A cube of side length 11.0 cm and made of unknown material floats at the surface between water and oil. The oil has a density of 810 kg/m^3.

a)If the cube floats so that it is 70% in the water and 30% in the oil, what is the mass of the cube?
b)What is the buoyant force on the cube?

To find the mass of the cube, we can use the fact that the cube is 70% in water and 30% in oil.

Step 1: Find the volume of the cube submerged in water.
The volume of the cube submerged in water can be calculated as:
Volume_water = (70/100) * Volume_cube

Step 2: Find the density of water.
The density of water is known to be 1000 kg/m^3.

Step 3: Calculate the mass of the cube submerged in water.
Mass_water = Volume_water * Density_water

Step 4: Find the volume of the cube submerged in oil.
The volume of the cube submerged in oil can be calculated as:
Volume_oil = (30/100) * Volume_cube

Step 5: Find the density of oil.
The density of oil is given to be 810 kg/m^3.

Step 6: Calculate the mass of the cube submerged in oil.
Mass_oil = Volume_oil * Density_oil

Step 7: Calculate the total mass of the cube.
Total_mass = Mass_water + Mass_oil

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To find the buoyant force on the cube, we can use the relationship between buoyant force, displaced volume, and the density of the fluid.

Step 8: Calculate the volume of the cube that is submerged in water.
Volume_submerged = Volume_water

Step 9: Calculate the buoyant force.
Buoyant_force = Density_water * Volume_submerged * gravity

Note: gravity is approximately 9.8 m/s^2.

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Now let's calculate the values step by step:

Step 1: Find the volume of the cube submerged in water.
Volume_water = (70/100) * (11.0 cm)^3

Step 2: Find the density of water.
Density_water = 1000 kg/m^3

Step 3: Calculate the mass of the cube submerged in water.
Mass_water = Volume_water * Density_water

Step 4: Find the volume of the cube submerged in oil.
Volume_oil = (30/100) * (11.0 cm)^3

Step 5: Find the density of oil.
Density_oil = 810 kg/m^3

Step 6: Calculate the mass of the cube submerged in oil.
Mass_oil = Volume_oil * Density_oil

Step 7: Calculate the total mass of the cube.
Total_mass = Mass_water + Mass_oil

Step 8: Calculate the volume of the cube that is submerged in water.
Volume_submerged = Volume_water

Step 9: Calculate the buoyant force.
Buoyant_force = Density_water * Volume_submerged * gravity

Now you can plug in the values and calculate the answers.

To solve these problems, we need to use the concepts of density and buoyant force. The buoyant force is the force exerted on an object when it is immersed in a fluid (in this case, water). It is equal to the weight of the fluid displaced by the object.

a) To find the mass of the cube, we first need to determine the volume that is submerged in water and the volume submerged in oil.

Given that the cube floats so that it is 70% in the water, the submerged volume in water can be calculated as follows:
Volume in water = 0.70 * (side length)^3

Volume in water = 0.70 * (11.0 cm)^3
Volume in water = 0.70 * 1331 cm^3
Volume in water = 931.7 cm^3

Similarly, the submerged volume in oil can be calculated by multiplying the remaining percentage (30%) by the total volume of the cube:
Volume in oil = 0.30 * (side length)^3

Volume in oil = 0.30 * (11.0 cm)^3
Volume in oil = 0.30 * 1331 cm^3
Volume in oil = 399.3 cm^3

Now, we can calculate the mass of the cube by using the densities of water and oil.

Given that the density of oil is 810 kg/m^3, we need to convert the volume of oil to cubic meters:
Volume in oil = 399.3 cm^3 = 0.0003993 m^3

The mass of the cube can be calculated as:
Mass = Volume * Density

Mass = 0.9317 cm^3 * 1000 kg/m^3 (density of water)
+ 0.0003993 m^3 * 810 kg/m^3 (density of oil)

Mass = (0.9317 * 1000 + 0.0003993 * 810) kg
Mass ≈ 931.7 kg + 0.3234 kg
Mass ≈ 932 kg (rounded to the nearest kilogram)

Therefore, the mass of the cube is approximately 932 kg.

b) To find the buoyant force on the cube, we use the formula:
Buoyant force = Weight of the fluid displaced

The weight of the fluid displaced by the cube is equal to the weight of the water displaced, as that is the fluid the cube is submerged in.

The volume of water displaced by the cube is the same as the volume submerged in water:
Volume of water displaced = 931.7 cm^3 = 0.0009317 m^3

Using the density of water (1000 kg/m^3), we can calculate the buoyant force as follows:
Buoyant force = Volume of water displaced * Density of water * Acceleration due to gravity

Buoyant force = 0.0009317 m^3 * 1000 kg/m^3 * 9.8 m/s^2

Buoyant force ≈ 9.126 N

Therefore, the buoyant force on the cube is approximately 9.126 N.

the volume of the cube is 11^3 cc

the mass of the cube is:

11^3x0.7x1 g/cc + 11^3x0.3x0.81 g/cc

bouyant force = mass of cube x g