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 2.7g/cm3 the water density is 1g/cm3
What is the buoyant force on the cylinder?
Repeat the calculation if the object were inside Glycerin ( density: 1.26g/cm3)
Vs = pi*r^2 * h = 3.14*10^2*25 = 7850 cm*3 = Vol. submerged = Vol. of water displaced.
Fb = 7850cm^3 * 1g/cm^3 = 7850 g.
To calculate the buoyant force on the submerged cylinder, you need to consider the density of the fluid it is submerged in, as well as the volume of the cylinder. The formula for buoyant force is:
Buoyant force = Fluid density * Volume * Acceleration due to gravity
Given:
- Radius of the submerged cylinder = 10 cm
- Height of the cylinder = 25 cm
- Density of aluminum = 2.7 g/cm^3
- Density of water = 1 g/cm^3
- Density of glycerin = 1.26 g/cm^3
First, let's calculate the buoyant force in water:
1. Calculate the volume of the submerged cylinder:
Volume = π * r^2 * h
Volume = π * (10 cm)^2 * 25 cm
*Note: Since the radius was given in centimeters (cm), the volume will be in cubic centimeters (cm^3).
2. Calculate the buoyant force in water:
Buoyant force (water) = (Density of water) * (Volume) * (Acceleration due to gravity)
Buoyant force (water) = 1 g/cm^3 * (Volume) * 9.8 m/s^2
*Note: Since the density was given in grams per cubic centimeter (g/cm^3), the buoyant force will be in newtons (N) using the acceleration due to gravity in meters per second squared (m/s^2).
Now, let's calculate the buoyant force in glycerin:
1. Calculate the volume of the submerged cylinder:
Volume = π * r^2 * h
Volume = π * (10 cm)^2 * 25 cm
2. Calculate the buoyant force in glycerin:
Buoyant force (glycerin) = (Density of glycerin) * (Volume) * (Acceleration due to gravity)
Buoyant force (glycerin) = 1.26 g/cm^3 * (Volume) * 9.8 m/s^2
Finally, you can solve these calculations to find the buoyant forces on the submerged cylinder in both water and glycerin.