Обучение по природни науки и върхови технологии

https://doi.org/10.53656/nat2022-3.06

2022/3, стр. 231 - 254

IS IT SIMPLE TO EXPLAIN THE SIMPLE EXPERIMENTS? HOW DO SOLID BODIES FLOAT?

Dragia Ivanov
OrcID: 0000-0003-1721-1376
E-mail: draiva@uni-plovdiv.bg
Faculty of Physics and Technology
Plovdiv University “Paisii Hilendarski”
24 Tsar Asen St.
4000 Plovdiv Bulgaria
Stefan Nikolov
OrcID: 0000-0001-5498-9940
E-mail: stnikolov@uni-plovdiv.bg
Faculty of Physics and Technology
Plovdiv University “Paisii Hilendarski”
24 Tsar Asen St.
4000 Plovdiv Bulgaria

Резюме: This paper considers the floating of solid homogenous bodies with different simple shapes. The stable floating positions attained by the bodies are examined and some qualitative rules are derived to determine those positions. The sensitivity of those stable positions to the exact proportions of the bodies is shown.

Ключови думи: floating; hydrostatics; educational experiments

I. Introduction

The problems concerning the flotation of solid bodies have been considered since antiquity, mostly with regard to ships. Despite this, there still are interesting things to explore in this field (Bogner & Rüde 2013; Erdös, Schibler & Herndon 1992a; Erdös, Schibler & Herndon 1992b; Lauturp 2011; Wegner 2003), some of which are subject to exploration in this paper.

A stationary solid body  submerged in water is acted  upon by two forces – a gravitational force G and a buoyancy force FB . The gravitational force is a volume force, acting upon each little part of the body. The effective point of application (center of gravity – CG) of this force is fixed in a solid body and doesn’t change irrespective of the position and orientation of the body in the liquid, its participation in any motion, whether it is homogenous or not. Buoyancy force is an electromagnetic surface force. It only acts upon the points of the body in contact with water. The net buoyancy force is a sum of the elementary force of normal reaction of the liquid acting upon the body. Every one of the elementary forces is determined by Pascal’s law of hydrostatic pressure. For a static body in equilibrium the net buoyancy force is constant and does not depend on the orientation of the body in the liquid. It is also equal to the gravitational force ( FB = G ). This is in fact the requirement for the flotation of stationary bodies.

The question about the effective point of application of the buoyancy force (center of buoyancy CB) turns out to be very important in practice. For a homogenous ( ρ = const ) static body the CG is always above the CB. The two centers are positioned on the same vertical line, the two forces compensate each other and the floating body is in equilibrium (Fig. 1).

Figure 1. A homogenous floating body

If the body is not homogenous (ρ ≠ const ) it can happen that the CG is actually below the CB (Fig. 2). Like in the previous case, if the two forces act along the same vertical line the body will be in equilibrium.

Figure 2. A non-homogenous floating body

Figure 3. A floating body out of equilibrium

It is possible for a body to fulfill the flotation requirement but not to be in mechanical equilibrium. If the effective points of application of the two forces are not on the same vertical line the sum of their torques is not zero (Fig. 3). The body will rotate within the liquid until the two forces act along the same vertical line. Therefore, a more complete flotation requirement should also include a requirement for zero net torque.

Figure 4.1. A long thin body in water is unstable when vertical

Figure 4.2. Once tilted, the long thin body rotates under the torque of the two forces

Figure 4.3. The long thin body is stable in a horizontal position

It is well known from mechanics that a body placed on a flat surface is more stable when its CG is lower and/or its supporting contact surface is larger. A similar situation happens when the body is immersed in a liquid. Let us, for example, immerse a relatively thin, long cylinder (a pencil) vertically in water (Fig. 4.1). The body quickly starts rotating under the action of the two forces. (Fig. 4.2) and transitions to a stable horizontal position (Fig. 4.3). It is obvious without the need for calculations that in the initial position the CG and CB are far apart and the “supporting” surface is very small. In the final position the distance between CG and CB is very small and the “supporting” surface is much larger. In both the initial and final state, the forces act along the same vertical line.

We can define the main rules for stable flotation of a solid body in a liquid:

1. The potential energy of the body-liquid system should be minimal

2. The center of gravity and center of buoyancy should be on the same vertical line

3. The distance between the two centers should be minimal

4. The maximal cross-section of the submerged part of the body should be horizontal

From the point of view of pure physics requirement 1 is sufficient to describe stable equilibrium but it is very difficult to apply in practice. The other rules may not always be true, especially for complex, non-homogenous bodies (like ships and boats) but for the simple homogenous objects we explore bellow they effectively equate to rule 1 while being easier to apply purely geometrically.

II. Rectangular prism

Let us consider a homogenous wooden rectangular prism with density ρB 0.5 g cm3 and sizes a=60mm, b=40mm, c=15mm (Fig. 5). We immerse in a vessel with water in an arbitrary orientation. Upon the action of the two forces the prism quickly rotates itself into its stable position. In this position the two largest faces of the prism are horizontal. (Fig. 6). The prism has two equivalent stable positions with either one of the two largest being the “bottom” while the other is the “top”. Which one of the two stable positions is reached depends on the initial position of the prism and any initial motion the may have been imparted on it during the immersion.

