physics competitions vol. 14 no 2 2012 - ipn startseite —...

Physics Competitions Vol. 14 No 2 2012

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ISSN 1389 – 6458 Physics Competitions published biannually by The World Federation of Physics Competitions

— Contents Page

WFPhC, Executive Committee; Advisory Board, Award Committee 2

Editorial 6

REPORTS ON COMPETITIONS AND ARTICLES The Final Round of the First World Physics Olympiad .......................... 8 Herry J. Kwee, Yohanes Surya

The Junior League of Young Physicists´ Tournament ............................ 39 Alexandr A. Kamin, Alexandr L. Kamin

Integrating Aspects of Geography in Physics Teaching ......................... 56 Gróf Andrea Amazing Science ..................................................................................... 67 Paul F. Pshenichka The HUNVEYOR-Project ....................................................................... 74 György Hudoba Front page: Picture of Estonian dancers, welcoming the participants of the 43rd IPHO in

Tallinn/Estonia (picture: Gunnar Friege)


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— Executive Committee

HELMUTH MAYR — President Austria / retired physics and physics didactics teacher, Vienna Federal Coordinator of the Austrian Physics Olympiad [email protected] HENDRA KWEE — Vice-President Indonesia / General secretary of APhO, Surya Institute [email protected] GUNNAR FRIEGE — Vice-President Germany / Institute of Mathematics and Physics Education, Leibniz University Hannover Welfengarten 1; D-30167 Hannover [email protected] STEFAN PETERSEN — Secretary Germany / Leibnitz Institute for Science and Mathematics Education at the University of Kiel Olshausenstraße 62; D-24118 Kiel [email protected] INGIBJÖRG HARALDSDOTTIR — Treasurer Iceland / Kopavogur Gymnasium, Digranesvegi, IS-200 Kopavogur [email protected] ANDRZEJ KOTLICKI — Member Canada / University of British Columbia, Department of Physics and Astronomy 6224 Agricultural Road, Vancouver B.C., Canada V6T 1Z1 [email protected] PAUL PSHENICHKAL — Member Ukraine / Representative of ICYS [email protected] NATALYA KAZACHKOVA — Member Ukraine / [email protected]


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— Awards Committee

JAN MOSTOWSKI - Chairman Poland / Polish Academy of Science, Warszawa [email protected] MASNO GINTING Indonesia / Komplek Puspiptek Blok II H no. 13Tangerang Selatan-Banten, 15310 [email protected] ANDREI LAVRINENKO Denmark / Technical University of Denmark, DK-2800 Lyngby [email protected] JUAN LEON Spain / IFF/CSIC, Serrano 113-B, ES-28006 Madrid, http//quinfog.iff.csic.es [email protected] MONIKA RAHARTI Indonesia / Surya Institute [email protected]

— Advisory Board

GIULIANA CAVAGGIONI Italy / Italian Association for the Teaching of Physics [email protected] ANDREI LAVRINENKO Denmark / Technical University of Denmark, DK-2800 Lyngby [email protected] ANDRZEJ NADOLNY Poland / Polish Academy of Science, Warszawa [email protected]

mailto:[email protected]




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— Regional Representatives

Dr. Alan Alliosn / Australia Mr. Michael A. Cotter / Ireland Dr. Gagik V. Grigoryan / Armenia Prof. MSc. Ozimar Pereira / Brazil

— Editor-in-Chief HELMUTH MAYR Austria / retired physics and physics didactics teacher, Vienna Federal Coordinator of the Austrian Physics Olympiad [email protected]

— Editorial Board HELMUTH MAYR Austria / retired physics and physics didactics teacher, Vienna Federal Coordinator of the Austrian Physics Olympiad [email protected] GUNNAR FRIEGE Germany / Institute of Mathematics and Physics Education, Leibniz University Hannover, Welfengarten 1; D-30167 Hannover [email protected] STEFAN PETERSEN Germany / Leibnitz Institute for Science and Mathematics Education at the University of Kiel Olshausenstraße 62; D-24118 Kiel [email protected]




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— Aims of Federation

1) To promote excellence in, and research associated with, physics education through the use of school physics competitions;

2) To promote meetings and conferences where persons interested in physics

contests can exchange and develop ideas of use in their countries;

3) To provide opportunities for the exchanging of information for physics educa-tion through published material, notably through the Journal of the Federation;

4) To recognize through the WFPhC Awards system persons who have made

notable contributions to physics education through physical challenge around the world;

5) To organize assistance provided by countries with developed system for com-

petitions for countries attempting to develop competitions;

6) To promote physics and to encourage young physicists.


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— Editorial Dear Reader!

This is the first journal of the World Federation of Physics Competitions published on our new homepage and it is now free of charge. Since April 2012 a new team of the Executive Committee has been working. This is the second journal the new team has produced. Beside that we are trying hard to check all our members worldwide. Due to that it might be you have received a mail from our secretary. I am asking you to help us to get a proper list and I thank you for your help. You can see that the layout of our journal has been changed and we hope for the better. In connection with that we have to apologise for the bad quality of the photos in our last journal. It was due to a technical problem, which cannot happen in future. From 01-03-2013 to 03-03-2013 there was a meeting of the Executive Committee in the city of Kiel in Germany. There we decided that in future the Federation will run as follows:

Becoming a member of the WFPhC is free of charge.

Each WFPhC-member gets a newsletter, normally three times a year.

The journal of the Federation will be published on the home page normal-

ly twice a year.

As in the past, there will be organized a Congress every two years. The

next Congress will be in 2014.

Further information about this Congress will be published on this homep-

age soon. The picture on the front-page shows Estonian dancers welcoming the participants of the 43rd International Physics Olympiad in Tallinn/Estonia on the arrival day. Estoni-ans capital was the venue of this event with a fantastic atmosphere and extremely challenging problems on a very high standard.


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There will be an article about this great event in our next journal. In this journal you can find an interesting article about the 1st World Physics Olympiad, then being a new type of competition. It successfully took place in Indonesia. You can also find a description of the so-called Junior League of the Young Physicists´ Tournament, hav-ing taken place in Ukraine with remarkable success. A very good interaction between the secondary school subjects physics and geography is presented in the next text, written by a Hungarian colleague. “Amazing Science” gives an insight into the way children can be brought to approach science competitions at the point of becoming secondary school students, very well done in Ukraine. The Hunveyor-Project, de-scribed in the next article, can bring didactical information on how teaching of physics can be done in a way very close to a competition. There have been outstanding re-sults in Hungary. We invite you to become a member of our federation and to take part in our world-wide activities. All over the world there are so many projects in physics education of secondary school students using different kinds of competitions or similar pro-grammes. We feel everybody should know about these great events. Hence we ask you to send us an interesting article to be published in this journal. If you wish to write a text, I recommend to have a look at our homepage and to click “authors´ tem-plates”. Thank you! I want to point out that authors are responsible for their articles including all the fig-ures. In addition I have to say that an authors´ opinion is not necessarily the editors´ view. I truly hope you can enjoy this journal and all its interesting points.

December 2012 (Helmuth Mayr) president


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The Final Round of the First World Physics Olympiad

held in Lombok, West Nusa Tenggara Indonesia: Problems and Results

Herry J. Kwee and Yohanes Surya Faculty of Physics Education Department, Surya College of Education, Banten, Indonesia

Abstract A brief report of the final round of the first World Physics Olympiad (WoPhO) held in Lombok, West Nusa Tenggara, Indonesia is presented. The theoretical and experimental problems are presented and the mark distribution is discussed.

— 1. Introduction

The final round of the first WoPhO was held in Lombok, West Nusa Tenggara, Indo-nesia from December 28th, 2011 to January 3rd, 2012 and was organized by Surya College of Education and Indonesian Society for the Promotion of Science under the auspices of Surya Institute. WoPhO is a secondary school level individual physics competition initiated by one of the authors, Yohanes Surya. It is a unique competition that lasts for a full year and consists of three rounds: selection, discussion and final round. The selection round is meant to provide as many opportunities as possible to students to participate in an Olympiad-level physics competition. Problems are presented online and any student who is eligible1 can participate. For the first WoPhO selection round, 345 students from all over the world register to participate. The discussion round provides an op-portunity for the participants and the general public to discuss the problems and solu-tions of the selection round and other physics Olympiad-level problems. And the final round, which is organized very similar to the International and Asian Physics Olympi-ad (IPhO and APhO) provides an opportunity for every participants to challenge the APhO and IPhO gold medalists. Just like in APhO and IPhO, there are 5 hours at the students´ disposal to solve the three theoretical problems and another 5 hours for the experimental tasks. There were 122 students from 13 countries who participated in the first WoPhO final round, even though the distribution was not evenly spread. The majority of students were from the host country, Indonesia. 1 Students who have not started college or reached 20 years of age by June 30th of competition year.


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Another unique characteristic of WoPhO is the fact that the problems for the final round are not provided by the host country but are selected from a competition (or simply called WoPhO problem competition). Anyone can participate in this competi-tion, in fact one of the winners of this first WoPhO problem competition was a high school student and another one was a university student. Three theoretical problems were chosen from thirty one entrants and two experimental problems were chosen from four entrants. The number of entries for experimental problems was much lower than for theoretical problems due to the amount of work needed to prepare a good experiment and its apparatus. In section 2, we present the theoretical problems. In section 3, we present the experimental problems. In section 4, we present the summary of the result of the final round.

— 2. Theoretical Examination

Theoretical Problem No. 1: Motion of a Rolling Rod

In this problem, the motion of a uniform rod (stick) with length L , ended with caster-wheels at both ends, will be investigated on a flat surface. The casters at each end of the rod can spin freely and independently (see Figure 1) and have a negligible mass compared to the rod. The friction between the rod and the caster-wheels is negligible. The diameters of the caster-wheels are a bit larger than the diameter of the rod, but both diameters are much smaller than the length of the rod. The gravitational accel-eration is g .

Figure 1: Sketch of the rod with the caster-wheels.

The rod is placed on a horizontal flat surface and pushed such that each end of the rod get different horizontal initial velocity ( 1v and 2v , pointing in the same direction)

perpendicular to the axis of the rod. The casters roll without slipping on the surface.


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Calculate the initial velocity 0v of the center of the rod and the initial angular ve-

locity 0ω of the rod using 1v , 2v and L ! [0.8 points]

Describe the motion of the center of mass of the rod! Determine the parameter(s) of its orbit! [0.8 points]

What should be the minimum value of the coefficient of static friction µ for the

casters to not slip on the surface? [0.6 points]

In the following sections the case of the inclined surface will be considered. The an-gle between the inclined surface and the horizontal plane is α . If α is infinitesimally small, the motion of the rod slightly changes: the motion of the center of mass is approximately the same as in the previous section but a constant drift velocity driftv added to the solution. Use a coordinate system as in Figure 2.

Calculate the magnitude and the direction of driftv as a function of the small α ,

the initial velocities of the two ends of the rod ( 1v and 2v , pointing in the same di-

rection) and the gravitational acceleration g ! [1.9 points]

Sketch the orbit of the center of mass of the rod! [0.5 points]

If α is finite, the details of the motion of the rod changes. Place the rod on the in-clined plane along the steepest line of the surface (so the rod is parallel with the in-clined edges of the plane). Consider that the initial velocity 0v of the center of mass of

the rod is perpendicular to the axis of the rod and the initial angular velocity 0ω is

perpendicular to the surface as shown in Figure 2.

Figure 2: The initial conditions of the rod

Calculate the time evolution of the ve-locity ( ) ( ( ), ( ))x yt vt v t=v of the center of mass

of the rod in the Cartesian coordinate system shown in Figure 2. [0.8 points] Depending on the magnitude of the 0v

and 0ω , it can occur, that the center of the rod

stops for a moment during its motion. Express the condition(s) for such a behavior using the parameters 0v , 0ω , g , α and L ! [0.8 points]

Determine the maximum displacement of the center of the rod in the direction of the steepest line ( y -direction) as function of 0v and 0ω ! [1.2 points]


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Investigate another situation where the rod is placed horizontally on the inclined sur-face. Consider that the initial angular velocity 0ω of the rod is perpendicular to the

surface but the initial velocity of the center of the rod is zero (see Figure 3).

Figure 3: The initial conditions of the rod

Describe the motion of the center of mass of the rod! Determine the pa-rameter(s) of its orbit! [1.6 points] What should be the minimum val-ue of the coefficient of static friction µ in

this case for the casters to not slip on the surface? [1.0 points]

— Theoretical Problem No. 2: Why Maglev Trains Levitate

Maglev is a technology for magnetic suspension (levitation) and propulsion of trains or other vehicles. Since there is no friction force between the train and the rails, Mag-lev trains reach record velocities approaching 600 /km h .

