The Mariana trench is located in the Pacific Ocean at a depth of about 11 000 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 = 0.109 m)? (b) For comparison, determine the weight of a jetliner whose mass is 2.98 x 105 kg.
a= 6190000 N
b= 6313632.7 N
To determine the force exerted on the observation window of an underwater vehicle exploring the Mariana Trench, we can use the formula:
F = P * A
Where:
F = Force exerted by the water
P = Pressure exerted by the water
A = Area of the observation window
(a) To find the force, we first need to calculate the pressure exerted by the water at that depth. The pressure at a depth in a fluid can be determined using the formula:
P = ρ * g * h
Where:
P = Pressure
ρ = Density of the fluid
g = Acceleration due to gravity
h = Depth
Given that the density of seawater is 1025 kg/m^3 and the depth is 11,000 m, and the acceleration due to gravity is approximately 9.8 m/s^2, we can substitute these values into the equation to find the pressure:
P = 1025 kg/m^3 * 9.8 m/s^2 * 11,000 m
Calculating this will give us the pressure exerted by the water at that depth.
(b) To find the weight of a jetliner, we can use the formula:
Weight = mass * g
Given that the mass of the jetliner is 2.98 x 10^5 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can substitute these values into the equation to find the weight.
Using these steps, we can find the answers to both parts of the question.