a) find the total force on the bottom of a cylinder gasoline storage tank 15.0 m high with radius 23.0 m. b) find the total force on the side of a tank.
a) The total force on the bottom of the cylinder gasoline storage tank is equal to the weight of the tank, which is equal to the volume of the tank multiplied by the density of gasoline and the acceleration due to gravity.
Total force = Volume of tank x Density of gasoline x Acceleration due to gravity
Total force = (π x (23.0 m)2 x 15.0 m) x (0.7 kg/L) x (9.8 m/s2)
Total force = 1.2 x 106 N
b) The total force on the side of the tank is equal to the pressure of the gasoline multiplied by the area of the side of the tank.
Total force = Pressure of gasoline x Area of side of tank
Total force = (1.0 x 105 Pa) x (2π x 23.0 m x 15.0 m)
Total force = 6.9 x 106 N
a) To find the total force on the bottom of the cylinder gasoline storage tank, you need to calculate the pressure at the bottom and multiply it by the area of the bottom surface.
Step 1: Calculate the pressure at the bottom
The pressure at the bottom of a liquid column can be calculated using the formula:
Pressure = Density x Gravitational acceleration x Height
Given:
Density (ρ) = density of gasoline = 750 kg/m^3 (approximate value)
Gravitational acceleration (g) = 9.8 m/s^2 (standard value)
Height (h) = 15.0 m
Plugging in the values:
Pressure = 750 kg/m^3 x 9.8 m/s^2 x 15.0 m
Step 2: Calculate the area of the bottom surface
The area of the bottom surface of a cylinder can be calculated using the formula:
Area = π x Radius^2
Given:
Radius (r) = 23.0 m
Plugging in the values:
Area = π x (23.0 m)^2
Step 3: Multiply the pressure by the area to find the total force on the bottom
Total force = Pressure x Area
You can now calculate the total force on the bottom of the cylinder gasoline storage tank by multiplying the pressure at the bottom by the area of the bottom surface.
b) To find the total force on the side of the tank, you need to calculate the pressure along the height of the tank and multiply it by the surface area of the side.
Let's go step by step to calculate the total force on the side of the tank.
Step 1: Calculate the pressure along the height of the tank
The pressure at any point along the height can be calculated using the formula:
Pressure = Density x Gravitational acceleration x Height
Given:
Density (ρ) = density of gasoline = 750 kg/m^3 (approximate value)
Gravitational acceleration (g) = 9.8 m/s^2 (standard value)
Height (h) = 15.0 m
Plugging in the values:
Pressure = 750 kg/m^3 x 9.8 m/s^2 x (height of the point along the side)
Step 2: Calculate the surface area of the side of the tank
The surface area of the side of a cylinder is given by the formula:
Area = 2π x Radius x Height
Given:
Radius (r) = 23.0 m
Height (h) = 15.0 m
Plugging in the values:
Area = 2π x 23.0 m x 15.0 m
Step 3: Multiply the pressure by the surface area to find the total force on the side
Total force = Pressure x Area
You can now calculate the total force on the side of the cylinder gasoline storage tank by multiplying the pressure along the height by the surface area of the side.
To find the total force on the bottom and side of a cylindrical gasoline storage tank, we need to understand the basic principles of pressure and how it is related to force.
a) Total force on the bottom of the tank:
The force exerted on the bottom of the tank is the weight of the gasoline above it. We can calculate this force using the formula:
Force = Pressure × Area
For our calculation, we need to find the pressure at the bottom and the area of the bottom surface.
1. Calculate the pressure at the bottom:
Pressure (P) = Density × Gravity × Height
The density of gasoline is approximately 720 kg/m³, and gravity is 9.8 m/s².
So, P = 720 kg/m³ × 9.8 m/s² × 15.0 m
2. Calculate the area of the bottom surface:
Area (A) = π × Radius²
Radius (r) = 23.0 m
Now, we can calculate the force:
Force = Pressure × Area
b) Total force on the side of the tank:
The force exerted on the side of the tank is due to the pressure of the gasoline acting on the vertical wall.
The force per unit area acting on the side of the tank results from the hydrostatic pressure.
We can calculate this force using the formula:
Force = Pressure × Area
For our calculation, we need to find the pressure on the side and the area of the side surface.
1. Calculate the pressure on the side:
Pressure (P) = Density × Gravity × Height
Using the same density and gravity values as before and considering the height of the tank, P = 720 kg/m³ × 9.8 m/s² × 15.0 m
2. Calculate the area of the side surface:
Area (A) = Circumference × Height
Circumference = 2 × π × Radius
Now, we can calculate the force:
Force = Pressure × Area
By following these steps and plugging in the given values, you can find the total force on the bottom and side of the cylinder gasoline storage tank.