A swimming pool has dimensions 26 m x 32 m and a flat bottom. When the pool is filled to a depth of 3 m with fresh water, what is the total force due to the water on the bottom?
density = 1000 kg/m^3
volume = 26 * 32 * 3 = 2496 m^3
so mass = 2.496*10^6 kg
so weight = 9.81*mass = 24.486 *10^6 N
= 2.45*10^7 N
To find the total force due to the water on the bottom of the swimming pool, we need to calculate the pressure exerted by the water and then multiply it by the area of the bottom of the pool.
First, let's calculate the pressure exerted by the water:
Pressure (P) = Density (ρ) × Gravity (g) × Depth (h)
The density of fresh water is approximately 1000 kg/m³, and the acceleration due to gravity is 9.8 m/s². The depth of the pool is 3 m.
P = 1000 kg/m³ × 9.8 m/s² × 3 m
P = 29400 Pa (Pascal)
Now, let's calculate the area of the bottom of the pool:
Area (A) = Length (L) × Width (W)
The length of the pool is 26 m, and the width is 32 m.
A = 26 m × 32 m
A = 832 m²
Finally, to find the total force on the bottom of the pool, we multiply the pressure by the area:
Force (F) = Pressure (P) × Area (A)
F = 29400 Pa × 832 m²
F = 24412800 N (Newton)
Therefore, the total force due to the water on the bottom of the pool is approximately 24,412,800 Newtons.