IPhO 2025

Problem 1 (10 points) A look through the glass sphere In the photo on the first page of the problem sheet, the Eiffel Tower can be seen in the glass sphere as an upside-down image. The glass sphere has a diameter of 9.5 cm and, for paraxial rays, can be treated approximately like a thin lens with a focal length of 7.0 cm. The photo was taken with a mobile phone camera whose very small lens is located at a distance of about 30 cm from the centre of the glass sphere. Using the photo, estimate the distance from the Eiffel Tower at which it was taken. To do this, use two different methods, once using the image in the glass sphere and once without. Compare the results obtained. Note: feel free to research the data you need about the Eiffel Tower.

Topic: Geometric Optics, Order-of-Magnitude Estimation Metodi: Thin Lens & Mirror Equation, Ray Tracing, Order-of-Magnitude Estimation Competenze: Estimation & Approximation, Physical Reasoning, Diagrammatic Reasoning Objects: Sphere, Lens Fonte: Testo (PDF) — p.2

Problema 1 (10 punti) Un’occhiata attraverso la sfera di vetro Nella foto sulla prima pagina del foglio di problemi, la Torre Eiffel può essere vista nella sfera di vetro come un’immagine al vertice. La sfera di vetro ha un diametro di 9,5 cm e, per i raggi parazziali, può essere trattato approximately like a thin lens with a focal length of 7,0 cm. La foto è stata scattata con una telecamera del telefono cellulare il cui piccolo obiettivo è situato a una distanza di circa 30 cm da Il centro della sfera di vetro. Usando la foto, stima la distanza dalla Torre Eiffel alla quale è stata presa. Per fare questo, utilizzare due metodi diversi, una volta usando l’immagine nella sfera di vetro e una volta senza. Compare i risultati ottenuti. Nota: sentitevi liberi di ricercare i dati che vi servono sulla Torre Eiffel.

The following points are added: A look through the glass sphere In the photo on the first page of the problem sheet, the Eiffel Tower can be seen in the glass sphere as an upside-down image. The glass sphere has a diameter of 9.5 cm and, for paraxial rays, can be treated approximately like a thin lens with a focal length of 7.0 cm. The photo was taken with a mobile phone camera whose very small lens is located at a distance of about 30 cm from The center of the glass sphere. Using the photo, estimate the distance from the Eiffel Tower at which it was taken. To do this, use two different methods, once using the image in the glass sphere and once without. Compare the results obtained. Note: feel free to research the data you need about the Eiffel Tower.

Problem 2 (10 points) Planetary observation Two planets move, as sketched alongside, on circular orbits in a common plane and with the same sense of revolution around a star of mass M = 2.0 $\cdot$ 1030 kg. From one of the planets, an astronomer has measured the angle shown in the following figure between the central star and the other planet as a function of time. One unit on the horizontal time axis corresponds to one Earth year a. The size of one unit of the angle axis is not given. 2.a) Using the data from the graph, show that the radius of the orbit of the outer planet is about 1.4 times as large as the radius of the orbit of the inner planet. 2.b) State which angle (in degrees) one unit on the vertical axis corresponds to. 2.c) Determine the radii of the planetary orbits.

Topic: Astrophysics, Gravitation Metodi: Kepler’s Laws, Newton’s Law of Gravitation, Experimental Data Analysis Competenze: Experimental Data Analysis, Graph Linearization, Estimation & Approximation Objects: Planet, Star Fonte: Testo (PDF) — p.2

Problema 2 (10 punti) Observazione planetaria Due pianeti si muovono, come disegnato insieme, su orbite circolari in un comune piano e con lo stesso senso di rivoluzione attorno a una stella di massa M = 2.0 $\cdot$ 1030 kg. Da uno dei pianeti, un astronomo ha misurato l’angolo mostrato nella figura seguente tra la stella centrale e il altri pianeti in funzione del tempo. One unit on the horizontal time axis corrisponde a un anno terreno a. La dimensione di una unità dell’asse angolare non è data. 2.a) Usando i dati del grafico, mostrare che il raggio di orbita del pianeta esterno è circa 1,4 volte superiore a quello di grande come il raggio dell’orbita del pianeta interno. 2.b) Stato a cui corrisponde un angolo (in gradi) di una unità sull’asse verticale. 2.c) Determinare i radii delle orbite planetarie.

