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 various items have different weight- any of us can easily bring juicy food from the market ripe melon, but you’ll have to work hard on 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 shows us the density of matter in 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. Density solids, 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 precisely because of this strange feature water, 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
- Organizing time.
- Updating knowledge.
- Analysis of the textbook text, identification of dominant elements of knowledge, written answers to questions.
- Checking the assimilation of electronic knowledge in the order of their logical sequence.
- Lesson summary.
- Homework.
1. Organizational moment.
2. Updating knowledge.
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?
3. Independent study of the material using ESD.
Students independently study the textbook material and provide written answers to questions in their notebooks.
Questions for DEZ |
Source of knowledge |
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| 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 body weight 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. |  |
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| 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. |
4. Checking the assimilation of electronic knowledge in the order of their logical sequence.
The teacher calls the student to the board, takes his notebook with questions, checks for answers, and asks questions from the notebook in order.
5. Summing up the lesson.
The teacher asks several of the most important questions from the ECD notebook on the topic.
The bodies around us are made up of various substances: iron, wood, rubber, etc. The mass of any body depends not only on its size, but also on the substance of which it consists. Bodies of the same volume, consisting of different substances, have different masses. For example, having weighed two cylinders made of different substances - aluminum and lead, we will see that the mass of the aluminum cylinder is less than the mass of the lead cylinder.
At the same time, bodies with the same masses, consisting of different substances, have different volumes. Thus, an iron bar weighing 1 ton occupies a volume of 0.13 m 3, and ice weighing 1 ton occupies a volume of 1.1 m 3. The volume of ice is almost 9 times greater than the volume of an iron bar. That is, different substances can have different densities.
It follows that bodies with the same volume, consisting of different substances, have different masses.
Density shows the mass of a substance taken in a certain volume. That is, if the mass of a body and its volume are known, the density can be determined. To find the density of a substance, you need to divide the mass of the body by its volume.
The density of the same substance in solid, liquid and gaseous states is different.
The densities of some solids, liquids and gases are given in tables.
Densities of some solids (at normal atmospheric pressure, t = 20 ° C).
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Solid |
ρ , kg/m 3 |
ρ , g/cm 3 |
Solid |
ρ , kg/m 3 |
ρ , g/cm 3 |
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Window glass |
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Pine (dry) |
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Plexiglas |
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Rafinated sugar |
Polyethylene |
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Oak (dry) |
Densities of some liquids (at normal atmospheric pressure t = 20 ° C).
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Liquid |
ρ , kg/m 3 |
ρ , g/cm 3 |
Liquid |
ρ , kg/m 3 |
ρ , g/cm 3 |
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The water is clean |
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Whole milk |
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Sunflower oil |
Liquid tin (at t= 400°C) |
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Machine oil |
Liquid air (at t= -194°C) |
7th grade
Muharramova Gulnara Munipovna, physics teacher
Lesson objectives: 1. Educational:- introduce a new characteristic of the body (substance) - density;
Find out the physical meaning of density;
Derive the calculation formula, density units;
2. Developmental: - formation of independent thinking, ability to compare,
analyze, draw conclusions;
3. Educational: - development cognitive interest students to this topic and
the subject as a whole, broadening one’s horizons;
Careful and careful handling of devices;
accuracy of notes in notebooks, availability of textbooks
and writing instruments.
lesson type: lesson in learning new material
methods: verbal-visual-practical
equipment: lever scales with weights, two bars
Demonstrations: demonstration of a set of bodies of the same mass, the same volume
Technical equipment: computer, screen, multimedia projector
I Organizational moment
Give the correct psychological attitude: “I can see from your faces that you are in a good mood today. Let’s work in class today so that your mood remains the same, and maybe becomes even better.”
Create a normal working mood: “Let’s start the lesson.”
II. Updating of reference knowledge
Teacher. In previous lessons we studied the first form matter - substance. What is a substance? Let us recall the internal structure of matter.
Matter consists of molecules (atoms) with spaces between them. Molecules move... Molecules interact...
Teacher- Name the states of matter of matter.
Gas, liquid and solid.
III. Motivation educational activities students
Teacher Imagine that geologists have discovered oil deposits. They know the volume of deposits. How to determine the mass of oil? Obviously, we can calculate the mass of oil if we know the mass per unit volume (1 m3) and volume. Therefore, knowledge of the mass per unit volume of a substance has great importance For practical activities person. In physics it received a special name - density.