There are three types of Maglev systems -- EMS (Electromagnetic Suspension), EDS (Electro-dynamic Suspension), and the experimental Inductrack technology. In this problem you are going to explore the physical principles of Inductrack suspension on a simplified model of a Maglev train. The principle of magnetic propulsion will not be considered here because it has a lot in common with the physics of magnetic levita-tion. Shown in Figure 4 is a schematic side view of an Inductrack train-car. When at rest or moving at a low speed, the car lies with its wheels on the rails like any ordi-nary train. The car, however, detaches from the rails at a specific takeoff velocity 𝑣𝑡 due to the system described below: two long parallel arrays of permanent cubic-shape magnets of size a = 5 cm, each is located at the bottom of the car. The mag-netic dipole moments of the neighboring magnets are tilted at an angle of 45° relative to each other (the so called Halbach array). As a result a static magnetic field is pro-duced below each array with components of the magnetic field given by the equa-tions:

0 exp( )sin( )xB B ky kx= − (2.1)

0 exp( )cos( )yB B ky kx= − (2.2)


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where the x-coordinate is measured from the rear end of the car in the direction of motion and y-coordinate from the bottom of the car in a downward direction. The pa-rameter k is the wavenumber of the magnetic field. The amplitude of the magnetic field is 0 1.4 B T= .

Figure 4: A schematic side view of an Inductrack train-car. The arrows show the directions of magnetic moments of the cubic magnets in the Halbach array. The wheels and the rails of the train are not shown for convenience.

Two inductive arrays of horizontal rectangular wire frames of the same width a made of permanent magnets are arranged along the rail as seen from the top view Figure 5. The length of the inductive frames as well as the distance between them is b. Each inductive array is located below the corresponding Halbach array at a dis-tance corresponding to the y-coordinate of the inductive array (see Figure 4). As-sume that the equations (2.1) and (2.2) for the components of the magnetic field hold only for the inductive frames, which are located below the car, while the magnetic field outside the car area is strictly zero.

Figure 5: A schematic top-view of an Inductrack train-car. The wheels and the rails of the train are not shown for convenience.

Note: In the real Inductrack trains, the frames of the inductive array are electrically connected and form a continuous ladder-like array. In order to simplify the theoretical consideration, we use a simplified model shown in Figure 5.

Helpful mathematics formulas:

sin( ) sin( ) 2sin( ) cos( )2 2

x y x yx y − +− = (2.3)


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cos( ) cos( ) 2sin( )sin( )2 2

y x x yx y − +− = (2.4)

Assume that the train car is infinitely long (i.e. equations (2.1) and (2.2) hold for all values of the x-coordinate.

a) Electromotive force in the inductive wires Derive a relationship between the wavenumber of the magnetic field k and the

lateral size of the cubic magnets in the Halbach array a. Calculate k numerically. [0.3 points]

Suppose that the train moves with a constant velocity v in the positive direction of the x-axis. Consider an inductive frame whose center in the initial moment 0t = is located below the car at a point of coordinate cx relative to the car. Derive an

expression for the electromotive force (EMF) ε induced in the frame as a func-tion of the time t and the other parameters already defined. [1.5 points]

What is the angular frequency ω of the induced EMF. [0.4 points]

b) Current in the inductive wires Each frame in the inductive array is characterized by a self-inductance L and a re-sistance R. The mutual inductance between different frames is negligible compared to L. The current I induced in the frame varies with time according to the equation: 0( ) sin( )cI t I t kxω ψ= − +

Obtain expressions for the amplitude 0I and the phase-shift ψ of the alternat-

ing current induced in the frame. [2.0 points] Note: The positive direction of circulation of the induced current in the frame is related to the positive direction of the y-axis according to the right-hand rule.

c) The dynamics of the train Derive formulas for the time-averaged components xF and yF acting on a single

inductive frame in terms of velocity v, the distance between the Halbach array and the inductive array y, and the others parameters already defined. Sketch qualitative graphs of xF and yF versus train velocity v for a fixed value of the dis-

tance y. [3.0 points] Consider a train-car of a large but finite length (l and b). Derive expressions for

the magnitude of the total lift (vertical) and drag (horizontal) forces LF and DF

acting on the car. [1.2 points]


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For a given value of a, what is the minimum aspect ratio /b a for which the lift force is maximum for given values of the distance y, velocity v, resistance R, and the inductance L. [1.0 points]

Consider a train-car of length 10 l m= and mass 10000 kgm = . Assume that the

aspect ratio /b a corresponds to the optimal value found in 3(c). The inductance

and the resistance of the inductive frames are 71.0 10 L H−= × and 51.0 10 R −= × Ω

respectively. The acceleration due to gravity is 29.8 /g m s= . Assume that the dis-

tance between the Halbach array and the inductive array is 0 y m= , when the

train is at rest. Obtain an expression and calculate the takeoff velocity tv , the velocity at which

the train detaches from the rails. [0.3 points] What is the distance y between the train and the rails at an operating velocity of

360 km/h?

— Theoretical Problem No. 3: Mirage

The refractive index of the air varies with temperature. Cold air is denser than warm air and has therefore a greater refractive index. Thus a temperature gradient in the atmosphere is always associated with a gradient of the refractive index. Under cer-tain conditions, this gradient of the refractive index could be strong enough so that light rays are bent to produce a displaced image of distant objects. This amazing phenomenon is called a mirage. Mirages can be categorized as "inferior" and "superior". Inferior mirages can be seen on deserts and highways, and superior mirages occur over the sea. To describe in detail the phenomenon of the mirage, we need to analyze the path of light rays in media with a refractive index gradient.

Figure 6: Left: A superior image. Right: An inferior image


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The path of a light ray and the trajectory of a mass point Media with a refractive index gradient can be treated as being formed from thin ho-mogeneous layers with different refractive indices. The path of a light ray can be de-termined then by analyzing refractions of the light ray at interfaces between these thin homogeneous layers. But there exists a more convenient way for determining the path of a light ray in media with a refractive index gradient. Instead of analyzing the propagation of the light, one may study the motion of a mass point that moves along the path of the light ray, driven by a conservative force. The potential energy of the conservative force field depends on the distribution of the refractive index. Once the potential energy is established, one may study the motion of the mass point by using well developed tools in classical mechanics, and find the trajectory of a mass point which is also the path of the light ray.

Refraction of a light ray at the interface between a medium with a refractive index 1n

and a medium with a refractive index 2n is shown in Figure 7a. The angles 1i and 2i

obey the Snell's law: 1 1 2 2sin sinn i n i= . (2.1)

The path of a mass point in a conservative force field is illustrated in Figure 7b. The speed of the mass point is 1v in the region with the potential energy 1pE , and 2v in the

region with the potential energy 2pE .

Find expressions for 1v and 2v so that the relation 1 1 2 2sin sinn i n i= holds also for the trajectory of the mass point. You may use an arbitrary constant expression

0v with the dimension of speed in your expressions. [0.2 points]

Figure 7:

(a) Left: Refraction of a light ray. (b) Right: Deviation of a mass point in a conservative force field


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Assume that the mass of the mass point is m, and the total energy of the mass point equals to zero. Find the potential energies 1pE and 2pE in 0v , 1n and 2n

[0.2 points] The trajectory of a mass point with a mass m in a conservative force field is the

same as the path of a light ray in a medium with a refractive index ( )n r which is

a function of the position. The total energy of this mass point is zero. Find ex-pressions for the potential energy ( )pE r of the conservative force field and the

speed of the mass point ( )v r [0.4 points]

To describe the motion of a mass point, one expresses the position of the mass point as a function of time: ( )r t . To describe the trajectory of a mass point, one needs to express the position of the mass point as a function of the distance s traveled by the mass point from the start point of the trajectory to the current po-sition: ( )r s . Derive a differential equation for the trajectory ( )r s of a mass point with a mass m and a total energy E that moves in a conservative force field. [0.6 points]

Hint: in a conservative force field, ( )r t satisfies Newtons´ second law:

2

2 ,pd rm Edt

= −∇

(2.2) where ,( )

ˆ ˆ ˆ .

ds v rdt

x y zx y z

=

∂ ∂ ∂∇ = + +

∂ ∂ ∂

(2.3)

Derive the light ray equation (a differential equation for the path of a light ray) by using the results obtained in (c) and (d). [0.6 points]

Hint: 2 ( ) 2 ( ) ( )f r f r f r∇ = ∇

The inferior mirage When an inferior mirage appears, an image of a distant object can be seen under the real object. A direct image of that object is seen because some of the light rays enter the eye in a straight line without being refracted. The double images seem to be that of the object and its upside-down reflection in water. For exhausted travelers in the desert it seems like that there is a lake of water in front of them.

An inferior mirage occurs when a strong positive gradient of refractive index is pre-sent near the ground. We use the following model to describe the variation of the refractive index of the air with elevation:


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2

2 020

for 0( )

for ,n z h z

n zn h z h

αα

+ ≥ ≥=

+ > (2.4)

with 20 1 1n − and 1hα .

Figure 8: The geometry for analyzing an inferior mirage

Find the path of a light ray (i.e. z as a function of x) that enters in an observer's eye at an angle θ (see Figure 8). The height of the observer eye is H. [1.9 points]

Due to the inferior mirage, the observer can see an inverted image of the upper part of a camel at a large distance. The parameters for the refractive index of the air are 5 13.0 10 m α − −= × , 0.50 mh = . The height of the observers eye is

1.5 mH = , and the height of the camel is 2.2 ml = . Find the minimum values for the distance mD between the observer and the camel so that the observer still

can see the inverted image of the upper part of the camel. You may use the ap-proximation 2

0 1n ≈ . [0.7 points]

As a result of the light refraction in the region with refractive index gradient, the observer cannot see the lower part of the camels legs. Find the height of the low-est point ( ml ) on the camel at the distance mD that can still be seen by the ob-

server. [0.7 points] Find the distance d between the observer and the imaginary lake of water.

[0.3 points]


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The superior mirage When a superior mirage occurs, light rays that were originally directed above the line of sight of the observer will reach the observer's eyes. Thus, an object ordinarily be-low the horizon will be apparently above the horizon. A superior mirage occurs when a negative gradient of refractive index is present over a body of water or over large sheets of ice. We use the following model to describe the refractive index of the atmosphere (see Figure 9):

[ ]

[ ]20 0 02

20 0

1 ( ) for ( ) 0( )

1 for ,

( )n r r b r r

n rn b r r b

ββ

− − ≥ − ≥=

− − > (2.5)

where 0r is the radius of the earth, 0b r and 1bβ .

Figure 9: The geometry for analyzing a superior mirage

Find the path of a light ray (i.e. r as a function of φ ) within the range

0( ) 0b r r≥ − ≥ . Use γ , the angle between the light ray and the vertical direction at

the sea level as the parameter of the path. [1.4 points] Hint: The trajectory of a mass point with mass m, angular momentum L and total energy E in a conservative force field with

0pmAE Er

= − + (2.6) is ,1 cos

r ρε φ

=−

(2.7)

Where 22

02 3 2

2( ), and 1 .E E LLm A m A

ρ ε −= = + (2.8)

We also have


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00 02

0 0

1 1 if | | .r r r r rr r r

−≈ − − (2.9)

Find the minimum value of ( )mβ β at which the superior mirage occurs. Use the

following values for 0n and 0r : 0 1n ≈ , 60 6.4 m10r = × . [0.8 points]

Under a certain atmospheric condition, with 100 mb = and 7 16.0 10 m β − −= × , cal-

culate the largest distance MD at which the surface of the sea can be seen by an

observer at an altitude 10 my = (y is the altitude of the observer's eye).

[1.4 points]

Useful formula: 21cos 12

φ φ≈ − for 1φ .

For comparison, calculate the largest distance MD′ at which the surface of the

sea can be seen by an observer at the same altitude 10 my = , when the refrac-

tive index of the air is constant. [0.3 points] Calculate the angular difference ϑ∆ between the apparent horizon when a supe-

rior mirage occurs as and the apparent horizon in a normal day, seen at the same altitude 10 my = . [0.5 points]

— 3. Experimental Examination Experimental Problem No.1: Granular Material

The vast majority of mechanics experiments normally conducted in high school phys-ics laboratories are those that have to do with solid objects such as spheres, springs, carts, and rods. Moreover, these solid objects are additionally assumed to be ideal rigid objects such as the ones usually dealt with in any classroom discussion involv-ing dynamics. This approach unfortunately omits the exploration of another class of solid objects that are rather ubiquitous in real life, granular materials. These are ma-terials consisting of many small grains or particles; while each grain or particle is a solid object, the collective behavior of any group of those grains or particles is usually nothing like their more rigid counterparts. The following experiments depart from the common high school mechanics experiments in that they are designed to explore many aspects of the behaviors of granular materials.

