Final answer:
The buoyancy force on the submarine is approximately 21,139,326 Newtons.
To calculate the buoyancy force on the submarine, we need to determine the volume of the submarine and use Archimedes' principle. The volume of a cylinder is calculated using the formula V = πr^2h, where r is the radius and h is the height. The buoyant force is equal to the weight of the water displaced by the submarine.
Step-by-step explanation:
To calculate the buoyancy force on the submarine, we need to first determine the volume of the submarine and then use Archimedes' principle.
The volume of a cylinder is calculated using the formula V = πr^2h, where r is the radius and h is the height (or length in this case) of the cylinder.
Given that the radius (r) of the submarine is 13.0 m and the length (h) is 115.0 m, we can calculate the volume:
V = π(13.0)^2(115.0)
= 67230π m^3
Using Archimedes' principle, the buoyant force is equal to the weight of the water displaced by the submerged submarine.
The weight of the water displaced can be calculated using the formula F = ρgV, where ρ is the density of the water and g is the acceleration due to gravity.
Given that the density of seawater is 1.020 times the density of fresh water (ρ = 1000 kg/m^3), and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the buoyant force:
F = (1.020)(1000 kg/m^3)(9.8 m/s^2)(67230π m^3)
Using the value of π as approximately 3.14, we can simplify the equation:
F ≈ 21,139,326 N
Therefore, the buoyancy force on the submarine is approximately 21,139,326 Newtons.