Students write down the topic of the lesson. The teacher communicates the objectives of the lesson. (Slide)
Know:
1.What is density?
2.How is density determined?
3. Formula for calculating density
4. Density units.
Be able to:
Knowing the density, learn to determine chemical composition substances.
IV. Perception and assimilation of educational material
Teacher- Tell us how the volume of a body shaped like a parallelepiped is determined. What device is needed for this?
Ruler. The volume is equal to the product of the dimensions of the three sides V=a b c.
Teacher- The volume of bodies of arbitrary shape cannot be measured using a ruler. To do this, you can use the simplest method.
A measuring cylinder (beaker) is used to measure volumes of liquids and solids. If you pour liquid into a measuring cylinder and determine its volume, and then lower a solid into it, the liquid level will rise. The difference between these two volumes is equal to the volume of the solid. (Slide)
Teacher Measure the volume of the bars using a ruler and write down the results on a piece of paper that I put on everyone's desk. What answers did you get?
The volumes of the bodies turned out to be the same.
Teacher- What else have you learned to identify in past lessons?
A lot of bodies.
Teacher- Right. Using what device?
Using lever scales.
Teacher- Right. Determine the mass of the bars using a scale on your desk. Record the result on the same sheet. Are the masses of different bodies the same?
Teacher- Bodies from different materials, but of the same volume have different masses. (Slide)
For clarity, let’s put an iron cylinder on one pan of the scale and an aluminum cylinder on the other.
What facts are visible from observation?
One body is made of iron, the other is made of aluminum. V iron = V aluminum. The mass of iron is greater than the mass of aluminum.
Teacher- How to explain this?
The mass of the substance contained in 1 cm 3 is different, i.e. density is different.
Teacher - If you take two bars, one made of copper, the other of aluminum, you can see that the volume of the aluminum cylinder is almost four times larger than the copper one (put on scales). Why are the scales in balance?
They have equal masses
Teacher An iron beam weighing 1 ton has a volume of 0.13 m 3, and ice weighing 1 ton has a volume of 1.1 m 3, i.e. almost 9 times more (Slide) . Bodies made of different substances with the same mass have different volumes. (Slide)
Teacher- What can you offer to explain what you saw?
The mass of 1 cm 3 is different, that is, the densities of the bodies are different.
Teacher- Let’s explain the meaning of the word density using knowledge about the internal structure of matter.
Iron and aluminum atoms have different masses and different spaces between them.
Teacher– What determines the density of a substance?
A physical quantity that shows how much mass is per unit volume of a substance is called density. (Slide)
To find the density of a substance, it is necessary to determine the mass and volume of the body.
The teacher offers an example.
Teacher. To find out how to find the density of a given substance, consider an example. A piece of ice with a volume of 4 m 3 has a mass of 3600 kg. Determine how much mass is contained in 1 m 3 of ice (ice density).
1 m 3 of ice contains 900 kg. Thus, the density of ice is 900 kg per 1 m 3.
Teacher How did we determine this?
3600 kg/ 4 m 3 = 900 kg/m 3
TeacherTo determine the density of a substance, you need to divide the mass of a body by its volume.
Hence, there is density physical quantity, equal to the ratio of body mass to its volume. The definition can be briefly written as follows: density = mass/volume.(Slide )
Let us introduce the following notation: ρ – density of matter ( greek letter, read “ro”), m is the mass of the body, V is its volume. Then we get a formula for calculating density: ρ=m/V(Slide)
Like any physical quantity, density has its own dimension.
In what units is density measured?
The student, analyzing the formula, says: kg/m 3 or g/cm 3
Teacher In the SI system, density is measured [kg/m3]. Density is often measured in [g/cm3].
Physical education minute. Guys, you already know that the effect on the nerve endings in our palms affects almost our entire body. Therefore, I invite you to clap and clap not just for fun, but with meaning. Let's imagine that our palms are molecules, and what does the movement of molecules depend on?
Therefore, listening to me, we think about how our palms should move. Fast or slow? So, it's very cold. A little warmer, a little warmer. Very hot. And it became cold again.
Now it won’t hurt for us to move. Let's imagine that we are liquid in a thermometer column. Temperature – 30 0, -10 0, 0 0, + 30 0, +50 0.
