Density of a substance - calculation of the mass and volume of a body. The preposition is at the beginning of mine

DEFINITION

Density is the amount of substance per unit volume of a body on average.

This amount can be determined in different ways. If we're talking about about the number of particles, we talk about the particle density. This value is denoted by the letter n. In SI it is measured in m -3. If we mean the mass of a substance, then enter the mass density. It is denoted by . In Si it is measured in kg/m3. Between and n there is a connection. So, if a body consists of particles of the same type, then

= m× n,

Where m- mass of one particle.

Mass density can be calculated using the formula:

This expression can be transformed so that the formula for mass in terms of volume and density is obtained:

Table 1. Densities of some substances.

Substance	Density, kg/m 3	Substance	Density, kg/m 3
Substances of the atomic nucleus
Compressed gases at the center of the densest stars		Liquid hydrogen
		Air near the Earth's surface
		Air at an altitude of 20 km
Compressed iron in the Earth's core		Highest artificial vacuum
	(7.6 - 7.8)×10 3	Gases of interstellar space
		Gases of intergalactic space
Aluminum
Human body

Regardless of the degree of compression, the densities of liquid and solid bodies lie in a very narrow range of values ​​(Table 1). The densities of gases vary within very wide limits. The reason is that in both solids and liquids the particles are closely adjacent to each other. In these media, the distance between neighboring particles is on the order of 1 A and is comparable to the sizes of atoms and molecules. For this reason, hard and liquid bodies have very low compressibility, which accounts for the small difference in their density. In gases the situation is different. The average distance between particles significantly exceeds their sizes. For example, for air near the Earth's surface it is 10 2 A. As a result, gases have high compressibility, and their density can vary over a very wide range.

Examples of problem solving

EXAMPLE 1

Exercise	Determine the molar concentration and mass fraction of sodium chloride in a solution obtained by dissolving 14.36 g of dry salt in 100 ml of water (solution density 1.146 g/ml).
Solution	First we find the mass of the solution: m solution = m(NaCl) + m(H 2 O); m(H 2 O) = r(H 2 O) ×V(H 2 O); m(H 2 O) = 1 × 100 = 100 g. m solution = 14.63 + 100 = 114.63 g. Let's calculate the mass fraction of sodium chloride in the solution: w(NaCl) = m(NaCl) / m solution ; w(NaCl) = 14.63 / 114.63 = 0.1276 (12.76%). Let's find the volume of the solution and the amount of sodium chloride in it: V solution = m solution / r solution ; V solution = 114.63 / 1.146 = 100 ml = 0.1 l. n(NaCl) = m(NaCl) / M(NaCl); M(NaCl) = Ar(Na) + Ar(Cl) = 23 + 35.5 = 58.5 g/mol; n(NaCl) = 14.63 / 58.5 = 0.25 mol. Then, the molar concentration of a solution of sodium chloride in water will be equal to: C(NaCl) = n(NaCl) / V solution ; C(NaCl) = 0.25 / 0.1 = 2.5 mol/l.
Answer	The mass fraction of sodium chloride in the solution is 12.76%, and the molar concentration of a solution of sodium chloride in water is 2.5 mol/l.

EXAMPLE 2

Exercise	What mass copper sulfate can be obtained by evaporating 300 ml of copper sulfate solution with mass fraction copper sulfate 15% and density 1.15 g/ml?
Solution	Let's find the mass of the solution: m solution = V solution ×r solution ; m solution = 300 × 1.15 = 345 g. Let's calculate the mass of dissolved copper sulfate: w(CuSO 4) = m(CuSO 4) / m solution; m(CuSO 4) = m solution ×w(CuSO 4); m(CuSO 4) = 345 × 0.15 = 51.75 g. Let's determine the amount of copper sulfate substance: n(CuSO 4) = m(CuSO 4) / M(CuSO 4); M(CuSO 4) = Ar(Cu) + Ar(S) + 4 ×Ar(O) = 64 + 32 + 4 × 16 = 98 + 64 = 160 g/mol; n(CuSO 4) = 51.75 / 160 = 0.3234 mol. One mole of copper sulfate (CuSO 4 × 5H 2 O) contains 1 mole of copper sulfate, therefore n(CuSO 4) = n(CuSO 4 × 5H 2 O) = 0.3234 mol. Let's find the mass of copper sulfate: m(CuSO 4 × 5H 2 O) = n(CuSO 4 × 5H 2 O) × M(CuSO 4 × 5H 2 O); M(CuSO 4 × 5H 2 O) = M(CuSO 4) + 5 × M(H 2 O); M(H 2 O) = 2 ×Ar(H) + Ar(O) = 2 × 1 + 16 = 2 + 16 = 18 g/mol; M(CuSO 4 × 5H 2 O) = 160 + 5 × 18 = 160 + 90 = 250 g/mol; m(CuSO 4 × 5H 2 O) = 0.3234 × 250 = 80.85 g.
Answer	The mass of copper sulfate is 80.85 g.