Problem 2 (10 points) The following is a list of the countries of the European Union: Two planets move, as sketched alongside, on circular orbits in a common plane and with the same sense of revolution around a star of mass M = 2.0 $\cdot$ 1030 kg. From one of the planets, An astronomer has measured the angle shown in the following figure between the central star and the other planet as a function of time. One unit on the horizontal time axis corresponds to One Earth year a. The size of one unit of the angle axis is not given. 2.a) Using the data from the graph, show that the radius of the orbit of the outer planet is about 1.4 times as large as the radius of the orbit of the inner planet. 2.b) State to which one unit on the vertical axis corresponds. 2.c) Determine the radii of the planetary orbits.

Problem 3 (10 points) Giant Magnetoresistance In 2007, the Nobel Prize in Physics was awarded for the discovery of Giant Magnetoresistance (GMR), a quantum-physical phenomenon, to the research groups around Albert Fert and Peter Grünberg. Owing to the effect, the electrical resistance of special, very thin layered systems can be deliberately influenced by an external magnetic field. Consider the example shown for a Co-Cu-Co layered system. On a very highly conductive substrate there are two equally large cobalt layers (Co, ferromagnetic), separated by a thin copper layer (Cu, approximately non-magnetic). Through the direct contact with the substrate, the magnetisation direction of the lower cobalt layer is fixed. The magnetisation of the upper cobalt layer, however, can be differently Angle measured from one of the planets between the star and the other planet. Sketch for the planetary observation. Best to hang the problems directly by the poster! Problems and further materials for download 1 2 3 4 5 6 7 8 $- 3$ $- 2$ $- 1$ 1 2 3 Time / a Angle oriented. Without an external magnetic field, the magnetisation directions of the layers are oriented antiparallel (Situation A). A strong external magnetic field leads to parallel orientation (Situation B). Perpendicular to the layered system a voltage is now applied, which leads to a current generated by electron transport. The spin orientation of the electrons is either parallel $(\to$ ) or antiparallel (←) to the magnetisation direction of the lower cobalt layer. This leads to different electrical resistances in the cobalt layers. For the description of the electrical resistance, assume the following: • In each case, half of the conduction electrons have spin orientation $\to$ and ←. The spin orientation does not change. • In a cobalt layer, electrons whose spin is aligned parallel to the magnetisation direction of the layer have a lower resistivity $(ρ ↑↑$ ) than electrons with antiparallel spin orientation $(ρ ↑↓$ ). • The electrical resistance of the substrate and the copper layer is negligible. • The external magnetic field does not affect the electron motion. 3.a) Draw an equivalent circuit sketch for the current flow through the Co-Cu-Co layered system for each of the situations A and B. 3.b) Show that the total resistances RA and RB of the layered system satisfy: RA > RB. 3.c) Using your equivalent circuit diagrams, calculate the relative change

of the resistance of the layered system due to the GMR effect. Express your result in terms of the ratio $α$ = $ρ ↑↑ / ρ ↑↓$ .

Topic: Circuits, Magnetism, Modern-Quantum Physics Metodi: Equivalent Circuit Reduction, Physical Modeling, Approximation & Series Expansion Competenze: Mathematical Modeling, Physical Reasoning, Diagrammatic Reasoning Objects: Electron Fonte: Testo (PDF) — p.2