The experiments consist of four independent parts. In the first part, we will investigate the static and dynamic properties of a granular material (dry sand) by measuring the


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angle of repose and the maximum angle of stability. This experiment accordingly gives us the information about coefficient of static friction of the sand grains. The mass flow rate of the dry sand through an orifice is investigated in the second exper-iment. In the third part, we will observe how the sand settles in a fluid. Having ob-tained the settling velocity of the sand sediment, we estimate the average size of a sand particle. Lastly, we model an asteroid impact crater using craters formed by balls dropped into dry, non-cohesive, granular media.

The following physical quantities are given:

Gravitational acceleration at surface of Earth: g = 9.81 m/s2

Average density of Earth's continental crust: ρE = 2.7 g/cm3 Average radius of Earth: RE = 6400 km Density of iron at room temperature: ρiron = 7.874 g/cm3 The explosive power of 1000 tons of TNT: 1 kiloton = 4.184x109 J Viscosity of water at room temperature: η = 8.94x10-4 Pa.s

Table 1: List of available apparatus and materials for experiment

Name Quantity Name Quantity Inclined plane with acrylic box + stand

1 Graduated Cylinder 1

Sand in the container with pink cover 1 Colored (red/blue) sand 1 Containers with different orifice size 6 A glass of water 1 Empty container without orifice 2 Ruler 1 Vernier caliper 1 Flashlight 1 Digital weight scale 1 Graph paper 1 Digital stopwatch 1 Tripod 1 Metal stand with release mechanism 1 Glass ball 1 Pile of sand in plastic basin 1 Spoon 1

ATTENTION: Do not mix different types of sands (sand in the container with pink cover, colored sand, and pile of sand in plastic basin are different.) Use the correct sand for each experiment.

Angle of Repose The hourglass is a fascinating and antique timekeeping device. Its distinctive geomet-rical shape makes it immediately recognizable, and, as some people claim, it has a certain elegance which modern timekeeping devices lack. Nevertheless, the geomet-ric shape of the common hourglass must exist for a reason, since one does not find


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cubic hourglasses. The reason, as it turns out, is that granular materials have a cer-tain parameter called the angle of repose, rθ which is a measure of the final angle

formed by the surface of a pile of granular material when it is poured onto a horizon-tal surface. The angle of repose rθ is measured with respect to horizontal surface.

In this problem, we will investigate the angle of repose of dry sand in a simple exper-iment. Initially, a flat rectangular container is filled with sand and the top surface of the sand is flattened out horizontally. The expanse of sand can be stable when its container is tilted as long as its slope is less than the angle of maximal stability, mθ . As the slope

is increased above mθ , some of the sand grains begin to flow and an avalanche oc-

curs.

Note: Use Sand in the container with pink cover

Figure 10: Configuration to determine maximum angle of stability.

Determine the angle of maximal stability, mθ . [1.0 points]

The angle you have just calculated, however, is not the angle of repose. If the sand is too compact it can affect your measurement result.

You may perform another experiment to determine the angle of repose of the sand, rθ . Draw a schematic diagram of your experiment. [1.0 points]

Determine the intergranular friction coefficient, sµ , which is the coefficient of stat-

ic friction between a sand grain and other sand grains. [0.5 points]


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Flow Rate of Granular Matter The mass flow rate of granular materials through an orifice due to gravitational force is generally independent on the geometry of the container. This statement holds as long as the dimensions of the container are sufficiently large compared to the size of the grains and the diameter of the outlet orifice. Note that it was this fact which, though perhaps unknown to the people of that time, enabled hourglasses to be rela-tively good timekeeping devices. In this case we will determine parameters that can affect the flow rate of sand through a circular orifice. Note: Use Sand in the container with pink cover Let us suppose that the mass flow rate of sand, W, through a circular orifice depends on the density of sand ρ , the acceleration due to gravity g, the orifice diameter D,

and the intergranular friction coefficient sµ . Based on this assumption, the flow rate

fulfills the equation ) ,( thraW C gDµ ρ= (2.1)

where ( )C µ is a dimensionless empirical factor which depends on the internal friction

coefficient of the sand and thra is a constant.

Find the theoretical value of thra . [0.5 points]

Measure the flow rate of sand using various orifice diameters and plot the de-pendence of lnW with respect to ln D . Using the same assumption used in de-

riving eq. (2.1) that expaW D∝ , determine the value of expa from the experiment.

[1.2 points]

The most widely accepted law that predicts the flow rate of grains through an orifice was proposed by Beverloo, which is modified from eq. (2.1) and has the form

( ) ,thraW C g D kdρ= − (2.2)

where d is the grain diameter and k is a dimensionless fitting parameter. According to the Beverloo law, the grains in fact do not flow through the whole orifice, but through an effective exit aperture whose diameter is given by ( ) D kd− .

Based on this law, determine the value of kd using linear regression from the da-ta you obtained. [0.8 points]


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Settling Rate of Sand

It is obvious that sand is a porous medium with different shapes and sizes of grains. In order to estimate the size of a sand grain, we can assume that the shape of the grain is spherical; however, the size of any individual grain might differ from that of the other grains. Despite this fact, we can still estimate the average size of sand par-ticles. In this experiment, you will observe the settling rate of sand particles in water and hence estimate the average radius of a sand grain.

Note: Use colored sand for this section. Plan your experiment very carefully before you begin your experiment, because you will not be able to recover the sand once it gets wet.

Determine the following quantities: Density of sand in air, mass of sand grains divided by the total volume (including

the volume of air inside the pores), Average density of sand grain, mass of sand grains divided by the total volume of sand grains. Density of sand in water, mass of sand grains divided by the total volume (includ-ing the volume of water inside the pores) [1.0 points]

Pour all the remaining colored sand into the graduated cylinder and fill it up with wa-ter. Close the cylinder using the plastic bag and the rubber band of the coloured sand, shake it well, and stand it in a vertical position. The sand will settle on the bot-tom with certain settling rate, which is the rate of the sediment height rises. Measure how fast the sand settles at various heights of the sediment and deter-

mine the settling rate of the sand within the region where the sand size is nearly homogenous. [1.0 points]

It is recommended to take measurements over the entire range of sediment volume in order to obtain the region where the sand size distribution is nearly uni-form/homogeneous. Derive an equation relating the sand settling rate and the density/ies of sand you

calculated before, taking note of the gravitational, Archimedean, and viscous forces. Give your estimation of the average size of the sand particles. [0.5 points]

The sand particle is assumed to be a spherical and any turbulent effect is neglected. You may also assume that a good shake causes the sand to be distributed uniformly. The formula for the viscous force is 6 ,viscous terminalF r vπ η= (2.3)

where r is the radius of the grain and η is the viscosity of water.


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Asteroid Impacts on Earths Surface When an asteroid impacts the surface of the Earth, it creates a large crater with circu-lar cross-section. The exact relation between the crater's dimensions, the physical properties of the impacting body, and the physical properties of the general area of impact is complicated and beyond the scope of this experiment. Nevertheless, there exists an empirical formula to estimate the diameter of an impact crater on the sur-face of the Earth based on experimental nuclear explosions at Yucca Flat, Nevada. From the experimental nuclear crater, the following empirical formula is obtained

1/

,af n

e

D c K Wσ

ρρ

=

(2.4)

where D is the diameter of the crater, fc is the so-called crater collapse factor

(whose value is 1 for craters m 3 k in diameter and 1.3 for craters m 4 k ), 1/0.074 km kiloto s nnK σ−= is an empirical constant, W is the kinetic energy of the as-

teroid just prior to impact, aρ is the mass density of the asteroid, eρ is the mean den-

sity of the target rocks at the point of impact and σ is a constant exponent. The di-ameter of the crater is defined by the peak of the "sand hill", not the outer most visi-ble boundary. The empirical formula above can be verified by modeling the collision using sand and glass balls. Note: Use the pile of sand in plastic basin Using the equipment provided, devise an experiment to determine the numerical

value of the constant exponent σ . After you make your measurement, you may need to loosen and flatten the surface of the sand again. If the sand is too com-pact it can affect your measurement result. [2.0 points]

Actually the σ of the typical asteroid is 25% bigger than the σ that we get from previous question. Estimate the diameter of a crater that would be caused by an iron meteorite of mass 710 kg drifting into Earth's path from very far away.

[0.5 points]

The students got detailed information about the use of the stopwatch in an appendix.


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Experimental Problem No. 2:

A Rotary Magnetic Drag System for Conductivity Measurement

Attention: Use the answer sheet provided to summarize your answer. Provide diagrams to help explaining your answer or your experiments, especially if your answer is not in English. Apparatus Rotary magnet assembly (x 1 pc) Copper plate (x 1 pc) "Black box" containing unknown metal X (x 1pc) Thin cardboard spacers (5 pcs) Thick cardboard spacers (2 pcs)

Power supply unit (x 1pc) Digital multimeter (DMM) – generic (x2 pcs). Digital multimeter (DMM) with frequency measurement (x1 pc). See Appendix A. Ruler (x 1 pc)

Figure 11: Experimental setup


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Important Experimental Data: Copper plate thickness: t = 0.6 mm Copper plate conductivity: σ = 6.0 x 107 (Ohm-m)-1 Metal X thickness: tX = 1.05 mm

— Introduction

Electrical conductivity measurement of a material is important for many applications such as metallurgy and semiconductor industries. Usually one measures conductivity (σ) (1/resistivity) by simple resistance measurement that requires making electrical contacts. This is troublesome and sometimes impossible due to the presence of insulating layer. Thus a contactless conductivity measurement technique is desired. In this problem we will explore a simple and fascinating system to perform contactless conductivity meas-urement utilizing magnetic drag or braking effect that occurs between fast moving mag-nets and a metal sheet. If a magnet moves with velocity v parallel to the plane of a non-magnetic, conducting ma-terial with conductivity σ and thickness t, it will experience a magnetic braking effect also known as eddy current braking effect as shown below:

Figure 12: The magnetic braking effect of a moving magnet near a metal sheet


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The magnetic braking force (using a magnetic dipole model and a thin metal sheet ap-

proximation) is given as: ,MB m

vF td

ασ= − (2.1)

where α is the magnetic braking coefficient of the system which depends on magnetic moment of the magnet and magnetic permeability of the metal sheet, σ and t are the conductivity and thickness of the metal, v is the velocity of the moving magnet, d is the distance between the center of the magnet and the metal and m is the distance power law factor to be determined in this experiment. The negative sign indicates a force that opposes the velocity thus it is called "magnetic braking". In this experiment we mount two strong magnetic pucks on a rotating disc driven by mo-tor as shown below. When the disc rotates and the metal plate is inserted underneath, the disc will slow down due to the magnetic braking effect. This effect can be exploited to measure the conductivity (or thickness) of a metal sheet.

Figure 13: Connection diagram of the rotary magnet setup

System Information: The motor is driven by a variable voltage power supply with coarse and fine control.

DMM (Digital Multimeter) #1 measures the motor voltage VM. DMM#2 measures the mo-tor current IM as a voltage across 1 Ω resistor. The Hall sensor serves as speed sensor. It provides a voltage pulse each time a magnet passes by. When the disc rotates, the Hall sensor frequency fH can be measured using DMM#3.


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To demonstrate the magnetic braking effect, a metal plate is placed at a distance d from the rotating disc. Note that d is measured from the center of the magnets (see Figure 13). Thick and thin card board spacers are provided to vary the distance d. There are two metals provided: a copper plate (with a known conductivity σ and thickness t) and an unknown metal X inside a "black box" (with a known thickness tX). See Section 1: “Important Experimental Data”

Attention: The disc can rotate up to fH = 200 Hz. In general, useful data can be ob-tained approximately < 120 Hz. Do not run the motor at maximum frequency (around 200 Hz) for too long. To save battery power, don't run the motor unnecessarily. Turn off the power if not in use.

— Experiment and Questions

This experiment is divided into four small sections: A. Introduction: Speed Sensor and Basic Operation [1.5 points] B. Basis System Characterization [2.0 points] C. Magnetic Braking Effect Characterization [4.5 points] D. Conductivity Measurement of an Unknown Metal X [2.0 points] --

A: Introduction: Speed Sensor and Basic Operation [1.5 points]

This section will help to familiarize yourself with the experimental setup. First we will try to understand the operation of the Hall effect sensor that measures the rotation frequen-cy. We will observe the voltage signal coming from the Hall sensor. Set the DMM #3 to DC Voltage mode. Turn the rotating disc (mounted on the motor) manually so that the magnet passes through the Hall sensor.