Figure 5. The rectangular prism

Figure 6. The rectangular floating in one of its stable positions

Let us determine the position of the CG and CB for three possible positions of the prism with a different pair of side horizontal (Fig. 7) starting with the one that the prism normally takes (Fig. 8). The CG is in the geometric center O of the figure, a distance c/2 from the base. This is the effective point of application of the gravitational force which has a magnitude G = mg = VBρBg = abcρBg . The buoyancy force is applied in point A, in the geometric center of the submerged part of the body, which is a similar prism to the whole body but with the side c replaced with h. The buoyancy force is FB =VW ρW g =hac ρW g . In equilibrium FB = G which yields BWhcρρ= . The distance between the CG and CB is 1.122222BBWWchcссx . Analogously we find the distances between the CG and CB for the other two cases. Ultimately 112BWсx,212BWbxρρ= and 312BWaxρρ= , i.e. x1 < x2 < x3 .

Figure 7.1. The prism in one possible position – large side up

Figure 7.2. The prism in a possible position long thin side up

Figure 7.3. The prism with the smallest side up

Figure 8. The floating prism in detail

The shortest distance between the CG and CB is attained in the case when the body is stable in the water. The respective horizontal cross-sections of the body have areas S1 > S2 > S3 .

We can make the following conclusions:

1. In the stable position of the body the gravity force and the buoyancy force are along the same vertical line with the point of application of the buoyancy force below the point of application of the gravity force.

2. The gravity force and the buoyancy force are equal in magnitude and act in opposite directions.

3. In the stable position of the body, the distance between the CB and CG is smaller than in all the unstable positions. Because of this the body-water system has its lowest potential energy in the stable position.

4. The largest side of the body is submerged and horizontal.

These considerations are made for a distance c that is small (the prism is relatively thin). The a-b side is thus practically parallel to the water surface. If this condition is not observed, there are other stable positions possible that are not symmetric relative to the water surface and no sides of the prism are horizontal. The exact mathematical treatment of these cases turned out to be very complicated. It turned out, however, that the conclusions hold in many other cases when the immersed body is homogenous, less dense than the liquid and geometrically convex (no dimples). The general rules defined above can be used to relatively easily predict and explain the results in a number of different specific cases that we will outline bellow.

III. Examples

In this section we will present the experimental study of the static stable positions of different solid bodies with well-known basis shapes immersed in water. The bodies are made out of wood with a density less than water (ρB < ρW ). We can assume to a good approximation that the bodies are homogenous. We only explored geometrically convex bodies for which the CG is above the CB. We will check if the rules for stable equilibrium positions are applicable in each case. All bodies were painted in contrasting colors on neighboring sides for improved visibility in the pictures. The paint also protects the wood from soaking up water, which was a problem in some of our initial experiments.

III.1. Cylinders

We studied cylinders with the same base (diameter 33 mm) but different heights ranging from 15 mm to 52 mm (Fig. 9). They’re all made of the same wood with ρ ≈ 0.5 g cm3 . It turned out that their floating behavior is very different based on their height (Fig. 10). The shortest cylinder floats with its base practically horizontal and axis vertical. The next one tilts slightly. The third cylinder has its axis at almost 45° with the fourth one being tilted even more. The tallest cylinder is floating practically on its side, with the axis essentially horizontal and the bases perpendicular to the water. The tilt of each of the cylinders is determined by the rules defined above. The main requirement is for the potential energy of the system to be minimal, but the exact position for which this is achieved is different depending on the specific height-to-diameter ratio. Playing around with each of the cylinders, trying to change its tilt it can be visually confirmed that in each case the stable position provides for the largest submerged horizontal cross-section.

Figure 9. The cylinders used for the experiments

Figure 10.1. The stable floating position of the shortest cylinder

Figure 10.2. The stable floating position of the mid-height cylinder

Figure 10.3. The stable floating position of the tallest cylinder

III.2. Square prisms

A set of three homogenous wooden prisms with a density of ρ ≈ 0.5 g cm3 , a square base with a 30 mm side and three different heights (15 mm, 30 mm, 50 mm). The middle on is actually a cube. The stable floating positions of each are shown on Fig. 12. The shortest one attains a position such that its square base is visually horizontal (Fig. 12.1). This prism has two distinct stable positions with each of the bases up. The second prism (cube) floats so that one of its vertices points up with the corresponding large diagonal close to vertical (Fig. 12.2). Three of the six sides of the cube show above the water symmetrically. The cube has eight stable positions with each of the vertices pointing up. The third, sufficiently tall prism attains a stable position such that one of its side/long edges points up, visually parallel to the water surface, and two of its larger side face above the water. This prism has four stable positions relative to each of the four side edges.

Figure 12.2. The stable floating position of the cube

Figure 12.3. The stable floating position of the tall prism

While experimenting with other prisms in between these extreme cases of height-to-base ratios we also obtained stable floating positions that were different in-between versions of the three we presented above. The most interesting ones were those closest to the cube with a height-to-base ratio close to one. Those are also the hardest to analyze due to the rather complex geometrical situations that can arise.

