Where is density used in life? Mass and density

Everything around us consists of different substances. Ships and bathhouses are built from wood, irons and cots are made from iron, tires on wheels and erasers on pencils are made from rubber. And different objects have different weights - any of us can easily carry a juicy ripe melon from the market, but we will have to sweat over a weight of the same size.

Everyone remembers the famous joke: “Which is heavier? A kilogram of nails or a kilogram of fluff? We will no longer fall for this childish trick, we know that the weight of both will be the same, but the volume will be significantly different. So why is this happening? Why different bodies and substances have different weights with the same size? Or vice versa, the same weight with different sizes? Obviously, there is some characteristic due to which substances are so different from each other. In physics, this characteristic is called the density of matter and is taught in the seventh grade.

Density of a substance: definition and formula

The definition of the density of a substance is as follows: density shows what the mass of a substance is in a unit of volume, for example, in one cubic meter. So, the density of water is 1000 kg/m3, and ice is 900 kg/m3, which is why ice is lighter and is on top of reservoirs in winter. That is, what does the density of matter show us in this case? An ice density of 900 kg/m3 means that an ice cube with sides of 1 meter weighs 900 kg. And the formula for determining the density of a substance is as follows: density = mass/volume. The quantities included in this expression are designated as follows: mass - m, volume of the body - V, and density is designated by the letter ρ (Greek letter “rho”). And the formula can be written as follows:

How to find the density of a substance

How to find or calculate the density of a substance? To do this you need to know body volume and body weight. That is, we measure the substance, weigh it, and then simply substitute the obtained data into the formula and find the value we need. And how the density of a substance is measured is clear from the formula. It is measured in kilograms per cubic meter. Sometimes they also use a value such as grams per cubic centimeter. Converting one value to another is very simple. 1 g = 0.001 kg, and 1 cm3 = 0.000001 m3. Accordingly, 1 g/(cm)^3 =1000kg/m^3. It should also be remembered that the density of a substance is different in different states of aggregation. That is, in solid, liquid or gaseous form. The density of solids is most often higher than the density of liquids and much higher than the density of gases. Perhaps a very useful exception for us is water, which, as we have already considered, weighs less in the solid state than in the liquid state. It is because of this strange feature of water that life is possible on Earth. Life on our planet, as we know, originated from the oceans. And if water behaved like all other substances, then the water in the seas and oceans would freeze through, the ice, being heavier than water, would sink to the bottom and lie there without melting. And only at the equator, in a small column of water, would life exist in the form of several species of bacteria. So we can say thank you to the water for our existence.

Purpose of the lesson: to study a new physical quantity “density of matter”.

Lesson Plan

1. Organizing time.
2. Updating knowledge.
3. Analysis of the textbook text, identification of dominant elements of knowledge, written answers to questions.
4. Checking the assimilation of electronic knowledge in the order of their logical sequence.
5. Lesson summary.
6. Homework.

How are the masses of bodies at rest before interaction compared based on the acquired velocities?

What is the unit of mass?

How is body weight determined?

Students independently study the textbook material and provide written answers to questions in their notebooks.

Questions for DEZ	Source of knowledge
1. What can be said about body masses made from different substances with equal volume?	A.V. Peryshkin, N.A.Rodina. Physics textbook for 7th grade. With. 48	Bodies that have equal volumes and are made from different substances have the same masses.
2. What explains that bodies made from different substances have different masses with equal volume?	With. 48	This is explained by the fact that different bodies have different densities.
3. Density formula.	With. 49
4. What is the density of a substance called?	With. 49	Density is a physical quantity equal to the ratio of the mass of a body to its volume.
5. What is the physical meaning of the density of matter?	With. 49	Density shows how much mass is contained in a unit volume.
6. What is the unit of density?	With. 49	The unit of density is the density at which a unit of volume contains a unit of mass of a substance.
7. What is the SI unit of density?	With. 49	The SI unit of density is the density when one cubic meter of a substance contains one kilogram of mass.
8. Get the name of the density unit.	With. 49
9. Obtain the designation for the unit of density.
10. Derive the formula for calculating body mass from the formula for the density of a substance.	With. 52
11. Derive from the formula for the density of a substance the formula for calculating the volume of a body.	With. 53
12. Why do you need to know the density of a substance?	With. 52	The density of a substance needs to be known for various practical purposes. An engineer, when creating a machine, can calculate in advance the mass of parts of the future machine based on the density and volume of the material. The builder can determine what the mass of the building under construction will be, etc.

The teacher calls the student to the board, takes his notebook with questions, checks for answers, and asks questions from the notebook in order.

The teacher asks several of the most important questions from the ECD notebook on the topic.

