On august 12, 2000, the russian submarine kursk sank to the bottom of the sea, 350 feet below the surface
a) find the force on a 6 foot square metal sheet held horizontally at the depth of the kursk.
b) find the force on a 6 foot square metal sheet held vertically at the depth of the kursk. (the bottom of the sheet is at a depth of 350 feet.)

A) The answer is 3,596,866.62 N

Step 1. Calculate the water pressure at the bottom of the ocean where the Kursk sank because: Force (F) = Pressure (P) * Area (A). P = ?
Step 2. Calculate the area (A) of a 6 foot square metal sheet: A = ?
Step 3. Calculate the force on a 6 foot square metal sheet held horizontally at the depth of the Kursk: F = ?

Step 1. The water pressure at the bottom of the ocean is:
P = ρ * g * h
ρ - the density of the sea water: ρ = 1,027 kg/m³
g - the gravitational acceleration: g = 9.8 m/s²
h - the height: h = 350 ft = 106.68 m
P = 1,027 * 9.8 * 106.68 = 1,073,691.53 kg/m*s²

Step 2. The area of a 6 foot square metal sheet is:
A = s²
s - the side of the square: s = 6 ft = 1.83 m
A = (1.83 m)² = 3.35 m²

Step 3. The force on a 6 foot square metal sheet held horizontally at the depth of the Kursk is:
F = P * A
P = 1,073,691.53 kg/m*s²
A = 3.35 m²
F = 1,073,691.53 kg/m*s² * 3.35 m² = 3,596,866.62 N

b) The answer is 3,535,165.59 N.

Step 1. Calculate the water pressure at the bottom of the ocean where the Kursk sank because: Force (F) = Pressure (P) * Area (A). P = ?
Step 2. Calculate the area (A) of a 6 foot square metal sheet: A = ?
Step 3. Calculate the force on a 6 foot square metal sheet held horizontally at the depth of the Kursk: F = ?

Step 1. The water pressure at the bottom of the ocean is:
P = ρ * g * h
ρ - the density of the sea water: ρ = 1,027 kg/m³
g - the gravitational acceleration: g = 9.8 m/s²
h - the height: h = 350 ft - 6 ft = 344 ft (Since it is vertically held, the height of the metal sheet must be subtracted from the total depth)
h = 344 ft = 104.85 m= 104.85 m
P = 1,027 * 9.8 * 104.85 = 1,055,273.31 kg/m*s²

Step 2. The area of a 6 foot square metal sheet is:
A = s²
s - the side of the square: s = 6 ft = 1.83 m
A = (1.83 m)² = 3.35 m²

Step 3. The force on a 6 foot square metal sheet held horizontally at the depth of the Kursk is:
F = P * A
P = 1,055,273.31 kg/m*s²
A = 3.35 m²
F = 1,055,273.31 kg/m*s² * 3.35 m² = 3,535,165.59 N