>>Calculation of body mass and volume

3. How can you find the mass of a body based on its density and volume?

Experimental task.

Take a bar of soap shaped rectangular parallelepiped, on which its mass is indicated. After taking the necessary measurements, determine the density of the soap.

Submitted by readers from Internet sites

physics library, physics lessons, physics program, physics lesson notes, physics textbooks, ready-made homework

Lesson content lesson notes supporting frame lesson presentation acceleration methods interactive technologies Practice tasks and exercises self-test workshops, trainings, cases, quests homework controversial issues rhetorical questions from students Illustrations audio, video clips and multimedia photographs, pictures, graphics, tables, diagrams, humor, anecdotes, jokes, comics, parables, sayings, crosswords, quotes Add-ons abstracts articles tricks for the curious cribs textbooks basic and additional dictionary of terms other Improving textbooks and lessonscorrecting errors in the textbook updating a fragment in a textbook, elements of innovation in the lesson, replacing outdated knowledge with new ones Only for teachers perfect lessons calendar plan for a year guidelines discussion programs Integrated Lessons

Lesson developments (lesson notes)

Basics general education

Line UMK A.V. Peryshkin. Physics (7-9)

Attention! The site administration is not responsible for the content of methodological developments, as well as for the compliance of the development with the Federal State Educational Standard.

Methodological development physics lesson for grade 7 on the topic “Calculating the mass and volume of a body based on its density.

Class: 7

Lesson objectives: repeat the topic “Body Density”, learn to determine the volume of a body and its mass from a known density, learn to solve problems using these formulas.

Lesson objectives: apply acquired knowledge in a new situation; develop interest in a subject by doing different tasks: practical and theoretical.

Didactic materials and equipment for the lesson: presentation, posters " International system units", "Prefixes for forming multiples and submultiple units", individual cards with test tasks; scales with weights, beaker, ruler, soap, potato, stone.

Lesson Plan

I. Organizational moment

II. Updating knowledge

1. Frontal survey on theoretical material

2. Fill out the table (orally)

				ρ

3. Name the number you made from the numbers of the correct formulas.

1. v = S/t;
2. v = St;
3. S = vt;
4. ρ = mv;
5. ρ = m/V;
6. m = ρ/ V.

3. Express in SI.

4.8 t; 502 g; 175 g; 35 cm; 2341 mm; 584 l; 3846 cm 3; 0.00567 g/cm 3

III Checking the data

Test work on the topic “Mass. Density"

Option 1

1) When heated, the body expands. Moreover, the density of the substance from which it is made is...

A) does not change b) increases V) decreases G)

2) A body weighing 42 g in the shape of a parallelepiped was made from a certain substance. The parallelepiped has the following dimensions: height 1 cm, width 2 cm, length 3 cm. Determine its density.

3) After placing a body on one pan of the scale and a set of weights on the other (20 g, 500 mg, 200 mg, 100 mg, 10 mg, 20 mg, 20 mg and 50 mg), the scales came into equilibrium. What is the body mass?

Option 2

1) When cooling, the body contracts. Moreover, the density of the substance from which it is made is...

A) does not change b) increases V) decreases G) increases, then decreases

2) The canister has dimensions: height 3 dm, width 1 dm, length 5 dm. The weight of an empty canister is 1 kg, filled - 13 kg. What is the density of the liquid?

3) After placing a body on one pan of the scale and a set of weights on the other (50 g, 500 mg, 200 mg, 100 mg, 10 mg, 10 mg, 20 mg and 50 mg), the scales came into equilibrium. What is the body mass?