Problema 3 (10 punti) Giant magnetoresistance Nel 2007, il Premio Nobel di Fisica fu assegnato per la scoperta di Giant Magnetoresistance (GMR), un fenomeno quantistico fisico, al I gruppi di ricerca intorno a Albert Fert e Peter Grünberg. A causa dell’effetto, la resistenza elettrica di sistemi speciali a strati molto sottili può essere deliberatamente influenzata da un campo magnetico esterno. Considerate l’esempio mostrato per un sistema strato Co-Cu-Co. Su un substrato molto altamente conduttivo ci sono due strati di cobalto (Co, ferromagnetico), separati da un sottile strato di rame (Cu, circa non magnetico). Attraverso il contatto diretto con il substrato, la direzione di magnetizzazione del livello inferiore di cobalto è fissa. La magnetizzazione del livello superiore di cobalto, tuttavia, può essere differente Angolo misurato da uno dei pianeti tra la stella e l’altro pianeta. Sketch per l’osservazione planetaria. Best to hang i problemi direttamente da Il poster! Problemi e altri materiali per download 1 2 3 4 5 6 7 8 $- 3$ $- 2$ $- 1$ 1 2 3 Tempo / a Angolo orientato. Senza un campo magnetico esterno, le direzioni di magnetizzazione dei strati sono orientate antiparallelamente (situazione A). Un forte campo magnetico esterno porta ad orientamento parallelo (situazione B). Perpendicolare al sistema strato, una voltage è ora applicata, che porta a un corrente generato dal trasporto elettronico. L’orientamento spin degli elettroni è sia parallelo $(\to$ ) che antiparallelo (←) la direzione di magnetizzazione del livello inferiore di cobalto. Questo porta a diversi resistenze elettriche nei livelli di cobalto. Per la descrizione della resistenza elettrica, supponiamo: • In ogni caso, metà degli elettroni di conduttività hanno orientamento spin $\to$ e ←. The spin orientation non

Cambiare. • In un strato di cobalto, gli elettroni il cui spin è allineato parallelo alla direzione di magnetizzazione del strato hanno una resistenza inferiore $(ρ ↑↑$ ) rispetto agli elettroni con orientamento spin antiparallelato $(ρ ↑↓$ ). • La resistenza elettrica del substrato e del copro è trascurabile. • Il campo magnetico esterno non influisce sul movimento degli elettroni. 3.a) Disegnare uno schema di circuito equivalente per il flusso corrente attraverso il co-cu-co sistema stratificato per ciascuna delle situazioni A e B. 3.b) Sosteni che le resistenze totali RA e RB del sistema strato soddisfano: RA > RB. 3.c) Utilizzo dei diagrammi di circuiti equivalenti per calcolare il cambiamento relativo

di resistenza del sistema stratificato a causa dell’effetto GMR. Esprimere il risultato in termini del rapporto $α$ = $ρ ↑↑ / ρ ↑↓$ .

Problem 3 (10 points) Giant magnetic resistance In 2007, the Nobel Prize in Physics was awarded for the discovery of Giant Magnetoresistance (GMR), a quantum-physical phenomenon, to the The research groups around Albert Fert and Peter Grünberg. Because of the effect, the electrical resistance of special, very thin layered systems can be deliberately influenced by an external magnetic field. Consider the example shown for a co-cu-co layered system. On a very highly conductive substrate there are two equally large cobalt layers (Co, ferromagnetic), separated by a thin copper layer (Cu, approximately non-magnetic). Through the direct contact With the substrate, the magnetisation direction of the lower cobalt layer is fixed. The magnetisation of the upper cobalt layer, however, can be differently Angle measured from one of the planets between the star and the other planet. Sketch for the planetary observation. Best to hang The problems directly by The poster! Problems and further materials for download 1 2 3 4 5 6 7 8 $- 3$ $- 2$ $- 1$ 1 2 3 Time / a Angle of use The Commission is not prepared to take any further action. Without an external magnetic field, the magnetisation directions of the layers are oriented antiparallel (situation A). A strong external magnetic field leads to parallel orientation (situation B). Perpendicular to the layered system a voltage is now applied, which leads to a current generated by electron transport. The spin orientation of the electrons is either parallel $(\to$ ) or antiparallel (←) to the magnetisation direction of the lower cobalt layer. This leads to different electrical resistance in the cobalt layers. For the description of the electrical resistance, assume the following: • In each case, half of the conduction electrons have spin orientation $\to$ and ←. The spin orientation does not Change the way you look. • In a cobalt layer, electrons whose spin is aligned parallel to the magnetisation direction of the layer have a lower resistivity $(ρ ↑↑$ ) than electrons with antiparallel spin orientation $(ρ ↑↓$ ). • The electrical resistance of the substrate and the copper layer is negligible. • The external magnetic field does not affect the electron motion. 3.a) Draw an equivalent circuit sketch for the current flow through the co-cu-co layered system for each of the situations A and B. 3.b) Show that the total resistance RA and RB of the layered system satisfy: RA > RB. 3.c) Using your equivalent circuit diagrams, calculate the relative change

of the resistance of the layered system due to the GMR effect. Express your result in terms of the ratio $α$ = $ρ ↑↑ / ρ ↑↓$ .

