Topicmc9a0904219abfc08_1528449000663_0Topic

Determining the density of bodies

Levelmc9a0904219abfc08_1528449084556_0Level

Second

Core curriculummc9a0904219abfc08_1528449076687_0Core curriculum

I. Using physical terms and quantities to describe phenomena and to identify their examples in everyday life.

Timingmc9a0904219abfc08_1528449068082_0Timing

45 minutes

General learning objectivesmc9a0904219abfc08_1528449523725_0General learning objectives

Identifying differences in body densities.

Key competencesmc9a0904219abfc08_1528449552113_0Key competences

1. Indicating the state of matter of bodies on the basis of their density.

2. Calculating the density of bodies.

Operational (detailed) goalsmc9a0904219abfc08_1528450430307_0Operational (detailed) goals

The student:

- recognizes the relationship between the state of matter of bodies and their density,

- specifies what density depends on.

Methodsmc9a0904219abfc08_1528449534267_0Methods

1. Learning through observation.

Forms of workmc9a0904219abfc08_1528449514617_0Forms of work

1. Individual work.

2. Work with the whole class.

Lesson stages

Introductionmc9a0904219abfc08_1528450127855_0Introduction

Density is a physical quantity which describes the body. To determine the density of the body, we need to measure its mass and volume and use the following formula:

If we know the density and the volume of the body, we can calculate its mass. For this purpose, the following formula should be used:

The body volume of a known mass and density is calculated using the formula:

Conclusion:

The density of the body can be determined only when we know its mass and its volume.

Proceduremc9a0904219abfc08_1528446435040_0Procedure

Task

Look at the Slideshow „Determining the volume of irregularly shaped bodies”.

In the presented example the measurement accuracy of the measuring‑glass is 1 ml = 1 cmIndeks górny 3³. This is the accuracy of determining the entire volume of water in the glass. However, our measurement is relative. We do not measure the volume of water but the difference between water volume with the key and after removing the key. Therefore, the measurement error is related only to the method of reading the water level and the meniscus height. Thus, the error of such measurement can be estimated as 0,2 ml = 0,2 cmIndeks górny 3³.

Question:

The volume of water with the dipped key was VIndeks dolny water + key Indeks dolny koniec_{water + key} = 26 cmIndeks górny 3³. The volume of water after removing the key was VIndeks dolny water_water = 25 cmIndeks górny 3³. Determine the volume of the key.mc9a0904219abfc08_1527752263647_0The volume of water with the dipped key was VIndeks dolny water + key Indeks dolny koniec_{water + key} = 26 cmIndeks górny 3³. The volume of water after removing the key was VIndeks dolny water_water = 25 cmIndeks górny 3³. Determine the volume of the key.

Answer:

VIndeks dolny key_key = VIndeks dolny water + key Indeks dolny koniec_{water + key} - VIndeks dolny water_water = 26 cmIndeks górny 3³ - 25 cmIndeks górny 3³ = 1 cmIndeks górny 3³

Because the error of such measurement can be estimated as 0,2 cmIndeks górny 3³, the final result of the experimental determination of the key volume can be written in the form:

VIndeks dolny key_key = 1,0 ± 0,2 [cmIndeks górny 3³]

Task

Do the experiment according to the instructions provided below.

Experiment

Research problem:

Do items made of the same material, having a greater mass, have a greater density.

Research hypothesis:

The greater the volume of bodies made of the same material, the greater their mass. The mass‑to‑volume ratio, i.e. the density, is constant.

The following equipment will be required:

- 3 copper nails of various sizes,

- a measuring‑glass,

- water,

- laboratory scales.

Experimentation process:

1. Measure the volume of all nails using the measuring glass.

2. Determine the mass of the nails using the laboratory scales.

3. Write the results of measurements in the notebook, for example in the adequatly table.

4. Make a graph of the dependence between the mass of the body on its volume.

Conclusion: 

The experiment shows that the mass of the body increases with the increase of its volume - the mass increases as many times as the volume increases. For the body of a given substance, the body‑volume ratio is constant. Bodies made of the same material have constant density, regardless of their mass and volume.

Task

Suggest the experiment in which you can determine the density of liquid.

Task

Familiarise yourself with the tables of body density. The bodies are in different physical states at the room temperature or below 0°C at atmospheric pressure of 1013 hPa.

[Table 1]

[Table 2]

[Table 3]

Task

Answer the following questions:

1. In what state of matter does the body have the lowest density?

2. In what state of matter does the body have the greatest density?

3. Does the change in the temperature affect the density of the body?

4. Does the molecular structure affect the density of bodies?

5. Why is ice density lower than water density?

Answers:

1. Bodies have the lowest density in the gas state.

2. Bodies in the solid state have usually the greatest density.

3. The change in the temperature affects the density of the body. The change in the temperature of the body is related to the change in average distances between the molecules or atoms that the tested body is made of.

4. The volume of the body depends on the average intermolecular distance. Therefore, the smaller the distance between the molecules of the body, the greater its density.

5. Ice density is lesser than water density, because the average distance of molecules in ice is greater than in water.

Task

Convert the following units:

2500 $\frac{kg}{m^3}$ to $\frac{g}{c{m}^3}$

7,2 $\frac{g}{c{m}^3}$ to $\frac{kg}{m^3}$

Answer:

$2500\frac{kg}{m^3}=2500\cdot \frac{1000}{1000000}\frac{g}{c{m}^3}=\frac{2500}{1000}\frac{g}{c{m}^3}=2,5\frac{g}{c{m}^3}$

$7,2\frac{g}{c{m}^3}=7,2\cdot \frac{0,001}{0,000001}\frac{kg}{m^3}=\frac{7,2}{0,001}\frac{kg}{m^3}=7200\frac{kg}{m^3}$

Lesson summarymc9a0904219abfc08_1528450119332_0Lesson summary

The quotient of the mass and the volume of a given body is called its density. Density is therefore a characteristic quantity of a given substance. Density is calculated with the formula $d=\frac{m}{V}$. To determine the density of the body, its volume and its mass should be known. The basic unit of density is the kilogram per cubic meter. In practice, we often express the density of bodies in smaller units, e.g. $\frac{g}{c{m}^3}$. The density of the substance varies with the temperature and/or pressure changes. The density of solids and liquids is much higher than the density of gases.

Selected words and expressions used in the lesson plan

densitydensitydensity

volume of the l bodyvolume of the l bodyvolume of the l body

irregular sahapeirregular sahapeirregular sahape

iceiceice

saturated water vaporsaturated water vaporsaturated water vapor

measurement accuracymeasurement accuracymeasurement accuracy

measuring glassmeasuring glassmeasuring glass

units conversionunits conversionunits conversion

determinedeterminedetermine

formulaformulaformula