How Buoyant Force Reduces the Weight of Immersed Objects in Fluids

Buoyant force plays a crucial role in how objects behave in fluids, such as water or air. When an object is submerged in a fluid, the fluid exerts an upward force, which can reduce the effective weight of the object. This phenomenon is governed by Archimedes' principle and affects the object's apparent weight, making it easier to handle or move underwater. This article will explore the principles behind buoyant force and its impact on the weight of objects in fluids.

Definition of Buoyant Force

Buoyant force is defined as the upward force exerted by a fluid on an object that is submerged in it. This force acts in opposition to gravity, which is why objects appear to float or feel lighter when they are partially or fully submerged in a fluid. The magnitude of the buoyant force depends on the fluid's properties and the volume of the object that is displaced.

Archimedes' Principle

According to Archimedes' principle, the buoyant force on an object is equal to the weight of the fluid that the object displaces. To put it simply, when an object is immersed in a fluid, it pushes aside a volume of fluid, and the weight of that displaced fluid creates the buoyant force. This principle is the key to understanding why objects can float in fluids.

Effective Weight Calculation

The effective weight of an object when submerged is calculated by subtracting the buoyant force from the object's weight in air. The formula is:

Effective Weight Weight of Object - Buoyant Force

This means that the buoyant force counteracts some of the weight of the object, making it seem lighter in the fluid. This reduction in apparent weight can have significant practical implications, such as making it easier to dive or float in water.

Example Calculation

Consider a block of wood that weighs 10 N in air. When this block is submerged in water, it displaces 6 N of water. According to Archimedes' principle, the buoyant force acting on the block is 6 N. Therefore, the effective weight of the block in water is:

Effective Weight 10 N - 6 N 4 N

As a result, the block feels lighter and only weighs 4 N when submerged, which would make it easier to handle underwater.

Pressure and Buoyant Force

In addition to buoyancy, fluid pressure also increases as you go deeper, based on the fluid's density. If you sum up the integrated pressure applied straight against the surface of the submerged object or up to the waterline if floating, you can find the buoyant force. However, there is a shortcut using Green's Theorem that can simplify this calculation.

Due to the linear increase in pressure for an incompressible fluid, if you multiply the density of the fluid by the volume of the submerged object, you can directly determine the buoyant force. This force will act vertically at the centroid of the submerged body. This shortcut makes the calculation of buoyant force easier and more efficient, but it remains rooted in the fundamental principles outlined by Green's Theorem.

Therefore, understanding both the principles of buoyancy and the practical applications of buoyant force can provide valuable insights into how objects behave in different fluids, leading to better design and engineering solutions in various industries, from maritime to aeronautics.