Problem 4 (10 points) Falling baking cups In the atmosphere, free fall is slowed by air friction. The friction force F is thereby proportional to the square of the falling speed v and can be expressed by Here A denotes the cross-sectional area of the falling body, $\rhoLuft$ the air density, and cW the so-called drag coefficient, which depends on the shape of the body. With paper baking cups, like the muffin cases seen in the photo, the slowed fall can be investigated experimentally. Besides several identical baking cups, you need for this a device for measuring time, such as a stopwatch, a tape measure or a folding rule, as well as an accurate scale, such as you can find for example at school. 4.a) Determine an expression for the terminal speed that a body can reach when falling with friction. 4.b) Drop five baking cups nested inside one another several times and measure the fall times for different fall distances. From this, produce a graph of the fall time as a function of the fall distance. Use it to determine approximately the fall distance after which the terminal speed is reached. Note that this fall distance can amount to several metres. 4.c) Now vary the number of baking cups nested inside one another and measure the terminal speed that establishes itself in each case. Using a suitable graph, determine the drag coefficient of your baking cups. In the evaluation, use for the density of air $\rhoLuft$ = 1.2 kg $m - 3$ and for the gravitational acceleration g = 9.81 m $s - 2$ . Junior problem (10 points) Lens construction A large but thin, symmetric lens is used to produce an image of the two points A and B in the adjacent figure. The points $A^{'}$ and $B^{'}$ are the real images of points A and B thereby produced. Construct in the figure the position of the lens and its focal points. Justify your procedure physically. Also state the focal length of the lens. 5.0 cm A $A^{'}$ B $B^{'}$ Situation A: no magnetic field Substrate -+ Co Cu Co Situation B: external magnetic field Substrate -+ Co Cu Co Magnetic field Magnetisation directions in the Co-Cu-Co layered system. Sketch of the points and their images produced by a lens. You can also find the figures for the problems on the IPhO website. Register now at www.ipho.info www.ipho.info for the competition! $\DeltaR$ = RA $-$ RB RA RA F = 1 A cW $\rhoLuft$ v 2

2 scienceolympiaden.de Show your talent! Students If you are a student, the IPhO and the PhysicsOlympiad in Germany offer you diverse opportunities to engage intensively with physics questions, to experience physics as an exciting scientific discipline, to test your own limits, and not least to meet interesting people. For the competition rounds there are learning materials and training problems that help you deepen your knowledge and problem-solving skills. At the seminars you meet many other young people enthusiastic about physics. Taking part is therefore worthwhile in any case, regardless of whether you make it to the higher rounds. What matters is to be there. Successfully completing the first round is already a special achievement and a real distinction. So, take heart! Teachers As a teacher, you can offer a challenge in physics to particularly capable or interested students with the problems of the PhysicsOlympiad and encourage them to engage more deeply with physics topics. The PhysicsOlympiad can thus serve as an instrument of individual support. The problems of the 1st round in particular are suitable not only for the best in a class.

