 mmHg × 288 m²
Finally, to find the increase in force, we can subtract the initial force from the final force:
Increase in force = Force (final) - Force (initial)
Now you can substitute the values into the equation and calculate the increase in force.