Final answer:
To calculate the buoyancy force on the submarine, you need to find the volume of the submarine first. Then, you can calculate the weight of the water displaced by the submarine and determine the buoyancy force using the formula W = mg.
Step-by-step explanation:
To calculate the buoyancy force on the submarine, we first need to find the volume of the submarine. The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height. Given that the radius is 13.0 m and the length is 115.0 m, the volume of the submarine is V = π(13.0 m)^2(115.0 m) = 68197.86 m^3.
The buoyancy force acting on the submarine is equal to the weight of the water displaced by the submarine. The weight of the water can be calculated using the formula W = mg, where m is the mass and g is the acceleration due to gravity.
The mass of the water is equal to the volume of the water multiplied by the density of seawater. The density of seawater is 1020 kg/m^3 (since the specific gravity is 1.020).
So the mass of the water is m = (68197.86 m^3)(1020 kg/m^3) = 69697519.2 kg.
Finally, we can calculate the buoyancy force using the formula W = mg, where g is the acceleration due to gravity (approximately 9.8 m/s^2).
Therefore, the buoyancy force on the submarine is W = (69697519.2 kg)(9.8 m/s^2) = 682356046.56 N.