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 = 0.201 m)? (b) For comparison, determine the weight of a jetliner whose mass is 3.38 x 105 kg.
Multiply the window area (in m^2) by the pressure (in Pascals), which is (density)*g*(depth).
That will give you the window force in Newtons.
For the airplane weight, use M*g
Two can play this passive agressive thing coward. Aint the info age grand.
To find the force exerted on the observation window of the underwater vehicle in the Mariana Trench, we can use the formula for pressure:
Pressure = Density x Gravity x Depth
where the density of seawater is 1025 kg/m^3 and the depth is 11,000 m.
(a) Calculating the force on the observation window:
To find the force, we need to multiply the pressure by the area of the observation window. The area can be calculated using the formula for the area of a circle:
Area = π x Radius^2
The radius of the observation window is given as 0.201 m.
First, we can calculate the pressure:
Pressure = Density x Gravity x Depth
= 1025 kg/m^3 x 9.8 m/s^2 x 11,000 m
= 1,124,450 N/m^2
Then we can calculate the area:
Area = π x Radius^2
= π x (0.201 m)^2
= 0.1277 m^2
Finally, we can find the force:
Force = Pressure x Area
= 1,124,450 N/m^2 x 0.1277 m^2
≈ 143,677 N
So, the water would exert a force of approximately 143,677 N on the observation window of the underwater vehicle in the Mariana Trench.
(b) Calculating the weight of the jetliner:
The weight of an object is given by the formula:
Weight = Mass x Gravity
where the mass of the jetliner is given as 3.38 x 10^5 kg, and the acceleration due to gravity is approximately 9.8 m/s^2.
Weight = Mass x Gravity
= 3.38 x 10^5 kg x 9.8 m/s^2
= 3.3144 x 10^6 N
Thus, the weight of the jetliner is approximately 3.3144 x 10^6 N.
To answer part (a) of the question, we need to calculate the force exerted by the water on the observation window of the underwater vehicle.
The force exerted by a fluid on an object can be calculated using the formula:
Force = Pressure × Area
where pressure is the pressure exerted by the fluid and area is the area on which the force is acting.
To find the pressure, we can use the formula:
Pressure = Density × Gravity × Depth
where density is the density of the fluid, gravity is the acceleration due to gravity, and depth is the depth at which the object is submerged.
In this case, the density of seawater is given as 1025 kg/m^3, and the depth of the Mariana trench is 11,000 m. The acceleration due to gravity can be approximated as 9.8 m/s^2.
Using these values, we can calculate the pressure:
Pressure = 1025 kg/m^3 × 9.8 m/s^2 × 11,000 m
Now, let's calculate the force exerted on the observation window. We know that the window has a radius of 0.201 m, so the area can be calculated using the formula:
Area = π × radius^2
Plugging this into the formula for force, we have:
Force = Pressure × Area
Now, let's calculate the force exerted by the water on the observation window of the underwater vehicle.
Finally, for part (b) of the question, we need to determine the weight of a jetliner whose mass is given as 3.38 x 10^5 kg.
The weight of an object can be calculated using the formula:
Weight = Mass × Gravity
where mass is the mass of the object and gravity is the acceleration due to gravity.
Using the given mass of 3.38 x 10^5 kg and an approximate value of 9.8 m/s^2 for the acceleration due to gravity, we can calculate the weight of the jetliner:
Weight = 3.38 x 10^5 kg × 9.8 m/s^2
Now, let's calculate the weight of the jetliner.