With a wide range of offerings, the PhysicsOlympiad aims to reach interested young people broadly and to inspire them lastingly for the natural sciences. To this end there are support offerings such as the Orpheus seminars and the accompanying materials for the 1st round, with which we want to support you in introducing topics of the PhysicsOlympiad. So please encourage your students to take part; for only those who do not take part can lose. Schools By encouraging participation in competitions, schools can sharpen their profile and use them, in the sense of enrichment, as a complement to school offerings. Competitions provide diverse, differentiated learning environments for participating students. In the area of STEM subjects, the Olympiads, at least in the later rounds, represent a competition aimed at particularly motivated and high-performing young people. Nevertheless, participation is not only worthwhile even in the entry rounds, but can also contribute to a lasting enthusiasm for STEM topics. Offerings such as the Orpheus seminars allow the support of a large number of participants. In many federal states, participation can incidentally be recognised as a special academic achievement or subject/seminar paper of your students for the Abitur. Interested in more than physics? The IPhO is one of the six nationwide scientific student competitions organised by the IPN – the ScienceOlympiads. In addition to the selection competitions for the international Olympiads in Biology (IBO), Chemistry (IChO) and Physics (IPhO), they also include the International JuniorScience Olympiad (IJSO), the European Olympiad of Experimental Science (EOES), and the Federal Environmental Competition (BUW). Together they address students from the beginning of secondary school until after the end of school, and, through close networking, offer the possibility of lasting support of scientific abilities and interests. Further information at: www.scienceolympiaden.de Many good reasons to take part in the PhysicsOlympiad Words of greeting The Federal Minister for Education and Research and the President of the Standing Conference of the Ministers of Education invite you to take part in the ScienceOlympiads, to which the PhysicsOlympiad belongs. © Bundesregierung -Guido Bergmann © Holger Kiefer Dear students, dear parents and teachers, STEM makes it possible. That sounds like a magic formula and has something of one about it. After all, mathematics, computer science, the natural sciences and technology are our levers for mastering the greatest tasks of humanity, such as climate change, the energy question or the protection of the environment in all its diversity, but also feeding the world and digitalisation. That young people get excited about STEM is one of the most important goals of our ministry and of the supported student competitions. For it is this next generation that we urgently need in STEM training and study professions. Their knowledge and skills determine what the world of tomorrow will look like. The urgency of letting the spark from school days carry over into working life has, however, never been as high as today. This also means: never before have so many doors stood open to those skilled in STEM. And to women skilled in it too, of course. More girls for STEM, that is a heartfelt concern of mine. Because we do not need clichés, but doers – in workshops, laboratories, and gladly also in the boss’s chair. Nationwide, around 10,000 students from the fifth grade upwards register each year for our competitions, enjoy experimenting, solving tricky problems, and meeting many others who like to ask, research, or get creative projects rolling. We are doing everything we can to ensure that it continues that way in 2024 too. Thanks to the numerous supporters who invest money, time and passion in this, above all the Leibniz Institute for Science and Mathematics Education

Topic: Newtonian Mechanics, Fluid Mechanics Metodi: Free-Body Diagram, Dimensional Analysis, Graph Linearization Competenze: Experimental Data Analysis, Graph Linearization, Estimation & Approximation Objects: — Fonte: Testo (PDF) — p.3

Problema 4 (10 punti) Coppe per il cottura Nell’atmosfera, la caduta libera è rallentata dalla friczione dell’aria. La forza di attrito F è quindi proporzionale al quadrato della velocità di caduta v e può essere espresso da Here A denota l’area cross-sectional del corpo che sta cadendo, $\rhoLuft$ l’aria densità, e cW il il cosiddetto coefficiente di drag, che dipende dalla forma del corpo. Con coppe di carta, come i muffin case visti nella foto, il lento Il caso può essere investigato sperimentalmente. Oltre a diversi identici tazze di cucina, ti serve questo a dispositivo per misurare il tempo, come un stopwatch, una misura a nastro o una regola di ripiegamento, nonché un accurate scale, come si può trovare per esempio a scuola. 4. (a) Determina un’espressione per la velocità terminale che un corpo può raggiungere quando cade con frizione. 4.b) Drop five baking cups nested inside each other several times and measure the fall times for different fall distances. Da questo, produce un grafico di tempo di caduta a funzione della distanza di caduta. Usalo per determinare circa la distanza di caduta dopo la quale la velocità terminale è raggiunta. Nota che in questo caso la distanza può arrivare a diversi metri. 4.c) Ora variare il numero di coppe di cottura piantate all’interno di un’altra e misurare la velocità terminale che si stabilisce in ogni caso. Usando un grafico appropriato, determinare il coefficiente di attrito delle vostre tazze da pasticcio. In questa valutazione, usate per la densità di aria $\rhoLuft$ = 1,2 kg $m - 3$ e per l’accelerazione gravitazionale g = 9,81 m $s - 2$ . Problema minore (10 punti) L’impianto di lenti Un grande ma sottile, lente simmetrica è usato per produrre un’immagine dei due punti A e B nel Figure adiacenti. I punti $A^{'}$ e $B^{'}$ sono le immagini reali dei punti A e B così prodotte. Construct in the figure la posizione della lente e i suoi punti focali. Giustificare la procedura fisicamente. Quindi, indicare la lunghezza focale della lente. 5.0 cm A $A^{'}$ B $B^{'}$ Situazione A: nessun campo magnetico Sostanti -+ Co Cu Co Situazione B: campo magnetico esterno Sostanti -+ Co Cu Co Magnetico campo Magnetizzazione direzioni in co-cu-co sistema stratificato. Sketch dei punti e delle loro immagini prodotte da una lente. È possibile trovare anche le cifre per i problemi sul sito IPhO. Registrare ora a www.ipho.info www.ipho.info per il La concorrenza! $\DeltaR$ = RA $-$ RB RA RA F = 1 A cW $\rhoLuft$ v 2