Sketch the voltage waveform for two full rotations, mark how the voltage changes with or without magnet near the sensor. Indicate the period of the waveform. [0.25 points]

Now switch DMM#3 to Frequency mode (Hz) to measure the Hall sensor frequency fH. No metal plate underneath. Turn on the motor Power Supply and increase the voltage gradually to speed up the rotation. Operate the motor < 150 Hz. Observe how the fre-quency reading fH increases with speed.


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Express the disc angular frequency ω (in rad/sec) in terms of Hall sensor frequency fH! [0.25 points]

Now insert the copper plate. Notice how the rotation slows down due to the magnetic braking effect. How does the magnetic braking effect work? To help answer this question, consider only interaction between the moving magnet and an "elemental ring" from the metal sheet as shown below. Draw all the necessary electromagnet fields involved in this diagram in the answer sheet. [1.0 points]

B. Basic System Characterization [2 points] The motor has an internal series resistance RM which is not negligible in this experiment. RM is the sum of resistance of the rotor coil inside the motor. Therefore when the motor is driven by a voltage source, not all of the power is converted to kinetic or rotational ener-gy. A fraction of the energy is turned into heat due to RM. Thus the real motor can be modeled as an ideal motor (whose coil has no resistance) plus a series resistance RM as shown below.

Figure 14. The equivalent circuit of the motor


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Determine the internal series resistance of the motor RM to at least two significant figures! Note: The series resistance is very small. Direct resistance measurement using ohm meter mode of the DMMs (Digital Multimeters) does not have enough accuracy. Try other method. You don't have to change the experimental setup. [0.7 points]

Now we will explore how the system behaves at various ranges of rotation speeds with no metal plate inserted. This is important to pick the operating range for further experi-ment. Under normal condition the motor should run smoothly, however at some frequen-cies the system vibrates strongly and become noisy and we want to avoid this. Do not insert the copper plate.

Increase the motor voltage gradually from 0 to near 200 Hz, record the Hall sensor frequency fH and the motor current IM (DMM#2). Plot both data with respect to voltage VM. Mark the range of frequencies where the system vibrates strongly and become noisy. Note that there is one dominant noisy region. [0.8 points]

What may cause this strong vibration/noise at certain frequencies? What anomaly do you observe in the motor current (IM) vs. voltage (VM) plot in this noisy region? [0.5 points]

C. Magnetic Braking Effect Characterization [4.5 points] Now we will study the characteristics of the magnetic braking effect with the copper plate provided. Here in section C and D, you can operate at low frequency (approximately fH < 120 Hz) and outside the dominant noisy region that you have identified in section B.

Derive expression for power dissipation PMB due to the magnetic braking force of the two magnets and the metal plate. Use (2.1) and express PMB in terms of the Hall sensor frequency fH. [0.5 points]

Perform experiments to verify the relationship of PMB and fH from your previous an-swer! [1.5 points]

Perform experiment to determine the magnetic braking force coefficient α (note that α is associated with one magnet) and distance power law factor m! [2.5 points] Note: To maintain the validity of the distance power law in Eq. (2.1) (due to magnetic dipole approximation) don't place the metal too close. Maintain sufficient distance, approximately d >8 mm.


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D. Conductivity Measurement of an Unknown Metal X [2.0 points] To obtain conductivity (assuming thickness is known), the distance between the magnet and the metal plate d needs to be determined accurately because the magnetic braking force falls off strongly with distance due to large power factor m. In actual industrial ap-plication, it is difficult or even impossible to obtain an accurate distance d without making a contact to the metal (remember this is a contactless method). However it is possible to perform the conductivity measurement without knowing the exact distance between the magnet and the metal plate d. This problem simulates this situation. We have an un-known metal X inside a "black box" as shown below. The thickness is known: tX = 1.05 mm. However its exact location from the surface (∆d0) is not known. In fact, you do not need to know it to obtain the conductivity σ.

Figure 15: The cross section of the "black box" containing the unknown metal X.

Perform an experiment to determine the conductivity of the metal X! [2.0 points]

Note: Please don't open the "black box". It will invalidate your answer. The students got detailed information about the use of the multimeter in an appendix.

— 4. Result

WoPhO is an individual competition, that is why we will present only students’ results. There will be no compilation of results by countries. The best overall participant is Kexin Yi from China with a score of 35.1 out of a total maximum of 50.0. The best result for a theoretical examination is also achieved by Kexin Yi with a score of 22.75 out of a total maximum of 30.0. The best experimental result is achieved by Eugen Hruska from Ger-many with a score of 13.5 out of a total maximum of 20.0. The average score for each problem is very low due to many guest participants from the host country. We will present here only the average score of the medalists. The overall average score of medalists is 17.32, the theoretical average score is 9.59 and the experimental average score is 7.73. The lowest average for a theoretical problem is for problem no. 3, “Mirage”, with an aver-age of 1.5, followed by problem no. 1, “Motion of a Rolling Rod”, with an average of 2.44


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and the highest average is for problem no. 2, “Why Maglev Trains Levitate”, with an av-erage of 5.66. For the experimental problems, the average of problem no. 2 is 4.28, fol-lowed by problem no. 1 with an average of 3.46. In the following, we present the result of the 10 best students for their overall examina-tion, both the theoretical and the experimental examination.

Table 1: The best 10 participants overall

1 Yi, Kexin China 35.10 2 Ants Remm Estonia 27.63 3 Eugen Hruska Germany 27.48 4 Attila Szabo Hungary 25.35 5 Danila Parinov Russia 23.80 5 Christian George Emor Indonesia 23.78 7 Lin Sen Singapore 22.63 8 Jan Pulmann Slovakia 22.45 9 Li Kewei Singapore 20.75 10 Evan Laksono Indonesia 20.15

Table 2: The best 10 participants for the theoretical examination

1 Yi, Kexin China 22.75 2 Ants Remm Estonia 18.68 3 Attila Szabo Hungary 14.40 4 Eugen Hruska Germany 13.98 5 Danila Parinov Russia 13.90 5 Christian George Emor Indonesia 13.63 7 Evan Laksono Indonesia 12.90 8 Jan Pulmann Slovakia 12.50 9 Ivan Ivashkovskiy Russia 11.98 10 Samuel Wirajaya Indonesia 11.83


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Table 3: The best 10 participants for the experimental examination

1 Eugen Hruska Germany 13.50 2 Yi, Kexin China 12.35 3 Lin Sen Singapore 11.40 4 Li Kewei Singapore 11.15 5 Attila Szabo Hungary 10.95 5 Christian George Emor Indonesia 10.15 7 Jan Pulmann Slovakia 9.95 8 Danila Parinov Russia 9.90 9 Wojciech Tarnowski Poland 9.60 10 Momchil Molnar Bulgaria 9.55

The authors would like to make two observations. First, WoPhO has been promoted as an opportunity for any student to challenge the win-ners of APhO and IPhO. However, all the gold medalists at the first WoPhO were still gold medalists of either the competition year APhO or IPhO, with only 2 exceptions. One of the two students, however, was a former gold medalist from the previous year IPhO and another one will be the absolute winner of the next IPhO. Second, the average score even for the medalists of the first final round of WoPhO was quite low. The problems were difficult and both the academic committee and the stu-dents acknowledged this fact. However, WoPhO is also a competition for the winners of the previous Olympiads and the level of difficulty of the problems in that regard can be justified.


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The Junior League of Young Physi-cists’ Tournament

1Alexandr A. Kamin and 2Alexandr L. Kamin 1Lyceum 24, Lugansk, Ukraine 2Specialized school 5, Lugansk, Ukraine

Abstract The purpose of the article is to describe the experience of the work with 13 to 15-year-old high school students solving inventive and research problems. The work was held within the Junior League of Young Physicists’ Tournament and included the solution to the problems and the de-fence of the solutions in the team fight. The properties of suitable problems, the procedure of work on such problems, the organization and peculiarities of the tournament fights for students of such age are described. Also, we pointed out the difference between the Junior League Tourna-ment and other competitions in physics. We showed why such work is reasonable for students and teachers alike.

— 1. Purpose and sense of the Junior League Tournament

The main problem for a school teacher of physics is to arouse and keep up the students´ interest in his subject. As we think, it is the main task for the students to master the sub-ject. Just the information about the importance and use of physics is not enough to arouse the students´ interest. The interest arises when physics is considered as a tool to solve nature’s riddles. Based upon the experience of 16 years, we are going to describe the way of teaching 13 to 15-years-old students. That way includes the solution to the inventive and research problems and the defense of the solution in a team fight. The fights are held within three days at the Opened Lugansk Young Physicists’ Tournament (Junior League).

—


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2. “Genres” of problems.

What properties must the problems that are to be solved have? According to our experi-ence, the greatest interest is caused by the following three types of problems:

Research problem: Some unclear phenomenon is taking place; it must be explained. For example, you show a photo, in which one can see a red-hot lava stream under the sur-face of the water and you ask to explain in which way this phenomenon is possible. Inventive problem: One has to suggest the idea of a device which is new in general. For example, the task is to design an engine which works just due to the atmospheric pres-sure. Reaching a maximum or a minimum: The task is to make clear the conditions of reaching the maximum (or minimum) of some physical parameter. For example, what is the height from which a wingless living being can fall down without any harm for itself ? It turns out that a problem formulated in such a way becomes an ‘open’ one: it allows several different approaches to solve it. During the discussion of the problems in the team and at the tournament it often turns out that different team members study different aspects of the initial problem, and none of them can exhaust the problem as a whole. That makes it essentially difficult both for the rivals and the jurors – there is a temptation for all of them to consider all the approaches to the task, excepting their own one, to be erroneous. It happened once in our practice, when a juror gave a low mark during the fight, because he regarded the Reporter’s solution to be wrong, and after the fight the Reporter convinced the juror that he was right. Unfortunately, that decision did not influ-ence the results of the game because the marks given during the fight may not be cor-rected after it. The general requirement of the task, irrespective of the ‘genre’, is that the wording of the task must be understandable to the students without any additional explanations. Thus, the terms of the problem must be expressed in a simple language, avoiding special terms. Maybe, such terms will be needed during the process of solving the problem, but its formulation must not contain any words whose meaning is unclear to your students. (See Appendix 1: the list of tasks for the Junior league YPT of 2012).

—


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3. The work on the tasks

When the students get acquainted with the tasks, the group (the students with the teach-er) meet to discuss the approaches to the tasks (in our practice – 2 or 3 times a week, every lesson lasts 2 or 3 academic hours). Here are simple rules of the work in the group, which are difficult, but necessary to follow:

1) First the students are to express their ideas; the suggested idea may be criticized only after all the versions are worded.

2) The versions may be criticized, but their authors may not. 3) Finally the team leader expresses his (her) considerations only when the students’

ideas have already been worded.

After such a discussion every task gets its ‘owners’, who want to work with it. If one task has several owners, they distribute their parts in solving the problem: for example, one of them is responsible for the theory, another one for the experiment. As a result of the work on the problem, its ‘owners’ must show a summarized solution and prepare its presentation. As a rule, during the presentation the rest of the group (in-cluding the leader) notice possible mistakes and suggest ways of correcting them. Often some new opportunities to improve the solution become visible at that stage. After that the task is ready for the presentation at the tournament. There arises one question: What can be called the solution to a tournament problem if there are different approaches to solving it and there cannot be any ‘canonical´ solution?

It seems to us that a good solution to a tournament problem must contain the following parts: 1) the brief ‘verbal’ explanation of the effect; 2) the theoretical derivation of a working formula from the numerical estimations; 3) the materials of the experiments or observations in which the effect was shown; 4) the comparison of the theoretical results with the experiment or observation. (See Appendix 2: an example of the solution to the tournament problem: A Spoonful of Water).

—


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4. The defense of the solutions in tournament fights

A tournament is a series of team fights. In each fight a group of teams (three or four, sometimes two) presents their solutions, playing the parts of the reporter, the opponent and the reviewer in turn, in front of a group of jurors (usually 5-10 members). The report-er presents the solution to a problem. The opponent must discover the strengths and weaknesses of the reporter’s solution and give a verdict – how well the problem is solved. The reviewer, in turn, must evaluate the reporter’s and the opponent’s job. There is an important aspect: The opponent must not render his (her) own version of the solution – he (she) has to consider into the reporter’s solution. The jury evaluates all the participants´ job, then the teams change their roles, so that within a fight each team plays each role once.

— 5. How to organize and hold a Tournament?

A tournament can take place under three necessary conditions:

1) There exists a group of authors, who write the tasks, which, firstly, have original con-tent (the detailed solution to the problems must not be published anywhere), and secondly, are worded in a form which is clear and interesting for students.

2) There is a team leader in the school (town, region) who will undertake to solve the

problems suggested by the authors with the students. The team leader can be a school teacher, a professor, a University student or a postgraduate.

