21. The Mariana trench is located in the Pacific Ocean at a depth of about 10300 m below the surface of the water. The density of seawater is 1025 kg/m3. If an underwater vehicle were to explore such a depth, what force would the water exert on the vehicle's observation window (radius = 0.13 m)?

Question

21. The Mariana trench is located in the Pacific Ocean at a depth of about 10300 m below the surface of the water. The density of seawater is 1025 kg/m3. If an underwater vehicle were to explore such a depth, what force would the water exert on the vehicle's observation window (radius = 0.13 m)?

Answer 1

p=ρgh+p₀ = 1025•9.8•10300+101325 =103564825 Pa

F=pA=pπr²=103564825•π•0.13²=5.5•10⁶ N

Answer 2

Thank you so much!

Answer 3

To find the force exerted by the water on the vehicle's observation window, we can use the formula:

Force = Pressure x Area

First, let's calculate the pressure at that depth. The pressure in fluids increases with depth and is given by:

Pressure = density x gravity x depth

where,
density = 1025 kg/m³ (density of seawater)
gravity = 9.8 m/s² (acceleration due to gravity)
depth = 10300 m (depth of the Mariana trench)

Plugging in the values, we get:

Pressure = 1025 kg/m³ x 9.8 m/s² x 10300 m

Now, let's calculate the area of the observation window. The area of a circle is given by:

Area = π x radius²

where,
radius = 0.13 m

Plugging in the radius, we get:

Area = π x (0.13 m)²

Now, let's calculate the force:

Force = Pressure x Area

Substituting the calculated values, we get:

Force = (1025 kg/m³ x 9.8 m/s² x 10300 m) x (π x (0.13 m)²)

Evaluating this expression will give us the force exerted by the water on the vehicle's observation window.

Answer 4

To calculate the force exerted by the water on the vehicle's observation window, we need to use the formula for pressure:

Pressure = Density × Acceleration due to gravity × Depth

First, let's find the pressure at the depth of the Mariana Trench.

Given:
Density of seawater (ρ) = 1025 kg/m^3
Depth (h) = 10300 m

The pressure (P) can be calculated as:
P = Density × Acceleration due to gravity × Depth

The acceleration due to gravity is approximately 9.8 m/s^2.

P = 1025 kg/m^3 × 9.8 m/s^2 × 10300 m

Now, let's calculate the force exerted by the water on the observation window.

The force (F) can be calculated using the formula:
F = Pressure × Area

Given:
Radius of the observation window (r) = 0.13 m

Area (A) of the window can be calculated as:
A = π × r^2

Now, let's calculate the force:

A = π × (0.13 m)^2
F = P × A

Once you substitute the values into the equations, you will be able to find the force exerted by the water on the vehicle's observation window.