We put iron and aluminum cylinders of the same volume on the scales. The balance of the scales has been disturbed. Why?

An imbalance means that the masses of the bodies are not the same. The mass of an iron cylinder is greater than that of an aluminum one. But the volumes of the cylinders are equal. This means that a unit volume (1 cm 3 or 1 m 3) of iron has a greater mass than aluminum.

The mass of a substance contained in a unit of volume is called matter density.

To find density, you need to divide the mass of a substance by its volume. Density is denoted by the Greek letter ρ (ro). Then

density = mass / volume,

ρ = m/V .

The SI unit of density is 1 kg/m 3. The densities of various substances are determined experimentally and are presented in the table:

How to understand that the density of water ρ \u003d 1000 kg / m 3? The answer to this question follows from the formula. Mass of water in volume V\u003d 1 m 3 is equal to m= 1000 kg.

From the density formula, the mass of a substance

m = ρ V.

Of two bodies of equal volume, the body with the greater density of matter has the greater mass.

Comparing the density of iron ρ w = 7800 kg / m 3 and aluminum ρ al = 2700 kg / m 3, we understand why in the experiment the mass of an iron cylinder turned out to be greater than the mass of an aluminum cylinder of the same volume.

If the volume of the body is measured in cm 3, then to determine the mass of the body it is convenient to use the density value ρ, expressed in g / cm 3.

Let's translate, for example, the density of water from kg / m 3 to g / cm 3:

ρ in \u003d 1000 kg / m 3 \u003d 1000 \ ( \ frac (1000 ~ g) (1000000 ~ cm ^ (3)) \) \u003d 1 g / cm 3.

So, the numerical value of the density of any substance, expressed in g / cm 3, is 1000 times less than its numerical value, expressed in kg / m 3.

Matter density formula ρ = m/V it is used for homogeneous bodies, i.e., for bodies consisting of one substance. These are bodies that do not have air cavities or do not contain impurities of other substances. The purity of the substance is judged by the value of the measured density. Is there, for example, some cheap metal added inside a gold bar?

As a rule, a substance in a solid state has a greater density than in a liquid state. An exception to this rule are ice and water, consisting of H 2 O molecules. The density of ice is ρ = 900 kg 3 , the density of water is ρ = 1000 kg 3 . The density of ice is less than the density of water, which indicates a less dense packing of molecules (i.e., large distances between them) in the solid state of matter (ice) than in the liquid state (water). In the future, you will meet with other very interesting anomalies (abnormalities) in the properties of water.

The average density of the Earth is approximately 5.5 g/cm 3 . This and other facts known to science made it possible to draw some conclusions about the structure of the Earth. The average thickness of the earth's crust is about 33 km. The earth's crust is composed mainly of soil and rocks. The average density of the earth's crust is 2.7 g / cm 3, and the density of rocks lying directly under the earth's crust is 3.3 g / cm 3. But both of these values ​​are less than 5.5 g/cm 3 , that is, less than the average density of the Earth. It follows from this that the density of matter located in the depths of the globe is greater than the average density of the Earth. Scientists suggest that in the center of the Earth the density of matter reaches 11.5 g/cm 3 , i.e. approaches the density of lead.

The average density of human body tissues is 1036 kg / m 3, the density of blood (at t\u003d 20 ° C) - 1050 kg / m 3.

A tree has a low density of wood (2 times less than cork) balsa. Rafts, life belts are made from it. A tree grows in Cuba eshinomena spiny-haired, the wood of which has a density 25 times less than the density of water, i.e. ρ ≈ 0.04 g / cm 3. Very high wood density snake tree. Wood sinks in water like a stone.

Finally, the legend of Archimedes.

Already during the lifetime of the famous ancient Greek scientist Archimedes, legends were made about him, the reason for which were his inventions that amazed his contemporaries. One of the legends says that the Syracusan king Heron II asked the thinker to determine whether his crown was made of pure gold or a jeweler mixed a significant amount of silver into it. Of course, the crown should have remained intact. It was not difficult for Archimedes to determine the mass of the crown. It was much more difficult to accurately measure the volume of the crown in order to calculate the density of the metal from which it was cast and determine whether it was pure gold. The difficulty was that it had the wrong shape!

Once Archimedes, absorbed in thoughts of the crown, was taking a bath, where it occurred to him brilliant idea. The volume of a crown can be determined by measuring the volume of water displaced by it (you are familiar with this method of measuring the volume of an irregularly shaped body). Having determined the volume of the crown and its mass, Archimedes calculated the density of the substance from which the jeweler made the crown.