III.3. Cones

We carried out the immersion experiments with a set of homogenous wooden cones (Fig. 13) with a density ρ ≈ 0.5 g cm3 . They all have the same base with a diameter of 30 mm and progressively increasing heights of 25 mm, 33 mm and 48 mm. Upon immersion (Fig. 14) the shortest cone assumes a stable position with its axis visibly vertical, the tallest settles with its axis approximately horizontal and the middle-height cone has a stable position with its axis at an in-between angle. The short one could be put in a stable position both point-up and point-down but the point-down position was relatively easy to turn over with a little outside force while the point-up was much more stable in this sense. The in-between tilted position of the mid-height cone is with the point up, too, which also indicates that the point-up position is the more stable one. The exact angle of tilt for the mid-height cone depends on the precise height-to-diameter ratio.

Figure 13. The cones used for the experiments

Figure 14.1. The point-up stable floating position of the short cone

Figure 14.2. The point-down stable floating position of the short cone

Figure 14.3. The stable floating position of the mid-height cone

Figure 14.4. The stable floating position of the tall cone

III.4. Square pyramids

We carried out floating experiments with a set of wooden (ρ ≈ 0.5 g cm3 ) homogenous pyramids with a square base with a 35 mm side. The heights of the pyramids are 30 mm, 40 mm and 70 mm (Fig. 15). Upon immersion in water the pyramids attain one of their stable equilibrium positions (Fig. 16). The shortest pyramid is visibly upright, with its axis apparently vertical. Like with cones, a point-up and a point-down position are possible. The mid-high pyramid obtains a tilt in its axis and one of its side edges gets on top. Four such positions are possible, with each of the edges on top. The highest pyramid positions itself with its axis approximately horizontal and one of the edges on top for a set of four possible stable equilibrium states.

Figure 15. The pyramids used for the experiments

Figure 16.1. The point-up stable floating position of the short pyramid

Figure 16.2. The point-down stable floating position of the short pyramid

Figure 16.3. The stable floating position of the mid-height pyramid

Figure 16.4. The stable floating position of the tall pyramid

III.5. Spherical caps

Figure 17 depicts a body formed by a sphere cut through with a plane (a spherical cap). No matter what part of the sphere the cap constitutes, upon immersion it always orients itself such that the flat part is parallel to the water surface. In this case there is an interesting peculiarity. Depending on the initial position of the body in the water it can orient itself flat side up or flat side down, i.e. it has two stable positions. The experiments showed that when we immerse the body at an angle to the water the critical angle αc that separates these two states is more than 90° (Fig. 18.1). When the angle between the flat part of the body and the water is in the interval 0° < α < αc the body tends toward the stable position, with the spherical part above water and the flat part below (Fig. 18.2, Fig. 19.1). When the angle is αc < α< 180° (Fig. 18.3) the spherical cap moves towards the stable position with the flat side on top (Fig. 18.4, Fig. 19.2). If we drop the spherical cap randomly in the water, the first position (flat side down) is more frequently obtained, it is in a way more stable. Both positions represent local minimums of potential energy of the body-water system, but the flat-side-down is the global minimum. Transition between the two positions requires an outside action since the intermediate positions are energetically unfavorable. An analogous behavior with two stable positions that are not equally stable was observed for the short cone and pyramid discussed above. It can also be obtained with a piece of cylinder cut along a plane parallel to its axis (Fig. 20).

Figure 17. The spherical cap

Figure 18.1. The cap at less than the critical angle

Figure 18.2. The flat-down position attained by the cap if at less than the critical angle initially

Figure 18.3. The cap at more than the critical angle

Figure 18.4. The flat-up position attained by the cap if at more than the critical angle initially

Figure 19.1. The cap in the flat-down stable floating position

Figure 19.2. The cap in the flat-up stable floating position

Figure 20.1. A half-cylinder in a stable floating position with the flat down

Figure 20.2. A half-cylinder in a stable floating position with the flat up

IV. Floating of light bodies

In the previous section we performed the experiments with bodies of relatively large density (still less than the water) so that a significant part of the body was under the water and the CG was at the water surface or below. It is possible to have many situations when the average density of the body is significantly lower than that of the liquid. Such bodies sink very little in the water and essentially float on top of it (Fig. 21). In those cases, the stability of the body can be more easily analyzed by treating it as if the body is just lying on a solid surface. Such experiments can be performed with bodies made out of expanded polystyrene, cork or other similar low-density materials.

V. Floating of non-homogenous bodies

In most practical situations the floating bodies are not solid homogenous objects. In those cases, it is possible for the CG to be both below and above the CB. This can be examined qualitatively with some simple experiments.

On a long thin stick (a pencil works well) we wound a piece of metal wire. Solder wire is very suitable as it is soft and can be wound tightly and won’t spring back and loosen. At first, we position the metal winding close to the end of the pencil. It positions itself vertically (Fig. 22.1). Obviously, the CG of the overall body is below the CB. If the pencil is perturbed from the equilibrium position it quickly moves back as the torque by the pair of forces acting on the body is quite large.