2 sciencesolymppiaden.de Mostra il tuo talento! Studenti Se sei uno studente, l’IPhO e l’Olimpiade di Fisica in La Germania offre diverse opportunità a impegnarsi intensamente con le domande di fisica, a sperimentare la fisica Come una disciplina scientifica eccitante, per testare i vostri limiti, e non ultimo per incontrare persone interessanti. Per i round di competizione ci sono materiali di apprendimento e problemi di formazione che aiutarti a approfondire le tue conoscenze e le tue capacità di risoluzione dei problemi. Al seminario incontrerai molti altri giovani entusiasti di fisica. In ogni caso, è quindi utile prendere parte. Indipendentemente dal fatto che tu lo faccia

Rondate superiori. Cosa importa
E’ di essere lì. Completare con successo Il primo round è già un risultato speciale e una vera distinzione. Allora, prendi il cuore! Docenti Come insegnante, puoi offrire una sfida in fisica • studiare con studenti particolarmente capaci o interessati le problematiche del PhysicsOlympiad e incoraggiarli a impegnarsi più profondamente con fisica
I temi. Il PhysicsOlympiad può In questo modo servono come strumento di sostegno individuale. I problemi del 1° Le misure di sicurezza e di sicurezza sono particolarmente adatte non solo per il settore
Il migliore di una classe.

Con una vasta gamma di offerte, il PhysicsOlympiad mira a raggiungere i giovani interessati di diffusione e di ispirazione duratura per Le scienze naturali. A questo fine ci sono offerte di supporto come i seminari di Orpheus e i materiali che accompagneranno il primo round, con cui vogliamo supportarti nell’introduzione

E’ un’occasione per i nostri studenti. Quindi, per favore, incoraggi i tuoi studenti per partecipare; solo coloro che non partecipano possono perdere. Scuole Incoraggiando la partecipazione a competizioni, le scuole Can sharpen their profile e usarli, nel senso dell’enrichimento, come complemento alla scuola offerte. Competitions provide ambienti di apprendimento diversificati per gli studenti partecipanti. In questo settore, la Le Olimpiadi, almeno in seguito La Commissione ha inoltre adottato una proposta di direttiva che prevede che le parti sociali, quali le parti sociali, le parti sociali e le parti sociali, siano Giovani ad alto rendimento. Tuttavia, la partecipazione non è solo utile anche nei round di entrata, ma può anche contribuire a L’entusiasmo per i temi STEM è duraturo. Offerte come i seminari di Orpheus consent the support of a Numero di partecipanti. In molti stati federali, la partecipazione può essere incidentalmente riconosciuta come un particolare risultato accademico o Paper di tema/seminar dei vostri studenti per l’abitur. Interessato più della fisica? L’IPhO è uno dei sei a livello nazionale scientific student competitions organised by the IPN
Le ScienceOlympics. In aggiunta alla le selection competitions for the international Olympiads in Biology (IBO), La ricerca e la ricerca sono stati sviluppati in un campo di ricerca e di ricerca. La ricerca internazionale JuniorScience Il programma di formazione professionale (IJSO), l’Olimpiade europea Il programma di ricerca è stato sviluppato in Federal Environmental Competition (BUW). Insieme si rivolge agli studenti dal principio di scuola secondaria fino a dopo la fine di scuola, e, attraverso una rete stretta, offrono la possibilità di sostenere duratamente le capacità e gli interessi scientifici. Informazioni aggiuntive: www.scienceolympiaden.de Molti buoni motivi per partecipare al PhysicsOlympiad Parole di saluto Il Ministro federale per l’istruzione e la ricerca e il Presidente della Conferenza permanente dei ministri dell’istruzione invitare a partecipare alle ScienceOlympiads, alle quali appartiene la PhysicsOlympiad. © Governo federale - Guido Bergmann © Holger Kiefer Cari studenti, Cari genitori e insegnanti, STEM lo rende possibile. Sembra una formula magica e ha qualcosa di uno su di esso. Dopo tutto, la matematica, l’informatica, le scienze naturali e la tecnologia sono i nostri fegati per il dominio dei più grandi compiti di La questione dell’energia La protezione dell’ambiente in tutta la sua diversità, ma anche il mondo e la digitalizzazione. Che i giovani eccitato per STEM è uno degli obiettivi più importanti del nostro ministero e di tutti i concorsi studenteschi supportati. Perché è questa prossima generazione che abbiamo urgentemente bisogno nelle professioni di formazione e studio STEM. Le loro conoscenze e le loro capacità determinano come sarà il mondo di domani. L’urgenza di lasciare che la scintilla di scuola si trasmetta nella vita lavorativa non è mai stata così alta come oggi. Questo significa anche: non ci sono mai state così tante porte aperte per coloro che hanno la capacità di STEM. E anche alle donne che ne sono abili, naturalmente. Più ragazze per STEM, cioè Una preoccupazione di cuore. Perché non abbiamo bisogno di cliché, ma ci si fa in laboratori, in laboratori e anche nella sedia del capo. In tutto il paese, circa 10.000 studenti della quinta elementare si iscrivono ogni anno per le nostre competizioni, godere di sperimentare, risolvere problemi difficili, e incontrando molti altri che amano chiedere, ricercare, o Get creative projects rolling. Stiamo facendo tutto il possibile per assicurarci che continuerà così anche nel 2024. Grazie ai numerosi sostenitori che investono denaro, tempo e passione in questo, soprattutto l’Istituto Leibniz per la scienza e le matematiche Educazione

