Topicm3b638b9b5869d04b_1528449000663_0Topic

Determining matter density

Levelm3b638b9b5869d04b_1528449084556_0Level

Second

Core curriculumm3b638b9b5869d04b_1528449076687_0Core curriculum

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

Timingm3b638b9b5869d04b_1528449068082_0Timing

45 minutes

General learning objectivesm3b638b9b5869d04b_1528449523725_0General learning objectives

Determining the densitydensitydensity of bodies with regular structure.

Key competencesm3b638b9b5869d04b_1528449552113_0Key competences

1. Using mass, volume and density concepts.

2. Determining the relationship between massmassmass, volumevolumevolume and densitydensitydensity.

Operational (detailed) goalsm3b638b9b5869d04b_1528450430307_0Operational (detailed) goals

The student:

- recognizes the notion of mass, volume, densitydensitydensity and their units,

- specifies what determines the magnitude of impacts.

Methodsm3b638b9b5869d04b_1528449534267_0Methods

1. Learning through observation.

Forms of workm3b638b9b5869d04b_1528449514617_0Forms of work

1. Individual work.

2. Work with the whole class.

Lesson stages

Introductionm3b638b9b5869d04b_1528450127855_0Introduction

Task 1

Answer the questions:

1. What is the weight of a physical body?

2. In what units do we determine the weight of the body?

3. What does the concept of body volumevolumevolume mean?

4. In which units do we determine the body volume?

5. Are there physical quantities that uniquely characterize the physical body?

6. Can bodies with the same dimensions have different masses?

Answer:

1. MassmassMass is a physical quantity telling us how much matter there is inside a particular physical body.

2. The unit of mass in the SI system is the kilogram.

3. The volume informs us about how much space the body occupies.

4. The unit of volume in the SI system is the cubic meter (mIndeks górny 3³).

5. There is no single physical quantity that could precisely describe the physical body. The unambiguity of the description of the physical body requires giving many of its properties e.g. mass, volumevolumevolume, colour, shape, temperature. The accuracy of the description depends on the type of observation.

6. Bodies of the same size can have different masses. Balls of the same diameter made of steel and wood have different masses.

Task 2

Learn identifying the letters and the units used to describe volume, weight, area and length.

[Table 1]

Procedurem3b638b9b5869d04b_1528446435040_0Procedure

Task 3

Calculate the volume of the figures presented below. Provide a mathematical notation of the formulas for the volume of a given figure.

[Illustration 1]

a)

Calculations:

$V=a·b·c=...$

b)

Calculations:

$V=\mathrm{\pi }·r^2·h=...$

c)

Calculations :

$V=V_1+V_2=a·b·c+\mathrm{\pi }·r^2·h=...$

Answer:

a) $V=a\cdot b\cdot c=6cm\cdot 4cm\cdot 12cm=288c{m}^3$

b) $V=\pi \cdot r^2\cdot h=3,14\cdot {\left(3cm\right)}^2\cdot 8cm=226,08c{m}^3$

c) $V=V_1+V_2=a\cdot b\cdot c+\pi \cdot r^2\cdot h=3cm\cdot 2cm\cdot 7cm+3,14\cdot {\left(\frac{4cm}{2}\right)}^2\cdot 8cm=$

$=(42+100,48)c{m}^3=142,48c{m}^3$

Task 4

Look at the figure and:

1.  Check the changes in massmassmass and volumevolumevolume of the cubes presented in figures (a), (b) and (c) which are made of aluminum.

2. Compare the results with the volumes and masses of bars made after melting two cubes (d) and melting three cubes (e).

3. Compare the mass‑volume ratio in every variant.

[Illustration 2]

(a) $V_a=1c{m}^3,m_a=2,7g,\frac{m_a}{V_a}=\frac{2,7g}{1c{m}^3}=2,7\frac{g}{c{m}^3}$

(b) $V_b=1c{m}^3+1c{m}^3=2c{m}^3,m_b=2,7g+2,7g=5,4g,\frac{m_b}{V_b}=\frac{5,4g}{2c{m}^3}=2,7\frac{g}{c{m}^3}$