The purpose of the lesson:

• consolidate students' knowledge about density
• show how to determine the mass and volume of a body by its density
• solve calculation problems

Lesson structure:

1. Org. moment
2. Repetition of material
3. Learning new material
4. Fixing the material
5. Homework

1. Org. moment
2. Repetition of material

The lesson uses a presentation (Appendix 1)

• Do all bodies have the same volume and the same mass? (slide 2)
• Why?
• Do all bodies of the same mass have the same volume? (slide 2)
• Why?
• what does it depend on?
• What is the density of a substance? (slide 3)
• Density is a physical quantity equal to the ratio of the mass of a body to its volume.
• write down the density formula. (slide 4)

• get the density name in SI (slide 4)

Today in the lesson we will calculate the mass and volume of bodies based on density, write down the topic of the lesson in your notebook.

Lesson topic: determining the mass and volume of a body based on the density of the substance. (slide 8)

Write the formula for calculating density in your notebook

what will the mass of the body be equal to if we know the density of the body and its volume?, who will write it down?

– to calculate mass from its density and volume, you need to multiply the density by its volume. (slide 9)

No. 1 - everyone solves the problem themselves

We check:
Task
Answer: m=2825g. (slide 12)

Attention! What will the volume of the body be equal to if we know the mass and density of the substance?

; - to calculate the volume of a body from its density, you need to divide the mass of the body by its density (slide 13)

The problem is solved on the board and remains as a sample solution.

No. 2 - everyone solves the problem themselves

1. A steel part of a machine has a mass of 7890 g. Determine its volume if the density of steel is 7.8. (Appendix 3)

We check:
Task
Answer: V=1023.077 cm 3 (slide 16)

• Homework §22 ex. No. 8 (slide 17)
• Open task 3 (slide 18)

No. 3 - everyone solves problems themselves

Task report form No. 3 (slide 19)– please note that you must fill in the field with your last name

Last name student name_____________________________________________

fill in the calculated physical quantity with its units of measurement in the appropriate cells (slide 19)

Date of completion______________________________________

• Everyone has such a form on their desk; you fill out the corresponding cells in which you write only numerical values.
• Close Excel. Save the change to the document. (slide 21)

Lesson over thanks! (slide 22)

Used Books:

1. Physics textbook 7, author – A.V. Peryshkin – Moscow – “Enlightenment”
2. Methodological materials 7,- L.A.Kirik – Moscow – “ILEKS”
3. Multi-level independent and control work 7, - L.A. Kirik - Moscow - “ILEKS”
4. Collection of problems in physics - V.I.Lukashik - Moscow - “Enlightenment”

DEFINITION

Weight is a scalar physical quantity that characterizes the inertial and gravitational properties of bodies.

Any body “resists” attempts to change it. This property of bodies is called inertia. So, for example, a driver cannot instantly stop a car when he sees a pedestrian suddenly jumping onto the road in front of him. For the same reason, it is difficult to move a wardrobe or sofa. Under the same influence from surrounding bodies, one body can quickly change its speed, while another, under the same conditions, can change much more slowly. The second body is said to be more inert or have greater mass.

Thus, the measure of the inertia of a body is its inertial mass. If two bodies interact with each other, then as a result the speed of both bodies changes, i.e. in the process of interaction, both bodies acquire .

The ratio of the acceleration modules of interacting bodies is equal to the inverse ratio of their masses:

The measure of gravitational interaction is gravitational mass.

It has been experimentally established that the inertial and gravitational masses are proportional to each other. Selecting the proportionality factor equal to one, they talk about the equality of inertial and gravitational masses.

In the SI system The unit of mass is kg.

The mass has the following properties:

1. mass is always positive;
2. the mass of a system of bodies is always equal to the sum of the masses of each of the bodies included in the system (additivity property);
3. within the framework, mass does not depend on the nature and speed of movement of the body (invariance property);
4. the mass of a closed system is conserved during any interactions of the bodies of the system with each other (law of conservation of mass).

Density of substances

The density of a body is the mass per unit volume:

Unit density in SI system kg/m .

Different substances have different densities. The density of a substance depends on the mass of the atoms of which it is composed and on the packing density of atoms and molecules in the substance. The greater the mass of atoms, the greater the density of the substance. In different states of aggregation, the packing density of the atoms of a substance is different. In solids, the atoms are very tightly packed, so substances in the solid state have the highest density. In the liquid state, the density of a substance does not differ significantly from its density in the solid state, since the packing density of atoms is still high. In gases, molecules are weakly bound to each other and move away from each other over long distances; the packing density of atoms in the gaseous state is very low, therefore, in this state, substances have the lowest density.

Based on data from astronomical observations, the average density of matter in the Universe was determined; the calculation results indicate that, on average, outer space is extremely rarefied. If we “spread” matter throughout the entire volume of our Galaxy, then the average density of matter in it will be equal to approximately 0.000 000 000 000 000 000 000 000 5 g/cm 3 . The average density of matter in the Universe is approximately six atoms per cubic meter.

Examples of problem solving

EXAMPLE 1

EXAMPLE 2

EXAMPLE 3