According to the legend, the density of the crown material turned out to be less than the density of pure gold, and the dishonest jeweler was caught cheating.

Do not lift a strong man. A lead sinker for a fishing rod can easily be lifted even by a toddler. It turns out that the above expressions are wrong? Wait to draw conclusions - let's figure it out.

1. We carry out some measurements and make calculations

On fig. 2.8 you see two bars, both bars are made of the same substance - lead, but have different sizes. Our task is to find the ratio of the mass of each bar to its volume.

Rice. 2. 8. Two lead bars with different volumes

Rice. 2.5 Measurement of the masses of lead bars having different volumes

First, measure the length, width and height of the bars and calculate their volumes. (If you take the measurements correctly and do not make mistakes in the calculations, then you will get the following results: the volume of the smaller bar is 4 cm 3, the larger bar is 10 cm 3.)

Having determined the volumes of the bars, we weigh them. We place one of the bars on the left pan of the scales, and weights on the right pan (Fig. 2.9). The scales are in balance, your task is to count the mass of weights.

It remains for us to find the ratio of the mass of each bar to its volume, i.e., to calculate what the mass of lead with a volume of 1 cm 3 is for the smaller and for the larger bars. Obviously, if the mass of the smaller bar is 45.2 g and it occupies a volume of 4 cm3, then the mass of lead with a volume of 1 cm3 for this bar is 45.2: 4 = 11.3 (g). Having performed similar calculations for a larger bar, we get 113: 10 \u003d 11.3 (g). Thus, the ratio of the mass of a lead bar to its volume (the mass of lead per unit volume) is the same for both larger and smaller bars.

If we now take bars made of another substance (for example, aluminum) and repeat the same steps, then the ratio of the mass of the aluminum bar to its volume will also not depend on the size of the bar. We again get a constant number, but different than in the experiment with lead.

2. We define the density of matter

The physical quantity that characterizes a given substance and is numerically equal to the mass of a substance of a unit volume is called the density of the substance.

The density is denoted by the symbol p and is calculated by the formula

where V is the volume occupied by a substance of mass m.

Rice. 2.10. Density is numerically equal to the mass per unit volume. The figure shows the mass of 1 cm 3 of the substance

Density is a characteristic of a substance that does not depend on the mass of the substance and its volume. If the mass of a substance is doubled, for example, then the volume that it occupies will also double*.

From the definition of the density of a substance, we obtain a unit of density. Since the SI unit of mass is the kilogram and the unit of volume is the cubic meter, the SI unit of density is the kilogram per cubic meter (kg/m3).

1 kg / m 3 is the density of such a homogeneous substance, the mass of which in a volume of one cubic meter is equal to one kilogram.

In practice, the density unit of grams per cubic centimeter (g / cm 3) is also very often used.

Density units kilogram per cubic meter (kg / m 3) and grams per cubic centimeter (g / cm 3) are interconnected by the ratio:

3. Compare the densities of different substances

The densities of different substances and materials can differ significantly from each other (Fig. 2.10). Let's look at a few examples. The density of hydrogen at a temperature of 0 C and a pressure of 760 mm Hg. Art. is 0.090 kg / m 3 - this means that the mass of hydrogen with a volume of 1 m 3 is 0.090 kg, or 90 g. The density of lead is 11,300 kg / m 3. This means that lead with a volume of 1 m 3 has a mass of 11,300 kg, or 11.3 tons. The density of the substance of a neutron star reaches 1018 kg/m 3 . The mass of such a substance with a volume of 1 cm 3 is equal to 1 billion tons. The table below shows the densities of some substances.

Density, however, changes significantly in the case of changes in temperature and the state of aggregation of the substance. We will get acquainted with the reasons for the change in the density of matter further.

Table of densities of some substances in the solid state

Table of densities of some substances in the liquid state

Table of densities of some substances in the gaseous state

(at a temperature of O o C and a pressure of 760 mm Hg. Art.)

4. Learning to calculate the density, mass and volume of a physical body

In practice, it is often necessary to determine what substance this or that physical body consists of. To do this, you can use this method. First, calculate the density of this body, i.e., find the ratio of the mass of the body to its volume. Further, using the data of the density table, find out which substance corresponds to the found density value.

