A metal cube, 2.00cm on each side, has a density of 6600 kg/m3.
Find its apparent mass when it is totally submerged in water.
The first step is to find the volume of the cube, which is (2.00cm)3 = 8.00 cm3.
Next, we need to convert the density to the same units as the volume, so we divide 6600 kg/m3 by 1,000,000 to get 6.6 g/cm3.
We can use the formula for density to find the mass of the cube:
Density = Mass/Volume
Rearranging, we get:
Mass = Density x Volume
Mass = (6.6 g/cm3) x (8.00 cm3)
Mass = 52.8 g
So the mass of the cube is 52.8 g.
Now we need to find the apparent mass when the cube is submerged in water. The cube will displace a volume of water equal to its own volume, so the apparent mass is:
Apparent mass = Mass of cube + Mass of displaced water
The density of water is 1 g/cm3, so the mass of the displaced water is:
Mass of displaced water = Density of water x Volume of displaced water
Volume of displaced water = Volume of cube = 8.00 cm3
Mass of displaced water = (1 g/cm3) x (8.00 cm3) = 8.00 g
Apparent mass = 52.8 g + 8.00 g = 60.8 g
Therefore, the apparent mass of the cube when it is totally submerged in water is 60.8 g.
To find the apparent mass of the metal cube when it is totally submerged in water, we can use Archimedes' principle.
Archimedes' principle states that when an object is submerged in a fluid, it experiences an upward buoyant force equal to the weight of the displaced fluid.
The first step is to find the volume of the cube. Since it is a cube, we can calculate the volume using the formula:
Volume = (side length)^3
Plugging in the given side length of 2.00 cm:
Volume = (2.00 cm)^3 = 8.00 cm^3
Next, we need to convert the volume to cubic meters since the density is given in kg/m^3. Since 1 m = 100 cm, there are (100 cm)^3 = 1,000,000 cm^3 in 1 m^3. So:
Volume = 8.00 cm^3 × (1 m^3 / 1,000,000 cm^3) = 8.00 × 10^-6 m^3
Now we can calculate the apparent mass using the formula:
Apparent mass = Density × Volume
Plugging in the given density of 6600 kg/m^3 and the calculated volume of 8.00 × 10^-6 m^3:
Apparent mass = 6600 kg/m^3 × 8.00 × 10^-6 m^3
Multiplying the values, we get:
Apparent mass = 0.0528 kg
Therefore, the apparent mass of the metal cube when it is totally submerged in water is 0.0528 kg.