We then move the metal winding up the pencil, closer to the middle. The stable position is tilted relative to the water surface (Fig. 22.2). The distance between the CG and CB is smaller. When the pencil is perturbed from the equilibrium it moves back more slowly, as the torque created by the two forces is less.

When we move the metal winding in the middle of the pencil, its equilibrium position is horizontal (Fig. 22.3). In this case the CG is actually above the CB and very close to it. In this case the pencil is slowest to return to equilibrium if it is perturbed. This experiment shows that a floating body is more stable when its CG is lower. This is very important for ship design and ship sailing. In fact, some cargo ships are dangerous to sail when empty because cargo normally brings the CG down and without it the CG move too high, making the ship very unstable. Some modern sailing boats have keels that protrude below the main hull for this exact purpose – to bring the CG lower. Some of them even have lead weights at the end of the keel. The keel also provides some hydrodynamic effects as the boat moves through the water but this is beyond the scope of this paper.

Figure 21. A lightweight body made of expanded polystyrene floating as if on a solid surface

Figure 22.1. A pencil with a weight at the end floats vertically

Figure 22.2. A pencil with the weight closer to the center can float stably at an angle

Figure 22.3. A pencil with the weight at about the middle floats horizontally

VI. Conclusions

The results of the numerous experiments performed confirm the stability rules formulated in the beginning of the paper. These rules can be used to predict some of the behavior of solid bodies floating in water and may even be used to perform some exact calculations for specific cases. The experiments can be used in an educational setting to start off the exploration of the topic of floating.

REFERENCES

BOGNER, S. & RÜDE, U., 2013. Simulation of floating bodies with the lattice Boltzmann method, Computers & Mathematics with Applications. 65 (6), 901 – 913, https://doi.org/10.1016/j.camwa.2012.09.012.

ERDÖS, P., SCHIBLER, G., & HERNDON, R. C., 1992a. Floating equilibrium of symmetrical objects and the breaking of symmetry. Part 1: Prisms, American Journal of Physics. 60, 335 – 345. https://doi. org/10.1119/1.16877.

ERDÖS, P., SCHIBLER, G., & HERNDON, R. C., 1992b. Floating equilibrium of symmetrical objects and the breaking of symmetry. Part 2: The cube, the octahedron, and the tetrahedron, American Journal of Physics. 60, 345 – 356, https://doi.org/10.1119/1.17130.

LAUTRUP, B., 2011. Physics of Continuous Matter: Exotic and Everyday Phenomena in the Macroscopic World (2nd ed.), Boca Raton: CRC Press. 41 – 55, https://doi.org/10.1201/9781439894200.

WEGNER, F., 2003. Floating Bodies of Equilibrium, Studies of Applied mathematics. 111, 167 – 183, https://doi.org/10.1111/1467-9590.t01-100231.

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RHEOLOGICAL PROPERTIES OF BATTER FOR GLUTEN FREE BREAD

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АДАПТИРАНЕ НА ОБРАЗОВАНИЕТО ДНЕС ЗА УТРЕШНИЯ ДЕН

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ZAGREB CONNECTION INDICES OF TiO2 NANOTUBES

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GEOECOLOGICAL ANALYSIS OF INDUSTRIAL CITIES: ON THE EXAMPLE OF AKTOBE AGGLOMERATION

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БЛАГОДАРЯ ВИ!

Александър Панайотов

ТЕМАТА ВЪГЛЕХИДРАТИ В ПРОГРАМИТЕ ПО ХИМИЯ И БИОЛОГИЯ

Радка Томова, Елена Бояджиева, Миглена Славова , Мариан Николов

BILINGUAL COURSE IN BIOTECHNOLOGY: INTERDISCIPLINARY MODEL

V. Kolarski, D. Marinkova, R. Raykova, D. Danalev, S. Terzieva

ХИМИЧНИЯТ ОПИТ – НАУКА И ЗАБАВА

Елица Чорбаджийска, Величка Димитрова, Магдалена Шекерлийска, Галина Бальова, Методийка Ангелова

ЕКОЛОГИЯТА В БЪЛГАРИЯ

Здравка Костова

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SYNTHESIS OF FLUORINATED HYDROXYCINNAMOYL DERIVATIVES OF ANTI-INFLUENZA DRUGS AND THEIR BIOLOGICAL ACTIVITY

Boyka Stoykova, Maya Chochkova, Galya Ivanova, Luchia Mukova, Nadya Nikolova, Lubomira Nikolaeva-Glomb, Pavel Vojtíšek, Tsenka Milkova, Martin Štícha, David Havlíček

SYNTHESIS AND ANTIVIRAL ACTIVITY OF SOME AMINO ACIDS DERIVATIVES OF INFLUENZA VIRUS DRUGS

Radoslav Chayrov, Vesela Veselinova, Vasilka Markova, Luchia Mukova, Angel Galabov, Ivanka Stankova