For example, if a block with a volume of 3 m 3 has a mass of 2700 kg, then it is obvious that the density of the block is:

According to the table, we find that the block consists of ice.

In the examples given above, we considered the so-called homogeneous bodies, that is, bodies that do not have voids and consist of one of its substances (an ice block, lead and aluminum bars). In such cases, the density of the body is equal to the density of the substance of which it consists (density of an ice block = density of ice).

If there are voids in the body or it is made of various substances (for example, a ship, soccer ball, person), then they talk about the average body density, which is also calculated by the formula

where V is the volume of a body with mass m.

The average density of the human body, for example, is 1036 kg/m 3 . Knowing the density of the substance from which the body is made (or the average density of the body), and the volume of the body, it is possible to determine the mass of a given body without weighing. Indeed, if p = m/V, then m = pV. Accordingly, knowing the density and mass of the body, you can find its volume:

• Summing up

The physical quantity that characterizes a given substance and is numerically equal to the mass of a substance of a unit volume is called the density of the substance.

The density of a substance and the density of a body can be calculated by the formula

In SI, density is measured in kilograms per cubic meter (kg/m3). Often also use the unit of density grams per cubic centimeter (g / cm 3). These units are related to each other by the ratio:

Knowing the mass of the body and its density, you can find the volume of the body:. Accordingly, according to the known volume of the body and its density, you can find the mass of the body: m = pV.

• Control questions

1. Does the ratio of the mass of a substance to the volume occupied by this substance depend on its mass? from volume? from the kind of substance?

2. What is called the density of matter?

3. The density of platinum is 21,500 kg/m 3 . What does this mean?

4. How to determine the density of a substance?

5. What units of density do you know?

6. How to express the density in grams per cubic centimeter (g / cm 3), if it is given in kilograms per cubic meter (kg / m 3)?

7. How to calculate the mass of a body from its density and volume?

8. How to determine the volume of a body, knowing its density and mass?

• Physics and technology in Ukraine

Donetsk Institute of Physics and Technology HAH Ukraine

In the 60s of the last century in the Donbass - the most important industrial region of Ukraine - there was an urgent need to organize scientific research, maximally focused on meeting the needs of the region. For this purpose, the Donetsk Scientific Center of the Academy of Sciences of the Ukrainian SSR was established in 1965, one of the key centers of which was the Donetsk Institute of Physics and Technology (DonFTI). The research results of the Institute staff were recognized by the scientific community of Ukraine and many foreign scientists. DonFTI maintains extensive research and production relations with dozens of foreign institutes and industrial enterprises in Switzerland, the USA, Germany, and Spain.

• Exercises

1. Find the density of air and the density of lead from the table. What do they mean? What quantities are we actually comparing when we say "light as air", "heavy as lead"?

Density is the most important feature that distinguishes steel from precious metals.

Table "Density of steel and precious metals", metal densities are shown in ascending order.

Density determination

Density is the ratio of the mass of a body (weight of an object) to its area or volume.

How is density measured?

The units of measurement for the density of metals in the international system of measurement are kg/m³ and g/cm³.

We do not accidentally compare density of precious metals and steel density. Today, stainless steel jewelry is at the peak of popularity. Such products are quite practical and unpretentious in care, and the price is so tempting that jewelry steel successfully competes with silver and even platinum. Moreover, outwardly it is not possible to distinguish stainless steel jewelry from jewelry made of platinum, silver, palladium or white gold. Take a look at the photo.

1.Steel. 2.Silver 3.White gold 4.Platinum 5.Palladium

All these products have a light silver color and luster in common. So here distinctive feature compared metals is precisely the density, which has a direct impact on the weight of the jewelry.

Unspoken rule: jewelry made of steel will always be lighter than jewelry made of precious metals presented. When comparing jewelry in the same weight category.

stigma jewelry metals- second hallmark

You can also determine which metal is in front of you by the brand. To do this, you need to know the standards for samples of precious metals, both Russian (Ukrainian) and foreign. Because in different countries, samples of precious metals may differ, not to mention a gross violation of the law and consumer rights - fake jewelry .

In the photographs above, you can see the distinctive markings of the metals. For steel - steel(sometimes you can find a specific steel grade, for example, L316), for silver - 925 test, for white gold - 585 sample, for platinum - 950 proof, for palladium - also 950 proof. Please note that the marking of platinum - Pt and palladium - PD, - tells us about an imported product.