(c) $V_c=1c{m}^3+1c{m}^3+1c{m}^3=3c{m}^3,m_c=2,7g+2,7g+2,7g=8,1g,\frac{m_c}{Vc}=\frac{8,1g}{3c{m}^3}=2,7\frac{g}{c{m}^3}$

(bIndeks dolny 1₁) $V_{b1}=2\cdot 1c{m}^3=2c{m}^3,m_{b1}=2\cdot 2,7g=5,4g,\frac{m_{b1}}{V_{b1}}=\frac{5,4g}{2c{m}^3}=2,7\frac{g}{c{m}^3}$

(cIndeks dolny 1₁) $V_{c1}=3\cdot 1c{m}^3=3c{m}^3,m_{c1}=3\cdot 2,7g=8,1g,\frac{m_{c1}}{V_{c1}}=\frac{8,1g}{3c{m}^3}=2,7\frac{g}{c{m}^3}$

[Interactive illustration]

Conclusions:

1. The weight to volumevolumevolume ratio in all cases was the same and was $2,7\frac{g}{c{m}^3}.$ 
This ratio does not depend on the way of examining individual cubes or combining them into one whole bar (e.g. by melting) as a rod. Thus, the ratio of body mass to its volume is a physical quantity that characterizes the properties of the body

2. DensitydensityDensity is a new physical quantity describing the properties of the body. Density of the body is determined on the basis of its mass and volume.

Density can be written mathematically in the form of the following formula:

Task 5

Determine the minimum and maximum density of a cuboid with the dimensions $4cm·6cm·7cm$ and the mass of 250 g, knowing that the ruler measures with 1 mm accuracy and the scale weighs with 2 g accuracy. Draw the conclusion obtained from the above calculation.m3b638b9b5869d04b_1527752263647_0Determine the minimum and maximum density of a cuboid with the dimensions $4cm·6cm·7cm$ and the mass of 250 g, knowing that the ruler measures with 1 mm accuracy and the scale weighs with 2 g accuracy. Draw the conclusion obtained from the above calculation.

Answer:

Minimum volume, $V_{min}=3,9cm\cdot 5,9cm\cdot 6,9cm=158,77c{m}^3.$

Maximum volume, $V_{max}=4,1cm\cdot 6,1cm\cdot 7,1cm=177,57c{m}^3.$

Minimum mass, $m_{min}=248g.$

Maximum mass, $m_{max}=252g.$

Minimum density, $d_{min}=\frac{V_{min}}{m_{max}}=0,63\frac{g}{c{m}^3}.$

Maximum density, $d_{max}=\frac{V_{max}}{m_{min}}=0,72\frac{g}{c{m}^3}.$

Real density, $d_{av}=\frac{V_{av}}{m_{av}}=0,67\frac{g}{c{m}^3}.$

Conclusion:

The measurement result differs most often from the real value of the measured quantity. We say that the result of each physical measurement is burdened with measurement uncertaintymeasurement uncertaintymeasurement uncertainty.

In our case, we can write that the densitydensitydensity of the measured cuboidcuboidcuboid was:

This uncertainty results both from the measurement method and the accuracy of the used instrument. An inaccurate reading of the results from the scale of the instrument may also be the reason of uncertainty. The properties of the tested subject can also influence the uncertainty of measurement.

Task 6

Learn the transformations of the formula for density calculation:

Lesson summarym3b638b9b5869d04b_1528450119332_0Lesson summary

DensitydensityDensity is a physical quantity that is often used to describe the physical properties of the studied physical body. For bodies of regular shaped, the volumevolumevolume determination procedure can be simplified. For this purpose, the mathematical relations that associate the volume of the body with its linear dimensions should be used. To determine the density of the body, we need to measure its massmassmass and volume and then 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 volumevolumevolume of known mass and density is calculated using the formula:

This uncertainty results both from the measurement method and the accuracy of the used instrument. An inaccurate reading of the results from the scale of the instrument may also be the reason of uncertainty. The properties of the tested subject can also influence the uncertainty of measurement.

Selected words and expressions used in the lesson plan

cubecubecube

cuboidcuboidcuboid

cylindercylindercylinder

densitydensitydensity

massmassmass

measurement uncertaintymeasurement uncertaintymeasurement uncertainty

solid bodysolid bodysolid body

steamsteamsteam

volumevolumevolume