3) There is an organizing committee capable of setting organizational issues: making

a list of tasks, sending the list to the leaders of the participating teams, forming a qualified and authoritative jury, appointing the date of the Tournament, providing the participants and the jury with meals and lodgings for that period, writing the neces-sary documents and summing up the results of the Tournament.

—


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6. What does the participation in the Tournament achieve?

For the students: a) The Tournament reveals the purport of studying physics and thus it is a remedy from

its formal studying. b) It deepens the understanding of the laws of physics. c) It trains the creative thinking in the field of physics, the skill of finding the original but

simple solutions to the research and inventive problems. d) It forms the skills of the creative work in a team, including that of the scientific discus-

sions. e) It allows to use the sections of physics and mathematics studied in the lessons for

solving real problems, and not artificial ones – that is much more interesting. f) The Tournament teaches how to defend one´s own point of view in a well-reasoned

way, which raises the success in studying both at school and at the university. g) The Tournament gives the experience of working not only with text-books, but also

with scientific literature – articles, books, special Internet publications. For teachers: a) The work at the Tournament tasks arouses a stable students’ interest in physics and

other exact sciences and the wish to go in for those sciences. b) The students master the material in the usual lessons much better. c) The students participating in the Tournaments show good success in other physics

competitions – i.e. olympiads and children’s scientific conferences. d) The teacher that takes part in solving the Tournament tasks, grows professionally: he

(she) masters the new approaches faster, his (her) explanations become clearer to the students.

e) The constant work with original tasks raises the teacher’s interest in his (her) work and protects him (her) from the ‘professional burn out’.

—


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7. The difference between the Junior League Tournament and other physics competitions

1) Differences from the Olympiads: a) The problems suggested at the Olympiads have, as a rule, only one way of solving a

problem and only one correct answer – the time given to solve the problems is sev-eral hours. The problems, suggested at the Tournaments do not have unambiguous answers and allow several ways of solving problems. Those problems usually require the combination of the theoretical and experimental approaches. Respectively, it may take the team (together with its leader) several days or several weeks to solve the one problem.

b) At the Olympiad every participant solves the problems individually; at the Tourna-ments the whole group, including the team leader, takes part in solving the problems.

2) Difference from the children’s scientific conferences. At the children’s scientific conferences (Sakharov Readings, ICYS) every participant solves and presents one problem, defending its solution before an adult Jury. At the Jun-ior League YPT a team of 6 members must solve about 10 problems, so one participant can be responsible for 2 or 3 problems. The opponents and the reviewers are not adults, but the students of the same age from other teams. What does it result in? The main ef-fect is that the solution to the problem is evaluated by people who have also been in the position of solving it.

3) The difference from the ‘grown-up’ Tournament (for the school-leaving classes). In the All-Ukrainian Tournament the age of the participants is usually 14 to 18 years, in the International Tournament up to 19 years. In the Junior League YPT the age is limited to 15 years. According to the regulations, the team taking part in the Junior league YPT must consist of a student of the 8th and 9th year, except one or two 10th-year students. At that, a 10th year student may speak only once in each fight – either as a reporter, or as an opponent or a reviewer. Two purposes are reached by that: firstly, the problem solu-tion can be developed at a higher scientific level, and secondly, the older participant be-comes a ‘playing coach’ of the team and teaches his less experienced fellows how to work with the tournament tasks. And the rule, limiting the speeches of the 10th-year stu-dents is introduced in order for the tournament not to become a competition among the tenth-graders only. In the ‘grown-up’ Tournament the mathematics is often used, which was usually studied in the first and second years at University up to the differential equa-tions. In the Junior League, as a rule, the results must be received with the help of alge-bra and elementary geometry. Most frequently the list of JL YPT tasks include such parts


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of Physics as mechanics (including the motion in liquids and gases), thermal phenome-na, elements of acoustics, geometrical optics and photometry. Electricity is absent due to the fact that only the electric circuit theory is studied quantitatively in the relevant age.

— 8. Brief history of the Junior league YPT

The Tournament for the students of the 8th to 9th year (3 and 2 years before leaving the school) has been held in Lugansk every year in April or May since 1997. It is interesting that the initiators of the Junior league were not adults, but high school students, partici-pants of the All-Ukrainian Tournament. Since that time about a half of the problems have been suggested not but teachers, but by the school and university students, who were the prize-winners of the All-Ukrainian YPT. 16 such tournaments have been held by 2012. The number of the teams, taking place in the tournaments of the last years, is 10 to 14. From 2000 the tasks of the Junior League YPT are published in the All-Ukrainian journals for teachers of physics, and some regions of Ukraine (Kharkov, Kiev, Lvov, Lutsk, Crimea) hold their own regional tournaments with those tasks. We notice that from 2000 the majority of the prize-winners of the All-Ukrainian YPT (for senior students) were the prize-winners of the Junior League YPT in Lugansk. They are the teams of Kiev, Kharkov, Odessa, Lugansk, Alchevsk, Sevastopol and Dnepropetrovsk. The winners of the International Student Physical Tournament in 2011 took part in the Junior League teams three times: Alexander Kryuchkov, Igor Vakulchik, Ilya Pozhidayev and Alexander Litvinov were the members of Lugansk team; Anastasiya Gaevaya and Anastasiya Va-silchenkova were the members of Kharkov team. It is interesting that very often the sen-ior students who participated in the ‘big’ Tournament help the team leader of the Junior League. Such a job is an invaluable experience for them – the first steps in teaching. And during the Junior League tournament itself such high school students are jury members – together with the University students and adults.

—


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9. Conclusions

In the article we describe the experience of sixteen years of work (from 1997 to 2012). That work included the making of the Tournament tasks, solving them in the optional les-sons together with the students, the organizing and conducting of the Tournament fights. What are our conclusions?

1) The work of the Tournament team resembles that of a real research group or labora-tory (consisting of adults). It arouses the stable interest in physics and other exact sciences and the wish to go in for those sciences. It clears up the purport of studying science and thus is a remedy from formal studying.

2) Time spent on the solving of tournament problems is the time spent on mastering physics through one´s own experience; such a level of mastering adds much to the knowledge received in the regular lessons of physics.

3) The active participants of Tournament teams show great success while studying at the University and during their further work.

4) As a rule, a Tournament team, which successfully performs during several years be-comes a possible institution in an educational establishment (town, region) when supported by the administration organizationally and financially.

— Acknowledgements

The authors like to thank all the teachers – our colleagues at the All-Ukrainian and Junior League Young Physicists’ Tournaments and all the students who were preparing those Tournaments with us and took part in it enthusiastically. There are dozens of such people whose names we are not going to mention, but who we remember and love.

—


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Appendix 1

16th Opened Lugansk Young Physicists’ Tournament Tasks (Junior League)

1. Invent a Laser Broom yourself. In the photo you may see the Earth surrounded by space rubbish (that photo is the result of NASA’s computer simulation). According to modern calculation there are up to 600 000 ob-jects of a diameter of 1 cm at the Earth’s orbit. But even the smallest objects are very danger-ous because of space velocities. Consider the idea of cleaning the near-Earth space by irradi-ating the ‘rubbish’ particles with a laser. Imagine

the optimal design of a cleaning device. What will happen to the particle after being irra-diated? What optimal characteristics must the laser have? How much time will the clean-ing of the near-Earth space take? Calculate it theoretically and make the numerical esti-mations.

2. Wedding aerodynamics. There is the custom of fasting toy balloons to the car of newlyweds. Describe the behavior of the balloons while the car is moving, do so theoreti-cally and research experimentally. Make the numerical estimations.

3. Ripples of the water. Assume a stone falling on the calm water surface far away from the shore. At what maximal distance can the waves from that stone be detected without instruments? What does that distance depend on and what is that dependence like? Can the point where the stone has fallen be found only in connection with those waves? If it can be – in which way can it be found? If not – why is it not possible?

4. Those are no funnels at all! In 1925 a vessel propelled by the rotation of two big upright cylinders crossed the At-lantic Ocean. Explain the operation principle of such a ship. Calculate the correlation between the parameters of the cylinders and the

speed of the vessel. Make the numerical estimations.


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5. Pow! Pow! – Oh, missed! Olga Zaytseva, a participant of the Biathlon World Cup in 2011, when shooting the rifle, missed her marks six times out of eight shots. She ex-plained her failure by the fact that a strong wind was blowing and the bullets were carried away ‘a target size wide!’ How believable is such an explanation from the physical point of view? Calculate the influence of the wind theoretically and make the numerical estima-tions. The Organizing committee of the Junior League YPT forbids the experiments with fire-arms without an Army representative!

6. Slingshot. What maximal speed can the projectile reach if shot with a slingshot? What must the parameters of such a slingshot be? What must the optimal parameters of the projectile be? The Organizing committee of the Junior League YPT forbids shooting at cats, dogs, birds, people and other living beings for practicing.

7. Mysterious fountain. Fasten a can to a rope. The can must be opened at the top, a small hole is made in its bottom. Fill the can with water and begin to rotate the rope ver-tically. At a certain angular velocity a water fountain arises from the hole. What maximal height of the fountain can be reached? Research the effect experimentally and theoreti-cally. Make the numerical estimation.

8. Scorching heat or beastly cold? In 1860 a meteorite dropped somewhere in India. Having drawn a fire trace in the sky, the red-hot body fell into a swamp. People were surprised very much when they found a block of ice at the place where the meteor-ite had fallen (the ice came to the surface itself). That meant that the heavenly flame brought ice to the warm land of India. 1) Explain that paradox. 2) Calculate and estimate numerically what mass the ‘red-hot body’ had before the con-

tact with the atmosphere of the earth, compared to the ‘block of ice’.

9. Rock musical instrument. If one is rotating a piece of a corrugated plastic pipe (a vacuum-cleaner hose, for example) over one´s head, one can hear a musical tone. Research experimentally and describe theoretically in which way the characteristics of the tone depend on the parameters of the rotation. Make the numerical estimations. The Organizing committee of the Junior League YPT warns: such sort of music doesn’t agree with some listeners’ taste!


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10. Bottom off! There is a record in the Guinness Book of Records saying that a kara-teka can strike the neck of a glass bottle in such a way that the bottom of the bottle is torn away, but the rest of the bottle remains unbroken. Explain the phenomenon, de-scribe it theoretically and make the numerical estimation.

11. Running horse, shaking ground. American Indians as well as medieval Rus-sian warriors put their ears to the ground in order to detect the approaching enemy caval-ry when it cannot be seen and heard in a usual way. At what distance can it be done? Describe the effect theoretically. Make the numerical estimations.

12. The die is cast! Why may not three noble dons play dice where they like? A. Strugatsky, B. Strugatsky. ‘Hard to Be a God’ Suppose, you have decided to play dice with the help of a matchbox. Find out from the physical point of view how many points must be marked on every face of the box. Re-search the problem experimentally, calculate theoretically and make the numerical esti-mations. Examine the cases both of an empty box and a full one. The Organizing committee of the Junior League YPT persists that all the winnings of the game must be remitted to the Junior League YPT fund. The tasks were suggested by: N. Boychenko, A Kamin jr, A.Kamin sr, S. Kara-Murza, A. Kryuchkov, I. Pozhidayev, A. Strugatsky, B. Strugatsky, R. Trofimenko, I. Vakulchik.

—


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Appendix 2

The solution to a Junior league YPT problem: “A spoonful of water” Turn a jet of water on a spoon – a tablespoon, a teaspoon or even a ladle. In which way does the jet be-have on the convex side of the spoon? Or on the con-cave side? What effects have you managed to find out? Estimate those effects quantitatively, describe the-oretically and explore in the experimental way.

Fig 1

Solution We have seen that the most interesting effect arises when the water jet meets the con-cave surface of the spoon. In that case we can see a water ‘leaf’, which is several times bigger than the spoon itself. (Fig 1).

It happens because the water, having struck against the spoon, spreads over the whole surface of the spoon at the same speed as it has struck the spoon. As the spoon is in-clined at some angle to the horizontal plane, a small water jet, having left the spoon, is flying further along a parabola. As the water is flowing along the spoon surface in all pos-sible directions, those parabolas form a ‘leaf’. Let us define the size of such a ‘leaf’.


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Measuring the jet speed The jet speed v can be found from the volume conservation (Fig.2): Within the time Δt a jet of the length Δl = v·Δt and the volume ΔV = sΔl = sv·Δt

(s is the jet cross section area, equal to πr2, where r is the jet radius) runs out from the

tap, when 2

1v Vt rπ

∆= ⋅∆

(1)

Thus, the jet speed can be measured by noting down the time within which the jet fills a vessel of a known volume. In the experiment a jar of the volume ΔV = 0.5 l = 5·10-4 m3 is filled within the time Δt =6 s. As the jet radius is r =5 mm we obtain v = 1,06 m/s.

