A large cube (one side measuring 1.0 m) is submerged in water, with the top face of the cube
8.7 m below the surface. Find
a) the force exerted by the water on each face of the cube.
b) the buoyant force on the cube.
top: force=area*weightwater=1*g*densitywater*1^3=1043E6*9.8 Pascals
bottom: force=above+1mwater, twice above.
net force on cube then is bottom-top, directed upward.
Sides: same force at top, times 1.5 to account for average depth being 1.5 meters.
To find the force exerted by the water on each face of the cube, we can use the concept of pressure.
a) The pressure exerted by a fluid at any depth is given by the equation P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the depth.
In this case, the depth is given as 8.7 m, and we are assuming that the density of water is 1000 kg/m^3.
So, the pressure at a depth of 8.7 m is P = (1000 kg/m^3) * (9.8 m/s^2) * (8.7 m) = 85,260 Pa.
The force exerted on each face of the cube can be found by multiplying the pressure by the area of each face, which is (1.0 m)^2 = 1.0 m^2.
So, the force exerted by the water on each face of the cube is F = P * A = 85,260 Pa * 1.0 m^2 = 85,260 N.
b) The buoyant force on the cube can be found by using Archimedes' principle, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
To find the weight of the fluid displaced by the cube, we need to find the volume of the cube submerged in water. Since the cube is completely submerged, the volume of water displaced will be equal to the volume of the cube. The volume of a cube is given by the equation V = (length)^3.
In this case, the length of the cube is 1.0 m, so the volume of the cube is V = (1.0 m)^3 = 1.0 m^3.
The density of water is 1000 kg/m^3, so the weight of the water displaced by the cube is equal to the volume of the water displaced multiplied by its density and acceleration due to gravity, which is W = V * ρ * g = 1.0 m^3 * 1000 kg/m^3 * 9.8 m/s^2 = 9,800 N.
Therefore, the buoyant force on the cube is equal to the weight of the water displaced, which is 9,800 N.