IV. Solving practical problems

1) There is a piece of stone in front of you. What measurements and calculations need to be performed to determine its density? What device is convenient to use to measure body volume? Not correct form? Formulate the problem with a solution.

2) Now you see a bar of soap. What measurements and calculations must be performed to determine the density of this body? What device is convenient to use to measure the volume of soap? Formulate the problem with a solution.

Formulation of the problem

3) Recently, one of the TV shows showed a story about peasant farm, where wonderful potatoes were grown. People come from all cities to buy potatoes, but only potatoes take a certain volume. I brought you something like this potato for class. Let's determine its volume. It’s just that it won’t fit into a beaker, or even into a casting glass. Your suggestions?

This is the topic of our lesson: Calculating the mass and volume of a body based on its density.

Complete this task in your notebooks: How to find the volume of a body if the mass of the body and its density are known?

Let's look at examples of problem solving.

1) In front of you in a beaker there are water, milk and sunflower oil. It is necessary to calculate the masses of these liquids, knowing their densities.

2) Next to the beakers there are plastic and steel balls, electronic balance. Using the table from the textbook, find out the densities of these substances. Calculate the volumes of the balls.

V. Independent solution of calculation problems

1. The mass of the cast iron ball is 800 g, its volume is 125 cm 3. Is this ball solid or hollow?
2. What is the mass of an iron sheet 1 m long, 80 cm wide, 1 mm thick?
3. An oak block has a mass of 800 g. Determine its volume if the density of oak is 800 kg/m 3.

VI. Reflection (summarizing the lesson, assessments)

Well, our lesson is coming to an end. I hope that you will be able to use the knowledge you have acquired not only in your lessons various subjects, but you will also use them in Everyday life. And now the section feedback. You see statements on the screen. Choose any one and complete it (orally).

Possible answers: Today I learned... It was interesting... It was difficult... I realized that... I learned... I was surprised...

VII. D/z

1) § 23 – teach

2) Come up with 3 interesting tasks to calculate the density, mass or volume of bodies used in everyday life (print on A4 with a solution and illustrations, bring these bodies to class to solve some problems)

Lesson topic: “Calculation of body mass and volume”
Lesson objectives: learn to determine the mass and volume of a body by its density.
Lesson objectives:
repeat body density, learn to determine the mass and volume of a body based on a given
density, learn to solve problems using these formulas, apply the obtained
knowledge in a new situation;
develop interest in the subject by performing various tasks: practical and
theoretical.
DURING THE CLASSES
1. Updating knowledge
2. Repetition of the topic “Density

Substances." Examination homework.
Discussion of questions:
1) What does the density of a substance show?
2) How to determine the density of a substance?
3)
Inflatable balloon squeezed with your hands. Do you think it has increased
the density of the air inside the ball or not.
4) When you, going on vacation to grandma or to camp, stuff everything with new and
new things, an already plump suitcase, which physical quantity do you
change: mass, density or volume?
5) The thickness and mass of aluminum and steel rods are the same. Which one of
Are the rods longer?
6) Does the density of water depend on its volume?
7) Find the error in the reasoning: “The density of 1 m3 of kerosene is 800 kg/m3. Then
the density of 2 m3 of kerosene is 1600 kg/m3.”
3. Studying new material. Calculation of body mass and volume based on its density
Mass (from the Latin massa - block, piece) of a body is a quantitative measure of its
inertia. Denoted by m
Inertia is an internal property of all bodies, the quantitative measure of which is
weight.
Knowing the density of substances is very important for various practical purposes.
An engineer, when creating a machine, can calculate in advance based on the density and volume of the material
the mass of the future car.
The builder can determine what the mass of the building under construction will be.
Assignment: “Think and answer” oral tasks for converting units of measurement to SI
100 g
O.45 t
4.5 t
450 g
450 c
4.5 c
45,000 kg
0.1 kg
450 kg
4,500 kg
0.45 kg
45,000 kg
Body volume
Body of regular shape V=abc (m3)
Body cylindrical V=Sh (m3)
Irregular body

