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
(a) If an underwater vehicle were to explore such a depth, what force would the water exert on the vehicle's observation window (radius = 0.14 m)?
(b) For comparison, determine the weight of a jetliner whose mass is 1.4 105 kg.
(a) force = (window area) x (pressure)
The pressure is
P = (water density)*g*(depth)
(b) jetliner weight = M g
Do the numbers
To find the force exerted on the observation window of an underwater vehicle exploring the Mariana trench, we need to first calculate the pressure at that depth using the formula:
Pressure = Density x Gravity x Depth
Let's calculate it step by step:
(a) Force exerted on the observation window:
1. Calculate the pressure at the given depth:
Pressure = Density x Gravity x Depth
where:
Density = 1025 kg/m^3 (density of seawater)
Gravity = 9.8 m/s^2 (acceleration due to gravity)
Depth = 10300 m (depth of the Mariana trench)
Plugging in the values:
Pressure = 1025 kg/m^3 x 9.8 m/s^2 x 10300 m
Pressure = 1.0185 x 10^8 Pa (Pascals)
2. Calculate the force using the formula:
Force = Pressure x Area
where:
Area = π x (radius)^2
Given: radius = 0.14 m
Plugging in the values:
Area = π x (0.14 m)^2
Area = 0.0616 m^2
Force = (1.0185 x 10^8 Pa) x (0.0616 m^2)
Force = 6.28 x 10^6 N (Newtons)
So, the water would exert a force of approximately 6.28 x 10^6 Newtons on the vehicle's observation window.
(b) Weight of a jetliner:
To determine the weight of a jetliner, we can use the formula:
Weight = Mass x Gravity
where:
Mass = 1.4 x 10^5 kg (mass of the jetliner)
Gravity = 9.8 m/s^2 (acceleration due to gravity)
Plugging in the values:
Weight = (1.4 x 10^5 kg) x (9.8 m/s^2)
Weight = 1.372 x 10^6 N (Newtons)
Therefore, the weight of the jetliner is approximately 1.372 x 10^6 Newtons.