Problem 4 (10 points) Falling baking cups In the atmosphere, free fall is slowed by air friction. The friction force F is therefore proportional to the square of the falling speed v and can be expressed by Here A denotes the cross-sectional area of the falling body, $\rhoLuft$ the air density, and cW the So-called drag coefficient, which depends on the shape of the body. With paper baking cups, like the muffin cases seen in the photo, the slowed The case can be investigated experimentally. Besides several identical baking cups, you need for this a device for measuring time, such as a stopwatch, a tape measure or a folding rule, as well as an accurate scale, such as you can find for example at school. 4. (a) Determine an expression for the terminal speed that a body can reach when falling with friction. 4.b) Drop five baking cups nestled inside each other several times and measure the fall times for different fall distances. From this, produce a graph of the fall time as a function of the fall distance. Use it to determine approximately the fall distance after which the terminal speed is reached. Note That this case distance can amount to several meters. 4.c) Now vary the number of baking cups nestled inside each other and measure the terminal speed that establishes itself in each case. Using a suitable graph, determine the drag coefficient of your baking cups. In the evaluation, use for the density of air $\rhoLuft$ = 1.2 kg $m - 3$ and for the gravitational acceleration g = 9.81 m $s - 2$ . The first is the ‘Junior Problem’ (10 points). Lens construction A large but thin, symmetric lens is used to produce an image of the two points A and B in the the adjacent figure. The points $A^{'}$ and $B^{'}$ are the real images of points A and B thus produced. Construct in the figure the position of the lens and its focal points. Justify your procedure physically. So state the focal length of the lens. 5.0 cm A $A^{'}$ B $B^{'}$ Situation A: no magnetic field Substrate -+ Co Cu Co Situation B: external magnetic field Substrate -+ Co Cu Co Magnetic field Magnetisation directions in the co-cu-co layered system. Sketch of the points and their images produced by a lens. You can also find the figures for the problems on the IPhO website. Register now at The Commission has also adopted a proposal for a regulation on the protection of the environment. The Commission has also adopted a proposal for a regulation on the protection of the environment. for the Competition! $\DeltaR$ = RA $-$ RB RA RA F = 1 A cW $\rhoLuft$ v 2

