A large aquarium has viewing ports so people can watch dolphins swim by. What is the net force on a rectangular window, 2.30 m wide and 1.20 m high, if the top of the window is 4.50 m below the surface of the water?
Well, water can be quite a pane sometimes! But let's dive into the question. To find the net force on the window, we need to consider the pressure exerted by the water.
Since the pressure in a fluid increases with depth, we'll need to take that into account. The pressure at the top of the window is lower than at the bottom, due to the height difference.
To calculate the net force, we'll use the equation:
Force = Pressure × Area
Now, let's calculate the pressure at the top and bottom of the window.
The pressure at the top is determined by the height from the surface:
Pressure at the top = ρ × g × h1
The pressure at the bottom is determined by the height from the bottom:
Pressure at the bottom = ρ × g × h2
where ρ is the density of water (about 1000 kg/m^3), g is the acceleration due to gravity (9.8 m/s^2), h1 is 4.50 m (distance from the surface to the top of the window), and h2 is 4.50 m plus the window height (5.70 m).
Now, let's calculate the net force by subtracting the pressure at the top from the pressure at the bottom. Then we'll multiply by the area of the window:
Net Force = (Pressure at the bottom - Pressure at the top) × Area
Area = width × height
Plugging in the values and crunching the numbers, we find the net force on the window. Just remember to keep swimming in the right direction with your calculations!
To determine the net force on the rectangular window, we need to consider the pressure difference between the inside and outside of the window.
Step 1: Determine the pressure at the surface of the water:
The pressure at the surface of the water is given by the equation: P = ρgh, where P is the pressure, ρ is the density of water, g is the acceleration due to gravity, and h is the height of the water column.
Using the given information, the height of the water column is 4.50 m. The density of water ρ is approximately 1000 kg/m^3. The acceleration due to gravity g is approximately 9.8 m/s^2.
Calculating the pressure at the surface of the water:
P = (1000 kg/m^3)(9.8 m/s^2)(4.50 m)
P ≈ 44,100 Pa (Pascals)
Step 2: Determine the pressure at the depth of the top of the window:
The pressure at a certain depth is given by the equation: P = ρgh, where P is the pressure, ρ is the density of water, g is the acceleration due to gravity, and h is the depth of the water column.
Using the given information, the depth of the top of the window is 4.50 m.
Calculating the pressure at the depth of the top of the window:
P = (1000 kg/m^3)(9.8 m/s^2)(4.50 m)
P ≈ 44,100 Pa (Pascals)
Step 3: Determine the net force on the window:
The net force on the window is given by the equation: F = P x A, where F is the net force, P is the pressure difference, and A is the area of the window.
Using the given information, the width of the window is 2.30 m and the height of the window is 1.20 m.
Calculating the area of the window:
A = (2.30 m)(1.20 m) = 2.76 m^2
Calculating the net force on the window:
F = (difference in pressure) x (area of the window)
F = (44,100 Pa - 44,100 Pa) x (2.76 m^2)
F = 0 N
Therefore, the net force on the rectangular window is 0 N, meaning there is no net force acting on the window.
To find the net force on the rectangular window, you need to consider the pressure exerted by the water on both the top and bottom sides of the window.
The pressure exerted by a fluid at a given depth can be calculated using the formula:
P = ρgh
Where:
P is the pressure exerted by the fluid (in Pascals, Pa)
ρ is the density of the fluid (in kg/m^3)
g is the acceleration due to gravity (approximately 9.8 m/s^2)
h is the depth of the fluid (in meters)
In this case, the depth of the water is the distance from the top of the window to the surface, which is 4.50 m. The water density can be assumed to be approximately 1000 kg/m^3.
Using the formula, the pressure exerted by the water on the top and bottom sides of the window can be calculated:
P_top = ρgh_top = (1000 kg/m^3)(9.8 m/s^2)(4.50 m) = 44100 Pa
P_bottom = ρgh_bottom = (1000 kg/m^3)(9.8 m/s^2)(4.50 m + 1.20 m) = 58800 Pa
Since pressure is a force per unit area, the net force on the window can be calculated by finding the difference between the pressure on the top side and the pressure on the bottom side, and then multiplying it by the area of the window:
Net force = (P_bottom - P_top) * Area
Where Area = width * height = (2.30 m)(1.20 m) = 2.76 m^2
Plugging the values into the equation:
Net force = (58800 Pa - 44100 Pa) * 2.76 m^2
Net force = 14700 Pa * 2.76 m^2
Net force = 40,572 N
Therefore, the net force on the rectangular window is 40,572 Newtons.
average force on the window is at the 1/2 way point down.
forceon window= (4.5m+1/2 *1.2)*area*densitywater*g
= 5.1m*(2.3*1.2)m^2*1E3kg/m^3*9.8N/kg
Now, that is net force, because above the water one would add atmospheric pressure, but on the inside of the window, one would subtract atmospheric pressure.