Density of a body

What´s density? What´s it used?

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The density is a magnitude used by the physics and chemistry to determine the amoun of mass contained in a given volume.

There are two types of densities:

ABSOLUT DENSITY: the density, which measure the mass per unit volume and is usually known by density.

Therefore, to calculate the density of a body you have to consider the following formula:

tabular{11}{11}{{rho = masa/volumen}} or that´s the same tabular{11}{11}{{ρ= m/v}}

where –mass is the number of particles that make up the substance or body. The mass is measured in grams.
          (What´s the difference between mass and weight of a body?)
         –and the volume is the total number of scattered molecules.
          The volume is in cubic units ( ${L^3}$ ).

RELATIVE DENSITY: is the density that compares the density of a substance with the density of water.

Is calculated using the followingo formula:

tabular{11}{11}{{relative density = {density of the substance}/{density of water}}} or that´s the same $tabular{11}{11}{{ρ_relative = {ρ_substance}/{ρ_water}}}$

The density of water is ${1000kg/m^3}$ or that´s the same ${1 g/cm^3}$

:?:Observes these two buckets, which belives it has greater density?

Because we know that density is the amount of mass contained in a given volume, it is easy to see that as the buckets are equal (have the same volume) and B in the cube is more number of particles (ie, higher mass), the density of the bucket B is greater than the density of the cube A. LOL

:?:Observe the following photograph of the globular cluster M13 or Hercules globular cluster:

We take two regions of the cluster, A and B.
For the same volume (square of 12*12 light years), we see that the area A accommodates smaller number of stars that the area B .

Which region has the lowest density?
A volume equal to the two areas, area B contains the largest number of stars in zone A, therefore the density of A is less than the density of B. LOL

In nature, the matter can be presented in three different states: solid, liquid or gaseous.

Let´s go to look some examples of densities of various elements and substances most common and known to us.

Some solids are:

	Sodium	Diamond	Silicon dioxide	Cesium chloride
densidad (g/cm³)	0.97	3.5	2.6	3.99

Some liquids are:

	Water	Ethanol	Essential Oil	Petrol
densidad (g/cm³)	1	0.79	0.92	0.71

Some gases are:

	Ozone	Carbon Dioxide	Air	Ammonia
densidad (g/cm³)	2.14	1.6	1.18	0.73

The data given in this section of gases, are data in normal pressure and temperature, ie:

pressure = 1 atmosphere temperature = 0º = 273 K

Example

A ball of radius 51.6 cm is composed of 40% iron and the rest is aluminium.

a)What is the area and volume of the ball? (What are the area and volume of a spherical body?)

b)What is the weight of the ball? (What is the weight of a body?)

a) The area of any sphere is:
$tabular{11}{11}{{ÁREA = 4.Pi.R^2}}$

As the radius of the ball is R=15.6 cm, the area is:

${Area(ball) = 4.Pi.15´6^2}$ = 3058 square centimeters.

The volume of a sphere is equal to:

$tabular{11}{11}{{VOLUME={4/3}.Pi.R^3}}$

As the radius of the ball is R=15.6 cm, the volume turns out to be:

${Volume(ball)={4/3}.Pi.15´6^3}$ = 15902.4 square centimeters.

b) To calculate the weight of the ball we need to know the densities of the materials that comprise it.
The density of iron is: ${{7.84} g/cm^3}$

The density of aluminium is: ${{2.7} g/cm^3}$

For the definition of density: tabular{11}{11}{{rho = mass/volume}} . Then the mass of the ball is:

{mass = rho*volume} . doubleright mass = (7.84×0.4 + 2.7×0.6)*15902´4 = 75759 grams

Therefore, for a body in the earth´s surface, where g = 9.8, the weight is:

weight = 75´759 x 9.8 = 742 Newton approximately.

BUOYANCY

What is buoyancy?

The density of a body is related to the buoyancy: a substance will float on the other if their density is lower.

:?:What happens when we launch a paper airplane to water?

The density of the paper is 0.77 g/cm³ and the density of water is 1 g/cm³, therefore, at the begining the paper fleet becouse the density of the sheet is lower than the density of water.

After a short period of time, just need to soak the sheet and become a grater density (particles bind water and cellulose), the blade falls to the bottom because the takes a higher density than the water.

:?:What about wood, lead and water?

— The wood floats on water while the lead sinks into it, and that lead has greater density than water and the wood density is lower..

:?:What about wood, lead and gasoline?

— However if we have galoline instead of water, wood sink and lead in gasoline, as thes density of gasoline is lower than that of lead and wood.