What is the total force on the bottom of a swimming pool 27.5m by 9.0m whose uniform depth is 1.9m? physics
What is the absolute pressure on the bottom of a swimming pool?
What will be the pressure against the side of the pool near the bottom?
Use the equation Pfluid=Density x height x gravity
(1000)(1.9)(9.8)=18,620
The TOTAL absolute pressure on the bottom and against the sides of the swimming pool is 18,620 + 1.01x10^5 = 119,620 Pa
Use the equation Pressure = Force/Area
Rearrange the equation to Force = Pressure x Area.
So, Force = 119,620 / (27.5x9) Which equals 29,605,950N.
FINALLY. this^^ is correct.
To find the total force on the bottom of the swimming pool, you can use the formula:
Force = Pressure * Area
First, let's find the pressure on the bottom of the pool:
The pressure at a certain depth in a fluid is given by Pascal's law, which states that the pressure at a depth is equal to the atmospheric pressure plus the pressure due to the weight of the fluid above it.
The atmospheric pressure is usually around 101.3 kPa (kiloPascals) or 101,300 Pa (Pascals).
The pressure due to the weight of the fluid can be calculated using the formula:
Pressure = Density * Gravity * Depth
Where:
- Density is the density of the fluid (water in this case), which is approximately 1000 kg/m³.
- Gravity is the acceleration due to gravity, which is approximately 9.8 m/s².
- Depth is the depth of the fluid (in this case, the uniform depth of the swimming pool), which is 1.9 m.
Let's calculate the pressure at the bottom of the swimming pool:
Pressure = Density * Gravity * Depth
= 1000 kg/m³ * 9.8 m/s² * 1.9 m
≈ 18,620 Pascals (Pa)
Now, to find the total force on the bottom of the swimming pool, we need to calculate the area of the bottom:
Area = Length * Width
= 27.5 m * 9.0 m
= 247.5 square meters (m²)
Finally, we can calculate the total force on the bottom of the swimming pool by multiplying the pressure by the area:
Force = Pressure * Area
= 18,620 Pa * 247.5 m²
≈ 4,608,150 N (Newtons)
Therefore, the total force on the bottom of the swimming pool is approximately 4,608,150 Newtons (N).
Now, let's move on to the next question:
To find the absolute pressure on the bottom of the swimming pool, we can use the same formula as before:
Pressure = Atmospheric pressure + Pressure due to the weight of the fluid
Using the same atmospheric pressure of 101,300 Pa and the pressure due to the weight of the fluid calculated earlier (18,620 Pa), we can add them together:
Absolute Pressure = 101,300 Pa + 18,620 Pa
= 119,920 Pa
Therefore, the absolute pressure on the bottom of the swimming pool is approximately 119,920 Pascals (Pa).
Finally, let's move on to the last question:
To find the pressure against the side of the pool near the bottom, we need to consider the hydrostatic pressure. The hydrostatic pressure is given by the formula:
Pressure = Density * Gravity * Depth
Using the same values as before:
- Density of water is approximately 1000 kg/m³
- Acceleration due to gravity is approximately 9.8 m/s²
- Depth near the bottom is 1.9 m
Pressure = 1000 kg/m³ * 9.8 m/s² * 1.9 m
≈ 18,620 Pa
Therefore, the pressure against the side of the pool near the bottom is approximately 18,620 Pascals (Pa).
To determine the total force on the bottom of a swimming pool with given dimensions, you can use the formula for pressure:
Pressure = Force / Area
First, we can calculate the area of the bottom of the swimming pool:
Area = Length * Width
Area = 27.5m * 9.0m
Area = 247.5m²
To find the total force on the bottom of the pool, you need to multiply the pressure by the area:
Force = Pressure * Area
However, you haven't provided the pressure, so I cannot calculate the exact force. Please provide the pressure value, and I'll be able to assist you with the calculation.
Moving on to the second question, the absolute pressure on the bottom of the swimming pool can be found using the formula:
Pressure = Density * Gravity * Depth
In this case, the density of water and gravity are constant values. The depth of the pool is given as 1.9m. By plugging in these values into the formula, you can calculate the pressure on the bottom of the pool.
Lastly, to determine the pressure against the side of the pool near the bottom, you can consider the hydrostatic pressure. Hydrostatic pressure is defined as:
Pressure = Density * Gravity * Height
The height in this case would be the depth of the pool. So, the pressure against the side of the pool near the bottom is the same as the pressure on the bottom of the pool, which can be calculated using the formula mentioned earlier.