a metal cube of side 2 cm is totally submerged in waterof the density of the object is 5000kg/m^3 find the mass apparent and buoyant force
a. V = S^3 = (2*10^-2)^3 = 8*10^-6 m^3 = vol. of cube = vol. of water disp.
M = V*Do = 8*10^-6 * 5*10^3 = 0.04 kg. = mass of cube.
b. M = V*D = 8*10^-6 * 1000 = 8*10^-3 kg. = mass of water disp.
Buoyant force = M*g = 8*10^-3 * 9.8 = ---N.
Note: 1000 = density of water in kg/m^3.
To find the mass of the submerged cube, we need to find its volume first.
The volume of a cube is given by the formula V = s^3, where "s" is the length of one side of the cube.
Given that the side length of the cube is 2 cm (or 0.02 m), we can find the volume:
V = (0.02 m)^3
V = 0.000008 m^3
Now, we can find the mass of the submerged cube using the density formula:
Density = Mass / Volume
Rearranging the equation, we have:
Mass = Density * Volume
Given that the density of water is 1000 kg/m^3, we can substitute the values:
Mass = 5000 kg/m^3 * 0.000008 m^3
Mass = 0.04 kg
So, the mass of the submerged cube is 0.04 kg.
To find the buoyant force, we use Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the submerged object.
The volume of water displaced by the cube is equal to the volume of the cube, which we calculated to be 0.000008 m^3.
The buoyant force can be calculated using the formula:
Buoyant force = Density of fluid * Volume of fluid displaced * g
Given that the density of water is 1000 kg/m^3 and the acceleration due to gravity is approximately 9.8 m/s^2, we can substitute the values:
Buoyant force = 1000 kg/m^3 * 0.000008 m^3 * 9.8 m/s^2
Buoyant force = 0.0784 N
So, the buoyant force acting on the submerged cube is 0.0784 N.
Apparent mass is the difference between the actual mass of the object and the mass of the fluid displaced by the object.
Apparent mass = Actual Mass - Mass of fluid displaced
Given that the actual mass of the cube is 0.04 kg and the mass of the fluid displaced is also 0.04 kg, we can calculate the apparent mass:
Apparent mass = 0.04 kg - 0.04 kg
Apparent mass = 0 kg
Therefore, the apparent mass of the submerged cube is 0 kg.
To find the mass, apparent weight, and buoyant force, you need to understand some basic principles of buoyancy.
1. Mass: The mass (m) of the object can be calculated by using the formula:
mass = density × volume
Given that the density (ρ) of the object is 5000 kg/m³ and the side of the cube is 2 cm, you can convert the side length to meters (0.02 m) and use it to find the volume (V) of the cube:
volume = (side length)³
Plugging in the values, you get:
volume = (0.02 m)³ = 0.000008 m³
Now, substitute the density and volume values into the mass formula:
mass = 5000 kg/m³ × 0.000008 m³
2. Apparent Weight: The apparent weight (Wapp) is the force experienced by the object in the fluid. It can be calculated using the formula:
apparent weight = weight of the object - buoyant force
Since the object is submerged, its weight is given by:
weight of the object = mass × gravitational acceleration
Gravitational acceleration (g) is approximately 9.8 m/s².
3. Buoyant Force: The buoyant force (Fb) is the upward force exerted on a submerged object. It can be calculated using the formula:
buoyant force = density of the fluid × volume of the object × gravitational acceleration
Given that the density of water is approximately 1000 kg/m³, you can substitute the values to calculate the buoyant force.
By following these calculations, you can find the required values.