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.
What is the buoyant force on the cylinder?
Repeat the calculation if the object were inside Glycerin ( density: 1.26g/cm3)
Fb = 7850cm^3 * 1g/cm^3 = 7850 g.
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.