2 The European Commission has also adopted a proposal for a directive on the protection of the environment. Show your talent! The students If you are a student, the IPhO and the PhysicsOlympic in Germany offers you various opportunities to engage intensively with physics questions, to experience physics As an exciting scientific discipline, to test your own limits, And not least to meet interesting people. For the competition rounds there are learning materials and training problems that help you deepen your knowledge and problem-solving skills. At the seminars You meet many other young people who are enthusiastic about physics. Taking part is therefore worthwhile in any case, Regardless of whether you make it to the higher rounds. What matters is to be there. Successfully completing The first round is already a special achievement and a real distinction. So, take heart! Teachers As a teacher, you can offer a challenge in physics to particularly capable or interested students with the The problem of the PhysicsOlympiad and encourage them to engage more deeply with physics The Commission’s proposal for a directive on the protection of workers’ rights The PhysicsOlympiad can This is a tool for individual support. The problems of the 1st The following are the main reasons for the Best in a class.

With a wide range of offerings, the PhysicsOlympiad aims to reach interested young people broadly and to inspire them lastingly for The natural sciences. To this end there are Support offerings such as the Orpheus seminars and the accompanying materials for the 1st round, with which we want to support you in introducing The first is the topic of the PhysicsOlympic. So please encourage your students To take part; for only those who do not take part can lose. Schools By encouraging participation in competitions, schools Can sharpen their profile and use them, in the sense of enrichment, as a complement to school The Commission will take the necessary measures to ensure that the Commission is able to take all necessary measures. Competitions provide The aim is to create a diverse and differentiated learning environment for participating students. In the area of STEM subjects, the The Olympic Games, at least in the later The main objective of the competition is to promote the development of a new approach to the high-performing young people. However, participation is not only worthwhile even in the entry rounds, but can also contribute to a I’m very excited about STEM. Offerings such as the Orpheus seminars allow the support of a large number of participants. In many federal states, participation can incidentally be recognized as a special academic achievement or subject/seminar paper of your students for the graduation. Interested in more than physics? The IPhO is one of six nationwide Scientific student competitions organised by the IPN The science olympics. In addition to the selection competitions for the international Olympiads in Biology (IBO), Chemistry (IChO) and Physics (IPhO), they also include The International JuniorScience The European Olympic Games (OILs), the European Olympic Games and the The European Commission has also launched a programme of research on the The Federal Environmental Competition (BUW). Together they address students From the beginning of secondary school until after the end The aim is to improve the quality of education and, through close networking, offer the possibility of The Commission shall, in accordance with Article 4 of Regulation (EC) No 1272/2009, adopt delegated acts in accordance with Article 5 of this Regulation. Further information at: The European Commission has also adopted a proposal for a directive on the protection of workers’ rights. Many good reasons to take part in the PhysicsOlympiad Words of greeting The Federal Minister for Education and Research and the President of the Standing Conference of the Ministers of Education invite you to take part in the ScienceOlympics, to which the PhysicsOlympic belongs. © Federal Government - Guido Bergmann © Holger Kiefer Dear students, Dear parents and teachers, STEM makes it possible. That sounds like a magic formula and has Something of one about it. After all, mathematics, computer science, the natural sciences and technology are our livers for mastering the greatest tasks of Humanity, such as climate change, the energy question The European Union is also a key player in the fight against climate change and the protection of the environment in all its diversity, but also feeding the world and digitalisation. That young people get excited about STEM is one of the most important goals of our ministry and of the supported student competitions. For it is this next generation The most important thing is that we need it urgently in STEM training and study professions. Their knowledge and skills determine what the world of tomorrow will look like. The urgency of letting the spark from school days carry over into working life has, however, never been as high as today. This Also means: never before have so many doors stood open to those skilled in STEM. And to women skilled in it too, of course. More girls for STEM, that is A heartfelt concern of mine. Because we don’t need clichés, but doers in workshops, labs, and gladly also in the boss’ chair. Nationwide, about 10,000 students from the fifth grade upwards register each year. For our competitions, enjoy experimenting, solving tricky problems, and meeting many others who like to ask, research, or Get creative projects rolling. We are doing everything we can to ensure that it It’s going to continue that way in 2024. Thanks to the numerous supporters who invest money, time and passion in this, The Leibniz Institute for Science and Mathematics is a very important institution in the world. Education

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