NEW DERIVATIVES OF OSELTAMIVIR WITH BILE ACIDS

Kiril Chuchkov, Silvia Nakova, Lucia Mukova, Angel Galabov, Ivanka Stankova

MONOHYDROXY FLAVONES. PART III: THE MULLIKEN ANALYSIS

Maria Vakarelska-Popovska, Zhivko Velkov

LEU-ARG ANALOGUES: SYNTHESIS, IR CHARACTERIZATION AND DOCKING STUDIES

Tatyana Dzimbova, Atanas Chapkanov, Tamara Pajpanova

MODIFIED QUECHERS METHOD FOR DETERMINATION OF METHOMYL, ALDICARB, CARBOFURAN AND PROPOXUR IN LIVER

I. Stoykova, T. Yankovska-Stefenova, L.Yotova, D. Danalev Bulgarian Food Safety Agency, Sofi a, Bulgaria

LACTOBACILLUS PLANTARUM AC 11S AS A BIOCATALYST IN MICROBIAL ELECYTOLYSIS CELL

Elitsa Chorbadzhiyska, Yolina Hubenova, Sophia Yankova, Dragomir Yankov, Mario Mitov

STUDYING THE PROCESS OF DEPOSITION OF ANTIMONY WITH CALCIUM CARBONATE

K. B. Omarov, Z. B. Absat, S. K. Aldabergenova, A. B. Siyazova, N. J. Rakhimzhanova, Z. B. Sagindykova

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TEACHING CHEMISTRY AT TECHNICAL UNIVERSITY

Lilyana Nacheva-Skopalik, Milena Koleva

ФОРМИРАЩО ОЦЕНЯВАНЕ PEER INSTRUCTION С ПОМОЩТА НА PLICКERS ТЕХНОЛОГИЯТА

Ивелина Коцева, Мая Гайдарова, Галина Ненчева

VAPOR PRESSURES OF 1-BUTANOL OVER WIDE RANGE OF THEMPERATURES

Javid Safarov, Bahruz Ahmadov, Saleh Mirzayev, Astan Shahverdiyev, Egon Hassel

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РУМЕН ЛЮБОМИРОВ ДОЙЧЕВ (1938 – 1999)

Огнян Димитров, Здравка Костова

NAMING OF CHEMICAL ELEMENTS

Maria Atanassova

НАЙДЕН НАЙДЕНОВ, 1929 – 2014 СПОМЕН ЗА ПРИЯТЕЛЯ

ИНЖ. НАЙДЕН ХРИСТОВ НАЙДЕНОВ, СЕКРЕТАР, НА СЪЮЗА НА ХИМИЦИТЕ В БЪЛГАРИЯ (2.10.1929 – 25.10.2014)

2014 година
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145 ГОДИНИ БЪЛГАРСКА АКАДЕМИЯ НА НАУКИТЕ

145 ANNIVERSARY OF THE BULGARIAN ACADEMY OF SCIENCES

ПАРНО НАЛЯГАНЕ НА РАЗТВОРИ

Б. В. Тошев Българско дружество за химическо образование и история и философия на химията

LUBRICATION PROPERTIES OF DIFFERENT PENTAERYTHRITOL-OLEIC ACID REACTION PRODUCTS

Abolfazl Semnani, Hamid Shakoori Langeroodi, Mahboube Shirani

THE ORIGINS OF SECONDARY AND TERTIARY GENERAL EDUCATION IN RUSSIA: HISTORICAL VIEWS FROM THE 21ST CENTURY

V. Romanenko, G. Nikitina Academy of Information Technologies in Education, Russia

ALLELOPATHIC AND CYTOTOXIC ACTIVITY OF ORIGANUM VULGARE SSP. VULGARE GROWING WILD IN BULGARIA

Asya Pencheva Dragoeva, Vanya Petrova Koleva, Zheni Dimitrova Nanova, Mariya Zhivkova Kaschieva, Irina Rumenova Yotova

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GENDER ISSUES OF UKRAINIAN HIGHER EDUCATION

Н.H.Petruchenia, M.I.Vorovka

МНОГОВАРИАЦИОННА СТАТИСТИЧЕСКА ОЦЕНКА НА DREEM – БЪЛГАРИЯ: ВЪЗПРИЕМАНЕ НА ОБРАЗОВАТЕЛНАТА СРЕДА ОТ СТУДЕНТИТЕ В МЕДИЦИНСКИЯ УНИВЕРСИТЕТ – СОФИЯ

Радка Томова, Павлина Гатева, Радка Хаджиолова, Зафер Сабит, Миглена Славова, Гергана Чергарова, Васил Симеонов

MUSSEL BIOADHESIVES: A TOP LESSON FROM NATURE

Saâd Moulay Université Saâd Dahlab de Blida, Algeria

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ЕЛЕКТРОННО ПОМАГАЛO „ОТ АТОМА ДО КОСМОСА“ ЗА УЧЕНИЦИ ОТ Х КЛАС

Силвия Боянова Професионална гимназия „Акад. Сергей П. Корольов“ – Дупница

ЕСЕТО КАТО ИНТЕГРАТИВЕН КОНСТРУКТ – НОРМАТИВЕН, ПРОЦЕСУАЛЕН И ОЦЕНЪЧНО-РЕЗУЛТАТИВЕН АСПЕКТ

Надежда Райчева, Иван Капурдов, Наташа Цанова, Иса Хаджиали, Снежана Томова

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Донка Ташева, Пенка Василева

