First, we need to find the density of the cube:
Density of wood = 600-900 kg/m^3 (approx.)
So, let's assume the density of the cube is 750 kg/m^3 (approx.), which is close to the middle of the density range for wood.
The volume of the cube = (side length)^3 = (15cm)^3 = 3375 cm^3 = 0.003375 m^3
The mass of the cube = Density x Volume = 750 kg/m^3 x 0.003375 m^3 = 2.53125 kg (approx.)
Buoyant force = Weight of fluid displaced = Density of fluid x Volume of fluid displaced x g
Volume of fluid displaced = Area of lower face x Depth submerged = (15cm x 15cm) x 0.05m = 0.1125 m^3
Buoyant force = 800 kg/m^3 x 0.1125 m^3 x 9.81 m/s^2 = 882 N
Now, let's find the pressure at the lower and upper face of the block:
Lower face:
Pressure at lower face = Pressure of oil at 5cm below interface + Weight of cube / Area of lower face
Pressure of oil at 5cm below interface = Density of oil x g x depth = 800 kg/m^3 x 9.81 m/s^2 x 0.05 m = 392.4 Pa
Weight of cube = mass of cube x g = 2.53125 kg x 9.81 m/s^2 = 24.85 N
Area of lower face = (15 cm)^2 = 0.0225 m^2
Pressure at lower face = 392.4 Pa + 24.85 N / 0.0225 m^2 = 1416.6 Pa
Force on lower face = Pressure x Area of lower face = 1416.6 Pa x 0.0225 m^2 = 31.87 N
Upper face:
Pressure at upper face = Pressure at lower face + Density of cube x g x depth
Depth = height of cube + depth submerged = 15 cm + 5 cm = 0.2 m
Pressure at upper face = 1416.6 Pa + 750 kg/m^3 x 9.81 m/s^2 x 0.2 m = 3941.1 Pa
Force on upper face = Pressure x Area of upper face = 3941.1 Pa x 0.0225 m^2 = 88.68 N
Therefore, the gauge pressure at the lower face of the block is 1416.6 Pa and at the upper face is 3941.1 Pa. The fluid exerts a force of 31.87 N and 88.68 N respectively at these points. The buoyant force on the block is 882 N. The mass and density of the cube are 2.53125 kg (approx.) and 750 kg/m^3 (approx.) respectively.
A cube with a side length of 15cm is made of wood. It floats at the interface between oil (p = 800kg/m^3) and water with its lower surface 5cm below the interface. What is the gauge pressure at the lower and upper face of the block? What force does the fluid exert at these points? What is the bouyant force on the block? What is the mass and density of the block?
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