What is the total force on the bottom of a swimming pool 20.5 m by 8.0 m whose uniform depth is 2.1 m?
density of water = 1000 kg/m^2
weight of water in pool = 1000 * 9.8*volume
= 1000 * 9.8 * 20.5 * 8 * 2.1 Newtons
To find the total force on the bottom of the swimming pool, we'll need to calculate the pressure exerted by the water and then multiply it by the area of the bottom.
Step 1: Calculate the pressure exerted by the water
Pressure (P) is defined as force (F) per unit area (A). In this case, the force is the weight of the water, and the area is the bottom of the pool.
The weight of the water is equal to the mass (m) times the acceleration due to gravity (g). The mass of the water is the density (ρ) multiplied by the volume (V).
The density of water is approximately 1000 kg/m³, and the volume of the water can be calculated by multiplying the area of the base (20.5 m by 8.0 m) by the uniform depth (2.1 m).
V = A * d
V = (20.5 m * 8.0 m) * 2.1 m
V = 344.4 m³
m = ρ * V
m = 1000 kg/m³ * 344.4 m³
m = 344,400 kg
The weight of the water is given by:
F = m * g
F = 344,400 kg * 9.8 m/s²
F ≈ 3,373,920 N
Now, let's calculate the pressure:
P = F / A
P = 3,373,920 N / (20.5 m * 8.0 m)
P ≈ 20,780 Pa
Step 2: Calculate the total force on the bottom of the pool
To find the total force (F_total), we need to multiply the pressure by the area of the bottom of the pool.
F_total = P * A
F_total = 20,780 Pa * (20.5 m * 8.0 m)
F_total ≈ 3,364,120 N
Therefore, the total force on the bottom of the swimming pool is approximately 3,364,120 Newtons.
To calculate the total force on the bottom of a swimming pool, we need to consider the pressure exerted by the water column above it.
The pressure exerted by a fluid is given by the equation:
Pressure = density × gravity × height
In this case, the fluid is water. The density of water is approximately 1000 kg/m³, and the acceleration due to gravity is approximately 9.8 m/s².
To calculate the force, we need to find the pressure at the bottom of the pool:
Step 1: Calculate the pressure:
Pressure = density × gravity × height
= 1000 kg/m³ × 9.8 m/s² × 2.1 m
Step 2: Calculate the area of the bottom of the pool:
Area = length × width
= 20.5 m × 8.0 m
Step 3: Calculate the force:
Force = Pressure × Area
Now, let's substitute the values and calculate:
Pressure = 1000 kg/m³ × 9.8 m/s² × 2.1 m = 20580 Pa
Area = 20.5 m × 8.0 m = 164 m²
Force = 20580 Pa × 164 m² = 3,376,320 N
Therefore, the total force on the bottom of the swimming pool is 3,376,320 Newtons.