Having struck the surface of the spoon, the water is spreading over the spoon at the same speed as it has hit the spoon. As the spoon is not horizontal, water jets leave the spoon, having the speed directed at some angle to the horizontal plane (Fig.3).

Having left the spoon, the jet moves along a parabola, as any inclined thrown body. Wa-ter is flowing along the spoon in all possible directions, so different portions of water will form parabolas lying in differ-ent vertical planes. One of such parabolas is shown in

Fig.3. All such parabolas form the water leaf, shown in Fig 1.

Below the spoon level the speed of the water drops. Forming the jets becomes greater than the speed v of the initial jet, so the leaf is broken into separate small jets and drops. That can also be seen in Fig 1.

Fig. 2


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The calculation of the ‘water leaf’ parameters.

Let us find the parameters of that ‘leaf’. To make it easy, let us consider the spoon to be a spherical segment, then water moves at the same angle to the horizontal plane in any direction (fig.3) If a portion of water flies out from the spoon at speed v at the angle α to the horizontal plane, it forms a parabola whose parameters can be calculated with the help of such formulas:

The flight time 0y 02v 2v sintg g

α= = (2)

The flight distance: L=2

0 0max 0

2v sin 2v sin cosv v cosoxx tg g

α α αα= = = (3)

The maximal height of the jet ascent: H=2 2

0y 0y 0max y ср

v v v sinv2 2

y tg g

α↓= = = (4)

Formulas (3) and (4) describes the leaf ‘radius’ and the height of the leaf ‘arch’. In order to find the thickness of the ‘leaf’, one must divide the water volume in the ‘leaf’ by its surface area S. The ‘leaf’ contains the water that has flowed out from the tap within the time t.

Evidently, the volume of the jet, which flowed out from the tap within the time t is equal to the volume of the water, which flew from the spoon edge to the ‘leaf’ bounds within the same time t: Vjet=Vleaf (5) The jet volume is 2

0vjetV r tπ= (6)

And the volume of the water that forms the ‘leaf’ is leafV S b= ⋅ ,

where S is the area of the ‘leaf’ surface and b is the ‘leaf’ thickness. Hence due to (5) ‘the leaf’ thickness is b =πr2v0/S (7)

In order to find the leaf area, let us consider it to be flat. Such an approximation is legiti-mate because, as we have found above, the ‘leaf’ radius L is 7 times greater than its height H. In the photo it can also be seen that the height of the leaf ‘arch’ is much less than the leaf ‘radius’. Thus, if we consider the ‘leaf’ to be flat, it gives: 2S Lπ=

Thus the ‘leaf’ thickness is 2 2

0 02 2

v vr t r tbL L

ππ

= = (8)


page 48 / 74

Having substituted (2) and (4), after simplifying we obtain.

2 00 2

2 2 2200

2v sinv

2v sin cos2v sin cos

rr ggb

g

α

α αα α= =

. (9)

That formula allows to calculate the ‘leaf’ thickness theoretically. We can make meas-urements and compare the theoretical values and the experimental ones. the leaf ‘radius’ L and the height of the leaf ‘arch’ H were measured in the photo; we did not manage to measure the ‘leaf’ thickness, so in the table we have presented only its theoretical mean-ing. In the table shows the theoretical and experimental values of L and H. The first val-ues in those columns are the theoretically, the second ones are experimental ones.

The results of the calculations and measurements:

Spoon radius cm

Spoon depth cm

tan α

α (deg)

Flight time, t(s)

Leaf radius L (cm)

Arc height H (cm)

Leaf thickness (mm)

Tea-spoon

2

0,5

0,25

14

0,057

6,4/12

0,8/0,7

0,4

Table-spoon

3,4

1

0,29

16

0,065

7,2/9,5

1/1

0,36

Ladle

4,5

2,7

0,6

31

0,12

12/5

3,6/5

0,24

Капица П.Л. Физические задачи, «Знание» Moscow (1966) Walker J. The flying circus of Physics. John Wiley and Sons, Inc. New York (1979) Камін О.Л, Камін О.О. Фізика (розвивальне навчання). «Основа», Kharkov (2009)


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Integrating Aspects of Geography in Physics Teaching

Gróf, Andrea Karinthy Frigyes Gimnázium, Budapest, Hungary

Abstract The underlying physical concepts and principles of the phenomena discussed in high-school ge-ography texts concerning physics are vaguely stated and explanations are superficial. In addition, there is no quantitative treatment, which would be essential for a deeper understanding. By way of three examples, this paper illustrates the application of the principles studied in physics to the quantitative treatment of geographic phenomena: The height of a tide is estimated, and then the same technique is used to estimate two other heights.

—

1. Introduction Hungarian high-school curricula contain two years of geography. Physical geography is taught in the first year, preceding most of, or, in some schools all physics instruction. Since the background knowledge in physics is lacking, students learn a significant part of their geography without really understanding it. Later on, as students receive the background knowledge in physics, it becomes possible to revisit geographic phenomena. The ability to establish and apply quantities represents a higher level of understanding than conceptual knowledge, even though the modelling of a complicated phenomenon to be approached within the limits of high-school mathemat-ics involves a great deal of simplification. Complexity of the treatment may vary in a wide spectrum, depending on the problem and on the extent to which the questions are struc-tured. The following example will be heavily mathematical at high-school level. However, with all the necessary guidance given, it works well with advanced students (18 year-olds) who can appreciate the power of mathematics.

—


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2. What would be the height of a tide on an Earth without continents?

The choice of tides was motivated by the observation that the treatment of tides in most geography books as well as a vast majority of popular science web pages (e.g. Figure 1) is based on the same misconception: the two lunar tidal bulges have two different rea-sons: the bulge facing the Moon is due to the attraction of the Moon while the one on the far side is due to the centrifugal force acting on the water rotating with the Earth around the centre of mass of the Earth-Moon system.

Figure 1.

Typical illustration. (To make it worse, this diagram gives the wrong impressions that the Moon orbits in the equatorial plane and that the centrifugal force is exerted by the Earth.) http://www.boatsafe.com/kids/earthtides.gif

This explanation is not only wrong because tides are caused by the non-uniform nature of the gravitational field, but it also involves a total confusion about the centrifugal force. Unfortunately, two hours of physics per week are not enough to introduce non-inertial reference frames. We do emphasize, however, in solving physics problems, that what happens is not a consequence of one force or another: all forces acting on an object should be considered. We also emphasize that the conclusion will not depend on the choice of the reference frame. The centrifugal force in itself cannot be the reason for the bulge since it only exists if a rotating frame is used. It is all right to use a rotating frame but the conclusion that there are two tidal bulges has to be the same in an inertial frame, too. To provide a better explanation, let us investigate the approximate range of water levels caused by the non-uniform gravitation of the Moon. (Naturally, textbook illustra-tions must exaggerate the size of the tidal bulges. But what is their true height?) For the sake of simplicity, assume a featureless Earth that consists of a rigid sphere surrounded by an ocean that will readily assume the equipotential shape. For further simplicity, only the effect of the Moon is considered, the effect of the Sun is disregarded.

http://www.boatsafe.com/kids/earthtides.gif


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Fig. 2

Figure 2 shows the Earth, the Moon and the notations that will be used. Since d ≈ 60R. (R is much smaller than d). f denotes the gravitational force per unit mass exerted by the Moon, at a particular location an angle θ away from the Earth-Moon axis.

The actual force per unit mass f can be considered the sum of f acting at the centre (that is the same everywhere and does not cause deformation) and a force ff − that is often called the tide generating force. The deformation of the ocean surface is only caused by

ff − and that result is independent of the reference frame. Since any stretching or com-pressing force will be counteracted by forces arising within the water, we need to concen-trate on the tangential (x) component of the tide generating force: if equilibrium is to be maintained, it is that component that needs to be compensated for by a sea surface slop-ing down in the opposite direction.

θαθ sin)sin( 22 dGM

rGMff MM

xx −+=− , where θαθ sin)sin(rd

=+

according to the sine rule for ΔEMP. By substituting and factorizing, an expression con-taining the difference of the inverse cubes of r and d is obtained:

θθθ sin11sinsin 3322

−=−⋅=−

drdGM

dGM

rd

rGMff M

MMxx

Using algebraic identities and the fact that r is about the same as d, this difference can be approximated as follows:

=−

=⋅−

≈++−

=−

=

− 35

2

32

22

32

33

33)(33)())((11

drd

ddrd

rdrrddrd

rdrd

drd

2

22

23

22

3

22

23

2)(3

)()(3

drd

dddrd

rddrd −

⋅=⋅−

≈+−

= , Hence

2

22

2 2sin3

drd

dGMff M

xx−

⋅⋅=− θ

Now we have the difference of the squares in the numerator, so the cosine rule


page 52 / 74

( 222 cos2 RRdrd −=− θ ) can be applied and the distance r is thus eliminated:

2

2

2 2cos2sin3

dRRd

dGMff M

xx−

⋅⋅=−θθ ,

−⋅⋅=−

2

2 21cossin3

dR

dR

dGMff M

xx θθ .

Finally, the tangential force per unit mass is expressed as a multiple of the gravitational acceleration g. (Any variation of g with position is ignored since this is only an estima-tion.)

Since 2RGMg E= , we have g

dR

dR

MMff

E

Mxx ⋅

−⋅

⋅⋅=− θθ sin2sin

23 3

Students are familiar with the idea of not making a distinction between the sine and tan-gent of an angle that is small. Since the angle of inclination of the sea surface is very small, the quantity multiplying g in the above expression can be considered the slope of the sea surface: For the surface to remain in equilibrium, this tangential force component needs to be balanced by a downhill component of the Earth’s gravity on the slope (Fig-ure 3).

Figure 3.

In the expression of the slope, the second term is only significant next to the first term when θ is close to 90°, but in that case, too, its value is very small because of R << d.


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Thus the maximum slope is found at θ ≈ π/4, where 12sin =θ . Since 8110123.0 ≈=

E

M

MM

and 6010166.0 ≈=

dR , the maximum slope is estimated to be

83

104.823 −×≈

⋅⋅

dR

MM

E

M ,

which means a rise of 8.4 cm over a distance of 1000 km. Slope means rise over unit distance. The total rise from low tide to high tide on our featureless ocean-covered Earth is obtained by adding up these rises for the total distance between a low and a high. That means values of θ between π/2 and 0, that is, over a distance of a quadrant circle, Rπ/2. Therefore the difference between the highest and lowest water levels is obtained by cal-culating the area under the curve in Figure 4:

Rxy 2sin10 8.42sin10 8.4 8-8- ⋅×=⋅×= θ

on the interval of 0=x to

2πRx = .

(The second term does not need to be considered since a small deviation from the sine 2θ curve at its tail where the values are

low does not influence a rough estimation.) If students do not know calculus, it is enough to tell them that the area under xy sin=

from 0 to π is 2 to get the area in question:

m 0.54 m106370104.8104.82

2 388 =×⋅×=×⋅⋅ −−R ,

which is not a very large height, but it is still an immense amount of water sloshing around as the Earth is turning underneath. It is important to note that the meaning of the word “tide” in everyday speech is not the rise and fall of a hypothetical continent-free ocean, but the rise and fall of water levels at a particular coastal location, which may be much larger than the result obtained, and which depends on many things, such as bulges reflected from continents (resonant motions of sea basins), shoreline topography (sea floor slope, estuaries and bays), position with respect to the Moon’s orbit, and the effect of the Sun.

—

Fig. 4


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3. How flat is the Earth?

Let us move on to another effect that determines the shape of the surface. Geography texts all mention the flattened shape of the Earth, but again, the distinction between ellip-soid, geoid and local topography is not made clear. The following estimation aims to determine the order of magnitude of the difference of polar and equatorial radii of the Earth-ellipsoid by only using the mean radius and the rotation period. For simplicity, it assumes an Earth that is covered in a thick layer of wa-ter, thicker than in reality, that will readily assume the ellipsoidal shape owing to rotation. A rotating reference frame attached to the Earth is used. This time, it is the tangential component of the centrifugal force (Figure 5) that needs to be compensated for by an appropriate sloping of the surface. With a calculation completely analogous to that car-ried out with tides, the tangential component is written as a multiple of g, with the coeffi-cient being a function of latitude φ.

Figure 5. The angular speed of the Earth is:

15 s 103.7360024

2 −−×=⋅

=Ωπ

. The tangential component of the centrifugal acceleration at a latitude φ is

ϕϕϕ 2sin2

sincos 22, ⋅Ω=⋅Ω⋅=

RRa xcf

Since this is only a rough estimation, we can calculate with the average radius of 6370 km.

