# Buoyant Force

## Introduction

Buoyancy is the upward force exerted on an object that has been immersed in the fluid. The fluid can be water, another liquid, or even gas, as long as it cannot penetrate the solid object fully. This upward force on the object is referred to as buoyant force or buoyancy and can be calculated using Archimedes’ principle, which states that the weight of the displaced fluid (liquid or gas) equals the weight of the volume of that object immersed in it.

The denser a material is, such as lead or gold, the more of an opposing force it has to buoyancy. If you drop a rock and an inflated balloon into the water at equal depth, both will sink because they have the same weight. However, since air is less dense than water, it creates less of an opposing force than the rocks do. This means that an object with a lot of air in it can float on top of liquid even though its overall weight is greater than that of other objects with less air in them. For example, when a boat sinks in water, it displaces enough of the surrounding fluid so that its overall density becomes less than that of seawater. The boat then floats back up to the surface until it displaces enough seawater again to create an opposing force against gravity.

## Buoyant Force

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It is an upward force exerted on an object when it is fully or partially immersed in a fluid. It results from gravity acting on both the mass of water and on its volume; thus, it can be expressed mathematically as:

$$\mathrm{F\:=\:\rho Vg}$$

where $\rho$ represents the density of water and g represents acceleration due to gravity.

### The magnitude of buoyancy force depends on two factors:

• The amount of fluid displaced by an object (i.e., ,volume),

• The difference between densities of liquid and solid objects (i.e.,relative density).

For example, if you place a rock into the water, it will sink because there is more mass than the volume of water displaced by that rock. If you put that same rock into honey, however, it will float because there is less mass than the volume of honey displaced by that rock.

## Archimedes' Principle

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Archimedes' Principle is a physical law that states that any object fully or partially submerged in a fluid (liquid or gas) at rest is acted upon by an upthrust equal to the weight of the fluid displaced by the object. The principle explains why boats float and why airplanes can fly. It also applies to buoyancy and submersion in liquids other than water (e.g., honey) or gases other than air.

The principle allows one to determine whether an object will float or sink in a given situation. As long as it is less dense than water, it will float on top; if it is denser than water (denser), it will sink.

## Archimedes' Principle related to Buoyant Force

Archimedes' principle relates to how things float on water. This law of buoyancy can be stated as any object completely or partially submerged in a fluid experiences an upward force equal to the weight of the fluid displaced by that object. If you've ever been stuck in quicksand or watched your cat try to get out of bathwater, you've seen Archimedes' principle in action.

## Cause of Buoyant Force

Buoyancy is caused by a difference in pressure. The pressure at which an object will float depends on its density relative to that of water. If an object’s density is greater than that of water, it sinks; if less, it floats.

For example, steel has a density of 7.85 g/cm3 (0.284 lb/in3) while water has a density of 1 g/cm3 (1 lb/ft3). Steel, therefore, sinks in water and does not experience buoyancy. On the other hand, wood has a density of 0.5 g/cm3 (1.92 lb/ft3), so it floats in water and experiences buoyancy. An object whose weight exceeds that of a liquid in which it is submerged tends to sink because there is more force pushing down on it than there is an upward force from the liquid. This imbalance creates what we call buoyant force: upward pressure from below balancing downward pressure from above.

## Applications Buoyant Force

### Hot Air Balloon

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A hot air balloon (or just a hot air balloon) is a lighter-than-air aircraft that is suspended and propelled by warm air rising from a heat source inside. The balloon envelope keeps its contents warmer than cool outside air by containing an ascending flow of heated buoyant gas that retains both its temperature and volume in spite of the reduction in external pressure. Hot air balloons that can be propelled through the use of an onboard burner are correctly referred to as thermal airships.

### Submarine

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A submarine uses buoyant force to displace water inside its hull and change its own density to move up or down in the water. This is why submarines are often called submersibles: they can submerge below sea level by filling their ballast tanks with seawater.

## FAQs

Q1. What are the three types of buoyancy?

Ans. Natural buoyancy: neither sinking nor floating

Positive Buoyancy: floating at the top of the surface

Negative Buoyancy: sitting at the bottom of the body of water

Q2. How are buoyancy and density related?

Ans. It is directly proportional to the density of a fluid.

Q3. What is the formula of buoyant force?

Ans. Fb is denoted as a buoyant force and Vf is a displaced fluid-

$$\mathrm{Fb\:=\:gp\:Vf}$$

Q4. Does buoyant force depend on liquid?

Ans. The buoyant force exerted on an object submerged in a liquid depends only on how much of an object is above water (in terms of volume) and not how much liquid is displaced by that portion of an object. The weight of displaced liquid does play a role in determining overall buoyancy.

Density = Mass/Volume.

Therefore, greater mass over any given volume increases density and thus decreases buoyancy by increasing weight relative to volume displacing it.