An in-ground swimming pool has the dimensions 20 m x 15 m. It is filled with water to a uniform depth of 3.00 m.What is the total force exerted on the bottom of the swimming pool?The density of water = 1.00 × 103 kg/m3.
Is there any Answer With this?
Well, let's dive into this question! To calculate the total force exerted on the bottom of the swimming pool, we need to find the weight of the water. To do that, we can use the formula:
Weight = Density x Volume x Gravity
First, let's find the volume of the water in the pool. The pool has a length of 20 m, a width of 15 m, and a depth of 3.00 m, so the volume is:
Volume = Length x Width x Depth
Volume = 20 m x 15 m x 3.00 m
Now, let's calculate the weight of the water. The density of water is given as 1.00 × 103 kg/m3, and the force of gravity is approximately 9.8 m/s2.
Weight = Density x Volume x Gravity
Weight = 1.00 × 103 kg/m3 x (20 m x 15 m x 3.00 m) x 9.8 m/s2
Now, you can put on your swimming goggles and calculate the total force exerted on the bottom of the swimming pool!
To calculate the total force exerted on the bottom of the swimming pool, we can use the formula:
Force = Pressure x Area
Step 1: Calculate the pressure exerted by the water.
To calculate the pressure, we can use the formula:
Pressure = Density x Gravity x Depth
Given:
Density = 1.00 × 103 kg/m3
Gravity = 9.8 m/s2
Depth = 3.00 m
Plugging in the values, we get:
Pressure = (1.00 × 103 kg/m3) x (9.8 m/s2) x (3.00 m)
Pressure = 29,400 Pa (Pascals)
Step 2: Calculate the area of the swimming pool.
The area of the swimming pool can be calculated using the formula:
Area = Length x Width
Given:
Length = 20 m
Width = 15 m
Plugging in the values, we get:
Area = 20 m x 15 m
Area = 300 m2
Step 3: Calculate the total force exerted.
Using the formula:
Force = Pressure x Area
Plugging in the values, we get:
Force = 29,400 Pa x 300 m2
Force = 8,820,000 N (Newtons)
Therefore, the total force exerted on the bottom of the swimming pool is 8,820,000 Newtons.
To find the total force exerted on the bottom of the swimming pool, we need to calculate the weight of the water.
The weight of an object can be calculated using the formula:
Weight = mass x gravitational acceleration
In this case, we need to find the mass of the water first. The formula to calculate the mass of an object is:
Mass = volume x density
The volume of water in the swimming pool can be calculated using the formula:
Volume = length x width x depth
Given that the dimensions of the pool are 20 m x 15 m x 3 m, we can calculate the volume as follows:
Volume = 20 m x 15 m x 3 m = 900 m^3
Now, we can calculate the mass of the water:
Mass = 900 m^3 x 1.00 × 10^3 kg/m^3 = 900,000 kg
Finally, we can calculate the weight of the water:
Weight = Mass x gravitational acceleration
The value of the gravitational acceleration is approximately 9.8 m/s^2.
Weight = 900,000 kg x 9.8 m/s^2 = 8,820,000 N
Therefore, the total force exerted on the bottom of the swimming pool is 8,820,000 Newtons.
consider a column of water 1cm^3 with a height of 300cm. It's weight will be
mass=300g
weight=.3*9.8 Newtons
force at bottom=that weight
total force on bottom of pool=force*area
-.3x9.8x20x15 Newtons