1) What conclusions can you draw?
Assignment: “Compare bodies”
2) Write down in a notebook and remember the scheme for calculating the mass and volume of a body according to its
density. Slide number 13.
,
.
We can easily find the mass m by multiplying the density by the volume.
4. Physical exercise:
Teacher: Everyone stood up. Guys, you will answer questions by show of hands. Answer
“yes” hands up and nod your head, answer “no” hands to the sides and shake your head
sides.
1) The bodies around us consist of various substances. (Yes)
2) Density is a physical quantity that is equal to the ratio of body mass to its
volume. (Yes)
3) Density of the same substance in solid, liquid and gaseous states
is the same. (No)
4) Density shows the mass of a substance per unit volume. (Yes)
5) The SI unit of density is 1 g/cm3. (No)
6) The density of 1 kg of water is 1000 kg/m3, and the density of 3 kg of water is 3000 kg/m3. (No)
7) The density of water is 1 g/cm3. (Yes)
5. Consolidation of the studied material. Problem solving.
1) Sample solution to the problem on page 53 of the textbook - let’s look at it.
2) Experimental task. Measure the volume of a wooden block and calculate its mass
using density table data. Check the result using a scale.
3) Task. How many kilograms of kerosene are in a five-liter bottle?
Given: Solution:
V ρ
V= 5 l= 0.005 m3 m=
ρ
= 800 kg/m
m= ? Answer: m= 4 kg.
3 m= 800 0.005 = 4 (kg)
4) Task. What is the volume in liters of an ice floe weighing 1.8 tons?
Given: Solution:
m= 1.8 t = 1800 kg V= m /ρ
ρ
= 900 kg/m
V= ? Answer: V= 2000 l.
3 V= 1800/900 = 2 m3= 2000 dm3= 2000 l
5) Solving problems from workbook No. 6, 7 page 45.
6. Reflection and summing up the lesson
It's interesting to know that...
Average density Earth 5500 kg/m3, Sun – 1400 kg/m3, Moon – 3300 kg/m3.
The density of human blood is 1050 kg/m3.
The average density of the human body is 1036 kg/m3. (Think if you can
determine the density of your body?)
Density is a wonderful characteristic!
Having determined the density, you can use the table to find out from what substance
the body is made. Knowing the density, you can determine the volume or mass of a body.

Lesson on the topic "Calculating the mass and volume of a body based on its density"

The purpose of the lesson: repeat the density of a body, be able to determine the mass and volume of a body based on a given density, learn to solve problems using these formulas, apply the acquired knowledge in a new situation;

Tasks:

educational (formation of cognitive UUD) :

consolidate the material studied on the topic “Density of Matter”;

be able to experimentally determine density solid using scales and a measuring cylinder, ruler;

consolidate problem solving skills on this topic.

educational (formation of communicative and personal UUD) :

work in a group - establish working relationships, collaborate effectively and promote productive cooperation; integrate into a peer group and build productive interactions with peers and adults

- developing (formation of regulatory UUD)

Broaden the horizons of students;

Foster careful and careful handling of equipment; accuracy of notes in notebooks

Form of work: individual - group.

Equipment: lever scales with weights, measuring cylinder (beaker), flask, key, block (pine), bag with buttons, bar of soap, vegetable oil.

There will be a file here: /data/edu/files/o1448041365.ppt (Calculation of body mass and volume)

There will be a file here: /data/edu/files/o1448041436.docx (Algorithm for the group leader)

The file will be here: /data/edu/files/j1448041511.docx (Tasks for groups)

Technical equipment: computer, screen, multimedia projector, lesson presentation Annex 1.

Handout: tasks for groups, algorithm for the experiment leader. Appendix 2.

Lesson Plan

1. Organizational moment - 1 min.

2. Updating knowledge - 8 min.

3. Motivation educational activities students to study the topic. -2 min

3. Consolidation of the studied material. - 14 min.

4. Physical education minute - 2 min.

5. Solving problems - 10 min.

6. Reflection - 2 min.

7.Homework - 1 min.

During the classes

1.Organizing time

Hello, sit down. Turn your attention to the board (slide No. 1). It is advisable to obtain any knowledge through experience, these words belong to the great scientist Leonardo da Vinci. How do you understand them? That's right, well done. Today in our lesson we will gain knowledge through experience.

2. Updating knowledge

But first, let's review the theory a little.

In what units is it measured?

What do you need to know to be able to find the density?