ДОЦ. Д.П.Н. АЛЕКСАНДЪР АТАНАСОВ ПАНАЙОТОВ

Наташа Цанова, Иса Хаджиали, Надежда Райчева

COMPUTER ASSISTED LEARNING SYSTEM FOR STUDYING ANALYTICAL CHEMISTRY

N. Y. Stozhko, A. V. Tchernysheva, L.I. Mironova

С РАКЕТНА ГРАНАТА КЪМ МЕСЕЦА: БОРБА С ЕДНА ЛЕДЕНА ЕПОХА В ГОДИНАТА 3000 СЛЕД ХРИСТА. 3.

С РАКЕТНА ГРАНАТА КЪМ МЕСЕЦА:, БОРБА С ЕДНА ЛЕДЕНА ЕПОХА, В ГОДИНАТА 000 СЛЕД ХРИСТА. .

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KNOWLEDGE OF AND ATTITUDES TOWARDS WATER IN 5

Antoaneta Angelacheva, Kalina Kamarska

ВИСША МАТЕМАТИКА ЗА УЧИТЕЛИ, УЧЕНИЦИ И СТУДЕНТИ: ДИФЕРЕНЦИАЛНО СМЯТАНЕ

Б. В. Тошев Българско дружество за химическо образование и история и философия на химията

ВАСИЛ ХРИСТОВ БОЗАРОВ

Пенка Бозарова, Здравка Костова

БИБЛИОГРАФИЯ НА СТАТИИ ЗА МИСКОНЦЕПЦИИТЕ В ОБУЧЕНИЕТО ПО ПРИРОДНИ НАУКИ ВЪВ ВСИЧКИ ОБРАЗОВАТЕЛНИ НИВА

Б. В. Тошев Българско дружество за химическо образование и история и философия на химията

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SCIENTIX – OБЩНОСТ ЗА НАУЧНО ОБРАЗОВАНИЕ В ЕВРОПА

Свежина Димитрова Народна астрономическа обсерватория и планетариум „Николай Коперник“ – Варна

BOTYU ATANASSOV BOTEV

Zdravka Kostova, Margarita Topashka-Ancheva

CHRONOLOGY OF CHEMICAL ELEMENTS DISCOVERIES

Maria Atanassova, Radoslav Angelov

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ОБРАЗОВАНИЕ ЗА ПРИРОДОНАУЧНА ГРАМОТНОСТ

Адриана Тафрова-Григорова

A COMMENTARY ON THE GENERATION OF AUDIENCE-ORIENTED EDUCATIONAL PARADIGMS IN NUCLEAR PHYSICS

Baldomero Herrera-González Universidad Autónoma del Estado de México, Mexico

2013 година
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DIFFERENTIAL TEACHING IN SCHOOL SCIENCE EDUCATION: CONCEPTUAL PRINCIPLES

G. Yuzbasheva Kherson Academy of Continuing Education, Ukraine

АНАЛИЗ НА ПОСТИЖЕНИЯТА НА УЧЕНИЦИТЕ ОТ ШЕСТИ КЛАС ВЪРХУ РАЗДЕЛ „ВЕЩЕСТВА И ТЕХНИТЕ СВОЙСТВА“ ПО „ЧОВЕКЪТ И ПРИРОДАТА“

Иваничка Буровска, Стефан Цаковски Регионален инспекторат по образованието – Ловеч

HISTORY AND PHILOSOPHY OF SCIENCE: SOME RECENT PERIODICALS (2013)

Chemistry: Bulgarian Journal of Science Education

45. НАЦИОНАЛНА КОНФЕРЕНЦИЯ НА УЧИТЕЛИТЕ ПО ХИМИЯ

„Образователни стандарти и природонаучна грамотност“ – това е темата на състоялата се от 25 до 27 октомври 2013 г. в Габрово 45. Национална конфе- ренция на учителите по химия с международно участие, която по традиция се проведе комбинирано с Годишната конференция на Българското дружество за химическо образование и история и философия на химията. Изборът на темата е предизвикан от факта, че развиването на природонаучна грамотност е обща тенденция на реформите на учебните програми и главна

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ЗА ХИМИЯТА НА БИРАТА

Ивелин Кулев

МЕТЕОРИТЪТ ОТ БЕЛОГРАДЧИК

Б. В. Тошев Българско дружество за химическо образование и история и философия на химията

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RECASTING THE DERIVATION OF THE CLAPEYRON EQUATION INTO A CONCEPTUALLY SIMPLER FORM

Srihari Murthy Meenakshi Sundararajan Engineering College, India

CHEMICAL REACTIONS DO NOT ALWAYS MODERATE CHANGES IN CONCENTRATION OF AN ACTIVE COMPONENT

Joan J. Solaz-Portolés, Vicent Sanjosé Universitat de Valènciа, Spain

POLYMETALLIC COMPEXES: CV. SYNTHESIS, SPECTRAL, THERMOGRAVIMETRIC, XRD, MOLECULAR MODELLING AND POTENTIAL ANTIBACTERIAL PROPERTIES OF TETRAMERIC COMPLEXES OF Co(II), Ni(II), Cu(II), Zn(II), Cd(II) AND Hg(II) WITH OCTADENTATE AZODYE LIGANDS

