The Mariana trench is located in the Pacific Ocean at a depth of about 11500 m below the surface of the water. The density of seawater is 1025 kg/m3.
(a) If an underwater vehicle were to explore such a depth, what force would the water exert on the vehicle's observation window (radius = 0.10 m)?
(b) For comparison, determine the weight of a jetliner whose mass is 1.1 105 kg.
Pressure = (density) x (acceleration of gravity) x (depth)
Multiply the pressure by the window area to get the force.
The jetliner mass should be written 1.1x10^5 kg
. Multipy that by g for the weight
I appreciate all of your help.
(a) To calculate the force exerted on the vehicle's observation window, we can use the formula:
Pressure = density × acceleration of gravity × depth
Given:
Density of seawater (ρ) = 1025 kg/m^3
Depth (h) = 11500 m
Acceleration due to gravity (g) = 9.8 m/s^2
Radius of the observation window (r) = 0.10 m
First, let's calculate the pressure at that depth using the given formula:
Pressure = ρ × g × h
Substituting the values, we get:
Pressure = 1025 kg/m^3 × 9.8 m/s^2 × 11500 m
Now, we can calculate the force exerted on the observation window by multiplying the pressure by the area of the window. The area of the window can be calculated using the formula:
Area = π × r^2
Substituting the values, we get:
Area = π × (0.10 m)^2
Finally, we can calculate the force using the formula:
Force = Pressure × Area
Substituting the values, we can calculate the force exerted on the vehicle's observation window.
(b) To determine the weight of the jetliner, we can use the formula:
Weight = mass × acceleration due to gravity
Given:
Mass of the jetliner (m) = 1.1 × 10^5 kg
Acceleration due to gravity (g) = 9.8 m/s^2
Substituting the values, we can calculate the weight of the jetliner using the formula:
Weight = (1.1 × 10^5 kg) × (9.8 m/s^2)
By multiplying the mass of the jetliner by the acceleration due to gravity, we can determine its weight.
(a) To find the force exerted on the vehicle's observation window at a depth of 11500 m, we can use the formula:
Pressure = density x acceleration due to gravity x depth
Given:
Density of seawater (ρ) = 1025 kg/m^3
Depth (h) = 11500 m
Radius of the observation window (r) = 0.10 m
Using the formula for pressure, we have:
Pressure = ρ x g x h
where g is the acceleration due to gravity.
Plugging in the given values:
Pressure = 1025 kg/m^3 x 9.8 m/s^2 x 11500 m
Pressure = 1.19 x 10^8 N/m^2
Now, to find the force exerted on the observation window, we need to multiply the pressure by the area of the window. The area of a circular window is given by:
Area = π x r^2
where π is a constant (approximately 3.14) and r is the radius.
Plugging in the given radius:
Area = 3.14 x (0.10 m)^2
Area = 0.0314 m^2
The force exerted on the observation window is:
Force = Pressure x Area
Force = 1.19 x 10^8 N/m^2 x 0.0314 m^2
To find the numerical value, multiply these two values:
Force = 3.74 x 10^6 N
Therefore, the water would exert a force of approximately 3.74 x 10^6 Newtons on the vehicle's observation window.
(b) To find the weight of the jetliner, we can use the formula:
Weight = mass x acceleration due to gravity
Given:
Mass of the jetliner (m) = 1.1 x 10^5 kg
Using the formula for weight, we have:
Weight = mass x g
Weight = 1.1 x 10^5 kg x 9.8 m/s^2
To find the numerical value, multiply these two values:
Weight = 1.08 x 10^6 N
Therefore, the weight of the jetliner is approximately 1.08 x 10^6 Newtons.