Teacher The densities of substances have already been determined by scientists. In the textbook on pages 50, 51 you will find a table of the densities of substances in solid, liquid and gaseous state. It is very important to note that the same substance in various states has different densities.
For example, the density of water is 1000 kg\m3, ice is 900 kg/m3, and water vapor is 0.59 kg/m3. Why are they different? (Slide)
Find the density of aluminum from the table.
2700 kg/m 3 or 2.7 g/cm 3
Teacher- What do the words mean: “The density of aluminum is 2700 kg/m3”?
According to the definition of density, 1 m 3 of aluminum has a mass of 2700 kg, and 1 cm 3 of aluminum has a mass of 2.7 g. Is it possible to talk about the density of the same substance in this way?
Yes, it is possible, because ρ = 2700 kg/m 3 = 2700 · 1000 g/ 1000,000 cm 3 = 2.7 g/cm 3.
Teacher-How many times is the number 2700 greater than 2.7?
1000 times.
Teacher- So, if you need to convert the value of 2700 kg/m 3 to g/cm 3 when calculating density, how many times should it be reduced?
Teacher- What arithmetic operation?
By division
Teacher- And, on the contrary, convert 2.7 g/cm 3 to kg/m 3?
Increase by 1000 times, multiply.
Teacher Look at the density tables in your textbook and find the substances with the highest and lowest densities for solids, liquids, and gases.
The densest solid substance is osmium - 22,600 kg/m3. The densest liquid is mercury (13600 kg/m3).
Teacher Well, now let’s find the chemical composition of the substance, knowing its density
Teacher writes on the board: the density of the substance is 19300 kg/m3. What is this substance?
The student, working with the table, answers that this substance consists of gold.
V. Formation of skills and abilities.
Teacher It is necessary to determine the density of the substance of bodies and, knowing it, find out the chemical composition of the material. How to determine this?
We calculated the volume of the bars, then using scales we found out the mass of the bodies. Finally using the formula ρ=m/V Let's determine the density of the substance. Using the table, we’ll see what specific density corresponds to which substance.
Teacher I evaluate the students' work... In general, the whole class successfully determined the chemical composition of the substance of the bars.
VI. Consolidation of new knowledge
Calculation tasks: (Slide)
Express body mass in kilograms: 2.5 t, 0.25 g, 300 g, 150 mg, 30 g, 3000 g.
VII. Lesson summary
Teacher What new did you learn?
1. Have you become acquainted with a new physical quantity - density?
2. The density of a substance determines how much mass of a substance is contained in a unit of volume (in 1 m 3, 1 cm 3)
3. Density is measured in 1 kg/m3 or 1 g/cm3
4. Learned to determine the density of a substance using the formula: ρ=m/V
5. Knowing the density of the body, we learned to determine the chemical composition of a substance.
6. Learn to work with tables of densities of solid, liquid and gaseous substances.
Teacher- Why do you need to know the density of a substance?
How to determine the mass of a brick using a ruler?
VIII. Homework
§ 21, story according to plan; Ex. 7 (1,2)orally; willing individual tasks
Determination of body volume
Determining the Density of a Solid
Determination of body volume
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№ |
Length A cm |
Width |
Height With cm |
Volume |
Body mass |
The density of the substance, ρ |
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g/cm 3 |
kg/m 3 |
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1 | |||||||
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2 | |||||||
Determining the Density of a Solid
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№ |
Length A cm |
Width |
Height With cm |
Volume |
Body mass |
The density of the substance, ρ |
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g/cm 3 |
kg/m 3 |
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1 | |||||||
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2 | |||||||
Determining the Density of a Solid
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№ |
Length A cm |
Width |
Height With cm |
Volume |
Body mass |
The density of the substance, ρ |
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g/cm 3 |
kg/m 3 |
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1 | |||||||
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2 | |||||||
Ministry of Education Russian Federation
GBOU "VSOSH TVER"
Physics 7th grade
"Density of matter"
Lesson developed by:
Physics teacher: Arefiev A.S.
October 2013
Technologies used : The lesson is based on problem technology with partial use of group and information technologies.
The purpose of the lesson: introduction of a new characteristic of a substance - density, consideration of its characteristics (definition, formula, units of measurement, methods of measurement).