With this radius

gR 32 107.1017.02

−×==Ω

(This maximum occurs at about 45° of latitude.) At a latitude φ, this requires a sea slope of 1.7 × 10–3 sin2φ for equilibrium. The total rise from pole to Equator is the area under the curve

Rxy 2sin107.1 3−×= over the interval 0=x to

2πRx = ,

which is km 11 =×⋅×=×⋅⋅ −− m106370107.1107.12

2 333R .


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The actual values of polar and equatorial radii are 6357 km and 6378 km, their difference is 21 km. So the estimation gives the correct order of magnitude, and we cannot expect more since it was based on an over-simplification of the situation. Note that the 21 km difference is much greater than the height variations owing to tides. Naturally, this oblate spheroidal shape serves as a baseline to which tidal heights should be added. It is also instructive to compare this difference of the order of 10 km to the deviation of the geoid (the true equipotential surface) from the ellipsoid. The map of Figure 6 shows this devia-tion, which does not exceed 110 m anywhere.

Figure 6. Deviations from the ellipsoid. [3]

—


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4. What is the rise of the ocean surface across the Gulf Stream?

Figure 7. Deviations of mean sea surface from marine geoid. [4]

Figure 7 shows the deviations of the mean ocean surface from the marine geoid: all with-in the range of plus 1.5 metres to minus 1.5 metres. We can observe the regions where strong and steady ocean currents flow, for example next to the east coasts of continents. These currents are discussed by all geography texts, the Gulf Stream being the best known of them since it also features a lot in predictions and guesses about climate change that receive a lot of public attention. The Gulf Stream can be observed as a dark orange band in the false-colour image of Figure 8 where colours indicate surface tem-perature. Since one degree on the globe corresponds to about 110 km, we can estimate the width of the Gulf Stream to be 100 km. It does not have sharp boundaries, so this will pass as an order-of-magnitude estimation. Geography texts also mention that the Coriolis force plays a role in the formation of these currents, although again, without a thorough explanation (most of them do not even say that it depends on speed). In addition to the missing explanation, students may be interested to hear that ocean currents also involve a sloping of the sea surface, and this slope is easy to estimate. In the estimation, we will concentrate on the region marked with the white arrow in Figure 8, where the Gulf stream flows northwards at N30° latitude.


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The horizontal Coriolis acceleration is aCor = 2v ×ω where ω is the local vertical component of the Earth’s angular velocity (ω = Ω·sinφ) as shown in Figure 9.

Figure 8 Figure 9

http://oceanmotion.org/images/gatheringdata/modern-gulf-sst.jpg

If a parcel of water at 30° latitude is travelling northwards on the surface at uniform speed v, its Coriolis acceleration is eastwards as shown in Figure 10.

vvaCor ⋅Ω=⋅= ϕω sin22 .

To keep the equilibrium, the sea surface is sloping up towards the east and the slope is obtained if the Coriolis acceleration is divided by g.

Figure 10

http://oceanmotion.org/images/gatheringdata/modern-gulf-sst.jpg


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With v in the order of 1 m/s substituted, the slope of the surface needs to be

565

10103.710

130sin103.72sin2 −−−

≈×=⋅°⋅×⋅

=⋅Ω

gvϕ

that is, about 1 metre over a distance of 100 km, which is the approximate width of the stream. The order-of-magnitude result agrees with reality. (Note that this is a sloping of the mean sea surface, since even ocean waves produce larger variations in height.)

— 6. Conclusion

These were a few examples of quantitative problems constructed to support understand-ing geography. The explanation given to the student necessarily involves a simplification. Even though a model may only describe a very restricted reality if its scope and limita-tions are made clear, it is always possible to elaborate the model later on when we have more background knowledge at hand. However, it is impossible to take that further step ahead from the hazy explanations provided by geography texts. Phenomena addressed by geography texts that lend themselves to physics problems include winds, cyclonic ro-tations, air humidity, thermals, the forming of precipitation, water and earthquake waves, the slope angle of sand dunes, the earth-atmosphere energy budget and many others. In addition to a link between disciplines, the discussion of such phenomena also provides an opportunity to synthesize knowledge across different chapters of physics, such as mechanics and thermal physics.

— References

H.V. Thurman, Introductory Oceanography, Merrill: Columbus, Toronto, London, Melbourne (1984); J.A. Adam, , Mathematics in Nature. Modelling Patterns the Natural World, Princeton University Press (2003); X. Li and H.J. Götze, “Tutorial: Ellipsoid, geoid, gravity, geodesy, and geophysics” Geophysics 66:1660-1668 (2001) I.Jánosi and T. Tél, Introduction to Geophysical Flow Dynamics, (in Hungarian) L. Eötvös Univer-sity Physics Institute, Budapest (2011) http://www.lhup.edu/~dsimanek/scenario/tides.htm http://www.britannica.com/EBchecked/topic/229667/geoid/9322/The-concept-of-the-geoid http://en.wikipedia.org/wiki/Reference_ellipsoid

http://www.lhup.edu/~dsimanek/scenario/tides.htm

http://www.lhup.edu/~dsimanek/scenario/tides.htm

http://www.britannica.com/EBchecked/topic/229667/geoid/9322/The-concept-of-the-geoid

http://www.britannica.com/EBchecked/topic/229667/geoid/9322/The-concept-of-the-geoid

http://en.wikipedia.org/wiki/Reference_ellipsoid


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AMAZING SCIENCE Paul F. Pshenichka Lyceum #1, Chernivtsi, Ukraine. Physics and Astronomy Teacher.

[email protected] , www.ql.cv.ua

This article is mainly about the technique of project-based training in science education. The method is based on the concept of individualizing the stu-dents’ creative abilities. A student must bring all of his/her knowledge to develop an investigation and prepare further on a presentation using PPT or a poster. The student must use written and spoken language, art and graphics, background study and history of a subject, mathematics, learn about sci-entific thinking and processes, develop organiza-tional skills, and conjure up some serious curiosity about its topic. In fact, curiosity, the conversion of that curiosity into a problem statement, and finding ways to overcome a chain of obstacles is what sci-ence is all about.

You may ask: why did we choose the project meth-od? The answer will be: due to its effectiveness and naturalness. Starting in the early childhood, we im-plement a couple of vital projects. We begin to per-ceive the world around us; we learn how to crawl and walk and how to speak. All this is done by cop-ying and repetition. And all these heroic and ingen-ious things are done without fear of failure. Children are remarkably persistent and quick in forming their intellect i.e. - the ability to obtain information and use it. The child's mind knows no boundaries; it is inquisitive and consistent, continuing the instinct of self-preservation. Later on, they are learning to turn the pages of illustrated children's books, then – to be a quick reader, and then – put together puzzles. Here the intelligence is often failing, demanding the creative mind, which appears miraculously, without any tension, as by itself.

Fig. 1. By putting together puzzles the child has to use its creative mind.

Fig. 3. A small investigation during the break.

Fig. 2. Lecture conducted by a FermiLab engineer.


http://www.ql.cv.ua/


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The engagement in a large number of projects requires a number of scientific advisors. These requirements have been successfully met by es-tablishing a scientific organization named “Qua-sar” (the key idea) that united the students’ efforts of different age groups, who were engaged in sci-ence. “Quasar” has become a powerful organiza-tional and intellectual amplifier where students’ creative beginnings and makings in different spheres of science can develop in full at the earli-est age. The Youth Scientific Society (YSS) “Quasar” is an officially registered non-state, non-profit organ-ization. It unites high school students, university students and young scientists with the main aim to promote the youth scientific interests and to support gifted schoolchildren.

Since 1992 the "Quasar’s" 229 high school stu-dents have participated in 103 conferences, Olympiads and competitions, have carried out 130 scientific projects in the fields of physics, mathematics, astrophysics, computer science and ecology. To the present day, they have been awarded 97 diplomas, two gold medals, four sil-ver and seven bronze medals at various national and international scientific conferences, tourna-ments, fairs and Olympiads. The Society was founded in 1991 and is, actually, a small independent youth academy of sciences. It is a prototype of school with no classes, les-sons, grades, examinations and terms of gradua-tion. Members of this school are both students and teachers, they make up an active environ-ment, where their creative beginnings and work in different spheres of science can develop in full at the earliest age possible. The students enter the association at the age of 12 – 14 (Fig. 3) and then are involved in scientific activities through a sys-tem of optional courses and seminars. They start by solving simple problems and go on dealing with more and more difficult questions, learn how to design their solutions in the form of scientific work and to give speeches at scientific confer-ences. The YSS members remain in the society, if they wish, as college students, post-graduate

Fig. 5. Team work. Discovery of a new effect.

Fig. 4. 18-23 of April 2008 YSS “QUASAR” organized the ICYS-08 in Chernivtsi, Ukraine.

Fig. 6. An unexpected optical effect discovered during a regular investigation of a glass sphere.


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students and scientific researchers. They actively help the younger members of the YSS and each other in the fulfillment of scientific work, and gain-ing extracurricular knowledge. The members of the YSS are studying or working in Ukraine, Rus-sia, the USA, the Netherlands, Great Britain, Switzerland, France, Germany, Denmark, Israel and Canada. When they come home on vacation, they take part in seminars and deliver lectures as part of optional courses. YSS currently participates in 9 international and 4 Ukrainian national projects, keeps in touch with 17 educational and research organizations, in-cluding research institutes, universities, and sci-ence magazines. 1999 the Canada Fund supported the YSS “Qua-sar”.

18-23 of April 2008 YSS “Quasar” organized the International Conference of Young Sci-entists ICYS-08 in Chernivtsi, Ukraine (Fig. 4).

Students are able to study during a break and after school on their own, if they are motivated by a gen-uine interest. In that case, they need a coach rather than a teacher, who can be a peer, a student, a graduate student or a scholar. A small, but real problem can develop into a project lasting several years and the gained experience during this time is often more important than the problem, no matter whether it is solved or not.

In modern science, problems are solved by teams – the project can unite students, knowledge and abili-ties complement each other. The need for mutual help holds the group together, there is always a leader among them, and the shared interest in this case helps to overcome contradictions and differ-ences of the characters – so that a group gives birth to a team. In the picture (Fig.5) you can see the team that won a prize in a serious contest pre-senting the project which is a small discovery.

A discovery can be planned or can occur randomly, but in any case it is a very rare event (Fig. 6). The Linear Vibrotransporter – a problem that was previously formulated and then solved in two steps. The problem of transitive chaos which was demonstrated using a small jumping ball, gave a new modification of

Fig. 7. Discovery of the “Rotating Ball Effect”.

Fig. 8. “Physics-8. A Step to the Next Century”


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the problem while the ping-pong ball was replaced by a tennis ball (Fig.7). A random er-ror led to the discovery of a new effect. How often have you been witness of a discovery?

The collaboration within the society coherently fosters student independent research with a greater sense of self-reliance. The effective undertaking of a scientific project requires an exchange of ideas, which is accomplished by the interaction of students in society. To broaden their interaction with likeminded people we participate in a great number of sci-entific conferences, competitions and Olympiads (further information is attached). Work-ing groups are created according to the students’ inclinations and function as a part of society, working in physics, mathematics, computer science, astrophysics, ecology, eco-nomics, and even sociology and linguistics. The efficiency of the group is restricted only to the availability of scientific advisors and equipment.

Separate elements of this method are used in my lessons, in textbooks and in extra cur-ricula education. My innovative ideas have been incorporated into our last two textbooks in physics (Fig.8) titled “Physics. A Step to the Next Century”.


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Many “Quasar” members cooperate with us after graduating from high-school. Now we can also receive the consultation from specialists working in famous laboratories (Fig. 2). A number of optional courses on modern scientific problems are taught during vacation sessions. A very interesting ex-change of ideas and knowledge is carried out at these meetings, which is a profitable mutual schooling for the participants. The students will benefit from this new learning platform due to their increased capacity to absorb new content and will thus turn information into knowledge quickly and effectively. There is a curious fact. A magnet at-tracts not only iron objects; it also attracts interest and attention. Students, who surrounded a power-ful magnet in the break instead of having lunch or lasting for entertainment, did not know at that mo-ment that all of them would become engineers (Fig. 9). The Quasar activities have been insepa-rable from the school educational process. Its ad-vantage stems from the self-organizing structure allowing for the involvement of a larger number of students leading to a higher quality of projects. As a mark of success we also consider the enthusi-asm with which students participate in research endeavours, their dedication to science and the fact that the numerous former Quasar members have become professional researchers at Harvard, Princeton, FermiLab, Leiden, Max Delbruck Insti-tute etc.

Below we present a selected list of projects that have received awards of a very high degree in different scientific conferences and competitions:

Warsaw, Poland. “The First Step to the Nobel Prize in Physics”. International Competition in Re-search Projects in Physics.

