The Mariana trench is located in the Pacific Ocean at a depth of about 11800 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 = 0.12 m)?
N
(b) For comparison, determine the weight of a jetliner whose mass is 1.1 105 kg.
N
To find the force exerted by the water on the vehicle's observation window, we can use the concept of pressure. Pressure is defined as force per unit area.
(a) To calculate the force exerted by the water on the observation window, we need to determine the pressure at that depth, and then multiply it by the area of the observation window.
The pressure at a certain depth in a fluid is given by the equation:
pressure = density × g × depth
where:
density is the density of the fluid (in this case seawater),
g is the acceleration due to gravity, and
depth is the depth below the surface of the water.
Given that the depth of the Mariana Trench is 11800 m and the density of seawater is 1025 kg/m3, we can substitute these values into the equation to find the pressure.
pressure = (1025 kg/m3) × (9.8 m/s2) × (11800 m)
pressure ≈ 1.20 × 107 Pa (Pascal)
Now, we can calculate the force exerted on the observation window using the equation:
force = pressure × area
Given that the radius of the observation window is 0.12 m, we can calculate the area of the window (assuming it's a circular shape):
area = π × (radius)^2
area = π × (0.12 m)^2 ≈ 0.045 m2
Substituting the pressure and area values into the equation, we can find the force exerted by the water on the observation window:
force = (1.20 × 107 Pa) × (0.045 m2)
force ≈ 5.4 × 105 N (Newton)
Therefore, the water would exert a force of approximately 5.4 × 105 N on the vehicle's observation window at a depth of the Mariana Trench.
(b) To determine the weight of a jetliner with a mass of 1.1 × 105 kg, we can use the equation:
weight = mass × gravity
where:
mass is the mass of the jetliner, and
gravity is the acceleration due to gravity.
Given that the mass of the jetliner is 1.1 × 105 kg and the acceleration due to gravity is approximately 9.8 m/s2, we can substitute these values into the equation:
weight = (1.1 × 105 kg) × (9.8 m/s2)
weight ≈ 1.08 × 106 N (Newton)
Therefore, the weight of the jetliner is approximately 1.08 × 106 N.