Tasks:
Educational:
Continue the formation of knowledge about nature, phenomena and laws in a unified system;
Repeat: the phenomenon of interaction of bodies; concept of body weight; inertia.
Educational:
Continue to form a scientific worldview and independent thinking;
Develop the ability to express your thoughts out loud.
Developmental:
Continue to develop the ability to analyze what you see;
Develop the ability to formulate hypotheses;
Develop the ability to work with tabular material;
Development of cognitive interest, intellectual and creative abilities;
Develop the ability to solve high-quality problems.
Equipment: multimedia projector; computer; presentation made with the help of PowerPoint programs; bodies of different volumes, but equal mass; scales; weights; bodies of equal volume but different masses.
Lesson plan:
Organizing time.
Repetition of covered material.
Learning new material.
Reinforcing the material learned
Homework, summing up.
During the classes:
Greeting students and marking absences in the journal. (2 minutes)
Three students are called to the board to solve experimental problems, the results of which will be needed when studying new material.
Equipment: scales, weights, bodies of various weights.
Task 1: Determine the masses of two wooden cylinders different sizes with an accuracy of 1g.
Task 2: Determine the masses of a wooden and aluminum block of the same volume with an accuracy of 1 g.
Task 3: Determine the masses of two bodies of different substances (bodies of equal mass) with an accuracy of 1 g.
The results are written on the board.
At the same time, the class answers test questions in order to review the material covered and test knowledge. (5 min) (Appendix 1) Then students exchange work with their desk neighbor and check the work (they write on a piece of paper in a different color the work they checked... and give a grade). The spoilage is shown on the screen (3 min). If a group of students has not yet finished measuring the masses, then the test can be checked together with the students.
Learning new material begins with posing a problem. (26 min.)
How can you experimentally determine body weight? Is it possible to calculate body weight theoretically?
The proposed task: How to determine the mass of a brick lying on a table using a ruler? (the guys may not be able to give an answer, then the conclusion is that we will definitely do this in class today).
Now we can look at the work of the expert group: m 1 m 2
How do you know which of two wooden cylinders has more mass?
m 1< m 2
Compare the masses of 2 bars of the same volume (wood and aluminum)
1 2 V 1 = V 2 m 2 > m 1
Compare the masses of 2 bodies of different volumes and different substances.
V 2 >V 1 ; m 1 = m 2
m 1 m 2
Bodies of the same mass are a steel body and a piece of bread weighing 125 g. (You can enter information about the battle of Moscow, that from November 20 to December 25, 1941, 125 g of bread was given to a non-working person, and 250 g to a working person; slide No. 5)
Analyzing the tasks completed by experts, the guys draw a conclusion.
Body weight depends on the volume of the body and the substance.
How does the mass and volume of a body depend on the substance? To answer this question, we introduce a new concept for us - density.
A designation for density is given and a mathematical relationship between density, volume and mass is constructed. m - mass V - volume, ρ - density
SI unit of density: 1 kg/m3, 1 g/cm3.
Let's convert the units from g/cm3 to kg/m3.
1 g/cm 3 = 0.001 kg/ 0.000001 m 3 = 10 -3 kg/10 -6 m 3 = 10 3 kg/m 3
The densities of many substances are known. Open page 50 of the textbook. Let's look at the tables of densities for three states of matter and find out what these numbers in the table mean?
Let's start with gold: the density of gold shows that gold with a volume of 1 m 3 has a mass of 19300 kg.
Students comment on several values to choose from
How is density related to internal structure substances?
Let's remember the 3 provisions of the ICT. (guys I name 3 positions)
The most convenient way to understand the concept of density is to consider the three states of matter.
m =Vρ
a= V = abc
b = m =ρ abc
ρ =1800 kg/m 3 Answer: m =
Consolidation of the studied material. (7 min.)
The guys answer questions to consolidate the material covered:
From what new characteristic substances did you meet?
How can you determine the density of a substance?
Does density depend on the mass and volume of a body?
Why do you need to know the density of a substance?
When is it more convenient to determine mass not experimentally, but by calculation?
If you have time, you can solve several quality tasks. For example:
Which of three spoons of the same mass - steel, aluminum or silver - has the greater volume?
Does the density of solids decrease or increase when heated?
Do the buckets have the same mass? drinking water and the same bucket of sea water?
5. Students who respond well in class are given grades and their homework is displayed on the screen. (2 min)
