In the figure, the radius of the submerged cylinder is 10 cm. The height is 25 cm. The cylinder is made of Aluminum whose density is the water density is
What is the buoyant force on the cylinder?
Repeat the calculation if the object were inside Glycerin ( density: 1.26g cm3
To calculate the buoyant force on a submerged object, we can use Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object.
Step 1: Calculate the volume of the cylinder.
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius of the cylinder and h is the height. In this case, the radius is 10 cm and the height is 25 cm.
V = π(10 cm)^2 * 25 cm
V = π * 100 cm^2 * 25 cm
V = 25000π cm^3
Step 2: Calculate the mass of the cylinder using the density of aluminum.
The volume of the cylinder can be used to determine its mass by multiplying it by the density of aluminum. The density of aluminum is not given, so we cannot complete this calculation without that information.
Step 3: Calculate the buoyant force using the density of water.
The density of water is 1 g/cm^3.
Buoyant force = weight of the fluid displaced
= density of fluid * volume of the fluid displaced * gravitational acceleration
Buoyant force = (1 g/cm^3) * (25000π cm^3) * (9.8 m/s^2) * (1 kg/1000 g)
Buoyant force = 7.75π N (approximately)
If the object were submerged in glycerin, we can repeat the calculation using the density of glycerin, which is given as 1.26 g/cm^3.
Buoyant force = (1.26 g/cm^3) * (25000π cm^3) * (9.8 m/s^2) * (1 kg/1000 g)
Buoyant force = 9.81π N (approximately)
Therefore, the buoyant force on the cylinder submerged in glycerin would be approximately 9.81π N.
To calculate the buoyant force on the cylinder, we need to use 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.
First, we need to find the volume of the cylinder. The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height. Given that the radius is 10 cm and the height is 25 cm, we can substitute these values into the formula:
V = π(10 cm)^2(25 cm)
= π(100 cm^2)(25 cm)
= 2500π cm^3
Next, we need to find the weight of the fluid displaced by the cylinder. The weight of a fluid is equal to its volume multiplied by its density, and we are given the density of water.
Let's assume the density of water is ρ_w g/cm^3, where ρ_w is the density of water in g/cm^3.
The weight of the fluid displaced by the cylinder in water is given by:
W_w = V ρ_w
= (2500π cm^3) ρ_w
Finally, the buoyant force on the cylinder in water is equal to the weight of the fluid displaced:
B_w = W_w
= (2500π cm^3) ρ_w
Now, let's calculate the buoyant force on the cylinder in water using the given densities:
Assuming the density of aluminum is ρ_Aluminum g/cm^3 and the density of water is ρ_w g/cm^3:
B_w = (2500π cm^3) ρ_w
To check the calculation if the object were in Glycerin density: 1.26g cm^3, we need to repeat the same process using the density of Glycerin instead of water.
Now, we can calculate the buoyant force on the cylinder in Glycerin using the given density:
Assuming the density of Glycerin is ρ_Glycerin g/cm^3:
B_g = (2500π cm^3) ρ_Glycerin
By substituting the density of Glycerin into the equation, you can find the buoyant force on the cylinder in Glycerin.