Category Awards: 1995, 2001.

Fig. 9. Students, who surrounded a powerful magnet in the break do not know in that moment that all of them will become engineers.

Fig. 11. International Astronomy School.

Fig. 10. The “Saharov Readings Con-ference”. Demonstration of the Linear Transporter Device.


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Category Honorable Mention: 1993 (2 papers); 1996, 1997, 1998, 2002.

Moscow, Russia. “The Open Russian Scientific Conference of High School Students” on physics, mathematics, computer science, ecology and chemistry.

1st Diploma: 1996 (Computer Science), 2000 (mathematics).

2nd Diploma: 1994 (Physics), 1996 (physics – two diploma), 1999 (physics)

Team Competition:

1st place: 1994 (mathematics), 1998 (physics)

2nd place: 1995 (physics), 2003 (physics)

"International Conference of Young Scientists, ICYS" on physics, mathematics, computer sciences and ecology.

1st Diploma: 1996 (physics), 1999 (ecology) – golden medal, 2001 (physics)

2nd Diploma: 1999 (physics) – silver medal.

3rd Diploma: 2006 (physics) – bronze medal, 2007 (physics, Computer Science) – bronze medals, 2009, 2012 (physics) – bronze medals.

Special Prise: 2010 (physics - team project, com-puter science)

Crimea. Ukraine. “International School and com-petition in Astronomy” (Fig. 11).

1st and 3rd Diploma: 1999

Moscow. Russia. “Moscow and Moscow Region Olympiad in Astrophysics and Space Physics”

1st and 3rd Diploma: 2000

Petersburg. Russia. “The Saharov’s readings” International Scientific Conference of High School Students in physics, mathematics, computer science, chemistry and biolo-gy (Fig. 10).

1st Diploma: 2000 (computer science), 2002, 2005, 2009 (physics)

Fig. 12. The “Intel-Techno Ukraine” Sci-ence Fair.


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2nd Diploma: 1995 (physics – two diploma), 1998 (physics).

Kiev, Ukraine. “Intel-Techno Ukraine”, Science and Engineering Fair (Fig. 12).

2nd Diploma: 2010 (physics) – team project.


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The HUNVEYOR Project, an integrated science education program

György Hudoba Alba Regia University Center, Óbuda University Székesfehérvár, Hungary

Abstract The HUNVEYOR project is a long term experimental complex teaching program. It is currently running at several educational institutions ranging from high school to university level in Hungary. The project (engineering, constructing and using an exploration robot) integrates many fields of science. The HUNVEYOR-4 is an advanced student-made Surveyor‐class environment monitor-ing, internet controllable robotic landing gadget with remote access, and suitable for “learning by experience” in many fields of physics.

— 1. Introduction

The 20th century gave a big boost for the technology and as a result our everyday life has been dramatically changed during the last 50 or 60 years. That was a great consequence of the cold war, especially of the “Space Race” announced by President Kennedy in Sep-tember 1962 at Rice University with his famous words: “We choose to go to the Moon.” Today we are living in the 21st century, in the so called “Space Age”. Our lives are in-creasingly dependent on technology: from shopping, banking and smart phones to life-support devices, computers and the internet have gone from luxury items to being ubiqui-tous lifestyle accessories. Everybody expects this evolution to be sustainable with no ob-stacles to growth. The once young pioneers of the technical revolution are gradually retir-ing, and the knowledge and work must be passed on to the younger generation. The reality is that interest in sciences and engineering is fading among the general popu-lation and also among the students. This is a world-wide phenomenon, and it is true to the Hungarian population as well. Our goal is to rekindle interest in careers in science and engineering. The HUNVEYOR project is our answer to this challenge.

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2. The aims of the HUNVEYOR project

The primary aim of the HUNVEYOR project is to gain interest among young people of ages 15 to 21. We aim to make careers in science and engineering attractive by involving students in research projects and developments at their academic institutions. We pro-vide them with personal experience by allowing them to become involved with master-minding, constructing and using advanced technological devices. We allow them to study real, complex situations outside “sterile” laboratory physics.

— 3. History and motivation

The HUNVEYOR project is a long term experimental complex teaching program running at several institutions ranging from high school to university level in Hungary. The educa-tional space probe building program was initiated in 1997 at the Roland Eötvös University (HUNVEYOR-1), and in course of time several other institutions joined the project. The name “HUNVEYOR” is an acronym for Hungarian UNiversity SurVEYOR. The “Surveyor” indicates that our template is the American built Surveyor-7 space probe that landed on the Moon in 1968. The surveying robot was fitted with a solar panel, an on board camera and several sensor devices. We believe that building a “space probe” in the Space Age is still an attractive project. Constructing, testing and using different sensors and devices (learning by personal experience) is an efficient way to teach physics. Let us assume, we are on the surface of Mars (or in any other location), and we want to know the local weather and numerous environmental parameters. We want to monitor these parameters in order to decide whether we humans would be able to establish a habitable space sta-tion in this environment. The measured data as well as the pictures can be retrieved on demand from the “Terrestrial Control Room” which can be reached from the web portal of the space probe: http://hunveyor.arek.uni-obuda.hu

—

http://hunveyor.arek.uni-obuda.hu/


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4. HUNVEYOR-4 in physics education

HUNVEYOR-4 is an advanced student-made Surveyor‐class environment monitoring robotic landing gadgets with remote access, engineered by the students of the Alba Regia University Centre, which is a campus of Óbuda University, located in Székesfehé-rvár. The solution (engineering, constructing and using an internet controllable explora-tion robot) integrates many fields of science including physics, electronics, robotics, com-puter and web programming and modelling. It involves creating space-inspired anima-tions, conducting planetary analog field studies and conducting various experiments. These experiments include monitoring the environment by measuring temperature, wind speed and direction, detecting soil pH, collecting magnetic dust (the so called “magnetic mat” experiment), and so on. With guidance by the teachers, the great bulk of the project is being done by the students of age 18 to 21.

Figure 1. HUNVEYOR-4 during a Martian analog terrestial field study

In the following below we go through some of the building elements of HUNVEYOR-4, pointing out some opportunities to discuss physics.

Building element:

Figure 2. The frame of HUNVEYOR-4


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Topics to discuss: force as vector, adding and subtracting vectors/forces, standing stability, pressure, vibrations, different macroscopic properties of matter, strength, stress, elasticity, thermal expansion

Building element:

Figure 3. The weather station

Topics to discuss:

temperature and its measurement, temperature scales, air pressure and its dependency on sea level, Pascal’s principle, vacuum, air flow, laminar and turbulent flow, electric discharges, lightning and detecting electromagnetic waves

Building element:

Figure 4. The webcamera

Topics to discuss:

various kinds of optics, light as ray and as wave, optical imaging and different aberrations, light and matter interaction, quantum properties of the light, detecting light, principles of the CCD

Building element:

Figure 5. The student made LED spectrometer

Topics to discuss:

the complete electromagnetic spectrum, spectral


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properties of the matter, emission and absorption, semiconductor physics: energy bands, electrons and holes, electron-hole recombination, the PN junction, LEDs and LDs

Building element:

Figure 6. The personal radiation detector

Topics to discuss:

particle radiation, radioactivity, stability and de-cay of elements, nuclear energy and power plants, elementary particles, cosmic rays, radio-active dating methods (like C14 dating), health issues

These are just a few examples of the numerous opportunities for teaching physics in the HUNVEYOR project. In addition to the device-specific topics there are other important fields to discuss. For example, what are the requirements for operating the space probe on a remote field, far from electric network? How would the space probe perform in space, i.e. in vacuum, where no air cooling is possible? These questions lead to discus-sions regarding energy and energy budget, determining the energy requirement of indi-vidual parts and of the complete device and establishing power sources, batteries and solar panels. Additional topics are heat dissipation, transportability and vibrations, radio communication, remote control and robotics. While using the device and taking meas-urements we can discuss the different kinds of errors, the statistical properties of the measurements and the importance of error estimation.

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5. Using the educational space probe

To provide an example, we review a planetary analog study. In this experiment we cap-ture magnetic dust particles on a slope. The first step is the calibration process, taking place in the laboratory, using different soil composition and slopes. The second step is taking actual measurements in the field. Comparing the results with the laboratory rec-ords allows students to infer the magnetic content of the soil gathered in the field. The Viking and the Mars Pathfinder space probes found magnetic materials while studying Martian dust, providing the motivation for this experiment. The tasks are simple enough to be carried out by students, however, the various components of the experiment make it more complex. The comparison to the natural environment provides an experience usually missed in “clean laboratory procedures”, providing exposure to the complexity of environmental measurements. Physical properties to be studied are as follows: - Sticking magnetic material on a slope - Blowing away particles by the wind - Changes in sticking behaviour by changing mixture composition Step one: calibration in the laboratory. We constructed a magnetic mat from refrigerator magnets (magnetic strength about

5 mT) covered by a white sheet of paper. We pre-pared different mixtures of sand, ferromagnetic mate-rials and gypsum. We aligned the slope and spread the mixture onto the top of the slope. The magnets captured part of the ferromagnetic dust and formed a pattern. We repeated the experiment with different compositions and recorded the results. The materials we used for the mixtures included sand (fine grained and coarse grained), rust (fine grained and coarse grained), iron (fine grained and coarse grained) and gypsum (CaSo4). From the calibration process we found that the minimal slope for sliding was 32,5 degrees for the coarse grained and 36 de-grees for the fine grained mixtures. Using this result we decided to use a 45 degree slope.

Figure 7. Using HUNVEYOR-4 during the calibration process


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For the friction coefficients we obtained µ=0.54 for the coarse grained mixture and µ=0.59 for fine grained mixture. We also calculated the sliding speeds at the top and at the bottom of the magnets. We found the numerical values of 1.3 m/s and 1.8 m/s for the coarse grained and 1.1 m/s and 1.6 m/s for the fine grained mixtures. All values refer to the slope aligned to 45 degrees.

Figure 8. left: fine grain two component, right: coarse grain three component patterns

Step two: field study We relocated the space probe to a Martian analog field some 20 km from our city and applied soil to the magnetic mat. Then, we took pictures with the webcamera of HUNVEYOR-4 as can be seen in figure 9.


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Figure 9. The Martian analogue terrestial field experiment

Comparing the results to the calibration records we concluded that the ferromagnetic component of the soil is nearly 5%

6. Conclusions The HUNVEYOR project has been successfully conducted in Hungary for more than ten years. The project forms an attractive background for meaningful, long term research, experiment and development and gives a wide variety of topics for studying physics. As a byproduct, students develop a lasting relationship with their teachers, furthering their ca-reer aspirations and options in science and engineering.

Acknowledgements Thanks to all of my students who contributed to the success of HUNVEYOR-4 in the past 11 years. I also thank my institution for supporting the project.

References Sz. Bérczi, V. Cech, S. Hegyi,T. Borbola, T. Diósy, Z. Köllõ , Sz. Tóth : Planetary geology educa-tion via construction of a planetary lander (1998), LPSC XXIX, #1267, LPI Houston

Sz. Bérczi, B. Drommer, V. Cech, S. Hegyi, J. Herbert, Sz. Tóth, T. Diósy, F. Roskó, T. Borbola: New programs with the Hunveyor experimental planetary lander in the universities and high schools in Hungary (1999), LPSC XXX, #1332, LPI Houston

Hegyi S., Kovács B., Keresztesi M., Béres I., Gimesi L., Imrek Gy., Lengyel I., Herbert J.: Exper-iments on the planetary lander station and on its rover units of the Janus Pannonius University, Pécs, Hungary (2000), LPSC XXXI, #1103, LPI Houston


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Hudoba, Gy., Sasvári G., Kerese P., Kiss Sz., Bérczi Sz.: HUNVEYOR-4 CONSTRUCTION AT KANDÓ KÁLMÁN ENGINEERING FACULTY OF BUDAPEST POLYTECHNIK, SZÉKESFEHÉRVÁR, HUNGARY (2003), LPSC XXXIV, #1543, LPI, Houston

Gy. Hudoba, Zs. I. Kovács, A. Pintér, T. Földi, S. Hegyi, Sz. Tóth, F. Roskó, Sz. Bérczi: New ex-periments (in meteorology, aerosols, soil moisture and ice) on the new Hunveyor educational planetary landers of universities and colleges in Hungary (2004), LPSC XXXV, #1572, LPI, Hou-ston

Györök, Gy.: Self Embedded hybrid Controller with programmable Analog Circuit. IEEE 14th In-ternational Conference on Intelligent Systems, Gran Canaria: pp. 1-4. Paper 59. (ISBN:978-4244-7651-0)

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