A swimming pool measures 10m x 7m x2m. Calculate the total force exerted by the water against the bottom.
Force = Pressure * Area
Pressure = density * height
density of water is 1 g/cm3, so pressure at a depth of 2m is
200cm * 1 g/cm3 = 200g/cm2
Convert mass to weight, and multiply by the area
To calculate the total force exerted by the water against the bottom of the swimming pool, we need to determine the pressure exerted by the water and then multiply it by the area of the bottom.
Step 1: Determine the pressure exerted by the water.
Pressure (P) is defined as the force (F) exerted per unit area (A). Mathematically, it can be expressed as P = F/A.
In this case, we want to find the force, so we rearrange the equation to F = P x A.
Step 2: Calculate the area of the bottom.
The area (A) of the bottom can be calculated by multiplying the length (L) and width (W) of the swimming pool.
A = L x W
In this case, the length is 10m and the width is 7m, so the area of the bottom is A = 10m x 7m = 70m².
Step 3: Calculate the pressure exerted by the water.
To find the pressure exerted by the water, we need to consider the depth (D) of the water and the density (ρ) of water. Pressure can be expressed as P = ρ x g x D, where g is the acceleration due to gravity (approximately 9.8 m/s²) and ρ is the density of water (approximately 1000 kg/m³).
In this case, the depth is 2m, so the pressure exerted by the water is P = 1000 kg/m³ x 9.8 m/s² x 2m = 19600 N/m².
Step 4: Calculate the total force exerted by the water.
Now that we know the pressure exerted by the water (19600 N/m²) and the area of the bottom (70m²), we can substitute these values into the equation F = P x A.
F = 19600 N/m² x 70m²
By multiplying these values, we get the total force exerted by the water against the bottom of the swimming pool.