Buoyant Force formula
Last updated on July 7th, 2023 at 10:11 am
In this post, our topic of discussion is the Buoyant Force formula. As we go through it here, we will use this formula to solve a sample numerical as well.
Remember that, the upward buoyant force caused by Buoyancy is equal to the weight of the displaced fluid.
Buoyant Force Formula
Note: Upward buoyant force caused by Buoyancy = the weight of the displaced fluid.
The magnitude of Buoyant force is expressed with the formula Fb = ρ g V
Here ρ is the density of the fluid, V is the volume of the fluid displaced, g is the acceleration due to gravity
Read our tutorial on Buoyancy.
Numerical Problem based on Buoyant Force formula (with solution)
The densities of water and ice are 1 g cm-3 and 0⋅917 g cm-3. Find the fraction of an iceberg floating above the water surface and the fraction below it.
SOLUTION
Let V = the total volume of the iceberg.
V1 = volume of the iceberg above the water surface
∴ V − V1 = volume of the iceberg below the water surface that provides the upthrust (buoyant force) to balance the weight of the entire iceberg while the iceberg floats.
By the law of floatation weight of the iceberg = weight of the water displaced by the immersed part of the iceberg.
V × 0.917 × g = (V − V1) × 1 × g
=>V1 = (1 − 0.917) V
=>V1/V = 0.083/1 = 1/12
Thus, 1/12th part of the total volume of the iceberg floats above the water surface.
∴ 11/12th part of the iceberg is submerged in water.
It means most of the iceberg is beneath the water.
Buoyant force – concepts
- Consider a body immersed in a liquid. Two forces act on it simultaneously.
- The weight (W) of the body is acting vertically down at its center of gravity (C.G).
- The upthrust or buoyant force (FB) is equal to the weight of the liquid displaced, acting vertically upwards.
- The point where the total upthrust due to the liquid displaced by the immersed part of the body acts is called the center of buoyancy.
- The weight of the body acts vertically down whereas the buoyant force acts vertically up.
