# Examples of objects floating on water

## The effect of the buoyancy force - formula & calculation

In this text we explain to you how the buoyancy of objects in liquids or gases works and which factors do it **Buoyancy** influence.

The Titanic is slowly sinking towards the bottom of the sea, but the iceberg is floating in the water. Why is it that solid objects behave differently in the same environment? In both cases the buoyancy acts on both objects. To explain the difference, let's take a look at the basic factors that are important for buoyancy.

### How is the buoyancy determined?

First and foremost, two important factors are involved in buoyancy. When we have an object that is in a liquid or in a gas (also in the remainder of the text **medium** called) is the **Density of this medium** ($ \ rho_ {M} $ or alternatively also $ ϱ_ {M} $). Imagine the difference that results when you drop an ice cube into a bowl filled with water, oil, or air. The second crucial factor is that **Volume of the object** ($ V_O $). A varying volume of an object also means a varying buoyancy force. How do these two factors relate to buoyancy?

According to Archimedes' law it means that the buoyancy force of an object is just as great as the weight of the medium that has been displaced by the object. As a formula it would look like this:

$ F_A, object = F_G, medium $

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### Calculation of the buoyancy force

The buoyancy force is therefore as great as the mass of the medium that has displaced the object. How do we calculate this mass? The mass of a body results from the density of the body multiplied by its volume ($ \ rho \ cdot V $). In the case of buoyancy we can also use this formula, but with a small difference. Since the mass of the displaced medium is sought for the buoyancy force, here we multiply the density of the medium ($ \ rho_ {M} $) by the volume of the object ($ V_O $). In the text about the mode of action of the weight force you can see that when calculating the weight force, the factor $ g $ of the acceleration due to gravity must also be taken into account. This is $ 9.81 \ frac {m} {s ^ 2} $.

A formula for calculating the buoyancy force can therefore be summarized as follows:

$ F_A, object = \ rho_M \ cdot V_O \ cdot g $

Let's take a look at an example of how to use this formula to calculate the buoyancy force. For this purpose, let's take the said Titanic from the text inbox. This has a volume of approximately $ 131,112 \; m ^ 3 $. The water in which the Titanic swam back then has a density of $ 1000 \ frac {kg} {m ^ 3} $. If we multiply these two values, taking into account the acceleration due to gravity $ g $, the following calculation results:

$ F_A, Titanic = 1000 \ frac {kg} {m ^ 3} \ times 131,112 \; m ^ 3 \ times 9.81 \ frac {m} {s ^ 2} $

$ F_A, Titanic = N $ 1,286,208,720

$ F_A, Titanic = 1,286,208.72 kN $

So the floating Titanic had a buoyancy of 1,286,208,720 Newtons. This force kept them on the surface of the sea. But why did it sink now? Why did some objects float in their medium, could they rise or also float? In all cases, the buoyancy is crucial. Let's take a look at the four phenomena of rising, sinking, floating and swimming.

### Rise, sink, float, swim

How a body behaves in a medium depends on the interaction of the **Weight of the object**($ F_G, O $) and from **his****Buoyancy**. Let us look at this balance of power in the four phenomena mentioned.

As you can see in this graph, the level of the **Weight force** and the **Buoyancy**plays a crucial role in the behavior of an object in a medium. If the buoyancy force is greater than the weight force, then **increases** the object up in the medium. It **sinks**if the weight is greater than the buoyancy. That was the Titanic's problem too. The water flowing in after the collision was added to the weight of the ship. As a result, the weight was too great to keep the ship afloat. In the event that the weight force and the buoyancy force are identical, **floats** the object in its medium. As you can see from the example on the far right, it can also happen that an object is initially in the medium and rises because the buoyancy force is greater than the weight force. After it has reached the surface and breaks through it, it displaces less of the medium than before. This reduces the buoyancy force until it is just as great as the weight. Then **swims** the object.

Now you know what the buoyancy force is, how it works and how it can be determined. You can now test your newly acquired knowledge on our tasks. Have lots of fun with it!

### Test your knowledge!

You have an object with the volume of $ 250 cm ^ 3 $ that is in water (density: $ 1 \ frac {g} {cm ^ 3} $). Determine its buoyancy.

For a floating object, the buoyancy force is ...

The buoyancy force is calculated from ...

If an object has a greater buoyancy than its weight, then ...

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