How to find the density of a substance? (write the formula on the board)

How to find the mass or volume of a body from the formula for the density of a substance?

3. Motivating students' learning activities to study the topic.

Setting goals and objectives for the lesson.

In previous lessons we got acquainted with physical quantity“Density” and did 2 laboratory works, during which they learned to experimentally find the volumes of bodies and the densities of various substances.

Tell me, how did you determine the volume of a body of arbitrary shape when doing laboratory work?

(Using a beaker. Water was poured into the beaker, the volume of liquid poured was measured, then a body of irregular shape was lowered into the beaker and the changed volume of liquid was measured again. They calculated how much the volume of liquid had changed, the change in volume will be the volume of the body of irregular shape.)

Knowing the density of substances is very important for practical purposes. For example, you can determine what volume to make a vessel in order to pour 1 kg of sunflower oil into it, or, when creating a machine, calculate the mass of the future machine in advance based on the density and volume of the material.

Since the density of any substance is calculated by the formula:

ρ= then from here you can find the mass and volume:

This is the topic of our lesson: “Calculating the mass and volume of a body based on its density.” Objective of the lesson: to be able to determine the mass, volume and density of bodies experimentally, to be able to solve problems using the density formula.

4. Consolidation of the studied material. Let's carry out experimental study. We will work in a group of 4 people. Each group has 1 experiment leader, 1 laboratory assistant and 2 statisticians. The head of the experiment gives tasks to the laboratory assistant and extras, and controls all the work in the group. All questions in the group are asked to the leader, and only the leader of the experiment can ask the teacher a question.

1 group Determine what substance the key is made of

Equipment: beaker, scales with weights.

2nd group Determine the mass of the block, knowing the type of wood from which it is made.

Equipment: block (pine), ruler

When completing tasks, do not forget about safety precautions when working with beakers, scales and bodies.

3 group Determine what substance the button is made of

Equipment: box with buttons, beaker with water, scales with weights

When completing tasks, do not forget about safety precautions when working with beakers, scales and bodies.

4 group Determine the density of soap

Equipment: soap, scales with weights, ruler

When completing tasks, do not forget about safety precautions when working with beakers, scales and bodies.

5 group Determine the density of vegetable oil

Equipment: flask with vegetable oil, scales with weights, beaker.

When completing tasks, do not forget about safety precautions when working with beakers, scales and bodies.

5. Physical education minute

- Let's depict how our bus travels. Turn the steering wheel to the left (children lean to the right)

- And now a sharp turn to the right. (children lean left)

- We're going straight. How noisy are our engines? (children voice)

- And now make a sharp left turn. (children lean to the right)

- And again now there is a sharp turn to the right. (children lean left)

- We're going straight. Abrupt stop. (children lean forward)

- We move off abruptly (children lean forward)

- Well done boys. What phenomenon did you depict?

- What is inertia?

6. Problem solving

1).Task No. 1. What liquid is poured into a vessel with a capacity of 100 liters if its mass is 93 kg?

2). Task No. 2. Determine the mass of a copper bar if its volume is 500 cm3.

Answer: 4450 g = 4.45 kg.

3)Task No. 3 Find the volume of an iceberg weighing 240 tons?

6. Reflection (summarizing the lesson, assessments)

In the right column, underline your answer from the options provided.
1. How did communication during work affect task performance?	Made it more efficient The task was slowed down It did not allow me to complete the task accurately and spoiled relationships in the group.
2. What difficulties did you experience while completing the task?	Lack of information, Lack of communication tools (speech samples, texts, etc.), Difficulties in communication.
3. What style of communication prevailed at work?	People oriented Task oriented.
5. Who or what played decisive role what happened in the group?	Team leader Reluctance to establish contact with most group members, Misunderstanding of the task assigned to collaboration, The task itself turned out to be uninteresting and difficult.

7. Homework.

§22 ex. 8 (No. 1,2,3)

Literature

“Physics” - 7th grade, A. V. Peryshkin M., 2004

Collection of problems in physics grades 7-8, V. I. Lukashik 2000

Know yourself, Library “First of September”, M., “ Chistye Prudy” 2009

Supplement “Physics” No. 17, 2001

Thematic planning in physics, grade 7 M., “Wako” 2005