Bipin B. Mahapatra, S. N. Dehury, A. K. Sarangi, S. N. Chaulia G. M. Autonomous College, India Covt. College of Engineering Kalahandi, India DAV Junior College, India

ПРОФЕСОР ЕЛЕНА КИРКОВА НАВЪРШИ 90 ГОДИНИ

CELEBRATING 90TH ANNIVERSARY OF PROFESSOR ELENA KIRKOVA

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SIMULATION OF THE FATTY ACID SYNTHASE COMPLEX MECHANISM OF ACTION

M.E.A. Mohammed, Ali Abeer, Fatima Elsamani, O.M. Elsheikh, Abdulrizak Hodow, O. Khamis Haji

FORMING OF CONTENT OF DIFFERENTIAL TEACHING OF CHEMISTRY IN SCHOOL EDUCATION OF UKRAINE

G. Yuzbasheva Kherson Academy of Continuing Education, Ukraine

ИЗСЛЕДВАНЕ НА РАДИКАЛ-УЛАВЯЩА СПОСОБНОСТ

Станислав Станимиров, Живко Велков

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COLORFUL EXPERIMENTS FOR STUDENTS: SYNTHESIS OF INDIGO AND DERIVATIVES

Vanessa BIANDA, Jos-Antonio CONSTENLA, Rolf HAUBRICHS, Pierre-Lonard ZAFFALON

OBSERVING CHANGE IN POTASSIUM ABUNDANCE IN A SOIL EROSION EXPERIMENT WITH FIELD INFRARED SPECTROSCOPY

Mila Ivanova Luleva, Harald van der Werff, Freek van der Meer, Victor Jetten

ЦАРСКАТА ПЕЩЕРА

Рафаил ПОПОВ

УЧИЛИЩНИ ЛАБОРАТОРИИ И ОБОРУДВАНЕ SCHOOL LABORATORIES AND EQUIPMENT

Учебни лаборатории Илюстрации от каталог на Franz Hugershoff, Лайциг, притежаван от бъдещия

2012 година
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ADDRESING STUDENTS’ MISCONCEPTIONS CONCERNING CHEMICAL REACTIONS AND SYMBOLIC REPRESENTATIONS

Marina I. Stojanovska, Vladimir M. Petruševski, Bojan T. Šoptrajanov

АНАЛИЗ НА ПОСТИЖЕНИЯТА НА УЧЕНИЦИТЕ ОТ ПЕТИ КЛАС ВЪРХУ РАЗДЕЛ „ВЕЩЕСТВА И ТЕХНИТЕ СВОЙСТВА“ ПО ЧОВЕКЪТ И ПРИРОДАТА

Иваничка Буровска, Стефан Цаковски Регионален инспекторат по образованието – Ловеч

ЕКОТОКСИКОЛОГИЯ

Васил Симеонов

ПРОФ. МЕДОДИЙ ПОПОВ ЗА НАУКАТА И НАУЧНАТА ДЕЙНОСТ (1920 Г.)

Проф. Методий Попов (1881-1954) Госпожици и Господа студенти,

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КОНЦЕПТУАЛНА СХЕМА НА УЧИЛИЩНИЯ КУРС П О ХИМИЯ – МАКР О СКОПСКИ ПОДХОД

Б. В. Тошев Българско дружество за химическо образование и история и философия на химията

ROLE OF ULTRASONIC WAVES TO STUDY MOLECULAR INTERACTIONS IN AQUEOUS SOLUTION OF DICLOFENAC SODIUM

Sunanda S. Aswale, Shashikant R. Aswale, Aparna B. Dhote Lokmanya Tilak Mahavidyalaya, INDIA Nilkanthrao Shinde College, INDIA

SIMULTANEOUS ESTIMATION OF IBUPROFEN AND RANITIDINE HYDROCHLORIDE USING UV SPECTROPHOT O METRIC METHOD

Jadupati Malakar, Amit Kumar Nayak Bengal College of Pharmaceutical Sciences and Research, INDIA

GAPS AND OPPORTUNITIES IN THE USE OF REMOTE SENSING FOR SOIL EROSION ASSESSMENT

Mila Ivanova Luleva, Harald van der Werff, Freek van der Meer, Victor Jetten

РАДИОХИМИЯ И АРХЕОМЕТРИЯ: ПРО Ф. ДХН ИВЕЛИН КУЛЕВ RADIOCHEMISTRY AND ARCHEOMETRY: PROF. IVELIN KULEFF, DSc

Б. В. Тошев Българско дружество за химическо образование и история и философия на химията

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TEACHING THE CONSTITUTION OF MATTER

Małgorzata Nodzyńska, Jan Rajmund Paśko

СЪСИРВАЩА СИСТЕМА НА КРЪВТА

Маша Радославова, Ася Драгоева

CATALITIC VOLCANO

CATALITIC VOLCANO

43-ТА МЕЖДУНАРОДНА ОЛИМПИАДА ПО ХИМИЯ

Донка ТАШЕВА, Пенка ЦАНОВА

ЮБИЛЕЙ: ПРОФ. ДХН БОРИС ГЪЛЪБОВ JUBILEE: PROF. DR. BORIS GALABOV

Б. В. Тошев Българско дружество за химическо образование и история и философия на химията

ПЪРВИЯТ ПРАВИЛНИК ЗА УЧЕБНИЦИТЕ (1897 Г.)

Чл. 1. Съставянето и издаване на учебници се предоставя на частната инициа- тива. Забележка: На учителите – съставители на учебници се запрещава сами да разпродават своите учебници. Чл. 2. Министерството на народното просвещение може да определя премии по конкурс за съставяне на учебници за горните класове на гимназиите и специ- алните училища. Чл. 3. Никой учебник не може да бъде въведен в училищата, ако предварително не е прегледан и одобрен от Министерството на народното просвещение. Чл.

JOHN DEWEY: HOW WE THINK (1910)

John Dewey (1859 – 1952)

ИНФОРМАЦИЯ ЗА СПЕЦИАЛНОСТИТЕ В ОБЛАСТТА НА ПРИРОДНИТЕ НАУКИ В СОФИЙСКИЯ УНИВЕРСИТЕТ „СВ. КЛИМЕНТ ОХРИДСКИ“ БИОЛОГИЧЕСКИ ФАКУЛТЕТ

1. Биология Студентите от специалност Биология придобиват знания и практически умения в областта на биологическите науки, като акцентът е поставен на организмово равнище. Те се подготвят да изследват биологията на организмите на клетъчно- организмово, популационно и екосистемно ниво в научно-функционален и прило- жен аспект, с оглед на провеждане на научно-изследователска, научно-приложна, производствена и педагогическа дейност. Чрез широк набор избираеми и факул- тативни курсове студентите

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УЧИТЕЛИТЕ ПО ПРИРОДНИ НАУКИ – ЗА КОНСТРУКТИВИСТКАТА УЧЕБНА СРЕДА В БЪЛГАРСКОТО УЧИЛИЩЕ

Адриана Тафрова-Григорова, Милена Кирова, Елена Бояджиева

ПОВИШАВАНЕ ИНТЕРЕСА КЪМ ИСТОРИЯТА НА ХИМИЧНИТЕ ЗНАНИЯ И ПРАКТИКИ ПО БЪЛГАРСКИТЕ ЗЕМИ

Людмила Генкова, Свобода Бенева Българско дружество за химическо образование и история и философия на химията

НАЧАЛО НА ПРЕПОДАВАНЕТО НА УЧЕБЕН ПРЕДМЕТ ХИМИЯ В АПРИЛОВОТО УЧИЛИЩЕ В ГАБРОВО

Мария Николова Национална Априловска гимназия – Габрово

ПРИРОДОНАУЧНОТО ОБРАЗОВАНИЕ В БЪЛГАРИЯ – ФОТОАРХИВ

В един дълъг период от време гимназиалните учители по математика, физика, химия и естествена

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„МАГИЯТА НА ХИМИЯТА“ – ВЕЧЕР НА ХИМИЯТА В ЕЗИКОВА ГИМНАЗИЯ „АКАД. Л. СТОЯНОВ“ БЛАГОЕВГРАД

Стефка Михайлова Езикова гимназия „Акад. Людмил Стоянов“ – Благоевград

МЕЖДУНАРОДНАТА ГОДИНА НА ХИМИЯТА 2011 В ПОЩЕНСКИ МАРКИ

Б. В. Тошев Българско дружество за химическо образование и история и философия на химията

ЗА ПРИРОДНИТЕ НАУКИ И ЗА ПРАКТИКУМА ПО ФИЗИКА (Иванов, 1926)

Бурният развой на естествознанието във всичките му клонове през XIX –ия век предизвика дълбоки промени в мирогледа на културния свят, в техниката и в индустрията, в социалните отношения и в държавните интереси. Можем ли днес да си представим един философ, един държавен мъж, един обществен деец, един индустриалец, просто един културен човек, който би могъл да игнорира придобив- ките на природните науки през последния век. Какви ужасни катастрофи, какви социални сътресения би сполетяло съвре

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MURPHY’S LAW IN CHEMISTRY

Milan D. Stojković

42-рa МЕЖДУНАРОДНА ОЛИМПИАДА ПО ХИМИЯ

Донка Ташева, Пенка Цанова

СЕМЕЙНИ УЧЕНИЧЕСКИ ВЕЧЕРИНКИ

Семейството трябва да познава училишето и училишето трябва да познава семейството. Взаимното познанство се налага от обстоятелството, че те, макар и да са два различни по природата си фактори на възпитанието, преследват една и съща проста цел – младото поколение да бъде по-умно, по-нравствено, физически по-здраво и по-щастливо от старото – децата да бъдат по-щастливи от родителите